Answers
From the given options, only the pair given in option B result in the composition equal to x.
[tex]F(x)= \frac{12}{x}-18 \\ \\ G(x)= \frac{12}{x+18} \\ \\ F(G(x))= \frac{12}{ \frac{12}{x+18} }-18 \\ \\ F(G(x))= \frac{12(x+18)}{12}-18 \\ \\ F(G(x))=x+18-18=x [/tex]
This proves, F(x) and G(x) are inverse of each other.
So the answer to this question is Option B
Related Questions
Hey can you please help me posted picture of question
Answers
Shirts x skirts x shoes
7 x 6 x 4
=168
So, there are 168 combinations- Letter answer B
write a cosine function for the graph?
Answers
Answer(s):
[tex]\displaystyle y = 4cos\:(4\theta \pm \pi) \\ y = -4cos\:4\theta[/tex]
Step-by-step explanation:
[tex]\displaystyle y = Acos(B\theta - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \\ Amplitude \hookrightarrow |A| \\ \\ Vertical\:Shift \hookrightarrow 0 \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \hookrightarrow \boxed{\pm\frac{\pi}{4}} \hookrightarrow \frac{\pm\pi}{4} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{\frac{\pi}{2}} \hookrightarrow \frac{2}{4}\pi \\ Amplitude \hookrightarrow 4[/tex]
OR
[tex]\displaystyle y = -Acos(B\theta - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \\ Amplitude \hookrightarrow |A| \\ \\ Vertical\:Shift \hookrightarrow 0 \\ Horisontal\:[Phase]\:Shift \hookrightarrow 0 \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{\frac{\pi}{2}} \hookrightarrow \frac{2}{4}\pi \\ Amplitude \hookrightarrow 4[/tex]
You will need the above information to help you interpret the graph. First off, keep in mind that this cosine graph will have TWO equations because the curvature begins upward from [tex]\displaystyle [0, -4][/tex] instead of downward from [tex]\displaystyle [0, 4],[/tex] telling you that one equation will have a “negative” symbol inserted in the beginning of the equation. Before we go any further though, we must figure the period of the graph out. So, in this case, sinse you ONLY have a graph to wourk with, you MUST figure the period out by using wavelengths. So, looking at where the graph hits [tex]\displaystyle [0, -4],[/tex]from there to [tex]\displaystyle [-\frac{\pi}{2}, -4],[/tex] they are obviously [tex]\displaystyle \frac{\pi}{2}\:unit[/tex]apart, telling you that the period of the graph is [tex]\displaystyle \frac{\pi}{2}.[/tex] Now, as you can see, the photograph on the right displays the trigonometric graph of [tex]\displaystyle y = 4cos\:4\theta.[/tex] Now, if you look hard enough, you will see that both graphs are “mirror reflections” of one another, meaning you can figure the rest of the terms out one of two ways. The first way is to figure the appropriate C-term out that will make the graph horisontally shift and map onto the original cosine graph [photograph on the left], accourding to the horisontal shift formula above. Also, keep in mind that −C gives you the OPPOCITE TERMS OF WHAT THEY REALLY ARE, so you must be careful with your calculations. So, between the two photographs, we can tell that the rightward graph is shifted [tex]\displaystyle \frac{\pi}{4}\:unit[/tex] on both sides of the y-axis, which means that in order to match the original graph, we need to shift the graph back, which means the C-term will be both negative and positive; and by perfourming your calculations, you will arrive at [tex]\displaystyle \boxed{\pm\frac{\pi}{4}} = \frac{\pm\pi}{4}.[/tex]So, one equation of the cosine graph, accourding to the horisontal shift, is [tex]\displaystyle y = 4cos\:(4\theta \pm \pi).[/tex] Now that we got this out the way, we can focuss on finding the second equation. Another way is to write an equation with a “negative” symbol inserted in the beginning [like I mentioned earlier]. Now, sinse we are writing an equation with the negative, the graph will not have a horisontal shift; so, C will be zero. With this said, the second equation is [tex]\displaystyle y = -4cos\:4\theta.[/tex] Now, the amplitude is obvious to figure out because it is the A-term, but of cource, if you want to be certain it is the amplitude, look at the graph to see how low and high each crest extends beyond the midline. The midline is the centre of your graph, also known as the vertical shift, which in this case the centre is at [tex]\displaystyle y = 0,[/tex] in which each crest is extended four units beyond the midline, hence, your amplitude. So, no matter how far the graph shifts vertically, the midline will ALWAYS follow.
I am delighted to assist you at any time.
34 + 4 ⋅ 5 = ____
PLEASE HELP ASAP FOR BRAINLIEST!!!!!
Answers
your answer is 80 hope this helped.
a salesman's commission on 150,000 sale is 3000. what is the percent?
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You can find this by multiplying 98% (0.98) and 150,000 to get 147,000. Then subtract 147,000 from 150,000 to get 3,000.
I hope this helps!
is 0.003km greater than, less than, or equal to 3 m
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does anyone have idea of a poem with using number 16
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When you add eight plus eight
Isn't that great?
When you divide two fifty six by sixteen
Darn, didn't that make your stomach turn green
I couldn't think of a better way to show you sixteen
Rather seems unseen
A better way to say Sixteen
You save $15,000.00. You place one-third in a savings account earning a 4.6% APR compounded annually. You then invest one quarter of the remaining balance in a 3-year U.S. Treasury bond earning a 5.2% APR compounded annually and the rest in a stock plan. Your stock plan increases in value 3% the first year, decreases 8% in value the second year, and increases 6% in value the third year. What is the balance of the savings account by the end of the third year?
$4,618.81
$2,910.63
$5,722.23
$3,910.02
Answers
1. You deposited 1/3 of 15,000 or 5,000 in a savings account that earns 4.6% compounded annually. If 5,000 is already in the savings account, there is still 10,000 left.
2. One-fourth(1/4) of 10,000 or 2,500 is invested in 3-year US Treasury bond earning 5.2% compounded annually. If 2,500 is invested, there is still 7,500 left.
3. The 7,500 was invested in the stock market.
For the savings account
The amount of money deposited in the savings account after three years will be
[tex]F_2=P\left(1+r\right)^t=5,000\left(1+0.046\right)^3=5,722.23[/tex]
Therefore, the balance of the savings account after three years is $5,722.23.
PLEASE PLEASE PLEASE HELP ME WITH ALGEBRA 1 PLEASE!?!?!?!?!!!?!?!?!?!?! I WILL GIVE LOTS OF POINTS AND BRAINLEST PLEEEEEEEEEEEEEEEEASE!!?!?!?!?!?!!?!?!?!?
What are the different ways you can solve a system of linear equations in two variables? What is the process for solving a system using each method?
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It is
________________________________
[tex]2x + y = 4, 2x - y = 0 is [[2 1], [2 -1] [4, 0][/tex]
Hope I helped have a good day
Please help Thankyou
Answers
----
The domain of a function is all the x values that return real y values.
If you look at your function, notice that x is in the denominator of [tex] \frac{1}{x+1} + 5[/tex]. Remember the denominator of a fraction can never equal zero because dividing by 0 isn't possible. That means x ≠ -1. All other x values work if you plug them in, so your answer must be the one that doesn't include x = -1.
As you look through your answer choices, remember that a bracket [ or ] means that the number is included and a parenthesis ( or ) means that the number is not included. The U means "union," which means both domains to the left and right of the U are included.
Your only choices that have "-1" are B and D. However, in D, there are closed brackets, and we want the "-1" to not be included. That means B is the only correct answer.
in order to make the function undefined, x must not be equal to -1 which makes the function 1/0 + 5.
It's either B or D
Refer to narrative 14-1. a house is selling for $150,000. a deposit of $20,000 was made when the sales contract was signed. the down payment is 30% and the balance will be financed with a 25-year mortgage at 11% and 4 discount points. if the sellers are responsible for the broker's commission (6% of the purchase price); $1,300 in other closing costs; and the existing mortgage, with a balance of $40,000; what proceeds will they receive on the sale of the property?
Answers
21 out of 25 cars have 4 doors what percentage have four doors
Answers
To find this, set up the current ratio as a fraction or 21/25. Then, multiply 21 by 100 and divide by 25 to find the percentage.
You do this using a similar like butterfly method - 21/25 x/100
Therefore, the answer is 84%
Hope this helps!
How many 2-digit numbers are multiples of neither 5 nor 7?
Answers
Answer:
Step-by-step explanation:
You take the amount of 2-digit numbers there are (90) and subtract it from the amount of two digit numbers that are multiples of 5 and 7 (29). You should get 61.
Answer: The number 2-digit numbers are multiples of neither 5 nor 7 is 61.
Step-by-step explanation: We are given to find the number of 2-digit numbers that are multiples of neither 5 nor 7.
Let A denote the set of 2-digit numbers that are multiples of 5 and B denote the set of 2-digit numbers that are multiples of 7.
Then,
A = {10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95}
and
B = {14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84, 91, 98}
That is, n(A) = 18 and n(B) = 13.
Now, the set of 2-digit numbers that are multiples of both 5 and 7 is given by
[tex]A\cap B=\{35, 70\}~~~~~~\Rightarrow n(A\cap B)=2.[/tex]
Therefore, the number of 2-digit numbers that are multiples of either 5 or 7 is given by
[tex]n(A\cup B)=n(A)+n(B)-n(A\cup B)=18+13-2=29.[/tex]
Now, there are 90 2 -digit numbers.
Thus, the number 2-digit numbers are multiples of neither 5 nor 7 is
90 - 29 = 61.
Hence, the total number of numbers is 61.
Which statements is true
A: all rectangles are squares
B: some trapezoids are parallelogram
C: all square are rhombues
D: no rhombuses are rectangles
Answers
all squares are rhombuses
Hope this Helped!
;D
Brainliest??
Hey can you please help me posted picture of question
Answers
The explanation is shown below:
The option A is theoretical probability, because they did not make any experiment to determine the probability, while in the others options, they had to make equal tests for to determine the probability.
For example, Lisa had to attempted 25 basketball free throws to determine which one them she could make and, then, determine the probability. While Kelli did not have to make any test.
A 12-foot ladder is leaning against a wall. The distance from the base of the wall to the base of the ladder is feet. Given this information, what can be determined about the triangle formed by the ground, wall, and ladder? Check all that apply.
Answers
We are given the length of the ladder and the distance of the base of the ladder from the wall. With that we can solve for the height of the triangle as well as the angle of inclination wrt to the floor and foot of the ladder or the wall to the tip of the ladder.
Pythagorean's theorem provides for the following formula
Square of hypotenuse (longest side of the triangle) equals the sum of the squares of the two other sides for right triangles.
Thus
Length of ladder being the hypotenuse we have below equation
Hypotenuse = 12
Distance from the base to the foot of ladder = 1 foot/feet
height = ?
12² = 1² + h²
h = √144-1
h=√143
Solving for inclination with respect to wall to tip of the ladder we can use rule of sine for right triangle
sineФ = opposite side / hypotenuse
sineФ = 1/12 = 0.083333
Ф = sin^-1 or inverse sine of 0.083333
Ф = 4.78017268 degrees
Note : If the distance between the base is not interpreted correctly, just change the value and plugin to the equation to get the result.
Answer:
A,B,D,E
Step-by-step explanation:
did it on edge
Find the feet of c and d
Answers
Use the Pythagorean theorem to find c.
15^2 + 20^2 = c^2
225 + 400 = c^2
c^2 = 625
c = 25
Side c measures 25 ft.
The two triangles are similar, so the lengths of corresponding sides are proportional.
120/20 = d/15
6 = d/15
d = 90
Length d is 90 ft.
Which of the following is the domain of the function G(F(x))?
F(x) = x + 4, G(y) =
G(F(x)) =
A. All numbers less than or equal to 4
B. All numbers less than or equal to -4
C. All numbers greater than or equal to -4
D. All numbers greater than or equal to 4
Answers
Justification:
1) G(F(x)) means apply first the rule F(x) and then apply the rule G(y) to the outcome of (Fx).
2) Mathematically that is:
G(F(x) = G (x + 4) = [tex] \sqrt{x+4} [/tex]
3) The the domain is all the numbers for which the expression inside the root are not negative, i.e x + 4 ≥ 0
⇒ x ≥ - 4
That is the option C. all number greater than or equal to - 4.
Assuming boys and girls are equally likely, find the probability of a couple having a baby boy boy when their fourth fourth child is born, given that the first three three children were all boys all boys.
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Then the information about the first three children is irrelevant.
So then the probability of fourth child being boy is 1/2, since boys and girls are equally likely.
Hope this helps.
(a) find the slope m of the tangent to the curve y = 5 + 5x2 − 2x3 at the point where x =
a. m = (b) find equations of the tangent lines at the points (1, 8) and (2, 9). y(x) = (at the point (1, 8)) y(x) = (at the point (2, 9))
Answers
The slope at (2, 9) is -4.
These values are computed numerically by the graphing calculator and shown in the column f'(x) in the graphic.
The derivative is y' = 10x -6x². At x=1, y' = 10-6 = 4; at x=2, y' = 20-24 = -4.
b) In point-slope form, the equations of the tangent lines are shown in the graphic.
The slope of the tangent will be "[tex]10a-6a^2[/tex]". The equation at point (1, 8) is "[tex]y = 4x+4[/tex]" and at point (2,9) is "[tex]y = -4x+17[/tex]".
Given equation is:
[tex]y = 5+5x^2-2x^3[/tex](a)
The slope of the tangent to the curve point where [tex]x = a[/tex] is:
→ [tex]\frac{dy}{dx} = m = 10x-6x^2[/tex]
→ [tex]= 10a-6a^2[/tex]
(b)
The equation of tangent at point (1,8) will be:
→ Slope, [tex]m = 10-6[/tex]
[tex]= 4[/tex]
→ [tex]y-8=4(x-1)[/tex]
[tex]y = 4x-4+8[/tex]
[tex]y = 4x+4[/tex]
and,
The equation of tangent at point (2,9) will be:
→ Slope, [tex]m = 10\times 2-6\times 2^2[/tex]
[tex]= 20-24[/tex]
[tex]= -4[/tex]
→ [tex]y-9=-4(x-2)[/tex]
[tex]y-9=-4x+8[/tex]
[tex]y = -4x+17[/tex]
Thus the above answer is right.
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hello can you please help me posted picture of question
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Here is something that may help you. ^.^
P(GG)=(8/12)(7/11)
P(GG)=56/132
P(GG)=14/33
The answer is .B! Please contact me for any further questions. Cheerio and have a lovely day.
picking a girl first = 8/12 = 2/3
picking a second girl = 7/11
picking both: 2/3 x 7/11 = 14/33
Answer is B
Algebraically determine if the relation y=10x is symmetric with respect to the x-axis, y-axis, the origin or has no symmetry
A.) y-axis
B.)no symmetry
C.)the origin
D.)x-axis
Answers
hope this helped
The ratio of the length to the width of a map is 8 to 5. The map is exactly 32 inches in length. What is the width of the map? A. 13 inches B. 20 inches C. 24 inches D. 32 inches
Answers
Length of the map = 32 inches
Let the width of the map = x inches
So,
Length : Width = 8 : 5
32 : x= 8: 5
x = 5/8 * 32
x = 20 inches
So, the width of the map is 20 inches
Answer:
B. 20 inches
Step-by-step explanation:
Remember that when dealing with ratios or unit rates you just have to do simple rules of three to calcuate what they are asking you, in this case you have that in the map for every 8 units in the length there will be 5 in the width, so how many will there be when the map is 32 inches in length?
[tex]\frac{8}{5}= \frac{32}{x}\\x=\frac{32*5}{8}\\ x=20[/tex]
So the width of a map with a length of 32 inches and a ratio of 8:5 will be 20 inches.
Michael bought a new soccer Jersey that was $24.99. after taxes the total cost was $28.99. What is the percent if increase
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Tax Percentage = 4/24.99 x 100 = 16%
Answer: 16%
What is the area, in cm2, of the circle shown above? Round your answer to the nearest tenth.
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A line passes through the (1, -6) and has a slope of 5. write an equation for this line
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y = m(x -h) +k
Your line's equation can be written as
y = 5(x -1) -6
This can be simplified to slope-intercept form
y = 5x -11
or standard form
5x -y = 11
hey can you please help me posted picture of question
Answers
( 2 - 8i ) + ( 5 - i )
Real part is added in real part and the complex part is added in complex part
= 2 +5 - 8i - i
= 7 - 9i
So, the answer is 7 - 9i
The diameter of a circle is 8 inches.What is the area?
A.8 inches
B.16 inches
C.32 inches
D.64 inches
Answers
The required correct answer is not listed among the given options. The area of the circle is approximately 50.24 square inches.
The area of a circle can be calculated using the formula A = πr^2, where A is the area and r is the radius of the circle. Since the given information provides the diameter (twice the radius), we need to first find the radius by dividing the diameter by 2.
Given: Diameter = 8 inches
Radius = Diameter / 2 = 8 inches / 2 = 4 inches
Now we can calculate the area using the formula:
= πr² = π * (4 inches)²
≈ 3.14 * 16 square inches
≈ 50.24 square inches
Therefore, the correct answer is not listed among the given options. The area of the circle is approximately 50.24 square inches.
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Final answer:
The area of a circle with an 8-inch diameter is calculated using the formula A = πr². The correct area is around 50.27 square inches, not one of the provided options.
Explanation:
The question asks for the area of a circle with a diameter of 8 inches. To find the area, we use the formula A = πr², where π is approximately 3.14159, and r is the radius of the circle. Since the diameter is 8 inches, the radius (r) is half of that, which is 4 inches.
To calculate the area:
Divide the diameter by 2 to find the radius: 8 inches / 2 = 4 inches.Square the radius: 4 inches ² = 16 square inches.Multiply by π (pi): π × 16 square inches ≈ 50.26548 square inches.The area of the circle is approximately 50.27 square inches, which means none of the given options A, B, C, or D is correct.
Evaluate Cot0 if sin0= square root of 6/5
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sin θ=opposite/hypotenuse
hence
opposite=√6
hypotenuse=5
thus the adjacent will be found using the Pythagorean theorem
c²=a²+b²
plugging in the value we get:
5²=(√6)²+b²
b²=25-6
b²=19
b=√19
thus
adjacent=√19
but
cotθ=1/tanθ
tanθ=√6/√19
hence:
cotθ=√19/√6
What is the quotient of -19/2 divided by 38/ 7
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BRAINLIEST!!!!!!!!
When you have two shapes to compare on a coordinate plane, you can determine the scale factor, knowing that the transformation was a dilation. Generate instructions you would give another student to determine the scale factor.
Answers
Locate two corresponding ordered pairs of the two shapes. Calculate how much the pre-image values were multiplied by to obtain the image values. This is your scale factor. You can calculate this by dividing the coordinates of the mage by the corresponding coordinates of the pre-image.
You can calculate the scale factor by dividing the coordinates of the image by the corresponding coordinates of the pre-image.
What is scale factor?A scale factor is defined as the ratio between the scale of a given original object and a new object, which is its representation but of a different size (bigger or smaller).
Assume that the initial coordinates are (x, y) and that the dilated coordinates are (x', y').
The dilation is therefore:
(x, y) → (x', y')
Now, let's assume that the dilation factor is k.
Therefore:
x' = kx
y' = ky
To get the initial coordinates and the final ones and then substitute in any of the above two equations to get the value of k, which is the scale factor,
For example =
Assume an original point at (2,4) is dilated to coordinates (4,8) we need to find the dilation factor.
Assume the dilation coefficient is k.
(x, y) are (2,4) and (x', y') are (4,8)
Therefore:
x' = kx → 4 = k×2 → k = 2
or:
y' = ky → 8 = k×4 → k = 2
Based on the above, the dilation coefficient would be 2.
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