All categories

1 year ago

If g (x)=4x+7 and h (x)=x-6, find g (h(x))

Mathematics

1 answer:

Lena [83]1 year ago

3 0

<h2>Answer:</h2>

$g(h(x))=4x-17$ .

<h2 /><h2>Step-by-step explanation:</h2>

<em>This is a problem of combination of functions. Let's find the combination of f(x) and g(x).</em>

<h2 /><h3>1. Write the full argument of g(x).</h3><h2> $g(x)=4x+7$ </h2><h2 /><h3>2. Insert the argument of h(x) as if it was an x value on g(x).</h3>

<em>Argument of h(x): </em> $x-6$ <em>.</em>

$g(h(x))=4(x-6)+7$

<h3>3. Apply the associative property of multiplication to solve the parenthesis.</h3>

$g(h(x))=[(4)(x)+(4)(-6)]+7\\ \\g(h(x))=[4x+(-24)+7\\ \\g(h(x))=4x-24+7$

<h3>4. Simplify by adding.</h3>

$g(h(x))=4x-17$ .

<em>Learn more about </em><em>combination of functions</em><em> here: </em>

<em>brainly.com/question/28263470 </em>

<em>brainly.com/question/28308849 </em>

You might be interested in

A TV that usually sells for $186.67 is on sale for 20% off. If sales tax on the TV is 8%, what is the price of the TV, including

Furkat [3]

Answer:

$161.28288 or $161.28 if rounded

Step-by-step explanation:

first find 10% of the original cost

186.67/10 =18.667

18.667 x 2 = 37.334 (20%)

186.67 - 37.334 = 149.336

to find the tax, mulitple 149.336 x 1.08

1.08 because, 100% of the cost, plus 8% of the cost for tax

= 161.28288

5 0

2 years ago

What is the value of the exponential expression below?

dimaraw [331]

Answer:

the answer is D which is 6

7 0

2 years ago

100 POINTS plz help Chuck drops a rock from a height of 70 m. How long will it take the rock to hit the ground?

lord [1]

Answer:

3.8

Step-by-step explanation:

We are going to plug in the values of the equation, so h(t)=-4.9^2+v0t+h0 will

now be h(t)=-4.9^2+0+70

Now we will find the a b and c of the equation, a=-4.9 b=0 c=70

Now we must find the discriminant of the equation, which the equation for that is D=b^2+(-4)(a)(c)

So D=1,372

Now we use the quadratic formula (see picture below for finished product)

4 0

3 years ago

Read 2 more answers

Genetic Defects Data indicate that a particular genetic defect occurs in of every children. The records of a medical clinic show

Dovator [93]

Complete Question

The complete question is shown on the first uploaded image

Answer:

The probability that there exist 60 or more defected children is $P(x \ge 60)=0.0901$

Looking at the value for this probability we see that it is not so small to the point that the observation of this kind would be a rare occurrence

Step-by-step explanation:

From the question we are told that

in every 1000 children a particular genetic defect occurs to 1

The number of sample selected is $n= 50,000$

The probability of observing the defect is mathematically evaluated as

$p = \frac{1}{1000}$

$= 0.001$

The probability of not observing the defect is mathematically evaluated as

$q = 1-p$

$= 1-0.001$

$= 0.999$

The mean of this probability is mathematically represented as

$\mu = np$

Substituting values

$\mu = 50000*0.001$

$= 50$

The standard deviation of this probability is mathematically represented as

$\sigma = \sqrt{npq}$

Substituting values

$= \sqrt{50000 * 0.001 * 0.999}$

$= \sqrt{49.95}$

$= 7.07$

the probability of detecting $x \ge60$ defects can be represented in as normal distribution like

$P(x \ge 60)$

in standardizing the normal distribution the normal area used to approximate $P(x \ge 60)$ is the right of 59.5 instead of 60 because x= 60 is part of the observation

The z -score is obtained mathematically as

$z = \frac{x-\mu }{\sigma }$

$= \frac{59.5 - 50 }{7.07}$

$=1.34$

The area to the left of z = 1.35 on the standardized normal distribution curve is 0.9099 obtained from the z-table shown z value to the left of the standardized normal curve

Note: We are looking for the area to the right i.e 60 or more

The total area under the curve is 1

$P(x \ge 60) \approx P(z > 1.34)$