how do i solve this question

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Answer 1

[tex]\bf \begin{cases} h(x)=(f\circ g)(x)\\ h(x)=\sqrt{x+5}\\ f(x)=\sqrt{x+2} \end{cases}\\\\ -------------------------------\\\\ (f\circ g)(x)\implies f[\ g(x)\ ]\implies f[\ g(x)\ ]=\sqrt{g(x)+2}\qquad thus \\\\\\ \sqrt{g(x)+2}=(f\circ g)(x)=h(x)=\sqrt{x+5}\qquad therefore \\\\\\ \sqrt{g(x)+2}=\sqrt{x+5}\impliedby \textit{squaring both sides}\\\\\\ g(x)+2=x+5\implies g(x)=x+5-2\implies \boxed{g(x)=x+3}[/tex]

Related Questions

Suppose a least-squares regression line is given by modifyingabove y with caret equals 4.302 x minus 3.293y=4.302x−3.293. what is the mean value of the response variable if x equals 20x=20

Answers

Final answer:

The mean value of the response variable y when x equals 20 in the least-squares regression line equation y = 4.302x - 3.293 is 82.041.

Explanation:

The given equation is y = 4.302x - 3.293, which is a least-squares regression line. In this formula, x is the independent variable and y is the resulting dependent variable or response. The goal is to find the mean value of the response variable when x is 20. This can be achieved simply by plugging 20 in place of x in our equation and calculating the resulting value for y.

We will substitute x = 20 into the equation y = 4.302x - 3.293. Therefore, the value of y when x is 20 is:

y = 4.302(20) - 3.293 = 82.041

So, when x = 20, the mean value of the response variable y or the predicted y value is 82.041.

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Which of the following is closest to 27.8 times 9.6? A. 280. B 300. C 2,800. D 3,000

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A 280. you really couldn't use a calculator?

The answer would be A because multiplying the 2 numbers give you 266.88

a rectangle has a width of 17 ft and a lenghth of 8ft....PLEASE HELP ME SOS!!! ASAP!!!

Answers

perimeter is 17 +17 +8 + 8 = 50 feet

area = 17 x 8 = 136 square feet

cost = 136 x $3.50 = $476.00

Kurt wants to have $25,000 in an investment account four years from now. the account will pay 0.2 percent interest per month. if he saves money every month, starting one month from now, how much will he have to save each month to reach his goal

Answers

Given:
F = 25000, future value
i=0.02 per month, compounded monthly
n=4*12=48 periods (months)
Need A=monthly deposit

The amount A is given by the formula
A=Fi/((1+i)^n-1) [can be derived from the annuity formula]
=25000*0.02/((1.02^48-1)
= 315.05

Answer: Kurt will need to save $315.05 each month to reach the goal of saving $25000 after 4 years.

Kurt will have to save an amount of $496.75 each month.

What is Compound Interest?

Compound interest is defined as the amount of interest which has been calculated on the principal amount as well as the amount accumulated over the previous period is also included.

Final amount of the account, A = $25,000

Interest rate, r = 0.2% = 0.002

Number of years, t = 4 years

Interest compounded monthly, so n = 12

Annuity can be found using the formula,

Annuity = 25,000 ÷ {[(1 + 0.002)^(12×4) - 1] / 0.002}

= 25,000 ÷ {[(1.002)⁴⁸ - 1] / 0.002}

= 496.75

Hence the amount Kurt needs to save each month is $496.75.

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Consider the following.
Point
(-5, 4)
Line
x + y = 7
(a) Write the slope-intercept form of the equation of the line through the given point and parallel to the given line.

(b) Write the slope-intercept form of the equation of the line through the given point and perpendicular to the given line.

Answers

x + y = 7....y = -x + 7....the slope here is -1

A. a parallel line will have the same slope
y = mx + b
slope(m) = -1
(-5,4)...x = -5 and y = 4
sub and find b, the y int
4 = -1(-5) + b
4 = 5 + b
4 - 5 = b
-1 = b
so ur parallel line is : y = -x - 1 <==

B. perpendicular lines have negative reciprocal slopes. That means our perpendicular line will have a slope of 1
y = mx + b
slope(m) = 1
(-5,4)...x = -5 and y = 4
now we sub and find b, the y int
4 = 1(-5) + b
4 = -5 + b
4 + 5 = b
9 = b
so ur perpendicular line is : y = x + 9 <==

find the volume of a sphere with a diameter of 25 cm. approximate pi as 3.14 and round your answer to the nearest hundredth

Answers

4/3[tex] \pi [/tex]r^3 is the forumla, and r = d/2, so 25/2 = 12.5 so r = 12.5 cm

4/3*[tex] \pi [/tex]*(12.5)^3 = 4/3*[tex] \pi [/tex]*1953.125 = 4/3 * 6132.8125 =
8177.08 cm

Branliest Please!

The formula for the volume of a sphere is:

V=4/3πr³

The diameter given is 25 cm, so that means the radius is 12.5 cm.

Now you just need to plug in the numbers and you will have:

V=(4/3)(3.14)(12.5)³

After plugging that all in the calculator, you should get the answer:

V=8,177.083333 cm³, which rounds to 8,177.08 cm³

I hope this helps!

$10,000 is invested at two different rates. $2,500 is invested at 4%, and the rest is invested at 5%. How much interest is earned at the end of one year? Show all work for full credit.

Answers

hmm is very straight forward, how much is whatever% of anything? is just (whatever/100) * anything.

[tex]\bf \textit{4\% of 2,500}\implies \cfrac{4}{100}\cdot 2,500\implies 100 \\\\\\ \textit{the rest is 7,500 at 5\%, what's 5\% of that?}\implies \cfrac{5}{100}\cdot 7,500\implies 375[/tex]

WILL GIVE BRAINLIEST...
You have 45 ft of the fence you enclose your yard, you are going to use the side of your house as one of the sides and put a fence down the width of the yard so your dog as a place to play, the length is three less than the width. What is the area of your yard?

Answers

We have 45 ft of the fence and we are going to use the side of the house as one of the sides ( on length ).
L = W - 3
2 W + L = 45
2 W + W - 3 = 45
3 W = 45 + 3
3 W = 48
W = 48 : 3
W = 16 ft
L = 16 - 3 = 13 ft
A = 16 * 13 = 208 ft²
Answer: The area of the yard is 208 ft².

The equation d=13/v shows that the density of a particular substance equals a mass of 13 grams divided by the volume of the substance. What happens to the density as the volume approaches 0?

Answers

d = M/V where M=mass and V = volume

Assume the Mass is 1 kg and the Volume = 1 cm³, so d= 1/1 kg/cm³

for V=0.1 → d = 1/0.1 = 10 kg.cm³
for V = 0.01 → d = 100.kg.cm³
for V = 0.001 → d = 1000.kg.cm³
for V = 0.000001 → d = 1,000,000.kg.cm³
and when Volume → 0. density →∞
.

Answer: the density approaches infinity

Step-by-step explanation:

A = h/2 * (a + b ); for h

Answers

[tex]A=\dfrac{h}{2}(a+b)\\ 2A=h(a+b)\\ h=\dfrac{2A}{a+b} [/tex]

h/2 * (a + b )=A
h/2=A/(a+b)
h=2A/(a+b)

(03.03 HC)

The table shows the outputs, y, for different inputs, x:

Input (x) 6 12 15 25
Output (y) 14 15 15 16

Part A: Do the data in this table represent a function? Justify your answer. (3 points)

Part B: Compare the data in the table with the relation f(x) = 7x − 15. Which relation has a greater value when x = 6? (2 points)

Part C: Using the relation in Part B, what is the value of x if f(x) = 6? (5 points)

Answers

part A the table does not show function because 15 is repeated which is a relationship.

If the measure of angle A is 40* and the length of side b is 15 inches, which can be the length of side a if it is possible to form two triangles

Answers

Because ∠A=40°, therefore ∠B + ∠C = 180.

To create two triangles, we could make a = 10 in.

From the Law of Sines,
a/sinA = b/sinB.

Therefore
10/sin(40) = 15/sin(B)
sin(B) = (15/10)*sin(40) = 0.9642
∠B = arcsin(0.9642) = 74.6°

Because the sine function is positive in quadrants 1 and 2, we could also have ∠B = 180 - 74.6 = 105.4°.
This means that
a/sin(105.4) = 15/sin(40°)
a = [sin(105.4)/sin(40)]*15 = 22.5 in

Answer:
We could have a = 10 in, or a = 22.5 in

A school did a survey among 100 students to find their sports preferences. The students were asked about their preferences for football or baseball. Out of the total 77 people who liked football, 48 also liked baseball. There were 65 people who liked baseball. Part A: Summarize the data by writing the values that the letters A to I in the table below represent. (5 points) Like football Do not like football Total Like baseball A D G Do not like baseball B E H Total C F I Part B: What percentage of the survey respondents did not like either football or baseball? (3 points) Part C: Do the survey results reveal a greater dislike for football or baseball? Justify your answer. (2 points)

Answers

PART A:

Total of students who like football = 77 students
Students who like football and baseball = 48 students
Students who like football and not baseball = 77 - 48 = 29 students

Students who do not like football = 100 - 77 = 23 students

Students who like baseball = 65 students
Students who like baseball but not football = 65 - 48 = 17 students

Students who do not like baseball = 100 - 65 = 35 students

These data can be represented in a two ways table as shown below

PART B:

The number of students who do not like either football or baseball is 29+17+6=52

The probability is 52/100 = 52%

PART C:

The number of students who don't like football is 17+6=23 students
The number of students who don't like baseball is 35 students

The survey result reveals a greater dislike for baseball

Find a nonzero vector normal to the plane

Answers

Find a nonzero vector normal to the plane z - 3 (x - 1) = -3 (4 - y).

The casino la bella fortuna is for sale and you think you might want to buy it, but you wantto know how much money you are going to make. all the present owner can tell you is thatthe roulette game red or black is played about 1000 times a night, 365 days a year. eachtime it is played you have probability 19/37 of winning the player’s bet of $10 and probability18/37 of having to pay the player $10.

Answers

Expected gain per player per game
10*(19/37)-10*(18/37)=0.27027
Expected gain per player per night (1000 games per night)
=1000*0.27027
=270.27
Expected gain per player per year (365 nights per year)
=270.27*365
=98648.65

Revenue is 98648.65 times the average number of players per game.

Final answer:

The expected value of the roulette game red or black is -$0.62 per game, indicating an expected average loss.

Explanation:

The expected value of the roulette game red or black can be calculated by multiplying the probabilities of winning and losing by their corresponding outcomes. In this case, the probability of winning ($10) is 19/37, and the probability of losing ($-10) is 18/37. Multiply these probabilities by their corresponding outcomes and subtract to get the expected value:

Expected value = (19/37 * $10) + (18/37 * -$10) = -$0.54 + (-$0.54) = -$0.62

This means that if you play this game repeatedly, over a long string of games, you would expect to lose an average of 62 cents per game.

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Two people are traveling and need to exchange the currency of their native country for the currency of the country they are visiting. drag each exchange to match the ratio of currency to currency in each category.

Answers

Answer:

The solution is shown in attached figure.

Step-by-step explanation:

In table 1,