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3 years ago

avocados cost $3 per pound. write and graph an equation in two variables that represents the cost of buying avocados

1 answer:

4 0

Pounds will be represented by x and the cost will be represented by y. The equation is Y=3x. For the graph just use substition for x and then calculate the outcome and graph it.

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A football is kicked into the air. The height of the football can be modeled by the equation

Alinara [238K]

Answer:

x = 0 and x = 1

Step-by-step explanation:

Given that,

A football is kicked into the air. The height of the football can be modeled by the equation :

$h = -16x^2 + 16x$

Where

h is the height reached by the ball after x seconds

When it touches the ground, h = 0

So,

$-16x^2 + 16x=0\\\\16x(-x+1)=0\\\\x=0\ and\ x=1$

So, it will touch the ground at x = 0 and x = 1 seconds.

6 0

3 years ago

What are the coordinates of the turning point for the function f(x) = (x - 1)3 - 3? A. (-1, -3)

Naddik [55]

ANSWER

The turning point is

$(1,-3).$

EXPLANATION

The function given to us is

$f(x) = (x - 1) ^{3} - 3$

At turning point,
$f '(x) = 0$

So we need to differentiate the given function and equate it to zero.

We using the chain rule of differentiation, we obtain,
$f '(x) =3 (x - 1) ^{2}$

We equate this to zero to obtain,

$3 (x - 1) ^{2} = 0$

We divide through by 3.

$(x - 1) ^{2} = 0$

We solve for x to get,

$x - 1 = 0$

$x = 1$

We substitute this x-value in to the function to obtain the corresponding y-value of the turning point.

$f(1) = (1- 1) ^{3} - 3$

$f(1) = 0 - 3$

$f(1) = - 3$

Therefore the turning point is

$(1,-3)$

C is the correct answer.

6 0

3 years ago

Read 2 more answers

HELPPPPP ME OUUTTTTTTT!!!!

klemol [59]

Answer:

20 degrees

Step-by-step explanation:

we can consider 33 to be the radius of a circle.

31 would then be the cos of the angle in that circle.

the regular cos function is defined for the standard circle with radius 1. so, that would be multiplied by 33 for this circle here.

31 = cos(?) × 33

cos(?) = 31/33 = 0.9393...

? = 20.05 ≈ 20 degrees

5 0

3 years ago

The one-to-one functions g and h are defined as follows

Debora [2.8K]

Answer:

$g^-^1(x)=-8$

$h^-^1(x)=\frac{x-4}{3}$

$(h^-^1 \ o\ h)(-3)=-3$

Step-by-step explanation:

When given the following functions,

$g=[(-2,-7),(4,6),(6,-8),(7,4)]$

$h(x)=3x+4$

One is asked to find the following,

1. Question 1

$g^-^1(4)$

When finding the inverse of a function that is composed of defined points, one substitutes the input given into the function, then finds the output. After doing so, one must substitute the output into the function, and find its output. Thus, finding the inverse of the given input;

$g^-^1(4)$

$g(4)=6\\g(6)=-8\\g^-^1(4)=-8$

2. Question 2

$h^-^1(x)$

Finding the inverse of a continuous function is essentially finding the opposite of the function. An easy trick to do so is to treat the evaluator (h(x)) like another variable. Solve the equation for (x) in terms of (h(x)). Then rewrite the equation in inverse function notation,

$h(x)=3x+4\\\\h(x)-4=3x\\\\\frac{h(x)-4}{3}=x\\\\\frac{x-4}{3}=h^-^1(x)$

$h^-^1(x)=\frac{x-4}{3}$

3. Question 3

$(h^-^1 \ o\ h)(-3)$

This question essentially asks one to find the composition of the function. In essence, substitute function (h) into function ( $h^-^1$ ) and simplify. Then substitute (-3) into the result.

$h^-^1\ o\ h$

$\frac{(3x+4)-4}{3}\\\\=\frac{3x+4-4}{3}\\\\=\frac{3x}{3}\\\\=x$

Now substitute (-3) in place of (x),

$=-3$

8 0

3 years ago

Find the x-intercepts of the parabola with vertex (-3,-18) and y-intercept at (0,0)

statuscvo [17]

Y + 18 = a(x + 3)^2
0 + 18 = a(0 + 3)^2 
18 = 9a 
2 = a

y = 2(x + 3)^2 - 18 
0 = 2(x + 3)^2 - 18 
18 = 2(x + 3)^2 
9 = (x + 3)^2 
± 3 = x + 3 
-3 ± 3 = x 
x = 0 or -6

(0, 0) and (-6, 0)

5 0

3 years ago