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2 years ago

Given that f ( x ) = 3 x − 7 and g ( x ) = 3 x + 9 , evaluate f ( g ( 2 ) )

Mathematics

1 answer:

Sergio [31]2 years ago

5 0

Answer:

Step-by-step explanation:

f ( x ) = 3 x − 7

g ( x ) = 3 x + 9

f(g(2))

First find g(2)

g(2) = 3(2)+9 = 6+9 = 15

Then find f(15)

f(15) = 3*15 -7 = 45 -7 =38

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The equation of the function h is h... PLEASE HELP MATH

Oduvanchick [21]

Answer:

Part A) $h(4) -m(16)=-4$

Part B) The distance between the y-intercepts is equal to 4 units

Part C) The value of h(x) will always be greater than the value of m(x) for any value of x

Step-by-step explanation:

Part A) What is the value of h(4) -m(16)

we have

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

For x=4

$h(4)=\frac{1}{2}(4-2)^2=2$

Find the equation of the line m(x)

Find the slope

take the points

(8,2) and (12,4)

The formula to calculate the slope between two points is equal to

$m=\frac{y2-y1}{x2-x1}$

substitute

$m=\frac{4-2}{12-8}$

$m=\frac{2}{4}$

$m=\frac{1}{2}$

Find the equation of the line in slope intercept form

$y=mx+b$

we have

$m=\frac{1}{2}$

$point\ (8,2)$

substitute

$2=\frac{1}{2}(8)+b$

solve for b

$b=-2$

$y=\frac{1}{2}x-2$

therefore

$m(x)=\frac{1}{2}x-2$

Find m(16)

$m(16)=\frac{1}{2}(16)-2=6$

$h(4) -m(16)=2-6=-4$

Part B) we know that

The y-intercept is the value of y when the value of x is equal to zero

Find the y-intercept of h(x)

For x=0

$h(0)=\frac{1}{2}(0-2)^2=2$

Find the y-intercept of m(x)

For x=0

$m(0)=\frac{1}{2}(0)-2=-2$

therefore

The distance between the y-intercepts is equal to 2-(-2)=4 units

Part C)

Graph both equations

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

$m(x)=\frac{1}{2}x-2$

using a graphing tool

see the attached figure

The value of h(x) will always be greater than the value of m(x) for any value of x

4 0

3 years ago

Click on the measurement that is equal to 24 kilograms

kenny6666 [7]

Answer:

24000 grams

Step-by-step explanation:

1kg = 1000 grams

So 24kg × 1000 = 24000 grams

3 0

3 years ago

A diver dives from a 10m springboard. the equation f(t) = -4.9t² + 4t + 10 models her height above the pool at time t. When will

Gennadij [26K]

Answer:

At time t = 0.408 sec diver will be at maximum height

Step-by-step explanation:

We have given equation of the height $f(t)=-4.9t^2+4t+9$

We know that velocity is the rate of change of distance with respect to time

So $v=\frac{df(t)}{dt}=\frac{df(-4.9t^2+4t+10)}{dt}=-9.8t+4+0=-9.8t+4$

At maximum height velocity will be zero

So $-9.8t+4=0$

t = 0.408 sec

So at time t = 0.408 sec diver will be at maximum height

5 0

3 years ago

You deposit $750 in an account that earns 7.5% simple interest. How much will be in the account after 5 years?

notka56 [123]

Answer:

$1,031.25 will be in the account

6 0

4 years ago

Read 2 more answers

Determine any data values that are missing from the table, assuming that the data represent a linear function.

Varvara68 [4.7K]

Answer:

c. 14

Step-by-step explanation:

Let the missing y value be y2.

If the data represent a linear function, then:

$\frac{6 - 2}{2 - 1} = \frac{y_2 - 6}{4 - 2}$

$\frac{4}{1} = \frac{y_2 - 6}{2}$

$4 = \frac{y_2 - 6}{2}$

Multiply both sides by 2

$4 \times 2 = \frac{y_2 - 6}{2} \times 2$

$8 = y_2 - 6$

Add 6 to both sides

$8 + 6 = y_2 - 6 + 6$

$14 = y_2$

The missing value is 14

6 0

3 years ago