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2 years ago

Complete the table of inputs and outputs for the given function g(x)=3-8x.

Mathematics

1 answer:

Andreas93 [3]2 years ago

6 0

Answer:

The answers to your questions are given below.

Step-by-step explanation:

From the question given above,

g(x) = 3 – 8x

Thus, we can complete the table given in question above as follow:

1. Determination of x

g(x) = 0

x =?

g(x) = 3 – 8x

0 = 3 – 8x

Collect like terms

0 – 3 = – 8x

– 3 = – 8x

Divide both side by –8

x = – 3 / –8

x = 3/8

2. Determination of g(x)

x = 0

g(x) =.?

g(x) = 3 – 8x

g(x) = 3 – 8(0)

g(x) = 3 – 0

g(x) = 3

3. Determination of x

g(x) = – 5

x =?

g(x) = 3 – 8x

– 5 = 3 – 8x

Collect like terms

– 5 – 3 = – 8x

– 8 = – 8x

Divide both side by – 8

x = – 8 / – 8

x = 1

4. Determination of g(x)

x = 3

g(x) =.?

g(x) = 3 – 8x

g(x) = 3 – 8(3)

g(x) = 3 – 24

g(x) = – 21

Summary

x >>>>>>>>>>>>>>> g(x)

3/8 >>>>>>>>>>>>> 0

0 >>>>>>>>>>>>>>> 3

1 >>>>>>>>>>>>>>>> – 5

3 >>>>>>>>>>>>>>> – 21

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f(x) = −16x2 + 24x + 16 Part A: What are the x-intercepts of the graph of f(x)? Show your work. (2 points) Part B: Is the vertex

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Answer:

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Step-by-step explanation:

f(x) = −16x^2 + 24x + 16

Set equal to zero to find the x intercepts

0 = −16x^2 + 24x + 16

Factor out -8

0 = -8(2x^2 -3x-2)

Factor

0 = -8(2x +1) (x-2)

Using the zero product property

2x+1 =0 x-2 =0

x = -1/2 x=2

The x intercepts are -1/2 ,2

Since the coefficient of x^2 is negative the graph will open down and the vertex will be a maximum

The x value of the maximum is 1/2 way between the zeros

(-1/2+2) /2 = 1.5/2 =.75

To find the y value substitute into the function

f(.75) = -8(2x +1) (x-2)

=-8(2*.75+1) (.75-2)

= -8(2.5)(-1.25)

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2 years ago

Elysse paid for her sandwich and drink with a $10 bill and received $0.63 in change. The sandwich cost $7.75 and sales tax was $

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Given

Elysse paid for her sandwich and drink with a $10 bill and received $0.63 in change.

The sandwich cost $7.75 and sales tax was $0.47.

Find out the cost of her drink

To proof

Let the cost of her drink be x.

As given in the question

Elysse paid for her sandwich and drink with a $10 bill and received $0.63 in change.

Elysse paid for her sandwich and drink = 10 - 0.63

= $ 9.37

sandwich cost $7.75 and sales tax was $0.47

Than the equation becomes

x = 9.37 - (7.75 + 0.47)

x = 9.37 - 8.22

x = $ 1.15

The cost of the drink is $ 1.15.

Hence proved

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2 years ago

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Answer:

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Step-by-step explanation:

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Box 2 is likely to take up more space if x is unlikely to be between 0 and 1.

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Answer: 8 (Pi - sqrt(3))

Discussion:

The area of the shaded region is that of the semicircle minus the area of the triangle..

Area of semicircle = 1/2 * Pi * R^2

Where R^2 is the square of the radius of the circle. In our case, R ( = OC)

= 4 so the semicircle area is

(1/2) * Pi * (4^2) = (1/2) * Pi * 16 = 8 Pi

Area of triangle.

First of all, angle ACB is a right angle ( i.e. 90 degrees).

* This is the Theorem of Thales from elementary Plane Geometry. *

so by Pythagoras

AC^2 + BC^2 = AB^2

But CB = 4 (given) and AB = 4*2 = 8 ( the diameter is twice the radius).

Substituting these in Pythagoras gives

AC^2 + 4^2 = 8^2 or

AC^2 = 8^2 - 4^2- = 64 - 16 = 48

Hence AC = sqrt(48) = sqrt (16*3) = 4 * sqrt(3)

We are almost done! The area of the triangle is given by

(1/2) b * h = (1/2) BC * AC = (1/2) 4 * (4 * sqrt(3)) = 8 sqrt(3)

We conclude the area area of the shaded part is

8 PI - 8 sqrt(3) = 8 (Pi - sqrt(3))

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