Which other expression has the same value as (-14) - (-8)? Explain your reasoning. *

ASAPPP!!!! HELP I WILL GIVE 100POINTS AND BRAINLIST Question 9 (Essay Worth 10 points)

Luda [366]

Answer:

Part A)

The x-intercepts are (-1/4, 0) and (4, 0).

Part B)

The vertex is a maximum because the leading coefficient is negative.

The vertex is (1.875, 72.25).

Part C)

We can plot the zeros and the vertex, and connect them with a curve.

Step-by-step explanation:

The function given is:

$f(x)=-16x^2+60x+16$

Part A)

To find the x-intercepts of the function, set the function equal to 0 and solve for x:

$0=-16x^2+60x+16$

We can divide both sides by negative four:

$0=4x^2-15x-4$

Factor:

$0=(4x+1)(x-4)$

Zero Product Property:

$x-4=0\text{ or } 4x+1=0$

Solve for each case:

$\displaystyle x=-\frac{1}{4}\text{ or }x=4$

Hence, our zeros are:

$\displaystyle \left(-\frac{1}{4}, 0\right)\text{ and } \left(4, 0\right)$

Part B)

Note that the leading coefficient of our function is negative.

So, our function will be concave down.

Hence, our vertex will be the maximum.

The vertex is given by:

$\displaystyle \left(-\frac{b}{2a}, f\left(-\frac{b}{2a}\right)\right)$

In this case, a = -16, b = 60, and c = 16.

Find the x-coordinate of the vertex:

$\displaystyle x=-\frac{(60)}{2(-16)}=\frac{15}{8}=1.875$

Substitute this back into the function to find the y-coordinate:

$f(1.875)=-16(1.875)^2+60(1.875)+16=72.25$

Hence, our vertex is:

$(1.875, 72.25)$

Part C)

Since we already determined the zeros and the vertex, we can plot the two zeros and the vertex and draw a curve between the three points.

The graph is shown below. Again, to do this by hand, simply plot the three points and connect them with a parabola. If necessary, we can also find the y-intercept.

7 0

2 years ago

Write each equation in slope-intercept form. underline the slope and circle the y-intercept in each equation 5x+3y=30

faust18 [17]

Answer:

The slope is

5

3

.

The y-intercept is

−

10

.

Explanation:

5

x

−

3

y

=

30

is the standard form for a linear equation. The slope-intercept form is

y

=

m

x

+

b

, where

m

is the slope, and

b

is the y-intercept. To convert from standard form to slope-intercept form, solve the standard form for

y

.

5

x

−

3

y

=

30

Subtract

5

x

from both sides of the equation.

−

3

y

=

30

−

5

x

Divide both sides by

−

3

.

y

=

30

−

3

−

5

x

−

3

=

y

=

−

10

+

5

3

x

Rearrange the right hand side.

y

=

5

3

x

−

10

m

=

5

3

,

b

=

−

10

graph{y=5/3x-10 [-10, 10, -5, 5]}

4 0

3 years ago

Read 2 more answers

What is the relationship between 0.04 and 0.004

Molodets [167]

0.04 is multiplied 10 times to get 0.004

4 0

3 years ago

Simplify each expression (e^2) (g) (g^4) (e^3) (e)( e^2) (e)

poizon [28]

Answer:

(e^2) (g) (g^4) (e^3)=e^b

(e)( e^2) (e)=ve^4

Step-by-step explanation:

4 0

2 years ago

The U.S. Bureau of the Census predicted that the population of Pennsylvania would be about 12.7 million in 2010 and then would i

liraira [26]

Answer:

y=0. 24x + 12. 7

Step-by-step explanation:

since you start with 12. 7 and gain .24 each year, you would multiply the years by. 24 and just add the 12. 7 I hope this makes sense. also I love your profile picture :)

3 0

2 years ago