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3 years ago

Which equation represents the relationship shown in the table?

Mathematics

2 answers:

Mila [183]3 years ago

5 0

Y=4x because 20/5 equals 4

zysi [14]3 years ago

4 0

Answer:

The equation is y = 4x

Step-by-step explanation:

From the table we can pick any 2 points $(x_1,y_1) \ \text{ and } \ (x_2, y_2)$ such, we can obtain the slope of the line given 2 points using the following equation

$m = \cfrac{y_2-y_1}{x_2-x_1}.$

Then we can compare to the given options, or alternatively find the y-intercept using any point of the line, to get a line equation that looks like $y = mx+b$

Finding the slope.

We can pick the first 2 points, that is (1,4) and (5, 20).

Replacing them on the slope equation give us,

$m=\cfrac{20-4}{5-1}$

Simplifying we get

$m=\cfrac{16}{4}\\m=4$

Thus the only option that has slope 4 is the line equation y = 4x which is the right answer for the exercise.

You might be interested in

Given: f(x) = 3x-7, g(x)=2x2 -3x+1, h(x)=4x+1, k(x) =-x2+3 Find: k(x) +g(x)

Afina-wow [57]

Answer:

k(x) + g(x) = x² - 3x + 4

General Formulas and Concepts:

Alg I

Combining like terms

Step-by-step explanation:

Step 1: Define

f(x) = 3x - 7

g(x) = 2x² - 3x + 1

h(x) = 4x + 1

k(x) = -x² + 3

Step 2: Find k(x) + g(x)

Substitute: k(x) + g(x) = -x² + 3 + 2x² - 3x + 1
Combine like terms (x²): k(x) + g(x) = x² + 3 - 3x + 1
Combine like terms (Z): k(x) + g(x) = x² - 3x + 4

7 0

2 years ago

Ann is adding water to a swimming pool at a constant rate. The table below shows the amount of water in the pool after different

N76 [4]

Answer:

(a) As time increases, the amount of water in the pool increases.

11 gallons per minute

(b) 65 gallons

Step-by-step explanation:

From inspection of the table, we can see that as time increases, the amount of water in the pool increases.

We are told that Ann adds water at a constant rate. Therefore, this can be modeled as a linear function.

The rate at which the water is increasing is the rate of change (which is also the slope of a linear function).

Choose 2 ordered pairs from the table:

$\textsf{let}\:(x_1,y_1)=(8, 153)$

$\textsf{let}\:(x_2,y_2)=(12,197)$

Input these into the slope formula:

$\textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{197-153}{12-8}=\dfrac{44}{4}=11$

Therefore, the rate at which the water in the pool is increasing is:

11 gallons per minute

To find the amount of water that was already in the pool when Ann started adding water, we need to create a linear equation using the found slope and one of the ordered pairs with the point-slope formula:

$y-y_1=m(x-x_1)$

$\implies y-153=11(x-8)$

$\implies y-153=11x-88$

$\implies y=11x-88+153$

$\implies y=11x+65$

When Ann had added no water, x = 0. Therefore,

$y=11(0)+65$

$y=65$

So there was 65 gallons of water in the pool before Ann starting adding water.

3 0

2 years ago

Read 2 more answers

the price of an item has been reduced by 40% the original price was $15 what is the price of the item now

harkovskaia [24]

This answer would be 21 because you’d just do 15 increased by 40% which gave me 21

3 0

3 years ago

A gate is 3 feet tall and casts a shadow 5 feet long. At the same time, a nearby building is 27 ft tall. If this is to be a prop

madam [21]

Answer:

the length of the shadow is 45 feet long

Step-by-step explanation:

8 0

3 years ago

Howhowhow?how??? how would you calculate

Liula [17]

Ok sooooooooooo

Lets say your two fractions are

13/26 and 20/40

you can divide the bottom number by the top one and if you get the same answer for both then they are equivalent. For these you get 2 for both, which means they are equivalent.

another example would be if your fractions are

2/5 and 4/10

You can say well 2*2 equals 4 And 5*2 equals ten so these are equivalent fractions.

3 0

3 years ago