By definition of inverse function,
[tex]F\left(F^{-1}(x)\right) = x[/tex]
so that
[tex]5F^{-1}(x) - 6 = x[/tex]
[tex]5F^{-1}(x) = x + 6[/tex]
[tex]F^{-1}(x) = \dfrac{x + 6}5[/tex]
Similarly,
[tex]G\left(G^{-1}(x)\right) = G^{-1}(x) - 4 = x \implies G^{-1}(x) = x+4[/tex]
Then the inverse of the composition [tex]F\circ G[/tex] is such that
[tex]\left(F \circ G\right) \left((F \circ G)^{-1}(x)\right) = x[/tex]
By definition of composition,
[tex](F\circ G)(x) = F(G(x))[/tex]
Applying [tex](F\circ G)^{-1}[/tex] to this recovers x, and this involves first inverting F, then G:
[tex](F\circ G)^{-1}(x) = G^{-1}\left(F^{-1}(x)\right)[/tex]
So, we find
[tex](F\circ G)^{-1}(x) = G^{-1}\left(F^{-1}(x)\right) = G^{-1}\left(\dfrac{x+6}5\right) = \dfrac{x+6}5 + 4 = \boxed{\dfrac{x+26}5}[/tex]
What is (16x+9)+(−9x−5) ?
Solve the equation or inequality. t/3+t/2−350=270
Answer:
t=744
Step-by-step explanation:
t/3+t/2-350=270 add 350 on both sides
t/3+t/2=620 convert both fractions containing t into a fraction with a common base
2t/6+3t/6 = 620 add the fractions containing t
5t/6=620 factor out the 5
5*(t/6)=620 divide both sides by 5
t/6=124 multiply both sides by 6 (note, you could have just divided 620 by 5/6 on both sides, or multiplided both sides by 6/5)
t=744
Math and Science If 7 giant solar power
plants generate 1.3 gigawatts (GW) of
energy to power 900,000 homes, how
many gigawatts can 21 giant solar plants
generate?
Answer:
Step-by-step explanation:
multiply everything by three to get your answer
write each power as a product of the same factor. Then find the value. 4^4
Answer:
256
Step-by-step explanation:
4^4 means 4raise to power 4. so, it's typically 4x4x4x4 which is 256
Liz is a salesperson at a department store. She gets paid an hourly wage plus a 5 percent commission on all her sales. Her pay is given by the formula below.
P = $6h + $0.05k
In this formula, h is the number of hours worked, and k is the dollar amount of sales. Liz worked 36 hours last week and sold $2,700 of merchandise. What was her total pay for the week?
Answer:
$351.00
Step-by-step explanation:
Our first step in this process is to find what the hours - represented by h - times $6.00 would result in. Since 36 ⋅ 6 results in $216.00, we know that $216.00 + $0.05k = last week's pay for Liz.
Our second step is to find what $0.05 is being multiplied by. We see in the given information that k represents the dollar amount of sales. Therefore, in the second step of this process, we'll be multiplying 0.05 by 2700, which results in $135.00.
We then add $216.00 - the remaining value to be added - to the second value of $135.00, making the answer to this math problem $351.00.
Hopefully this helped a bunch! And tell me if you need any further assistance. ( :
Please help meeeee please please c
Answer:
the item would cost $9000
0.000456 in scientific notation (Please answer fast this is on my final math exam!)
Answer:
0.000456 in scientific notation
= 4.56 × 10-4
Step-by-step explanation:
Can I have brainliest?
0.000456 in scientific notation is 4.56 × 10-4
Sort the expressions into the correct categories based on their value. Note that some expressions may not belong to any of the categories.
(help with the circled ones)
Answer:
the answer for (9squared divided by 3) - ( 3 x 5 ) = 12
Step-by-step explanation:
(9squared divided by 3) - ( 3 x 5 ) = 12
9x9 = 81
81 ÷ 3 = 27
27 - (3x5)
3 x 5 = 15
27 - 15 = 12
so it goes in the 12 box
4squared - ( 2 x 3 )
4squared = 4 x 4
4 x 4 = 16
16 - (2 x 3)
2 x 3 = 6
16 - 6 = 10
so it goes in the 10 box
All changes avec
7. The price of a plane ticket varies Inversely with the amount of tickets purchased at one time. If 2 plane tickets costs $350 each, how much will a ticket cost when purchasing 7 plane tickets?
O $25
O $100
O $1225
O $220
Answer:
1225
350/2=175
175 x 7 = 1225
The Shanghai Maglev Train takes 8 minutes to travel a distance of 30.5 kilometres.
Work out the average speed of the train.
Answer:
228.75 km/h
Step-by-step explanation:
average speed = total distance / total time
The Average speed is 228.75 Km/h.
What is speed- Distance Formula?Speed = Distance/TimeDistance = Speed X Time, and Time = Distance / Speed,Given:
Distance= 30.5 Km
Time= 8 min
= 8/60 hr= 2/15 hour
Now, Average speed= Distance / time
= 30.5 x 15/2
= 228.75 Km/ h
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The base of a triangle is 13 cm rounded to the nearest integer.
The perpendicular height of the triangle is 4.7 cm rounded to 1 dp.
Write the error interval for the area, a, of the triangle in the form m ≤ a < n.
Answer:
30.55 <_ a < 30.55
Step-by-step explanation:
a = 1/2 × b × h
a = 1/2 × 13 × 4.7
a = 30.55 cm^2
30.55 <_ a < 30.55
PLEASE HELPPPP !! Which points have positive y coordinates?
A) A and F
B) A and B
C) F and H
D) B and F
Solve the Equation [tex]\frac{5}{2}[/tex] · X = 1
[tex]\dfrac 52 \cdot x = 1\\\\\implies 5x = 2\\\\\implies x = \dfrac 25[/tex]
Answer:
5/2
Step-by-step explanation:
Please help!!!!!!!!!!!!!
Answer:
can you also send a graph that might help rn
Step-by-step explanation:
PLEASE HELP.
Use the drawing tool(s) to form the correct answer on the provided graph. The graph of f(x) = x is shown on the coordinate plane. Function g is a transformation of f as shown below. g(x) = f(-2/3x)
WILL GIVE 100 POINTS.
Step-by-step explanation:
Given function:
f(x) = xThe transformation of f(x) is g(x):
g(x) = f(-2/3x) = -2/3xThe graph of g(x) is attached below
The mean of 16, X, 3, 14,57 is 22. Find
Х
Answer:
20
Step-by-step explanation:
Given,
The mean of 16, X, 3, 14, 57 is 22.
Therefore,
(16+X+3+14+57)/5 = 22
(16+X+3+14+57) = 110
(90+X) = 110
X = 110-90
X = 20
The value of x will be 20.
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The mean of set 16, X, 3, 14, 57 is 22.
Now,
Since, The mean of 16, X, 3, 14, 57 is 22.
Hence, By definition of mean we get;
⇒ 16 + X + 3 + 14 + 57 / 5 = 22
Solve for x as;
⇒ 90 + X / 5 = 22
⇒ 90 + X = 22 × 5
⇒ 90 + X = 110
⇒ X = 110 - 90
⇒ X = 20
Thus, The value of x will be 20.
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is 5/8 greater than 61%? thanks i have late stuff that i need done
Answer:
5/8 is 62.5% which makes it greater
Step-by-step explanation:
Convert the fraction to a decimal and then just multiply it with 100
5/8 is 0.625
0.625×100 is 62.5
just add a %
then you get 62.5%
Identify if the table below shows a proportional relationship.
x
y
1
5
02
2
.
7
5
13
Proportional
Not Proportional
Answer:
i know answer i heard some were i think
What is an equation of the line that passes through the point (-7, -6) and is
parallel to the line 2 - y = 7?
Answer:
[tex]y = -6[/tex]
Step-by-step explanation:
Because is a line is of the form
[tex]y = mx + b[/tex]
and its parallel to the line
[tex]2 - y &= 7\\- y &= 5\\y = -5[/tex]
So that's meaning that the slope [tex]m[/tex] is equal to 0 then the equation now is of the form
[tex]y = b[/tex]
Then if pass for the point -6 and [tex]b[/tex] is the point of cut with the [tex]y[/tex] axis then our equation of the line is equal to
[tex]y = -6[/tex]
laura's family is going on a vacation. they will drive 4,180 miles over the next two weeks. about how many miles will they drive on average each week?
Answer:
l auras family will drive 2090 miles watch week because you decide by 2 because there are 2 weeks
what is the difference of 23xand 9 x
Answer:
14x
Step-by-step explanation:
.....................
Factor the following polynomial completely. x2n – y2n
Answer:
(x/y)^2n-2n
(x/y)⁰
=1
since any number raised to power of 0 is 1
1. Two students are asked to find the angle measures of AEFG, given that the triangle is isosceles. AEFG has an exterior angle at which has a measure of 110%. Their work is shown below.
Which answer is correct? Explain below.
Serin's Answer: The measure of Angle G is 70 degrees. Since the base angles are congruent, the measure of Angel F is also 70degrees.This leaves 40 degrees for Angle E.
Lam's Answer: The measure of angle G is 70degrees. Since an isosceles triangle has two congruent angles, the measure of Angle E and Angle F must be 55degrees
O Both are correct.
ONeither is correct.
Answer:
∆EFG has an exterior angle at G which has a measure of 110°. Which answer is incorrect ... Since external angle is 110 degrees, the internal is 70 degrees
Step-by-step explanation:
no problem we all get stuck
The angles can be ∠ G = 70°, ∠ F = 70° and ∠E = 40° or ∠ G = 70°, ∠ F = ∠ E = 55° hence both are correct so, option C is correct.
What is triangle?
Three straight lines coming together create a triangle. There are three sides and three corners on every triangle (angles). A triangle's vertex is the intersection of two of its sides. Any one of a triangle's three sides can serve as its base, however typically the bottom side is used.
Given:
The triangle is isosceles, and AEFG has an exterior angle at which has a measure of 110°,
Calculate the interior angles of the triangle as shown below,
∠ G = 180 - 110 (exterior angle)
∠ G = 70°
Since the remaining angles can be ∠ F = 70° and ∠E = 180 - 70 + 70 = 40°
or ∠ F = ∠ E = 55°
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T
Зл
Solve for the interval <<
2
2
3. 2 cos? 0-5 cos e = 3
(it put it in wrong so i put a picture of the question)
Answer:
540 g m/s.
Step-by-step explanation:
If you bought 12.6 gallons of gasoline as $1.20 per gallon, how much did the gasoline cost?
Answer:
15.12$
Step-by-step explanation:
Gallons = 12.6
Cost = $1.20
Gasoline Cost = ??
12.6 ×1.20
=15.12
Hence, gasoline will cost 15.12 $
pls mark me as brainliest! :D
Factor
10x + 100x + 250
Mr smith’s Pizza parlor
The questions are not readable. try uploading a better picture.
Do number 12 on the pic
Answer:
$21.83
Step-by-step explanation:
The amount spent will be the difference between the starting balance and the ending balance:
18.53 -(-3.30) = 18.53 +3.30 = 21.83
You spent $21.83 on lunch this week.
Natalie is graphing point T at (1,8). should she moves to the right 8 units or up 8 units? Explain
Answer:
move 1 to the right and 8 units up
Step-by-step explanation:
7. Write an equation for the line in slope- intercept form
Answer:
y equals -2x - 3
Step-by-step explanation:
hope it helps
(would appreciate mark brainliest)