Mathematics High School

## Answers

**Answer 1**

The **equation **of line is y = ( 1/4 )x + 13/4 , where the **slope **is m = 1/4

What is an Equation of a line?

The **equation **of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The **slope **m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the **equation **of line be represented as A

Now , the value of A is

Let the first point be P ( 0 , 1 )

Let the second point be Q ( 4 , 2 )

Now , the **slope **of the line is m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Substituting the values in the equation , we get

Slope m = ( 2 - 1 ) / 4

Slope m = 1/4

Now , the **equation **of line is given by y - y₁ = m ( x - x₁ )

Let the third point be R ( 3 , 4 )

And , y - 4 = ( 1/4 ) ( x - 3 )

On simplifying the equation , we get

y - 4 = ( 1/4 )x - 3/4

Adding 4 on both sides of the equation , we get

y = ( 1/4 )x + 13/4

Hence , the **equation **of line is y = ( 1/4 )x + 13/4

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## Related Questions

A rectangular paperboard measuring 23 in long and 17 in wide has a semicircle cut out of it, as shown below. What is the perimeter of the paperboard that remains after the semicircle is removed? (Use the value 3.14 for , and do not round your answer. Be sure to include the correct unit in your answer.)

### Answers

The **perimeter **of the paperboard that remains after the **semicircle **is removed is **89.69 In**.

What is the perimeter of the paperboard that remains?

A perimeter is defined as a **closed path **which encompasses, surrounds or outlines either a two dimensional shape or a one-dimensional length.

**Given data**

Length = 23 in

Width = 17 in

The **radius **of the semi circle = Half of the width of the paperboard = 17 / 2 = 8.5in

The **circumference **of the semi circle = π*radius = 3.14*8.5 = 26.69 In

The **perimeter **of the paperboard that remains after the semicircle is removed = Top + Left + Bottom + Right Circumference of the semi circle = 23 + 17 + 23 + 26.69 = 89.69 In

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60 -(-15)+(-13)=Calculate without using a calculator

### Answers

**Answer:**

**We can simplify the expression using the order of operations, which is commonly remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction):**

**First, we evaluate the expression inside the parentheses:**

**60 - (-15) + (-13) = 60 + 15 - 13**

**Next, we perform the addition and subtraction operations from left to right:**

**60 + 15 - 13 = 72**

**Therefore, 60 - (-15) + (-13) simplifies to 72.**

Eric has a loan of 35,000. This loan had a simple interest rate of 3% per year. What is the amount of interest that Erin will be charged in this loan at the end of the year?

### Answers

The **interest** **amount** is $1050.

What is simple interest?

It is the **interest** calculated on the **principal** with its given rate for the given number of **years**.

The **formula** used is PRT/100

Where P is the principal, R is the rate, and T is the time in years.

We have,

**Principal** P = 35,000 _____(1)

**Rate** R = 3% ______(2)

**Time** T = 1 year ______(3)

The **simple** **interest** formula.

SI = [tex]\frac{PRT}{100}[/tex]

**Substituting** the values from (1), (2), and (3) we get,

SI = [tex]\frac{35000\times3\times1}{100}[/tex]

SI = 1050

Thus,

The **interest** **amount **at the end of the year is $1050.

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How much does 1 oz weigh in Grams?

### Answers

Hello!

**Answer: **An ounce is 28 grams.

**Step-by-step explanation: **In a quarter ounce, there are 7 grams. Half an ounce weighs 14 grams. There are 3.5 grams in one-eighth of an ounce.

Hope this helps.

Have a great day! :)

~Ray

Every day, you run 5 miles in 40 minutes. Your friend runs 8 miles every day at the same pace as you. How long is your friends run

### Answers

Your friend’s run is **8 miles** long and takes 64 minutes (or 1 hour and 4 minutes) at the same** pace **as you.

Let’s first calculate your pace:

Your pace = **distance covered** / time taken = 5 miles / 40 minutes = 0.125 miles per minute

This means that you can cover 0.125 miles in one minute at your current pace.

Now, we know that your friend runs 8 miles every day, and if they run at the same pace as you, we can calculate how long it would take for them to cover that distance:

**Time taken** by your friend = distance covered / your pace

Substituting the values, we get:

Time taken by your friend = 8 miles / 0.125 miles per minute = 64 minutes

So your friend’s run is 8 miles long, and it takes them 64 minutes (or 1 hour and 4 minutes) to complete it at the same pace as you.

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a function is translated from f(x)=2⋅3x 4 to g(x)=2⋅3x−1. what is the effect on f(x)?

### Answers

The effect on f(x) is that it is **shifted one unit **to the left on the x-axis to obtain g(x).

Here,

In mathematics, a **graph **is a visual representation of a set of objects, called vertices or nodes, and the connections between them, called edges or links.

The **function **f(x) is translated to g(x) by subtracting 1 from the exponent of 3.

This means that g(x) is obtained by shifting f(x) one unit to the right on the x-axis.

The **coefficient **of 2 remains unchanged, which means that the overall scaling of the function remains the same.

**Therefore**, the effect on f(x) is that it is shifted one unit to the left on the x-axis to obtain g(x).

In other words, the graph of g(x) is obtained by taking the graph of f(x) and shifting it to the right by one unit.

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How to solve 4x-12=3x-3

### Answers

To solve 4x - 12 = 3x - 3, we must isolate the variable, x.

First, move all terms that contain the variable, x to one side, and all the constant terms to the other.

Let's move 3x to the other side. To do that, we can subtract 3x on both sides. This cancels out 3x on the right side since 3x - 3x equals 0.

4x - 12 - 3x = -3

Now, let's move -12 to -13. To do that, we can add 12 on both sides. -12 + 12 equals 0.

4x - 3x = -3 + 12

Now, combine the like terms.

x = 9

And that's it!

Selling price: $40.00

rate of sales tax: 4%

whats the sales tax?

### Answers

**The sales tax is calculated as a percentage of the selling price. In this case, the selling price is $40.00 and the rate of sales tax is 4%.**

**To calculate the sales tax, we can multiply the selling price by the rate of sales tax:**

**Sales tax = Selling price x Rate of sales tax**

**Sales tax = $40.00 x 0.04**

**Sales tax = $1.60**

**Therefore, the sales tax for a selling price of $40.00 and a rate of 4% is $1.60. The total cost of the item including sales tax would be $40.00 + $1.60 = $41.60.**

it takes all the correlations found in studies of a particular relationship and calculates a weighted average, called by?

### Answers

The weighted **average** of correlations found in studies of a particular relationship is called the meta-analytic **correlation**.

What is meta analysis?

Meta-analysis is a **statistical** technique that combines the results of multiple studies to arrive at an overall estimate of the strength and direction of a relationship or effect. In meta-analysis, the meta-analytic correlation is typically calculated by weighting the individual study correlations by their sample sizes or other relevant factors, such as the precision of the measurement instrument or the quality of the study design.

Why do we choose an average?

The **average**—the midpoint of the supplied data set—is established by adding together all the figures and dividing the sum by the quantity of statistics provided. The average value is the number with the most data display capacity. In our daily lives, the average computation frequently appears.

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What is 120ml to oz?

### Answers

the full answer is 4.05768 tbh i forgot how to round so just round that up

How many days is 1 million seconds?

### Answers

**Answer:**

≈11.574074

**Step-by-step explanation:**

First, how many seconds are in a day?

60x60x24=86400 seconds.

Now, divide

1,000,000/86,400

10000/864

5000/432

2500/216

1250/108

625/54

≈11.574 days

What is a number (from the choices given) that make this solution true?

x - 10 > 45

45

50

55

60

### Answers

**Answer:**

60 for sure

**Step-by-step explanation:**

when you subtract 60 from 10 you get 50 which is greater than 45, well it is so easy that a 1st grader can answer (don't mean anything bad)

In the diagram of MNP shown the midpoints of the sides MN and MP have been connected to form segment SR explain why quadrilateral SRNP must be a trapezoid￼

### Answers

We know that SR is parallel to MN and MP is parallel to NP. This means that **quadrilateral **SRNP has one pair of parallel sides (SR and MN), which is the definition of a trapezoid. Hence, quadrilateral SRNP must be a trapezoid.

Why is there a quadrilateral shape there?

A **quadrilateral** has four enclosed sides. Quadrilaterals include the following shapes: It was produced by Raphael. It has four sides. The shape has only one set of parallel sides and no straight angles.

In order to prove that quadrilateral SRNP is a trapezoid, we need to show that it has one pair of parallel sides.

We know that SR and MP are both medians of triangle MNP, which means they each pass through the midpoint of the opposite side. Let's call the midpoint of MN point Q.

Since SR passes through the midpoint of MN at point Q, we know that SR is parallel to side MN (by the converse of the midpoint theorem). Similarly, we can show that MP is parallel to side NP (by using the midpoint of MP and the midpoint of NP).

Therefore, we have shown that SR is parallel to MN and MP is parallel to NP. This means that **quadrilateral **SRNP has one pair of parallel sides (SR and MN), which is the definition of a trapezoid. Hence, quadrilateral SRNP must be a trapezoid.

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how much is 150 lb to kg?

### Answers

The **conversion rate **from pounds (lb) to kilograms (kg) is 1 kg = 2.20462262 lb.

To convert 150 lb to kg, we can use the** formula **kg = lb/2.20462262. When we plug in 150 for lb, we get kg = 150/2.20462262 = 68.0388555 kg. Therefore, 150 lb is equal to 68.0388555 kg.

The formula for converting lb to kg is kg = lb/2.20462262. To use this formula, divide the **number of pounds** by 2.20462262 to get the equivalent number of kilograms. Multiplying by the conversion factor of 2.20462262 is the same as **dividing **by 1, so the formula can also be written as kg = lb*2.20462262.

In summary, 150 lb is equal to 68.0388555 kg, and the formula to convert lb to kg is kg = lb/2.20462262 or kg = lb*2.20462262.The **conversion rate **from pounds (lb) to kilograms (kg) is 1 kg = 2.20462262 lb.

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How tall is a 153cm in feet?

### Answers

Answer:5.02 feet is the answer

Write a polynomial of least degree with roots 0 and -5.

Write your answer using the variable x and in standard form with a leading coefficient of 1.

### Answers

In **standard ****form,**** ****the polynomial of least degree **with roots 0 and -5 is:

p(x) = x² + 5x

How to Write a Polynomial with Least Degree?

If the polynomial has roots 0 and -5, then it must have factors of x and x + 5. To find the **polynomial of least** **degree**, we can multiply these factors together:

p(x) = x(x + 5).

Multiplying out the terms, we get:

p(x) = x² + 5x

This is a **polynomial** of degree 2 (quadratic), but we are asked for the **polynomi****al of least degree** with roots 0 and -5. However, since the leading coefficient is already 1, this is already in **standard form**. Therefore, the **polynomial of least degree** with roots 0 and -5 is:

p(x) = x² + 5x

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Factor the expression.

q² - r²s)

+ Szl zb

+

r4s²)

394

+

### Answers

The **factored expression** for this problem is given as follows:

q² - r² = (q - r)(q + r).

How to factor the expression?

The expression in the context of this problem is factored using the **subtraction of perfect squares **notable product, as follows:

a² - b² = (a - b)(a + b).

The **parameters a and b** for the expression q² - r² are given as follows:

a = q.b = r.

Hence the** factored expression **is given as follows:

q² - r² = (q - r)(q + r).

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over the last 2 decades the population of amherst, massachusetts has gone from 34,874 people to 39,714 people. what was the relative change in population rounded to the nearest percent?

### Answers

14% was the relative change in **population** rounded to the nearest percent.

Is relative change consistently favourable?

The absolute value can be substituted for the actual change in the formula above to generate a value for the relative change that is always non-negative if the relationship of the value with regard to the reference value (that is, larger or smaller) is **irrelevant **in a given application.When compared with the value of the signal during the prior time, relative change shows the relative change as a percentage.

To determine the relative change, we obtain,

We know that ,

Relative change = [tex]\frac{x_{2} -x_{1} }{x_{1}}[/tex],

[tex]x_{2}[/tex]=final value & [tex]x_{1}[/tex]= initial value

Relative change =[tex]\frac{39,714 -34,874}{34,874}[/tex]×100

⇒Relative change =0.139×100=14%.

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the domain of an exponential function is all real numbers. the domain of an exponential function is all real numbers. true false

### Answers

The **statement **"the domain of an exponential function is all real numbers" is generally **true**. An exponential function is a mathematical function of the form f(x) = a^x, where a is a positive **constant **and x can be any real number.

Since x can be any real number, the domain of an exponential function is all real numbers. This means that you can input any real number into an **exponential **function and get a valid output.

However, there are some special cases where the domain of an exponential function is restricted. For example, if the base a of the exponential function is negative, the **domain **of the function is limited to even integer values of x, because negative numbers raised to non-integer powers are not defined in the real number system.

In addition, if the function has other operations or **transformations **applied to it, such as addition or multiplication, the domain of the function may be restricted by these operations.

Overall, while the domain of an exponential function is typically all real numbers, it's important to consider any special cases or restrictions that may apply to a specific **function**.

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The functions f and g are defined by

[tex]f(x) = \frac{x}{x - 1} \: \\ g(x) = hx + k[/tex]

whereas x ≠ 1. the value of h and k are constants. given g(3) = 8 and gf(2) = 5, find the value of h and of k

### Answers

Therefore, the value of h is 3 and the value of k is 2. Hence, the** function **g(x) is:

g(x) = 3x + 2

A function example is what?

A **function**, a type of rule, creates one output from one input. A good example of this is the formula y=x2. Any input for x produces only one outcome for y. It is correct to state that y is a **function** of x because x serves as the input value.

To find the **values** of h and k, we need to first find the expressions for f(x) and g(x).

f(x) = x/(x - 1) (given)

gf(2) = g(f(2)) = g(2/(2 - 1)) = g(2)

We don't know the value of g(2), but we do know that gf(2) = 5, so:

g(2) = 5

g(x) = hx + k (given)

g(3) = h(3) + k = 8 (given)

Now, we have two **equations** in two unknowns:

h(3) + k = 8

h(2) + k = 5

Subtracting the second equation from the first, we get:

h(3) - h(2) = 3

h(3 - 2) = h(1) = 3

Substituting h(1) = 3 in the second equation, we get:

3 + k = 5

k = 2

Therefore, the value of h is 3 and the value of k is 2. Hence, the** function **g(x) is:

g(x) = 3x + 2

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The **values** of **h = 3 **and **k = -1/2**.

**What is a function?**

In mathematics, a **function** is a **relationship** between a set of **inputs** and a **set** of possible **outputs** with the **property** that each **input** is related to exactly one **output**. It is a rule that assigns to each input exactly one output.

We have:

gf(2) = g(f(2)) = g(2/(2-1)) = g(2)

and

g(3) = h(3) + k

From gf(2) = 5, we have:

f(2)g(2) = 5

2g(2) = 5

g(2) = 5/2

From g(3) = h(3) + k, we have:

h(3) + k = 8

So, we have two equations with two unknowns:

h(3) + k = 8

h/1 + k = 5/2

Solving for k, we have:

h/1 + k = 5/2

k = 5/2 - h

Substituting k in the first equation, we have:

h(3) + (5/2 - h) = 8

3h + 5 - 2h = 16/2

h = 3

Substituting h in the expression for k, we have:

k = 5/2 - 3/1

k = -1/2

Therefore, The **values** of **h = 3 **and **k = -1/2**.

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X - Y = 10

3x + y = 18

### Answers

**Answer:**

Point Form:

(7,−3)

Equation Form:

x=7, y= −3

**Step-by-step explanation:**

Solve for the first variable in one of the equations, then substitute the result into the other equation.

I’m so stuck please help

### Answers

**Answer: it is d**

**Step-by-step explanation:**

How do you find a perpendicular line through a given point?

### Answers

**Answer: To find a line that's perpendicular to a line and goes through a particular point, use the point's coordinates for (x1, y1) in point slope form: y - y1 = m (x - x1).**

What is the formula for angular velocity 2 pi t?

### Answers

The formula for **angular velocity** 2 pi t is ω = (2π/t).

The formula for **angular velocity** in terms of **time** is given by:

ω = Δθ/Δt

where ω is the** angular velocity**, Δθ is the change in the angle in **radians**, and Δt is the change in **time**.

For an object moving in a circular path, the angle through which the object moves in a given **time** period t is equal to 2π **radians**, which represents one complete **revolution** around the circle. Therefore, we can use the formula above to express the **angular velocity** of the object as:

ω = Δθ/Δt = (2π **radians**) / t

This simplifies to:

ω = (2π/t)

where t is the **time** taken for one complete **revolution** of the object. This formula shows that the **angular velocity** of an object in circular motion is inversely proportional to the **time** taken for one complete **revolution**. In other words, the faster an object moves in a circular path, the higher its **angular velocity**. Conversely, the slower the object moves, the lower its **angular velocity**.

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What are the half angle trig identities?

### Answers

The **formula** for half-angle identities is as below:

1. Sine of a Half Angle: sin(a/2)=±√(1−cosa)/2

2. Cosine of a** Half Angle:** cos(a/2)=±√(1+cosa)/2

3. Tangent of a Half Angle : tan(a/2)=1−cosa/sina=sina/1+cosa.

It is sometimes very crucial to determine the value of the **trigonometric** **functions** for half-angles. For instance, using some half-angle formula we can convert an **expression** with exponents to one without exponents, and whose angles are multiples of the original angle. It is to note that we get half-angle formulas from **double-angle formulas**. Both sin (2A) and cos (2A) are obtained from the double angle formula for the cosine.

The formula for half-angle **identities** is as below:

1.Sine of a Half Angle: sin(a/2)=±√(1−cosa)/2

2. **Cosine** of a Half Angle: cos(a/2)=±√(1+cosa)/2

3. Tangent of a Half Angle : tan(a/2)=1−cosa/sina=sina/1+cosa.

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Steven is comparing One-fourth and Four-fifths using benchmarks 0 and 1. Which statement is trueOne-fourth is closer to 1 than to 0.

Four-fifths is closer to 0 than to 1.

One-fourth is less than Four-fifths.

Four-fifths is less than One-fourth.

### Answers

The correct statement regarding the **fractions **is given as follows:

One-fourth is less than Four-fifths.

How to convert the fraction to decimal?

To convert a fraction to decimal, we must **divide **the numerator of the fraction by the denominator of the fraction.

Then the **decimals **that are equivalent to each fraction in this problem are given as follows:

1/4 = 0.25 -> closer to 0, as .25 < .5.4/5 = 0.8 -> closer to 1, as .8 > .5.

Hence the** correct statement** is given as follows:

One-fourth is less than Four-fifths.

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Which set of data contains two outliners

### Answers

**Answer:**

none as there is nothing to see

**Step-by-step explanation:**

What is the present of 1\4 and 1/2 round to the merits ten

### Answers

The **presents** of 1/4 and 1/2 **rounded** to the nearest tenth are 25.0% and 50.0%.

What is a percentage?

The **percentage** means the required value out of 100.

It is calculated by **dividing** the required value by the total value and **multiplying** by 100.

The percentage change is also calculated using the same method.

In percentage change we find the difference between the values given.

Example:

Required percentage value = a

total value = b

Percentage = a/b x 100

We have,

To find the **percentage** of 1/4 and 1/2, we need to **divide** each fraction by 1 and then **multiply** by 100.

So,

1/4

= 1/4 x 100

= 0.25 x 100

= 25%

And,

1/2 x 100

= 0.5 x 100

= 50%

Now,

**Rounding** 25% and 50% to the **nearest** **tenth**.

25% rounded to the nearest tenth.

= 25.0%

50% rounded to the nearest tenth.

= 50.0%

Thus,

The **presents** of 1/4 and 1/2 **rounded** to the nearest tenth are 25.0% and 50.0%.

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Rewrite the following fraction with a denominator of 100.

14/25

### Answers

Answer: 56/100

Multiple both by 4

Sam finished 20 problems. He finished 8 at school and 4 per hour at home.

Whats the equation?

### Answers

8 + 4x = 20

He already did 8

He does them at a rate of 4 per hour

20-8= 12

12/4 =3

He did 3 problems per hour