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2 years ago

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Given g(x)=Squareroot x-4 and h(x)=2x-8, what is g(h(10))

2 answers:

yan [13]2 years ago

8 0

Answer:

$g(h(10)) = 2\sqrt 2$

Step-by-step explanation:

Given

$g(x) = \sqrt {x - 4$

$h(x) = 2x - 8$

Required

$g(h(10))$

First, calculate $g(h(x))$

We have:

$g(x) = \sqrt {x - 4$

This gives:

$g(h(x)) = \sqrt {h(x) - 4$

Substitute $h(x) = 2x - 8$

$g(h(x)) = \sqrt {2x - 8 - 4$

$g(h(x)) = \sqrt {2x - 12$

Substitute $x = 10$

$g(h(10)) = \sqrt {2*10 - 12$

$g(h(10)) = \sqrt {20 - 12$

$g(h(10)) = \sqrt {8\\$

Split

$g(h(10)) = \sqrt {4} * \sqrt 2$

This gives

$g(h(10)) = 2\sqrt 2$

Gemiola [76]2 years ago

5 0

Answer:

Step-by-step explanation:

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The population of a certain community is known to increase at a rate proportional to the number of people present at time t. If

attashe74 [19]

Answer:

$t=7.85 years$

Step-by-step explanation:

We can write this rate as an ordinary differential equation.

$\frac{dP}{dt}=aP$

Where a is proportional constant, P the population variable, and t the time.

$\frac{dP}{P}=adt$

Integrating each side of the equation.

$\int \frac{dP}{P}=\int adt$

$ln(P)=at+c$

$P=e^{at+c}$

$P=e^{c}e^{at}=Ce^{at}$

To find C we need to use the initial condiction, it means evaluae P at t=0.

$P_{0}=Ce^{0}=C$

$P=P_{0}e^{at}$

Now, we use the sentence the population has doubled in 5 years.

$2P_{0}=P_{0}e^{a5}$

We can find "a" in this condition.

$2=e^{a5}$

$ln(2)=a5$

$a=\frac{ln(2)}{5}$

$a=0.14$

Finally, let's find how long will it take to triple.

$3P_{0}=P_{0}e^{0.14t}$

$3=e^{0.14t}$

$t=\frac{ln(3)}{0.14}$

$t=7.85 years$

I hope it helps you!

4 0

2 years ago

What grade average is 79.2 out of 120

mina [271]

Answer:

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Step-by-step explanation:

Divide 79.2 by 120 and multiply by 100

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3 years ago

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kykrilka [37]

Answer:

The only solution can be (0,-3) point.

Step-by-step explanation:

We have to judge whether the points in options are the solution to the graphed inequality or not.

The first point is (5,-5) which not included in the shaded region of the graph. Hence, it can not be a solution.

The second point is (6,0) which not included in the shaded region of the graph. Hence, it can not be a solution.

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The fourth point is (0,-3). It is on the firm red line which is included in the shaded region of the graph. Hence, it is a solution.

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3 years ago

Find the surface area of this rectangular prism: Don't forget to show the unit of measure.

Ann [662]

Answer:

See Explanation

Step-by-step explanation:

The question is incomplete as the attachment of the prism is not given.

From the attachment:

$L =10cm$ -- Length

$W = 4cm$ -- Width

$H=5cm$ -- Height

Required

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So, the volume is:

$Volume = Length * Width (* Height$

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diamong [38]

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