MATHEMATICS HIGH SCHOOL

In the xy-plane, the point (p,r) lies on the line with equation y=x+b, where b is a constant. The point with coordinates (2p,5r) lies on the line with equation y=2x+b. If p≠0, what is the value of r/p?

Answers

Answer 1

Answer:

Answer: 3/4

================================================

Explanation

The point (p,r) is on the line y = x+b

Plug in x = p and y = r to get r = p+b. Let's solve for b

r = p+b

b = r-p

This will be used later.

The point (2p,5r) is on the line y = 2x+b

Plug in those coordinates:

y = 2x+b

5r = 2*(2p)+b

5r = 4p+b

Next we replace b with r-p. This is valid because b = r-p.

5r = 4p+b

5r = 4p+r-p

5r = 3p+r

5r-r = 3p

4r = 3p

Then we follow the cross multiplication process in reverse.

4r = 3p

4r/4 = 3p/r

r = 3p/4

r/p = (3p/4)*(1/p)

r/p = 3/4 is the final answer

Answer 2

Answer:

Final answer:

Using the given coordinates and equations, we find that the value of r/p is 3/4 after a process of subtracting and simplifying two equations.

Explanation:

The question is related to the linear equations in the xy-plane. Given two points, (p,r) and (2p,5r) which lie respectively on the equations y = x + b and y = 2x + b.

We have two points on two different lines:

Point A: (p, r) lies on the line y = x + b.
Point B: (2p, 5r) lies on the line y = 2x + b.

Substituting the coordinates of the first point into the first equation gives r = p + b. Similarly, substituting the coordinates of the second point into the second equation gives 5r = 2(2p) + b, which simplifies to 5r = 4p + b.

Now, subtract the first equation from the second to eliminate b, resulting in 5r - r = 4p - p, which simplifies to 4r = 3p.

Dividing by 4p gives us r/p = 3/4. So, the value of r/p is 3/4.

Learn more about equations

brainly.com/question/33622350

#SPJ11

Related Questions

Two triangles are similar . The sides of the smaller triangle have lengths of 8,12, and 16 centimeters. The perimeter of the larger triangle is 54 centimeters. Find the length of the shortest side of the triangle.
Write an equation in slope-intercept form for the line: through (-6,3); horizontal
Find last year's salary if, after a 5 % pay raise, this year's salary is $34,125.
What is the soultion of - 21 = n - 8 what is n
What is the slope of ?

A certain forest covers an area of 2,000 square kilometers. Suppose that each year this area decreases by 6%. What is the function that bestrepresents the area of the forest each year and how much area remains after 12 years? Round your answer to the nearest square kilometer.Hint: Use the formula, f(x) = P(1 + r)x.

Answers

The question gives you the formula to use, but it's printed wrong.
The 'x' is an exponent after the (1 + r).

All you have to do is take the formula, and write the numbers into it
that are also given.

The key thing to spot is that the forest is decreasing, so the 'r' is negative,
just as if you had money in a savings account and every year the bank took
6% out of it.

So the formula to use is    f(x) = P (1 + r) ^x

P = 2000
r = -0.06
      f(x) = 2000 (1 - 0.06)^x
         = 2000 (0.94)^x

The amount left after 12 years is

   2000 (0.94)¹² =

   2000 (0.476) = 951.8 square kilometers.

hope this helps- i did the test :)

Answer:

the relative frequency of a blue on a spinner is 3/5.how many times would you expect a blue in 250 spins

Answers

$250\cdot\frac{3}5=\boxed{150\text{ times}}$

Faye and Andrew have written down the same negative number.Faye squares the number then multiplies by 2 and adds 4.
Andrew multiples the number by 21 then subtracts the result from 40.
They both finish with the same answer. What was the number?

Answers

x - the number

Faye squares the number: x²
then multiplies by 2: 2x²
and adds 4: 2x²+4

Andrew multiplies the number by 21: 21x
then subtracts the result from 40: 40-21x

They both finish with the same answer, so the results are equal.
$2x^2+4=40-21x \n2x^2+21x+4-40=0 \n2x^2+21x-36=0 \n2x^2+24x-3x-36=0 \n2x(x+12)-3(x+12)=0 \n2x-3=0 \ \lor \ x+12=0 \n2x=3 \ \lor \ x=-12 \nx=(3)/(2) \ \lor \ x=-12$

The number is negative so x=-12.

The number is -12.

Ben has some tiles. Each tile is the shape of a parallelogram. 6cm at the top and 10cm on the side He places the tiles in a row to make a shape with area 720cm2. How many tiles does he use?

Answers

Answer:

12 tiles

Step-by-step explanation:

First we need to find the area of the parallelogram, which can be found by the product of the two dimensions.

If the parallelogram has 6 cm and 10 cm, the area is 6 * 10 = 60 cm2

Then to find how many tiles are needed to fill the area of 720 cm2. we can do a rule of three:

1 tile -> 60 cm2

x tiles -> 720 cm2

x = 720 / 60 = 12 tiles

Find all solutions to the equation.

sin x = sqrt(3)/2

Answers

Answer:

$x=(\pi)/(3) and x=(2\pi)/(3)$

Step-by-step explanation:

We are given that $sin x=(\sqrt3)/(2)$

We have to find all solutions of the given equation

We know that $sin (\pi)/(3) =sin60^(\circ)=(\sqrt3)/(2)$

sin x is positive then the value of sin x will lie in I quadrant and II quadrant.The value of sin x is negative in III and IV quadrant .

We are given that sin x is positive then the solution will lie in I and II quadrant only.Therefore, the solution of sin x will not lie in III and IV quadrant .

$sin x =sin (\pi)/(3)$ ...(I equation )and $sin x =sin(\pi-(\pi)/(3))$ ...(II equation)

In II quadrant $\theta$ change into $(\pi-\theta )$

Cancel sin on both side of equation I

Then, we get

$x=(\pi)/(3)$

$sin x =sin ((3\pi-\pi)/(3))$

$sin x =sin (2\pi)/(3)$ ...(II equation )

Cancel sin on both side of equation II

Then we get

$x=(2\pi)/(3)$

Hence, the solutions of equation are

$x=(\pi)/(3) and x=(2\pi)/(3)$

The solutions of the equation are:

x = 60 degrees

x = 120 degrees

x = 420 degrees

x = 480 degrees, and so on.

We have,

The solutions to the equation sin(x) = √3/2 are any angles where the sine of the angle is equal to √3/2.

So,

sin 60 = √3/2

sin 120 = sin (π - 60) = sin 60 = √3/2

In trigonometry 180 is written as π.

Since (π - 60) is in the secondquadrant sin 60 is positive.

sin 420 = sin (360 + 60) = sin 60 = √3/2

In trigonometry 360 is written as 2π.

Since (2π + 60) is in the Firstquadrant sin 60 is positive.

Similarly,

sin 480 = sin (2π + 120) = sin 120 = sin (π - 60) = sin 60 = √3/2

Thus,

The solutions of the equation are:

x = 60 degrees

x = 120 degrees

x = 420 degrees

x = 480 degrees, and so on.

Learn more about solutionsofequations here:

brainly.com/question/545403

#SPJ6

What is the domain of the function shown in the graph 1) all real numbers
2)all real numbers less than 0
3)all real number greater than 0
4)all real numbers including 2 and 6

Answers

Answer:

The answer to your question is number 1) all real numbers.

Step-by-step explanation:

The Domain is all the set of numbers the x-axis could have.

In the graph, we notice a line that goes from zero to six, we could think that the domain is that interval but as the line has arrows, we can think that the line grows up in both senses, then the domain must be all real numbers.

Other Questions

Write 60/100 as a percent

If m(x)= x+5/x-1 and n(x)=x-3, which function has the same domain as (m*n)(x)?

Cuantos pedazos de cinta de 1/4 de metro se pueden obtener de un rollo de cinta que mide 15/2? 30 pedazos. 60 pedazos. 15 pedazos. 45 pedazos.

Convert the fraction to higher terms. Enter the value of the missing numerator 3/10=?/80

In the xy-plane, the point (p,r) lies on the line with equation y=x+b, where b is a constant. The point with coordinates (2p,5r) lies on the line with equation y=2x+b. If p≠0, what is the value of r/p?​

Answers

Answer: 3/4

Related Questions

Answers

Answers

Answers

Answers

Answers

Answers

In the xy-plane, the point (p,r) lies on the line with equation y=x+b, where b is a constant. The point with coordinates (2p,5r) lies on the line with equation y=2x+b. If p≠0, what is the value of r/p?