Given: F(x)= 5 x - 6 and G(x)= x - 4
(FoG)^-1=
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]
Someone plz help me :(
Answer:
B) 7 - 5x
Step-by-step explanation:
7 - 5x is the difference between the number 7 and the product of 5 and 'x'
Of the 32 teachers at Devon's high school, 22 are female. What is the ratio of the number of male teachers to the total number of teachers?
Write your answer as two numbers separated by a colon (for example, 2:3).
Answer:
10:32
Step-by-step explanation:
32-22=10 male teachers
Which of the following forms a Pythagorean triplet?
a)3, 4, 6 b) 5, 12, 13 c) 6, 7, 14 d) 8, 6, 16
(hey kid can you answer fast)
NO USELESS THINGS OR WRONG ANSWERS FOR I WILL REPORT YOU.
Answer:
b)
Step-by-step explanation:
i hope this help you
2H20 1) How many hydrogen atoms are represented by this much water? A) 1 B) 2 0.4 D) 6
Helpppppppppppp 70,000x379=????
Answer:
26,530,000
Step-by-step explanation:
this is quite easy, first you can write this question differently
Just view this problem as 7 x 379 which is 2653, now count how many zeros 70,000 has, which is 4 and add it to the answer 2653, which will give you 26,530,000
The multiplication or products of 70,000 and 379 is 26,530,000
How to multiply or find the product of valuesGiven:
70,000 × 379
= 26,530,000
Where from the left,
0 = unit position0 = Ten position0 = Hundred position0 = Thousand position3 = Ten thousand position5= Hundred thousand position6 = Million position2 = Ten million position.In words, 26,530,000 is written as twenty six million, five hundred and thirty thousand.
Learn more about multiplication;
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isaacs new panoramic television is 40 inches and 9 inches high. what is the diagonal size of Isaac’s television?
Answer:
41 inches
Step-by-step explanation:
To solve for the diagonal length of his television, we can use the formula:
a² + b² = c²
Square the length and width of the TV then add them together. Then find the square root of the sum.
40² = 1600
9² = 81
1600 + 81 = 1681
√1681 = 41
A HORIZONTAL line passes through point (-3, -1). Find the equation of this line. A) x = 1 B) x = 3 C) y = -1 D) y = 1
Answer: C) y = -1
Step-by-step explanation:
A horizontal line is represented by y = a constant. As such, the line must be y = -1, because the given point is (-3, -1), which has a y-coordinate of -1.
Answer:
D y=-1
Step-by-step explanation:
In horizontal lines, the equation is y=b. B is the location of the y-axis where the line crosses through it. Hope this helps :)
what is the solution of this equation?
2y=24
[tex]\huge\text{Hey there!}[/tex]
[tex]\large\boxed{\textsf{2y = 24}}\\\\\large\text{DIVIDE 2 to BOTH SIDES}\\\\\large\boxed{\mathsf{\dfrac{2y}{2}=\dfrac{24}{2}}}\\\\\large\text{CANCEL out: }\rm{\dfrac{2}{2}}\large\text{ because it gives you 1}\\\large\text{KEEP: }\rm{\dfrac{24}{2}}\large\text{ because it gives you the answer of the y-value.}\\\\\large\boxed{\mathsf{12= \dfrac{24}{2}}}\\\\\large\text{SIMPLIFY IT!}\\\\\large\boxed{\mathsf{y = 12}}\\\\\huge\text{Therefore, your answer is: \boxed{\mathsf{a = 12}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
Paul had 70 fliers to post around town. Last week, he posted 1/5 of them. This week, he posted 5/7
of the remaining fliers. How many fllers has he still not
posted
Answer:
Paul has not yet posted 6 fliers.
Step-by-step explanation:
How many did he post last week? (1/5)(70) = 14
This week? (5/7)(70) = 50
Already posted: 14 + 50 = 64
Not yet posted: 70 - 64 = 6
please help
Jay buys a certain brand of cereal that costs $15 per box. Luke changes to a super-saving brand of the same size. The equation shows the price, y, as a function of the number of boxes, x, for the new brand, y = 10x Part A: How many more dollars is the price of a box of Jay's original brand of cereal than the price of a box of the super-saving brand? Show your work. (5 points) Part B: How much money does Jay save each month with the change in cereal brand if he buys 8 cereal boxes each month? Show your work. (5 points)
A.
Jay's original brand is $5 more than the price of a box of the super-saving brand.
Since Jay's original brand costs $15 per box and the price of Luke's super-saving brand is y = 10x where x = number of boxes. For one box, x = 1.
So, y = 10x
y = 10 × 1
y = $10
So, Jay's brand costs $15 per box and Luke brand cost $10 per box.
So, the difference in price is per box is $15 - 10$ = $5
So, Jay's original brand is $5 more than the price of a box of the super-saving brand.
B.
Jay saves $40 per month with the change in cereal brand if he buys 8 cereal boxes each month
Since the difference in price for each box bought is $5. Jay saves $5 for every super-saving cereal brand he buys.
So, if he buys 8 cereal boxes per month, he saves $5 per box × 8 boxes per month = $40 per month.
So, Jay saves $40 per month with the change in cereal brand if he buys 8 cereal boxes each month
Learn more here:
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help please!! This is due 2 and a half hours. I can’t figure out the problem please help me
Answer:
g(x) = 2|x|: vertical stretch by a factor of 2.
h(x) = ⅓|x|: vertical compression by a factor of ⅓.
w(x) = 4|x|: vertical stretch by a factor of 4.
Step-by-step explanation:
Given the graph of an absolute value parent function, f(x) = |x|:
g(x) = 2|x|Multiplying the parent function by a number, where a > 1 causes a vertical stretch by a factor of a.
Hence, when a > 1, the graph is narrower than the parent function.
In the case of the function, g(x) = 2|x|, the graph represents a vertical stretch by a factor of 2. When a vertical stretch occurs, the y-coordinates will be twice of what the y-coordinates of the parent function. For instance, compare the y-coordinates of f(x) = |x| and g(x) = 2|x| when x = 1.
In the parent graph, f(x) = |x|: when x = 1, y = 1.
In g(x) = 2|x|, when x = 1, y = 2.
h(x) = ⅓|x|Multiplying the parent function by a number, where 0 < a < 1 causes a vertical compression by a factor of a.
Hence, when 0 < a < 1 , the graph is wider than the parent function.
In the case of the function, h(x) = ⅓|x|, the graph represents a vertical compression by a factor of ⅓. When a vertical compression occurs, the y-coordinates will be ⅓ of what the y-coordinates of the parent function.
If you compare the y-coordinates of the parent function, f(x) = |x|, and h(x) = ⅓|x|, when x = 1:
In the parent graph, f(x) = |x|: when x = 1, y = 1.
In h(x) = ⅓|x|: when x = 1, y = ⅓.
w(x) = 4|x|Using the same techniques presented in the previous sections of this post, we could focus on comparing the difference between the y-coordinates of the parent graph, f(x) = |x|, and w(x) when x = 1.
In the parent graph, f(x) = |x|: when x = 1, y = 1.
In w(x) = a|x|, when x = 1, y = 4.
This shows that the graph is vertically stretched by a factor of 4, where the graph appears narrower than the parent function.
Therefore, the function that represents the given graph is w(x) = 4|x|.
help me please bjsowownxnwkwndndiwijsjs
What is the height of the flagpole?
Use the dropdown menus to write an equation with infinitely many solutions.
4(2x + 3) – x =
A. 4 B. 5 C. 6 D. 7
x +
A. 12 B. 15 C. 16 D. 18
Answer:
4(2x + 3) - x = 7x + 12
Explanation:
That's what T4L/Edge said
how many times can 14 go into 97
Answer:
6 time
Step-by-step explanation:
97÷14=6•928
=6 or round it up to 7
Answer:
6
Step-by-step explanation:
97÷14=6.928
6 or round it up to 7
Which equation is the inverse of y = x2 +4?
y =-VI- 4
b. y = x-4
a
Cy=Vx+4
d. y= -x - 4
Anyone know the answer
Answer:
B. [tex]y=\pm\sqrt{x-4}[/tex]
Step-by-step explanation:
Swap the positions of the x and y variables then solve for y again.
[tex]y=x^2+4\\\\x=y^2+4\\\\x-4=y^2+4-4\\\\x-4=y^2\\\\\sqrt{x-4}=\sqrt{y^2}\\\\\pm\sqrt{x-4}=y[/tex]
Given that p varies directly as q and
[tex] \sqrt{q} [/tex]
varies inversely with t², show how p varies with t.
Answer:
p varies inversely with t⁴Step-by-step explanation:
Direct variation:
y = kx, where k is constantInverse variation:
y = k/x, where k is constantGiven:
p = kq (1)and
√q = k/t² (2)From the first equation we can see:
kq = p ⇒ q = (1/k)p ⇒ q = np, where n is a constantIt means if p varies directly as q, then q directly varies as p.
Square the second equation:
q = k²/t⁴ = m / t⁴, where m is constantSince p varies directly as q and q varies inversely with t⁴, we can state p varies inversely with t⁴.
What is the perimeter of PQR? Show your work.
(4,1),(8,2) in slope intercept form
Answer
y=1/4x
Step-by-step explanation:
2-1/8-4=1/4
Choose either of these points ( I will use 4,1 becuase it's easier)
1=1/4(4)=b
1=1+b
0=b
y=1/4x (you don't put the zero)
What is the base of 5^4?
Answer:
5 is the base
4 is the exponent
Which ordered pair represents the reflection of the point (−2,3) over the y-axis?
Answer:
there is no y axis because the term is kept in second of y and if that is negative then only y axis will there otherwise there will no y axis
The ordered pair represents the reflection of the point (−2,3) over the y-axis is (2, 3)
What is reflection of the points over the axis?A reflection of a point in the axes involved reflecting the image over the axes to create a mirror image.
Given that, a point is (-2,3) is being reflected over y-axis,
Rule of reflection over y-axis is, A(x, y) ↔ A'(-x, y)
Therefore, applying the rule to (-2,3):
(-2,3) ↔ (2, 3)
Hence, the reflected point is (2, 3)
For more references on reflection over axes, click;
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how to evaluate 3-(-10)
Answer:it's 13
please let me know if this is wrong
Answer:
Answer:
i am uncertain by the question
Step-by-step explanation:
10-3=7
10/3=3.333...
Answer:
the answer is "what are you doing step
bro"
Grace has $105 to buy a cake and pizza for her cousin’s birthday party. She knows she needs to set aside $25 for the cake, and the rest of the money she can spend on pizzas. Each pizza costs $9.25. How many pizzas can Grace afford to buy?
a.write and solve an inequality to answer the question
b. each pizza serves 4 people. if 22 people reply that they will attend the party, how many pizzas should grace buy? explain your reasoning.
im sorry its alot but this will help me lots
Answer:
A. She can buy 8 pizzas; B. At least 6 pizzas.
Step-by-step explanation:
Since Grace has $105, we can set our inequality to be less than or equal to that amount of money. We also know she needs to spend $25 on the cake no matter what. Assuming x is the amount of pizzas she can buy and each pizza costs $9.25, our inequality looks like this:
9.25x + 25 ≤ 105
To solve this inequality, we first subtract 25 from both sides, which gives us:
9.25x ≤ 80
Then we divide by 9.25 on both sides, giving us:
x ≤ 8.6486
Since Grace is only able to buy whole pizzas, the most she can buy is 8 pizzas.
If each pizza serves 4 people and there are 22 people attending, we need to be able to feed 22 or more people. We can use this inequality, where x is still the number of pizzas.
4x ≥ 22
Dividing both sides by 4, we get:
x ≥ 5.5
Again, assuming we can only buy whole pizzas, we would need at least 6 pizzas to feed the entire party.
Which statement describes the end behavior of the exponential equation y = 3^x?
A as x -> - ♾ , y -> - ♾
B as x -> - ♾ , y -> 0
C as x - > ♾ , y -> - ♾
a sequence is given by the rule 4n^2
work out the 3rd term in the sequence
Answer: See below.
Step-by-step explanation:
See attachment. It depends on what is considered the "third" term. If n=2 then the result is 16. If 3, the result is 36.
Figure ABCD is a trapezoid.
Find the value of x.
В,
2x + 1
17
X
3x + 8
A
D
X
= [?]
(BC + AD) / 2 = 17
(2x + 1 + 3x + 8) / 2 = 17
5x + 9 = 34
5x = 25
x = 5
Bo has $500 in his savings account. He plans to add $150 to his savings account every month. Recently, he purchased a tractor to use on his farm for $4,000. He plans to pay off the total price of the tractor over time by paying $200 a month from a separate account. How much will Bo have in his savings at the time he pays off the tractor in full? A. $3,500 B. $3,000 C. $2,150 D. $2,000.
Answer:
D. $2,000
Step-by-step explanation:
Found this answer somewhere and it made sense so I hope its correct :D
Answer:
it is 3500 You take 4000 divide by 200 which is 20 months then take 150 times 20 equals 3000 then add 500
Step-by-step explanation:
find the slope of the line through these pair of points. (17, –6), (–11, 7)
m = (Y2 - Y1)/(X2 - X1)
m = (7 - (-6))/(-11 - 17)
m = (7 + 6)/(-28)
m = 13/(-28) = -(13/28)
Airline fares are $200 for first class and $150 for business class. If a flight had
52 passengers who paid a total of $8500. How many first class passengers.
we’re on the trip?
Answer:
14 first class passengersStep-by-step explanation:
Set a system of equations as below:
x + y = 52200x + 150y = 8500Multiply the first equation by 150 and subtract from the second equation.
This will eliminate y, solve for x:
200x + 150y - 150x - 150y = 8500 - 150*5250x = 700x = 700/50x = 14