If f(x) = 2x - 8 and g(x) = square root of x - 5, what is (f ^ g)(30).

Answers

Answer 1

Final answer:

The output of the function (f ^ g)(30) in this context refers to first calculating the output of the g function given x = 30, then substituting this output into the f function. With g(30) = sqrt(x - 5) and f(x) = 2x - 8, we find that (f ^ g)(30) = 2.

Explanation:

To find (f ^ g)(30), we first need to find the output of the g function when x = 30 and then substitute this output into the f function. This is also known as the composition of functions.

First, let's find the output of the g function when x = 30. Given that g(x) = sqrt(x - 5), for x = 30, g(30) = sqrt(30 - 5) = sqrt(25) = 5.

Next, we substitute this output into the f function. Given that f(x) = 2x - 8, when x = 5, f(5) = 2(5) - 8 = 10 - 8 = 2.

Therefore, (f ^ g)(30) = 2.

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Answer 2

Final answer:

To find the value of [tex](f ^ g)(30)[/tex], substitute 30 into both f(x) and g(x) to find f(30) and g(30). Then substitute g(30) into f(x) to find the final value.

Explanation:

In this mathematics question, you're asked to find the value of [tex](f ^ g)(30)[/tex]where [tex]f(x) = 2x - 8[/tex]and g(x) = square root of x - 5. To calculate (f ^ g)(x), we first need to find the value x in both functions f and g. So, let's find f(30) and g(30) first.

Firstly, substitute x = 30 into f(x). So, [tex]f(30) = 2*30 - 8 = 52[/tex]. Now, substitute x = 30 into g(x). So, g(30) = square root of (30 - 5) = square root of 25 = 5.

Now, f ^ g(30) means we substitute the output of g(30) = 5 into f(x) which gives us [tex]f(5) = 2*5 - 8 = 2.[/tex]

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Related Questions

Express the given quantity as a single logarithm. ln x + a ln y − b ln z

Answers

The rules of logarithms tell you ...
• [tex]\ln(a)+\ln(b)=\ln(a \cdot b)[/tex]
• [tex]a \cdot \ln(b)=\ln(b^{a})[/tex]

[tex]\ln(x)+a \cdot \ln(y)-b \cdot \ln(z)=\ln\left( \dfrac{x \cdot y^{a}}{z^{b}} \right)[/tex]

Final answer:

To express ln x + a ln y - b ln z as a single logarithm, use the properties of logarithms.

Explanation:

To express ln x + a ln y - b ln z as a single logarithm, we will use the properties of logarithms. The key properties we will use are:

ln xy = ln x + ln y: The logarithm of a product is the sum of the logarithms of the factors.ln (x/y) = ln x - ln y: The logarithm of a quotient is the difference of the logarithms of the numerator and denominator.

Using these properties, we can simplify the expression:

ln x + a ln y - b ln z = ln x + ln(y^a) - ln(z^b)= ln (x(y^a)/(z^b))

So, the given quantity can be expressed as a single logarithm: ln (x(y^a)/(z^b))

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Which ordered pair is a solution of y = x - 4?

( -3, -7 )

( 3, -7 )

( -3, 7 )

( 3, 7 )

Answers

(-3, -7) is your answer

an order pair follows the (x, y) pair, in which (in this case), x = -3, and y = -7

plug in to the respective places inside the equation.

y = x - 4

(-7) = (-3) - 4

-7 = -7 (true)

Therefore, (-3, -7) is your answer

hope this helps

The correct answer is (-3,-7). This is because you can plug it in and the two sides are equal to each other. When you plug -3 in for x, you subtract for from it and get -7 since the y term is -7 the answer is -7=-7, thus (-3, -7) is the answer.

im posting several questions i need help with in an image

Answers

Answers:
(1) n = 4
(2) x = 30
(3) a = -4
(4) n =10
(5) n = -46.2

Explanation:
(1) Given
9n-8 = 28
9n = 28 + 8
9n = 36
n=4

(2) Given
-1-x = -31
-x = -31 + 1
x = +31 - 1
x = 30

(3) Given
9-4a = -5a + 5
-4a + 5a = 5 - 9
a = -4

(4) Given
n/2 = 5
n=5*2
n = 10

(5) Given
29.5 = -16.7 -n
n = -16.7 - 29.5
n = -46.2

1.
9n = 28 + 89n = 36n=4
2.
-x = -31 + 1x = 31 - 1x = 30

3.
9-4a = -5a + 5-4a + 5a = 5 - 9
a = -4

4.
n/2 = 5n=5*2 n =10

5.
29.5 = -16.7 -nn = -16.7 - 29.5n = -46.2

you have $120 to donate equally to several charities. Does this situaton represent direct or inverse variation? Explain.

Answers

This situation represents inverse variation.

The difference between direct and inverse variation is in direct variation, as one variable goes up the other does too, while in inverse, as one variable goes up the other falls.

In this case, as you donate to more charities, the amount you donate to each charity falls, because you donate an equal amount. This means it's inverse variation.

Hope this helps!

Which is the equation of a parabola with Vertex (0, 0) and directrix y = 4?

Answers

we know that

Vertex (0, 0) and directrix y = 4

is a vertical parabola------> open down (directrix above the vertex)
the equation is of the form
(y-k)=4p(x-h)²--------> y=4p*x²-------> vertex (0,0)

y=4
y=h-p-----> y=-p
p=-4

the equation of the parabola is
y=-16x²

the answer is
y=-16x²

see the attached figure

Answer:

D. x^2 = -16y

Step-by-step explanation:

got it right on edge

A = LW ; for L whats the answer step by step

Answers

divide W on each side ( A/W =L)

The answer is: " W = L / A " .
_________________________________________________
Explanation:
_________________________________________________
Given:
_________________________________________________
" A = LW " ; Solve for "L" ; {step-by step} ;
_________________________________________________
A = L * W ;

↔ L * W = A ;

Divide each side of the equation by "W" ;
to isolate "L" on one side of the equation; & to solve for "L" ;

→ { L * W } / L = A / L ;

to get:

→ W = L / A .
________________________________________________________
The answer is: " W = L / A " .
________________________________________________________

3/x+2 = 2/x−1 pleasee help

Answers

So you have:
[tex] \frac{3}{x} + 2 = \frac{2}{x} - 1 [/tex]

1) Start off by multiplying both sides by x to simplify the problem:
[tex]\frac{3}{x} + 2 = \frac{2}{x} - 1 \\ x(\frac{3}{x} + 2) = (\frac{2}{x} - 1)x\\ 3 + 2x = 2 - x [/tex]

2) Now isolate the x by moving all terms with x onto one side and all other terms onto the other side:
[tex]3 + 2x = 2 - x\\ 3x = -1[/tex]

3) Finally, divide by 3 on both sides to find the value of x:
[tex]3x = -1\\ x = \frac{-1}{3} [/tex]

------

Answer: x = [tex]\frac{-1}{3}[/tex]

some help help help help help help help help help help help help help help help help help help help help me please please please some

Answers

The answer would be 24. The answer would be 24 because 6+6+6+6 = 24, or a shortcut of 6*4 which would be 24. Hope this helps!

a plumber has a 36in. pipe that he has to cut into two pieces so that one piece is 8 in. longer than the other. find the length of each piece?

Answers

one piece is 14 in the other is 22 in

one is 22
and the other one is 14

A rectangular pyramid has a volume of 210 cubic centimeters. Find two possible sets of measurements for the base area and height of the pyramid.

Answers

To find 2 possible sets of dimensions you will use the formula for finding the volume of a prism.

V = 1/3Bh, where B is the area of the base.

210 = 1/3Bh
630 = Bh; this means the area of the B time the height must equal 630

Find 3 factors that will give you 630.

Ex #1: 10 cm (length) x 6 cm (width) x 9 cm (height)

Ex #2: 5 cm (length) x 9 cm(width) x 14 cm(height)

Answer:

630 cm 3 is the answer to the question

A cylindrical thermos has a radius of2 in. and is 5 in. high. It holds 10 f oz. To the nearest ounce, how many ounces will a similar thermos with a radius of 3 in. hold? Show your work

Answers

let
A--------> larger thermos with radius 3 in
B-------> smaller thermos with radius 2 in

we know that
scale factor=radius larger thermos/radius smaller thermos
scale factor=3/2----> 1.5

volume larger thermos=[scale factor]³*volume smaller thermos
volume larger thermos=[1.5]³*10 f oz-----> 3.375*10-----> 33.75 f oz----> 34 f oz

the answer is
34 f oz

A toy manufacturer needs a piece of plastic in the shape of a right triangle with the longer leg 2 cm more than the shorter leg and the hypotenuse 2 cm more than the longer leg. How long should the sides of the triangle be?

Answers

Short leg = 6, Long leg is 8, and hypotenuse is 10. Just for proof (6^2+8^2) = 100, the square root of that is 10.

The only Pythagorean triple that is an arithmetic sequence is (3, 4, 5). If the side lengths differ by 2 cm, they must be ...
6 cm, 8 cm, 10 cm

What is the simple interest that is missing from the table? p $375 r 2.2% t 3 years

Answers

I = Prt
I = 375*0.022*3 = $24.75

Express using a negative exponent.
1/z^9

Answers

According to the rules of indices:
1/a^b=a^-b
thus using this rule, our value will be expressed as follows:
1/z^9=z^-9
Hence the answer is: z^-9

How many gallons of punch will sadie make?

Answers

Sadie will make 3 gallons of punch.

First, let's convert all the measurements to the same unit, such as gallons.

1 gallon = 4 quarts

1 gallon = 8 pints

1 gallon = 16 cups

Now, let's convert each ingredient:

1. Lemon-lime juice: 8 quarts = 8/4 = 2 gallons

2. Vanilla ice cream: 4 pints = 4/8 = 0.5 gallons

3. Orange juice: 8 cups = 8/16 = 0.5 gallons

Now, let's sum up the amounts of each ingredient:

2 gallons (lemon-lime juice) + 0.5 gallons (vanilla ice cream) + 0.5 gallons (orange juice) = 3 gallons

Complete question: Using 8 quarts lemon-lime juice , 4 pints vanilla ice cream , 8 cups orange juice .How many gallons of punch will Sadie make?

Joel is mailing a large envelope to his cousin. The envelope has pictures inside, so he doesn't want to bend it.
The mail slot has the dimensions shown. The dotted line shows the widest part of the slot.

Answers

Answer: 25

Step-by-step explanation:

Pythagorean theorem

c=√a²±b²

So it was 7=A

And it was 24=b

solving that it gives us 25

This isn’t that much of help sorry but this is the basic info on how to solve it you can learn more by searching videos about the Pythagorean thermom.

Hope this helps-A

The maximum width of the slot is 25cm (Option A).

To find the maximum width of the mail slot, we need to calculate the length of the diagonal (the dotted line) in the rectangle. The diagonal of a rectangle can be found using the Pythagorean theorem.

Given:

- The length of the rectangle (one side) = 24 cm

- The height of the rectangle (other side) = 7 cm

The formula for the diagonal [tex]$ d $[/tex] is:

[tex]\[ d = \sqrt{(length)^2 + (height)^2} \][/tex]

Substituting the given values:

[tex]\[ d = \sqrt{24^2 + 7^2} \][/tex]

[tex]\[ d = \sqrt{576 + 49} \][/tex]

[tex]\[ d = \sqrt{625} \][/tex]

[tex]\[ d = 25 \, \text{cm} \][/tex]

So, the maximum width of the mail slot is 25cm.

Full Question:

Joel is mailing a large envelope to his cousin. The envelope has pictures inside, so he doesn't want to bend it.

The mail slot has the dimensions shown. The dotted line shows the widest part of the slot.

What is the maximum width of the mail slot?

A) 25

B) 31

C) 22

D) 20

If Dr. Suzuki rides his bike to his office, he averages 9 miles per hour. If he drives his car, he averages 27 miles per hour. His time driving is one third hour less than his time bicycling. How far is his office?

Answers

Speed
Riding speed = 9 mph
Driving speed = 27 mph

Time
If x hours is the time taken when riding, (x - 1/3) hours is the time taken when driving.

Distance in both instances is the same, D= Speed * time

Therefore,
9*x = 27(x-1/3)
9x = 27x - 27/2
9x = 27x - 9
(9-27)x = -9
-18x = -9
x = 9/18 = 1/2 hours

Distance, D = 1/2 *9 = 4.5 miles

What is the equation of the line perpendicular to 2x + 5y = 20 that contains the point (10, −4)?

Answers

perpendicular means a line that is opposite and reciprocal to the slope you have now

1) first solve for y

5y= -(2x) + 20
y= -(2/5)x + 4

so the slope is -2/5 so perpendicular is m= 5/2

so now use point slope

y-y1=m(x-x1)

m=5/2 and point is (10,-4)

plug and chug

y+4 = (5/2) (x-10 )

y= 5/2x - 25 - 4
y=5/2x - 29

hope i didnt make an adding error
but thats how you do it.

hope that helps

On a blueprint with a scale of 1cm = 2ft, the length of a wall is 12cm. If the scale of the blueprint were 1cm = 3ft, what will be the length of the wall?

(Please show work, I will mark brainliest)

Answers

I will assume that this question asks for the length of the wall on the new blueprint. It is not worded nicely.
The actual length of the wall is
12 cm * (2 ft / 1 cm) = 24 ft
On the new blueprint of 1 cm = 3 ft, the length on blueprint becomes
24 ft * (1 cm / 3 ft) = 8 cm
The length of the wall on the new blueprint is 8 cm.

hey can you please help me posted picture of question

Answers

The correct answer is option D.

The steps to find the inverse are listed below.

[tex]f(x)= \frac{2x}{7}+4 \\ \\ y= \frac{2x}{7}+4 \\ \\ y-4= \frac{2x}{7} \\ \\ 7(y-4)=2x \\ \\ x= \frac{7(y-4)}{2} \\ \\ f^{-1}(y)= \frac{7(y-4)}{2} \\ \\ f^{-1}(x)= \frac{7(x-4)}{2} \\ \\ [/tex]

Mission Control sends a signal to a Mars robot to travel to a mysterious rock 52.8 meters away. A return signal 59.0 minutes later tells scientists that the robot is at the rock. It took the signal 9.5 minutes to get from Earth to Mars, and the same time to get back. What was the robot’s average speed in meters per minute?

Answers

The response time includes the round-trip signal time plus the robot's travel time.
59 min = 2*(9.5 min) +travel time
59 min -2*(9.5 min) = travel time = 40 min

The speed is distance / travel time
speed = (52.8 m)/(40 min) = 1.32 m/min

The robot's average speed was 1.32 meters per minute.

PLEASE ANSWER!!! WILL MARK BRAINLIEST :D

When Alina was hungry she ate c cookies, which was 30% of all the cookies she had. How many cookies did she have in the beginning?

Answers

30/100=x
0.30a=x
x/0.30

WILL MARK BRAINLIEST IF RIGHT!!!
Meg described four triangles as shown below:

Triangle P: All sides have length 7 cm.
Triangle Q: Two angles measure 55°.
Triangle R: Two sides have length 8 cm, and the included angle measures 60°.
Triangle S: Base has length 8 cm, and base angles measure 55°.

Which triangle is not a unique triangle?

A) Triangle P
B) Triangle Q
C) Triangle R
D) Triangle S

Answers

I think its B) triangle Q

Answer:

It is q i think

Step-by-step explanation:

When flying at an altitude of 5 miles, the lines of sight to the horizon looking north and south make about a 173.7 degree angle. how much of the longitude line directly under the plane is visible from 5 miles high?

Answers

Final answer:

To find the visible part of the longitude line from an altitude of 5 miles, we can use the Law of Sines in combination with the given angle of 173.7 degrees. The resulting arc length signifies what portion of the Earth is visible from this altitude.

Explanation:

This question pertains to plane geometry and spherical geometry. Given that the angle formed by the lines of sight to the northern and southern horizons is 173.7 degrees when flying at an altitude of 5 miles, we can find the visible part of the longitude line using the Law of Sines.

Imagine a figure with a central angle of 173.7 degrees and a radius of 5 miles (the altitude of the airplane). Here, the radius of Earth is 3959 miles. Thus, from the center of the Earth to the airplane is a total of 3959+5 = 3964 miles.

Using the law of sines, we have: (sin(173.7 deg) / s) = (1 / 3964). Simplifying this gives us the arc length, s, which is the visible part of the longitude line. This visible part signifies the portion of the Earth you can see from the airplane's perspective.

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Final answer:

Using the horizon line formula, D = 112.88 km x √h, where h is the height in kilometers, we can determine the length of the longitude line visible from 5 miles up. This calculation takes into account, but barely modifies for not looking at a perfect 180-degree angle.

Explanation:

In order to find out how much of the longitude line directly under the plane is visible from 5 miles high, we need to apply some mathematical and geographical concepts. The key concept here is the idea of the horizon line, which is the furthest point you can see from a given point of elevation.

Using the formula D = 112.88 km x √h, where h is the height in kilometers (in this case, 5 miles or approximately 8.05 km), you would calculate D = 112.88 km x √8.05. This calculation gives you the distance to the horizon or how much of the line directly beneath the plane is visible.

However, the student's question also mentions an angle of 173.7 degrees - it represents nearly a complete observable circle from the airplane (as 180 degrees would be a complete straight line view). So, the observable part of longitude from the plane will also be correspondingly reduced by a very small amount, since we are not looking at a perfect 180 degrees.

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Calculate the number of integers divisible by 4 between 50 and 500, inclusive.

Answers

50 = 4*12.5
500 = 4*125

There are 125 -12 = 113 numbers between 50 and 500 that are divisible by 4.

Marta jogged 7/10 of a mile Monday. On Tuesday, she jogged 5/10 of a mile. What is the total distance Marta jogged on Monday and Tuesday?

Answers

To find the total, you have to add

7/10 + 5/10 = 12/10

12/10 simplified = 1 2/10 = 1 1/5

Your answer is 1 1/5 miles

Hope this helps :)

Sarawong is carrying six pages of math homework and four pages of english homework. a gust of wind blows the pages out of his hands and he is only able to recover seven random pages. what is the probability that he recovers at least five pages of his math homework

Answers

Final answer:

The probability that Sarawong recovers at least five pages of his math homework is 56.6%, using the combinatory principles of probability.

Explanation:

To solve the problem, we need to calculate the probability that Sarawong recovers at least five pages of his math homework after a gust of wind blows the pages out of his hands. This is a probability problem, which is under the field of mathematics. We first need to understand the total possibilities of the pages he could recover, which is combinations of six math pages and four English pages, that is 10 pages pick 7 pages. We add up the probabilities that he recovers 5, 6, or all 7 math pages. We also need to consider that there is no particular order in which the pages are recovered.

The total number of ways to select 7 pages from 10 can be calculated by 10 choose 7, which is 120.

The number of ways to select 5 math pages out of 6 and 2 English pages out of 4 is 6 choose 5 times 4 choose 2, which equals 60. The probability of this case is 60 / 120 which is 0.5.

The number of ways to select 6 math pages and 1 English page is 6 choose 6 times 4 choose 1, which is also 4. The probability is 4 / 120 which is 0.033.

The number of ways to select all math pages is 6 choose 6 and 4 choose 1, which totals 4. The probability is also 4 / 120 which is 0.033.

Therefore, the total probability that Sarawong recovers at least 5 of his math pages is 0.5 + 0.033 + 0.033 = 0.566, or 56.6%. This is the mathematical solution to the problem.

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What’s 3.192 rounded to the nearest hundredth ?

Answers

3.19 is the answer to your problemo.

Yes, the soulution is 3.19

This graph shows the solution to the inequalities y>3/2x-2 and y<3/2x-10. Does the system of inequalities have solutions? If so, which region contains the solution?

A) there is no solution
B) there is a solution, and it’s shown by region A.
C) there is a solution, and it’s shown by region C
D) there is a solution, and it’s shown by region B.

Answers

we know that

the region A satisfies only the inequality-------> y>3/2x-2

the region C satisfies only the inequality-------> y<3/2x-10

the region B
does not satisfy any of the two inequalities

there is no region that satisfies both inequalities

therefore
the answer is the option
A) there is no solution

Answer:

there is no solution

Step-by-step explanation:

Somebody helppppp pleassse

Answers

68,5+49,5=118

180-118=62,

Good luck!

X +68.5+49.5=180. The sum of all three angles =180 degrees in most triangles. X=62 degrees

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