A Line And The Point (3,4) Are Graphed In The Coordinate Plane.What Is The Equation Of The Line That (2024)

Mathematics High School

A Line And The Point (3,4) Are Graphed In The Coordinate Plane.What Is The Equation Of The Line That (1)

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 polynomial 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

A Line And The Point (3,4) Are Graphed In The Coordinate Plane.What Is The Equation Of The Line That (2024)
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