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2 years ago

The table represents a linear function. What is the slope of the function?

Mathematics

1 answer:

TEA [102]2 years ago

3 0

Answer:

-4

Step-by-step explanation:

The function is linear; therefore, the slope of the line joining any two points is the same.

We take any two points from the table and compute the slope or rise/ run between them— let is take points (-4, -2) and (-2, -10).

The slope $m$ of the line joining the points is

$m=\dfrac{\Delta y }{\Delta x } =\dfrac{-2-(-10)}{-4-(-2)} \\\\\boxed{m=-4}$

The slope of the function is -4.

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2 years ago

Tina was given the function y = x 2+ x – 5. For what x value(s) would y = 15?

ziro4ka [17]

Answer:

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Step-by-step explanation:

y = x^2 + x - 5

y = 4^2 + 4 - 5

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2 years ago

A water bottle holds 3 1/3 c of water. A bowl holds 2 1/4 times the amount in the water bottle. How much water does the bowl hol

kodGreya [7K]

First you would put both numbers into improper fractions.

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3 years ago

El señor Antonio Rodríguez compro en efectivo una televisión de plasma de $138,860.00. Le otorgan un descuento de la 20% ¿Cuanto

ella [17]

Answer:

$111,088

Step-by-step explanation:

Paso 1

Encuentra el descuento

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Descuento = 20% × $ 138,860

Descuento = $ 27,772

Paso 2

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Esto se calcula como:

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2 years ago

A chemical refinery needs a vat. They want the vat to be a rectangular prism (with square bases) that has a maximum volume of 1,

Alex17521 [72]

Answer:

For least material to be used lengths of square base and sides = 10 units.

Step-by-step explanation:

Let the lengths of the square base and the sides = x feet, x feet and y feet

Area of the square base = x² feet

Volume of the rectangular prism = Area of the square base × Height

= x²y cubic feet

1000 = x²y

y = $\frac{1000}{x^2}$ -------(1)

Material used in the prism = Surface area of the rectangular prism

= 2(lb + bh + hl)

Here, h = height of the prism

l = length of the base

w = Width of the base

Material to be used (S) = 2(xy + x² + xy) - Area of lid

S = 2(x² + 2xy) - x²

S = x² + 2xy

Now by substituting the value of y from equation (1),

S = x² + $2x(\frac{1000}{x^{2} })$

= x² + $\frac{2000}{x}$

For least amount of material used,

We will find the derivative of the given function and equate it to zero.

S' = 2x - $\frac{2000}{x^{2} }$

2x - $\frac{2000}{x^{2} }$ = 0

2x³ = 2000

x³ = 1000

x = 10 feet

From equation (1),

y = $\frac{1000}{(10)^2}$

y = 10 feet

Therefore, for least amount of the material used lengths of square base and sides will be 10 feet.

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3 years ago