Mathematics College

## Answers

**Answer 1**

Therefore , the solution of the given problem of **graphs** comes out to be curve of y = 4x – 3 can be plot by y=4x graph.

A graph is what?

Graphs are used by theoretical physicists to analytically and graphically display assertions rather than values. Typically, a graph **coordinate** point shows the relationship between several distinct objects. A graph is a particular kind of pas e carrier construction composed of groups and** lines**. The borders, also known as the channels, should be joined together with glue.

Here,

The methods below can be used to plot y = log4 x - 3 as a graph:

Move the y-axis of the graph of

=> y = log4 x down 3 units, making the horizontal asymptote y = -3 the new x-axis.

To acquire the graph of

=> y = log4 x – 3, reflect the resulting graph across the line y = x.

Here is a detailed explanation of how to plot y = log4 x - 3:

Diagram y equals 4x:

Plot the following y = 4x key locations first:

=> Y = 40 = 1 when x = 0.

=> If x = 1, then y = 41 = 4.

=> Y = 4-1 = 1/4 when x = -1.

The graph of y = 4x can be easily drawn using just these three values.

The curve of y = 4x is now 3 units lower:

To do this, take each y-coordinate and deduct 3 from it spots on the y = 4x graph. We now have the curve of y = 4x – 3:

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## Related Questions

a rectangular garden has dimensions of 5 feet by 12 feet. if the length and width of the garden are increased by the same amount, and the resulting area is 144 square feet, how much was each side increased?

### Answers

Based on the data, we can infer that the difference in **length** after the garden increment is **4 feet** on each **side**.

How to find how much the garden increased in length and width?

To find how much the garden increased in **length** and **width** we must carry out the following procedure:

First of all we must calculate the area of the garden:

side * side = area5 * 12 = 60

According to this result we know that the increase is more than half in the **values**. Therefore, we can add 3 or more **feet** to each side and recalculate the **area** of the garden.

5 + 3 = 812 + 3 = 158 * 15 = 120

In this case we add 3 **feet** to each side and calculate the area that would give these side measurements 8 and 15. The area would be 120, you still wouldn't have enough **length** on the sides to have an area of 144.

5 + 4 = 912 + 4 = 1616 * 9 = 144

In this case we add 4 **feet** on each side and calculate the area that would be given with these side measurements 9 and 16. The area would be 144, it would be the measurement mentioned in the statement.

Based on the above, we can infer that the **rise** is 4 feet on each **side**.

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A triangular prism is 32 centimeters long and has a triangular face with a base of 30 centimeters and a height of 20 centimeters. The other two sides of the triangle are each 25 centimeters. What is the surface area of the triangular prism?

### Answers

The **surface area** of the **triangular prism** is 1880 square centimeters.

How did we get the value?

To find the **surface area** of the **triangular prism**, we need to calculate the area of each of its faces and add them up.

First, let's calculate the area of the triangular base. The formula for the area of a triangle is:

Area = (base x height) / 2

Substituting the given values, we get:

Area = (30 x 20) / 2 = 300 cm²

Since the triangular prism has two identical triangular faces, the total area of the two triangular faces is:

2 x 300 cm² = 600 cm²

Now, let's calculate the area of the rectangular faces. The length of the **rectangular faces** is the same as the length of the prism, which is 32 cm. The height of the rectangular faces is the same as the height of the triangle, which is 20 cm. The formula for the area of a rectangle is:

Area = length x height

Substituting the given values, we get:

Area = 32 x 20 = 640 cm²

Since the triangular prism has two identical rectangular faces, the total area of the two rectangular faces is:

2 x 640 cm² = 1280 cm²

Finally, to find the total surface area of the triangular prism, we add the areas of the two triangular faces and the two rectangular faces:

600 cm² + 1280 cm² = 1880 cm²

Therefore, the surface area of the triangular prism is 1880 square centimeters.

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A parallelogram has a height of 5 units. One side of the parallelogram is AB⎯⎯⎯⎯⎯. The parallelogram has no right angles.

Draw the parallelogram using the Polygon tool.

Each segment of the grid represents 1 unit.

Keyboard Instructions

Initial graph state

The horizontal axis goes from 1.5 to 12.5 with ticks spaced every 1 unit(s).

The vertical axis goes from 1.5 to 12.5 with ticks spaced every 1 unit(s).

Point with coordinates (2, 3) labelled: A.

Point with coordinates (8, 3) labelled: B.

### Answers

Parallelogram, In Euclidean geometry, a **parallelogram** is a simple quadrilateral with two(2) pairs of parallel sides.

What is Parallelogram?

A parallelogram is a geometric object with sides that are parallel to one another in two(2) dimensions. It is a form of a **polygon** with four(4) sides (sometimes known as a quadrilateral) in which each parallel pair of sides have the same length.

A **Quadrilateral** is a closed shape and a type of polygon that has four sides, four(4) vertices and four angles. It is formed by joining(connecting) four non-collinear points. The sum of the interior angles of quadrilaterals(4 sides) is always equal to 360 degrees.

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The number of meters a student swam this week are listed.

600, 750, 800, 850, 900, 1100

What is the appropriate measure of variability for the data shown, and what is its value?

The mean is the best measure of variability and equals about 833.

The median is the best measure of variability and equals 825.

The range is the best measure of variability and equals 500.

The IQR is the best measure of variability and equals 150.

### Answers

**Answer: The range is the best measure of variability for the given data set and its value is 500.**

**The range is the difference between the maximum and minimum values in a data set, and in this case, the maximum value is 1100 and the minimum value is 600, so the range is 1100-600=500. The range gives us an idea of how spread out the data is, but it can be affected by outliers. In this case, it seems like a reasonable measure of variability since there are no extreme values that would greatly affect the range.**

**Step-by-step explanation:**

From the data of the number of meters swam by **students **, **range **is the best measure of **variability **and equals 500

What are domain and range?

The **domain **of a **function **is the set of values that we are allowed to plug into our function. This set is the x values in a function such as f(x). The range of a function is the set of values that the function assumes. This set is the values that the function shoots out after we plug an x value in.

The **range **is the set of outputs of a relation or function. In other words, it's the set of possible y values. Recall that ordered pairs are of the form (x,y) so the y coordinate is listed after the x. The output is listed after the input.

Given data ,

Let the **data **set be represented as A

Now , the value of A is

A = { 600, 750, 800, 850, 900, 1100 }

The appropriate measure of **variability **for the given data is the **range**. The range is the difference between the largest and smallest values in the data set.

And , range = 1100 - 600

R = 500

Hence , the **range **of the data set is R = 500

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Which function has an average change of -4 over the interval [-2,2]

### Answers

**Answer: B**

**Step-by-step explanation:**

2.

3.5 in.

4 in.

6 in.

What is surface area

### Answers

Given that three factors are given and the **surface area **is required, this means that we are dealing with a three-dimensional shape. Where the above is a **rectangular prism**, the surface area =** 118 In².**

What is the explanation for the above response?

**Surface area **is the measure of the total area that the surface of a three-dimensional object occupies.

To calculate the surface area of an object, you need to add up the areas of all its faces. The formula for finding the surface area of a **rectangular prism**, which has three pairs of congruent rectangular faces, is:

Surface area = 2(lw + lh + wh)

where l, w, and h are the length, width, and height of the rectangular prism, respectively.

So, if we have a **rectangular** **prism **with the following dimensions:

Length (l) = 3.5 inches

Width (w) = 4 inches

Height (h) = 6 inches

The **surface area **can be calculated as follows:

Surface area = 2(lw + lh + wh)

= 2(3.5 x 4 + 3.5 x 6 + 4 x 6)

= 2(14 + 21 + 24)

= 2(59)

= 118In²

Therefore, the **surface area **of this rectangular prism is **118 In².**

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**Full Question:**

Although part of your question is missing, you may be referring to this full question:

Given a rectangular prism with the following dimensions:

3.5 in.

4 in.

6 in.

What is surface area?

Question

The average daily balance of a credit card for the month of December was $5600, and the unpaid balance at the end of the

month was $6900. If the monthly interest rate is 2.5% of the average daily balance, what is the total balance on the next

billing date January 1? Round your answer to the nearest cent. Do not use commas to separate numbers or dollar signs. For

example, $5, 678.00 should be entered as 5678.00.

### Answers

**Answer:**

The first step is to determine the amount of interest charged for the month of December based on the average daily balance:

Average Daily Balance = $5600

Monthly Interest Rate = 2.5%

Interest Charged for December = Average Daily Balance * Monthly Interest Rate * Number of Days in December

Number of days in December is 31.

Interest Charged for December = $5600 * 0.025 * 31 = $4340.00

The total balance on the credit card on January 1 will be the sum of the unpaid balance at the end of December and the interest charged for December:

Total Balance on January 1 = Unpaid Balance at End of December + Interest Charged for December

Total Balance on January 1 = $6900 + $4340.00

Total Balance on January 1 = $11240.00

Rounded to the nearest cent, the total balance on the next billing date January 1 is $11,240.00.

The nearest cent, the total **balance **on the next billing date, January 1, is $12640.00.

To **calculate **the total balance on the next billing date, we need to consider the average daily balance for December, the unpaid balance at the end of December, and the monthly interest rate.

The monthly interest rate is 2.5% of the average daily balance. Let's calculate the **interest** charged for the month of December:

Interest charged = (2.5/100) * Average daily balance

= (2.5/100) * $5600

= $140

Next, let's calculate the total balance on the next **billing **date, January 1:

Total balance = Average daily balance + Interest charged + Unpaid balance

= $5600 + $140 + $6900

= $12640

Rounded to the nearest cent, the total **balance** on the next billing date, January 1, is $12640.00.

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when 40 is subtracted from the square of a number, the result is 3 times the number. find the positive solution

### Answers

**Answer: x = 8**

**Step-by-step explanation: **Let 'x' be the number we are looking for.

As per the question, equation will be : x^2 - 40 = 3x

x^2 - 3x - 40 = 0

Factor the equation. Or quadratic equation formula can also be used.

Factoring -

x^2 - 3x - 40 = 0

x^2 - 8x + 5x - 40 = 0

x(x-8) + 5( x-8) = 0

(x+5) ( x-8) = 0

x+5=0 , x-8 =0

x = -5 , x = 8

As we need to find the positive solution, x = 8 is the answer.

VERIFICATION -

= x^2 - 40

= ( 8 )^2 - 40

= 64 - 40

= 24

And 3 times 8 is also 24.

Therefore, if we subtract 40 from the square of 8, the result will be 3 times the number (which is 8).

A newspaper editor starts a retirement savings plan in which $275 per month is deposited at the beginning of each month into an account that earns an annual interest rate of 6.4% compounded monthly. Find the value of this investment (in dollars) after 20 years. (Round your answer to the nearest cent.)

### Answers

**Answer:**

**Step-by-step explanation:**

x= 20 (12) =240, Interest%= 6.4, Pv + 0, PMT= 275,temporarily skip FV,P/Y and C/Y= 12,

After 20 years, the value is $133,970.26

The **simple interest **value of the investment after 20 years is approximately $30,637.45

What do you mean by future value?

**Future value** (FV) is the value of an investment at a future date, based on a series of regular payments (or a lump sum) and assuming a certain interest rate over a period of time. In other words, it's the **amount** of money an investment will be worth after earning a certain rate of interest over a certain period of time.

What is simple interest?

**Simple interest** is a method of calculating interest on a loan or investment, where interest is only charged on the original principal amount. In other words, the interest is not compounded over time.

In the given question:

We can use the formula for the future value of an annuity:

FV = PMT x [(1 + r/n)^(n*t) - 1] / (r/n)

where: FV = future value

PMT = monthly payment

r = annual interest rate

n = number of compounding periods per year

t = number of years

Plugging in the given values, we have:

FV = 275 x [(1 + 0.064/12)^(12*20) - 1] / (0.064/12)

FV = 275 x (1.00533²⁴⁰ - 1) / 0.00533

FV = 275 x 111.034

FV = 30,637.45

Therefore, the value of the **investment** after 20 years is approximately $30,637.45.

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What is the ratio of the amount spent on staff salaries to the total budget for the youth programs?

1:10

1:8

1:5

1:4

1:2

### Answers

Answer:1:2

Step-by-step explanation:

1 of 431 of 43 Items

17:04

Skip to resourcesFeature

Find a Point on a Segment

Question 1

Find the point on PQ that divides the line segment directed from P to Q into the ratio of 1 : 3?

Responses

A (112

, 3)( 11 2 , 3)

B (52

, 5)( 5 2 , 5)

C (52

, 3)( 5 2 , 3)

D (112

, 5)( 11 2 , 5)

Question 2

Find the point on PQ that divides the line segment directed from P to Q into the ratio of 3 : 1?

Responses

A (112

, 3)( 11 2 , 3)

B (52

, 5)( 5 2 , 5)

C (52

, 3)( 5 2 , 3)

D (112

, 5)

### Answers

The points on **line segment **in Question 1 is C (52, 3)( 5 2 , 3) and the answer to Question 2 is A (112, 3)( 11 2 , 3).

**What is a line segment?**

A line segment is a straight line that is bounded by two distinct endpoints. It is the shortest distance between two points and is usually represented by an arrow. Line segments are an essential part of geometry, as they form the basis for many shapes, such as **triangles **and rectangles.

A line segment can be divided into two parts in a given **ratio **if the difference of the coordinates of the end points of the line segment is divided in the same ratio.

For Question 1, the ratio of the line segment is 1:3. To find the point on the line segment, we will divide the difference of the coordinates of the end points of the line segment into the ratio 1:3. The coordinates of the end points of the line segment PQ are (10,2) and (14,6). The difference of the coordinates of the end points of the line segment PQ is (14-10, 6-2) = (4,4). The difference of the coordinates (4,4) is divided into the ratio 1:3. After dividing the difference of the coordinates into the ratio 1:3, we get the **coordinates **of the point on the line segment PQ as (52,3).

For Question 2, the ratio of the line segment is 3:1. To find the point on the line segment, we will divide the difference of the coordinates of the end points of the line segment into the ratio 3:1. The coordinates of the end points of the line segment PQ are (10,2) and (14,6). The difference of the coordinates of the end points of the line segment PQ is (14-10, 6-2) = (4,4). The difference of the coordinates (4,4) is divided into the ratio 3:1. After dividing the difference of the coordinates into the ratio 3:1, we get the coordinates of the point on the line segment PQ as (112,3).

In conclusion, the point on the** line segment** PQ that divides the line segment into the ratio of 1:3 is C (52, 3)( 5 2 , 3) and the point on the line segment PQ that divides the line segment into the ratio of 3:1 is A (112, 3)( 11 2 , 3).

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I don't know What 5 + x + 3 simplified is, help me please?

### Answers

**Answer:**

5+x+3 simplified is x+8

**Step-by-step explanation:**

when you simplify something, you combine terms and write it in the simplest way you can. So combine 5 and 3 to get 8, and then the final answer of x+8

**Answer: **x+8

**Step-by-step explanation:**

"5 + x + 3" can be simplified by combining the numerical terms, which are 5 and 3, to get 8.

Then, just rewrite the expression as "x + 8." Therefore, "5 + x + 3" simplified is just "x + 8".

the solution to a system of linear equations is (0,4) one of the linear equations in the system is Y=8x+4

### Answers

Insufficient information

-> infinite number of lines can pass through a single point. We need another information do define the other line.

Which graph represents the solution set of the inequality x + 2 greater-than-or-equal-to 6 A number line goes from negative 9 to positive 9. A solid circle appears on positive 3. The number line is shaded from positive 3 through negative 9. A number line goes from negative 9 to positive 9. An open circle appears at positive 3. The number line is shaded from positive 3 through positive 9. A number line goes from negative 9 to positive 9. A closed circle appears at positive 4. The number line is shaded from positive 4 through positive 9. A number line goes from negative 9 to positive 9. An open circle appears at positive 4. The number line is shaded from positive 4 through negative 9.

### Answers

The shaded area to the right of 4 indicates all values larger than 4 being **inequality **included in the solution set, while the closed circle at 4 represents the number 4 being included in the solution set.

What is inequality?

A relationship between two terms or values which is not equal is known as an inequality in **mathematics**. Inequality follows imbalances, therefore. In mathematics, an inequality makes a link among two quantities that are not equal. Egality and inequality are different. Use the not similar **symbol **most frequently when two components are not equal (). Various inequalities are employed to contrast values of all sizes. By changing the two parts until only the **variables **are left, one can solve many straightforward inequalities. However a variety of factors support inequality: Negative values are split or added on either **side**. Switch between the left & right.

The graph below shows the set of solutions to the inequality where x + 2 is larger than or equal to 6:

From negative 9 to positive 9 is a number line. At positive 4, a closed circle appears. Positive numbers four through nine are shaded on the number line.

This means that the inequality will be satisfied by any value of x larger than or equal to 4. The graph includes the value 4 in the solution set since it has a closed circle there, and because it is shaded to the right of 4, it also includes all values higher than 4.

Here is an illustration of the graph:

|----|----|----|----|----|----|----|----|----|

-9 -8 -7 -6 -5 -4 -3 -2 -1 0

o

---->

4

----]

>

|----|----|----|----|----|----|----|----|----|

-9 -8 -7 -6 -5 -4 -3 -2 -1 0

The shaded area to the right of 4 indicates all values larger than 4 being included in the solution set, while the closed circle at 4 represents the number 4 being included in the solution set.

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A quadrilateral with vertices at A(4,-4), B(4, -16), C(12, -16), and D(12,-4) has been dilated with a center at the origin.

The image of D, point D', has coordinates (36, -12). What is the scale factor of the dilation?

ㅇㅎ

9

O 3

O 3

09

### Answers

**Answer:**

the scale factor = 3

**Step-by-step explanation:**

*the question is basically saying: how did (12,-4) jump to (36,-12)*

we can make d represent the scale factor used to get (12,-4) to (36,-12)

so,

12d = 36

-4d = -12

all there's left to do is to simply solve for d, which is 3

Help, please? lol its for like homework or whatev. helpppp!!

### Answers

Answer: $19800

To solve:

We need to multiply the annual income by the percent set for food. Since ‘food’ is 18% (.18 in decimal form) we can do 110000*.18 to get 19800

Hope this helped

DEDUCTION AND APPLICATION Do not use a calculator when answering Part 3. 3.1 Apply the compound angle expansion sin(x + y) = sin x cos y + cos x sin y to expa sin 2x and simplify your answer: sin 2x = sin(x+x) 3.2 Expand each of the following, using your answer from 3.1: 3.2.1 sin 100° = ..... 3.2.2 sin 46° = .... 3.2.3 sin 40° =. Write the following expressions as a single trigonometric ratio: 3.3.1 2 sin 19° cos 19° = 3.3.2 2 cos 40° sin 40° - 3.3.3 sin 25° cos155° .........

### Answers

**Answer:**

**Step-by-step explanation:**

3.1:

Using the compound angle expansion, we have:

sin 2x = sin(x + x) = sin x cos x + cos x sin x

sin 2x = 2 sin x cos x

Therefore, sin 2x = 2 sin x cos x.

3.2:

Using the result from 3.1:

3.2.1: sin 100° = 2 sin 50° cos 50° = sin 100° = 0.766

3.2.2: sin 46° = 2 sin 23° cos 23° = sin 46° = 0.719

3.2.3: sin 40° = 2 sin 20° cos 20° = sin 40° = 0.642

3.3:

Using the identity sin(a ± b) = sin a cos b ± cos a sin b:

3.3.1: 2 sin 19° cos 19° = sin 38° = sin (45° - 7°) = sin 45° cos 7° - cos 45° sin 7° = (1/√2)cos 7° - (1/√2)sin 7° = -sin (7° - 45°) = -sin 38°

Therefore, 2 sin 19° cos 19° = -sin 38°.

3.3.2: 2 cos 40° sin 40° = sin 80° = sin (45° + 35°) = sin 45° cos 35° + cos 45° sin 35° = (1/√2)cos 35° + (1/√2)sin 35° = sin (35° + 45°) = sin 80°

Therefore, 2 cos 40° sin 40° = sin 80°.

3.3.3: sin 25° cos 155° = (1/2)(sin 180°) = 0

Therefore, sin 25° cos 155° = 0.

A woman wants to measure the height of a nearby tower. She places a 7 ft pole in the shadow of the tower so that the shadow of the pole is exactly covered by

the shadow of the tower. The total length of the tower's shadow is 188 ft, and the pole casts a shadow that is 3.75 ft long. How tall is the tower? Round your

answer to the nearest foot. (The figure is not drawn to scale.)

Sun

Tower

Pole

Shadow of pole"

Shadow of tower

Ú

ft

X

### Answers

The **height** of the tower obtained from the 188 ft long tower's shadow, the 3.75 ft long pole's shadow, the 7 ft height of the pole, and the equivalent ratio of the corresponding sides of **similar triangles** is about 351 feet

What are similar triangles?

**Similar triangles** are triangles that have the **same** **shape** but may have different **sizes**.

**Height** of the pole = 7 ft

**Length** of the shadow cast by the tower = 188 ft

Length of the shadow cast by the pole = 3.75 ft

The **triangle** formed by the **length** of the shadows of the tower and the pole the tower and the pole and the **line** of sight from the tip of the shadow to the top of the tower and the pole are similar triangles, therefore, the ratio of the corresponding sides are the same, which indicates;

[tex]\frac{3.75}{188} = \frac{7}{Height \ of \ the \ tower}[/tex]

Height of the tower × 3.75 = 7 × 188

The height of the tower = 7 × 188/3.75 ≈ 351

The height of the tower is about 351 feet

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which one of the following greater

a, 20% of 45

b, 25% of 60

c, 2%of 800

d, 74% of 20

### Answers

**Answer:**

**2% of 800, which is 16**

To compare the values of a, b, c, and d, we can calculate each of them and then compare the results.

a) 20% of 45 = 0.20 x 45 = 9

b) 25% of 60 = 0.25 x 60 = 15

c) 2% of 800 = 0.02 x 800 = 16

d) 74% of 20 = 0.74 x 20 = 14.8

Comparing the values, we see that:

b > c > a > d

Therefore, the answer is option (b) 25% of 60.

Write the expression as the sine, cosine, or tangent of an angle.

### Answers

The simplified **expression** is: cos(13π/35)

What is trignometry?

Trigonometry is a branch of mathematics that studies the relationships between **angles** and the sides of triangles. It deals with functions such as sine, cosine, and tangent and their inverses, and is used extensively in fields such as engineering, physics, and astronomy.

We can simplify the given **expression** using the identity:

cos(A - B) = cos(A) cos(B) + sin(A) sin(B)

We can rewrite the given expression as:

cos(4π/7) cos(π/5) - sin(4π/7) sin(π/5)

= cos(4π/7 - π/5) [using the identity]

To simplify further, we can find a common denominator for 4/7 and 1/5:

4/7 = 20/35 and 1/5 = 7/35

Then, we can write:

4π/7 - π/5 = (20π/35) - (7π/35) = 13π/35

This expression cannot be further simplified using trigonometric identities, and is written only in terms of the cosine function.

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Can someone help me pleaseeee

### Answers

The **area **of the **triangles **are 81.77 square units, 333.50 square units, 207 square units and 52.21 square units

How to determine the area of the triangles

Given the triangles as the parameters, the **area **can be calculated as

Area = 1/2absin(C)

Using the above **formula **as a guide, we have the following **equations**

Triangle 7 = 1/2 * 15 * 13 * sin(57 degrees)

Triangle 7 = 81.77 square units

Triangle 8 = 1/2 * 28 * 24 * sin(83 degrees)

Triangle 8 = 333.50 square units

Triangle 9 = 1/2 * 23 * 18 * sin(90 degrees)

Triangle 9 = 207 square units

Triangle 10 = 1/2 * 15 * 7 * sin(96 degrees)

Triangle 10 = 52.21 square units

Hence, the **area **of **triangle **10 is 52.21 square units

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Please help with this pre calculus question

### Answers

The **distance **between the points z₁ = 3+7i and z₂ = -5-2i ** **is **12.04.**

What is distance?

**Distance **is the total movement of an object without any regard to direction.

To calculate the distance between the two complex expression, we use the

formula below

Formula:

d = √[(c-a)²+(d-b)²].................. Equation 1

From the question,

Given the question

z₁ = 3+7iz₂ = -5-2i

Where:

a = 3b = 7c = -5d = -2

Substitute these values into equation 1

d = √[(-5-3)²+(-2-7)²]d = √(64+81)d = √145d = 12.04

Hence, the **distance **is **12.04.**

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The scale drawing of a building has a height of 10 centimeters. The actual building is 20 feet high. How many centimeters in the scale drawing represent one foot on the actual building?

A. 1/2

B. 2

C. 10

D. 30

### Answers

1/2cm in the **scale drawing** represents one foot on the actual building.

**What is the scale factor?**

The ratio of the **scale **of an original thing to a new object that is a representation of it but of a different size is known as a **scale factor **(bigger or smaller). When both the original **dimensions **and the new dimensions are known, the **scale factor** may be determined. The following is a basic formula to determine a figure's scale factor: **Scale factor** is equal to the difference between the dimensions of the old and new shapes.

Here, we have

Given: The **scale drawing** of a building has a height of 10 centimeters. The actual building is 20 feet high.

we have to find how many centimeters in the** scale drawing** represent one foot on the actual building.

The answer will be 1/2 because 1 centimeter is equal to 2 feet in reality. But since we want to know the answer of how many centimeters is in 1 foot, we will divide that in half, to get an answer of 1/2 centimeter.

Hence, 1/2cm in the **scale drawing** represents one foot on the actual building.

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WILL GIVE THE BRAINLIEST AND 5 STARS!!!!

The vertices of △ABC are (−6, 2), (−4, 6), and (−2, 2), and the vertices of △DEF are (5,-2), (3, −6), and (1, −2). Which of these sequences of transformations of △ABC exhibit the congruence between the two triangles? Select TWO that apply.

Responses

a rotation of 180° about the origin and a translation of 1 unit left

a rotation of 180° about the origin and a translation of 1 unit left

a reflection across the x-axis and a translation 1 unit right

a reflection across the x-axis and a translation 1 unit right

a rotation of 180° about the origin and a translation of 1 unit right

a rotation of 180° about the origin and a translation of 1 unit right

a reflection across the x-axis, a reflection across the y-axis, and a translation 1 unit right

a reflection across the x-axis, a reflection across the y-axis, and a translation 1 unit right

a reflection across the y-axis and a translation 1 unit left

a reflection across the y-axis and a translation 1 unit left

a reflection across the x-axis, a reflection across the y-axis, and a translation 1 unit left

### Answers

The answer of the given question based on the **triangle **which is sequences of transformations of △ABC exhibit the congruence between the two triangles the answer is given below,

What is Congruent triangle?

Congruent triangles are two or more triangles that have same shape and **size**. In other words, they have same angles and same side lengths.

The congruence between the two triangles can be exhibited by the following two sequences of transformations:

a) a rotation of 180° about the origin and a translation of 1 unit left

c) a rotation of 180° about the origin and a translation of 1 unit right

Option b) and option e) involve a translation and a **reflection **that do not preserve orientation, so they do not result in a congruent triangle.

Option d) involves two reflections, which do not commute, so the order matters. This sequence of transformations would result in a reflection across the line y = x, followed by a translation of 1 unit right, followed by a reflection across the line x = -1, which does not result in a congruent triangle.

Option f) is similar to option d) in that it involves two reflections that do not commute. This sequence of transformations would result in a reflection across the line y = x, followed by a translation of 1 unit left, followed by a reflection across the line x = 1, which also does not result in a congruent triangle.

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A ship travels east from Port Lincoln 24 miles before turning north. When the ship becomes disabled

and radios for help, the rescue boat needs to know the fastest route to the ship. The rescue boat navigator

finds that the shortest route from Port Lincoln is 48 miles long. At what angle off of due east should the

rescue boat travel to take the shortest route to the ship? Round your answer to the nearest whole degree.

### Answers

**Answer:**

Rounding to the nearest whole degree, the rescue boat should travel at an angle of approximately 41 degrees off of due east to take the shortest route to the ship.

**Step-by-step explanation:**

We can use trigonometry to solve this problem. Let's draw a diagram to represent the situation:

A (rescue boat)

| \

| \

| \ C (disabled ship)

24 mi | \

| \

| \

|θ \

B-----------D (Port Lincoln)

48 mi

In the diagram, point B represents Port Lincoln, point C represents the disabled ship, and point A represents the rescue boat. Point D is the intersection of the eastward path and the northward path taken by the ship.

We are given that BD = 24 miles and CD = 48 miles. We want to find the angle θ, which is the angle between the line segments AB and AD.

To find θ, we can use the law of cosines:

cos(θ) = (BD² + CD² - AD²) / (2 x BD x CD)

Substituting the given values, we get:

cos(θ) = (24² + 48² - AD²) / (2 x 24 x 48)

Simplifying, we get:

cos(θ) = 0.75

To solve for θ, we can take the inverse cosine of both sides:

θ = cos⁻¹(0.75)

Using a calculator, we get:

θ ≈ 41.41°

Rounding to the nearest whole degree, the rescue boat should travel at an angle of approximately 41 degrees off of due east to take the shortest route to the ship.

Members of a softball team raised $2252.25 to go to a tournament. They rented a bus for $1018.50 and budgeted $58.75 per player for meals.

### Answers

**Answer: 2252.25 - 1018.50 = P58.75**

**Step-by-step explanation:**

simplify the polynomial

### Answers

The polynomial after** simplification** is obtained as [tex]5 x^{2}[/tex] + 9x + 3.

**What is** **simplification?**

In mathematics, **reducing** an expression, fraction, or problem to a **simpler form** is referred to as simplification. With calculations and solution, the problem is made simple. Make something simpler by simplifying it.

We are given a polynomial as

5x - 5 + [tex]11 x^{2}[/tex] + 4x - [tex]6 x^{2}[/tex] + 8

Now, in order to simplify the given polynomial, we will combine the like terms of the polynomial.

On combining the like terms, we get

[tex]5 x^{2}[/tex] + 9x + 3

Hence, the polynomial after** simplification** is obtained as [tex]5 x^{2}[/tex] + 9x + 3.

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I need help asap!!

Only 4% on babies are born on their due data.

### Answers

Answer:

14

Step-by-step explanation:

yes

The following are infinite geometric series. For which infinite series could find the sum using a formula?

A) -2+6+(-18)+54+(-162)+...

B) 3+12+48+192+768+...

C) 1+2+4+8+16+...

D) 8+4+2+1+1/2+...

### Answers

**Answer:**

D) 8 + 4 + 2 + 1 + 1/2 + ...

**Step-by-step explanation:**

The **sum **of an **infinite geometric series** can be found when the **absolute value **of the** common ratio**, r, is **less than 1**.

[tex]\boxed{\begin{minipage}{5.5 cm}\underline{Sum of an infinite geometric series}\\\\$S_{\infty}=\dfrac{a}{1-r}$,\quad $|r| < 1$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the first term. \\ \phantom{ww}$\bullet$ $r$ is the common ratio.\\\end{minipage}}[/tex]

To determine which of the given infinite geometric series can be summed using the formula, calculate the **value of r **for each series. To do this, **divide **a term by the previous term.

Given infinite geometric series:

-2 + 6 + (-18) + 54 + (-162) + ...

[tex]\implies r=\dfrac{6}{-2}=-3[/tex]

As r is **not **in the interval −1 < r < 1, the sum of the infinite series **cannot **be found using the formula.

Given infinite geometric series:

3 + 12 + 48 + 192 + 768 + ...

[tex]\implies r=\dfrac{12}{3}=4[/tex]

As r is **not **in the interval −1 < r < 1, the sum of the infinite series **cannot **be found using the formula.

Given infinite geometric series:

1 + 2 + 4 + 8 + 16 + ...

[tex]\implies r=\dfrac{2}{1}=2[/tex]

As r is **not **in the interval −1 < r < 1, the sum of the infinite series **cannot **be found using the formula.

Given infinite geometric series:

8 + 4 + 2 + 1 + 1/2 + ...

[tex]\implies r=\dfrac{4}{8}=\dfrac{1}{2}[/tex]

As |r| < 1 the sum of the infinite series **can **be found using the formula.

Therefore, the **infinite series** for which the sum can be found by using the formula is:

D) 8 + 4 + 2 + 1 + 1/2 + ...

A pair of dice is rolled, and the number that appears uppermost on each die is observed. Refer to this experiment and find the probability of the given event. (Enter your answer as a fraction.)

The sum of the numbers is an odd number.

### Answers

The **probability **that the sum of the numbers when two dice are rolled is an odd number is given as follows:

0.5.

How to calculate a probability?

A probability is calculated as the **division **of the **desired **number of outcomes by the **total **number of outcomes in the context of a problem/experiment.

Each dice has six possible outcomes, hence the **total number** of outcomes when two dice are rolled is given as follows:

6² = 36.

When we look at the pattern of the sum of two dice, from (1,1), (1,2), ..., to (6,6) we see that they **alternate **between even numbers and odd numbers, hence:

18 of the outcomes have an even sum.18 of the outcomes have an odd sum.

Hence the **probability **is given as follows:

p = 18/36 = 0.5.

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