Write an equation to determine Sarah’s age

If f(x)=x^4+6, g(x)=x-2 and h(x)= sqrt (x), then f(g(h(x)))=

patriot [66]

Answer:

x^2 + 4x * (3 - sqrt(x)) - 2(5 + sqrt(x))

Step-by-step explanation:

Firstly let us split this up, we need to first work out what g(h(x)) is:

h(x) = Sqrt(x) so g(h(x)) = g(sqrt(x)) = sqrt(x) - 2

Now to work out f(g(h(x))) = f(sqrt(x) - 2) = (sqrt(x) - 2)^4 + 6

= (sqrt(x) - 2) * (sqrt(x) - 2) * (sqrt(x) - 2) * (sqrt(x) - 2) - 6

= (x - 2 * sqrt(x) + 4) * (x - 2 * sqrt(x) + 4) - 6

= x^2 - 2x * sqrt(x) + 4x - 2x * sqrt(x) + 4x - 8 * sqrt(x) + 4x - 8 * sqrt(x) + 16 - 6

= x^2 - 4x * sqrt(x) + 12x - 16 * sqrt(x) + 10

= x^2 + 4x * (3 - sqrt(x)) - 2(5 + sqrt(x))

3 0

3 years ago

For a given input value b, the function f outputs a value a to satisfy the following equation. 4a+7b=−52 Write a formula for ) f

Sergio [31]

Answer: Our required formula becomes :

$a=f(b)=-13-\frac{7}{4}b$

Step-by-step explanation:

Since we have given that

$4a+7b=-52\\$

We need to write a formula for f(b) in terms of b So, it becomes

$4a=-52-7b\\\\a=\frac{-52-7b}{4}\\\\a=\frac{-52}{4}-\frac{7b}{4}\\\\a=-13-\frac{7b}{4}$

Hence, our required formula becomes :

$a=f(b)=-13-\frac{7}{4}b$

5 0

3 years ago

Read 2 more answers

In 2010, the average duration of long-distance telephone calls originating in one town was 9.4 minutes. A long-distance telephon

Zepler [3.9K]

<u>Answer</u>: No, we do not have sufficient evidence to conclude that the mean call duration, µ, is different from the 2010 mean of 9.4 minutes.

Step-by-step explanation:

As per given , we have

$H_0: \mu=9.4\\\\H_a:\mu\neq9.4$ , since $H_0$ is two-tailed so , the test is a two tail test.

Since population standard deviation is unknown, so we use t-test.

Critical value (two-tailed) for significance level of 0.01= $t_{n-1,\alpha/2}=t_{49, 0.005}\pm2.609228$

For n =50 , $\overline{x}=8.6$ and s= 4.8

Test statistic : $t=\dfrac{\overline{x}-\mu}{\dfrac{s}{\sqrt{n}}}$

$t=\dfrac{8.6-9.4}{\dfrac{4.8}{\sqrt{50}}}\approx-1.18$

Since test statistic value (-1.18) lies in critical interval (-2.609228, 2.609228), it means the null hypothesis is failed to reject.

We do not have sufficient evidence to conclude that the mean call duration, µ, is different from the 2010 mean of 9.4 minutes.

4 0

3 years ago

Need this help me will give brainllest to the one gives me all three answer

PilotLPTM [1.2K]

Answer:

the sum is -4

Step-by-step explanation:

3 0

3 years ago

Read 2 more answers

A rectangular box has length x and width 3. The volume of the box is given by y = 3x(8 – x). The greatest x-intercept of the gra

CaHeK987 [17]

Consider rectangular box with

length x units (x≥0);
width 3 units;
height (8-x) units (8-x≥0, then x≤8).

The volume of the rectangular box can be calculated as

$V_{box}=\text{length}\cdot \text{width}\cdot \text{height}.$

In your case,

$V_{box}=3\cdot x\cdot (8-x).$

Note that maximal possible value of the height can be 8 units (when x=0 - minimal possible length) and the minimal possible height can be 0 units (when x=8 - maximal possible length).

From the attached graph you can see that the greatest x-intercept is x=8, then the height will be minimal and lenght will be maximal.

Then the volume will be V=0 (minimal).

Answer: correct choices are B (the maximum possible length), C (the minimum possible height)

7 0

3 years ago