Which statements about the composite figure are true? Check all that apply.

kenny6666 [7]

Answer: A, A, C

Step-by-step explanation:

Educated Guess because none of them are going to be zero so it's either A or C but the point has a negative y so to plug it all in all of them have to be negative ex. -1 + -1 + -1 =-3

the x is -1 so both have to be negative in order to get -3

5 0

3 years ago

4. Determine whether f(x) = 1/3x + 5 and g(x) = 3x - 15 are inverse functions.

Ierofanga [76]

Answer:

YES! we conclude that f(x) = 1/3x + 5 and g(x) = 3x - 15 are inverse functions.

Step-by-step explanation:

Given

Given that the function f(x) and g(x) are inverse functions.

$f\left(x\right)\:=\:\frac{1}{3}x\:+\:5$

$g(x) = 3x - 15$

To determine

Let us determine whether f(x) = 1/3x + 5 and g(x) = 3x - 15 are inverse functions.

<u>Determining the inverse function of f(x) </u>

A function g is the inverse function of f if for y = f(x), x = g(y)

$y=\frac{1}{3}x+5$

Replace x with y

$x=\frac{1}{3}y+5$

Solve for y

$y=3x-15$

Therefore,

YES! we conclude that f(x) = 1/3x + 5 and g(x) = 3x - 15 are inverse functions.

4 0

2 years ago

What is the equation, in standard form, of a parabola that contains the following points?

svp [43]

Answer:

D

Step-by-step explanation:

the the 5 minus the 12 and the 0 minus the negative one all finds it way. back to the equation d

5 0

3 years ago

The base of an aquarium with given volume V is made of slate and the sides are made of glass. If slate costs five times as much

Y_Kistochka [10]

Answer:

x = ∛ 2*V/5

y = ∛ 2*V/5

h = V/ ∛ 4*V²/25

Step-by-step explanation:

Dimensions of the aquarium base is x*y

We call c₁ cost per unit area of the sides, then cost per unit area of slate is equal 5c₁.

let call h the height of the aquarium then volume of the aquarium is:

V = x*y*h where h = V / x*y

As the base is a rectangular one there are 2 sides x*h . and 2 sides y*h

According to this:

Ct (cost of aquarium ) = cost of the base + cost of the sides

cₐ ( cost of the base) = 5*c₁*x*y

c₆ (cost of the sides ) = c₁*2*x*h + c₁*2*y*h

C(t) = 5*c₁*x*y +2* c₁*x* V/x*y + 2* c₁*y* V/x*y or

C(t) = 5*c₁*x*y + 2*c₁*V/y *2*c₁* V/x

Taking partial derivatives en x and y we have:

C´(x) = 5*c₁*y - 2*c₁*V/x²

C´(y) = 5*c₁*x - 2*c₁*V/y²

C´(x) = C´(y) ⇒ 5*c₁*y - 2*c₁*V/x² = 5*c₁*x - 2*c₁*V/y²

or 5*y - 2*V/x² = 5*x - 2*V/y²

(5*y*x² - 2*V)/x² = ( 5*y²x - 2*V) /y²

(5*y*x² - 2*V)*y² = ( 5*y²x - 2*V)*x²

5*y³*x² - 2*V*y² = 5*y²x³ - 2*V*x²

5*y³*x² - 5*y²x³ = 2*V * ( y² - x²)

by symmetry x = y

Then using x = y and plugging that value on the derivatives

C´(x) = 5*c₁*y - 2*c₁*V/x²

C´(x) = 5*c₁*x - 2*c₁*V/x²

C´(x) = 0 ⇒ 5*c₁*x - 2*c₁*V/x² = 0

5*x - 2*V/x² = 0 ⇒ 5*x³ - 2*V = 0 ⇒ 5*x³ = 2*V ⇒ x³ = 2*V/5

x = ∛ 2*V/5 and y = ∛ 2*V/5 and h = V/ x*y h = V/ ∛ 4*V²/25

7 0

3 years ago

When a factory operates from 6 AM to 6 PM, its total fuel consumption varies according to the formula f(t)=0.9t^3−0.6t^0.5+10, w

Nataly [62]

Step-by-step explanation:

the answer is in the image above

7 0

3 years ago