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ra1l [238]
3 years ago
9

Find the constant of proportionality k. Then write an equation for the relationship between x and y

Mathematics
1 answer:
ExtremeBDS [4]3 years ago
6 0

Question:

Find the constant of proportionality k. Then write an equation for the relationship between x and y

\begin{array}{ccccc}x & {2} & {4} & {6} & {8} \ \\ y & {10} & {20} & {30} & {40} \ \ \end{array}

Answer:

(a) k = 5

(b) y = 5x

Step-by-step explanation:

Given

\begin{array}{ccccc}x & {2} & {4} & {6} & {8} \ \\ y & {10} & {20} & {30} & {40} \ \ \end{array}

Solving (a): The constant of proportionality:

Pick any two corresponding x and y values

(x_1,y_1) = (2,10)

(x_2,y_2) = (6,30)

The constant of proportionality k is:

k = \frac{y_2 - y_1}{x_2 - x_1}

k = \frac{30-10}{6-2}

k = \frac{20}{4}

k = 5

Solving (b): The equation

In (a), we have:

(x_1,y_1) = (2,10)

k can also be expressed as:

k = \frac{y- y_1}{x- x_1}

Substitute values for x1, y1 and k

5 = \frac{y- 10}{x- 2}

Cross multiply:

y - 10 = 5(x - 2)

Open bracket

y - 10 = 5x - 10

Add 10 to both sides

y - 10 +10= 5x - 10+10

y = 5x

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A car travels 240 miles in 4 hours. at this rate, how many miles will it travel in 8 hours
oksian1 [2.3K]
First you need to find the rate. This problem is based on the formula d = rt
d = distance
r = rate 
t = time.

The question is asking how many miles will it travel in 8 hours so to find this out we need to find the rate when the car travels 240 miles in 4 hours. We use this information and plug it into the model d = rt

d = 240
r = don't know yet
t = 4 hr
d = rt 
240 = 4r
240 / 4 = 4r / 4
60 = r
r = 60
So the car is going at a rate of 60 miles per hour. Now that we know this we can solve for how many miles the car will travel in 8 hours.
d = rt
d = r * t
d = 60 * 8
d = 480

So the car will travel 480 miles in 8 hours

Another way to think about this is that you know the car traveled 240 miles in 4 hours and the question is wanting to know how far the car will travel in 8 hours, which would be double the 4 hours so 240 + 240 = 480

8 0
3 years ago
Please help right away!!!
ira [324]
It depends on your goals.

typically it's B but it could be D
3 0
3 years ago
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sergey [27]
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6 0
2 years ago
1. Find the least common multiple of 6 and 9. oct common multiple of​
Marat540 [252]
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2 years ago
Two consecutive perfect squares have a difference of $99$. what is the value of the larger perfect square?
Fofino [41]

Answer:

2500

Step-by-step explanation:

Let the first square number be x^2 then the next square number is (x+1)^2.

The difference between these two consecutive numbers is 99.

This implies that:

(x+1)^2-x^2=99

We expand to get:

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Divide both sides by 2

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Therefore the value of the larger perfect number is

(49+1)^2=50^2=2500.

6 0
3 years ago
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