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]
Sara took skydiving lessons. The Skydome charges $45 per hour for lessons. Sara also gave her Skydiving Instructor a tip of $20. Define the unknown in the scenario and assign it a letter or symbol. math
Answer:
45+20=t t=65
Step-by-step explanation:
t is my assigned letter
Hope this helps
Which ordered pair is a solution of the equation?
7x-2y=-57x−2y=−5
Answer:
what ordered pairs?
Step-by-step explanation:
The graph f(x)=(x+2)^2-7is translated 5 units left, resulting in the graph g(x). Which equation represents the new function, g(x)?
Answer: G(x)=(x-3)^2-7
Step-by-step explanation: Translated 5 units to the left is a negative change and a change in the X axis
The equation represents the new function, g(x) will be G(x)=(x-3)²-7. The correct option is A.
What is translation?The process of changing the location of the image on the coordinate system will be known as the translation. A graph is the representation of the data on the vertical and horizontal coordinates so we can see the trend of the data.
It is given that the graph f(x)=(x+2)²-7 is translated as 5 units left, resulting in the graph g(x).
Translated 5 units to the left are a negative change and a change in the X axis. The graph is also attached with the answer below.
The equation represents the new function, g(x) will be G(x)=(x-3)²-7.
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miggy ask to solved the given quadratic equation x²+8x-20=0 using the quadratic formula,Help miggy to determine the following
Answer:
x = -10 or 2
Step-by-step explanation:
Un camión traslada 12 vehículos. Algunos son autos y otros son camionetas. Cada auto tiene una masa de 2 toneladas y cada camioneta de 3 toneladas. En total, el camión lleva una carga de 33 toneladas.
Escribe un sistema de ecuaciones que permita calcular cuántos vehículos de cada tipo traslada el camión. Usa a para representar la cantidad de autos y c para representar la cantidad de camionetas que traslada el camión.
El sistema de ecuaciones queda descrita por las siguientes expresiones:
[tex]a+c = 12[/tex]
[tex]2\cdot a + 3\cdot c = 33[/tex]
Donde [tex]a[/tex] y [tex]c[/tex] son las cantidades de autos y camionetas.
El enunciado es equivalente a un sistema de dos ecuaciones lineales con dos incógnitas. Una ecuación para la cantidad de vehículos trasladados por el camión y otra ecuación para la masa total trasladada:
[tex]a+c = 12[/tex] (1)
[tex]2\cdot a + 3\cdot c = 33[/tex] (2)
Donde:
[tex]a[/tex] - Cantidad de autos.[tex]c[/tex] - Cantidad de camionetas.El sistema de ecuaciones queda descrita por las siguientes expresiones:
[tex]a+c = 12[/tex]
[tex]2\cdot a + 3\cdot c = 33[/tex]
Donde [tex]a[/tex] y [tex]c[/tex] son las cantidades de autos y camionetas.
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What is the distance between point (2,6) and (5,2)?
Answer:
5 units
Step-by-step explanation:
Distance between two points can be found by using the pythagorean theorem
The distance in y = 4
The distance in x = 3
3² + 4² = c²
9 + 16 = c²
25 = c³
c = √25
c = 5
-Chetan K
Answer:
5
Step-by-step explanation:
[tex]\mathrm{Distance \:\:Formula:}\\\\\mathrm{d = \sqrt{(x_2 - x_1)^2 + (y_2-y_1)^2}}[/tex]
[tex]\underline{\mathrm{Plug \:the\: points:}}[/tex]
[tex]d = \sqrt{(x_2 - x_1)^2 + (y_2-y_1)^2}[/tex]
[tex]d = \sqrt{(5 - 2)^2 + (2-6)^2}[/tex]
[tex]\underline{\mathrm{Solve:}}[/tex]
[tex]d = \sqrt{(5 - 2)^2 + (2-6)^2}[/tex]
[tex]\sqrt{(5 - 2)^2 + (2-6)^2}[/tex]
[tex]\sqrt{3^2 + 4^2}[/tex]
[tex]3^2 = \sqrt{9+4^2} =\boxed{9}\\\\4^2=\sqrt{9+16} = \boxed{16}[/tex]
[tex]\sqrt{25}[/tex]
[tex]\sqrt{5^2}=5[/tex]
2) Write the following equations in the statement form.
a) 2a + 7 = 15
b) 4m - 6 = 2
pls I need help
Answer:
A) a = 4
B) m = 2
Step-by-step explanation:
A) 2a + 7 = 15
2a + 7 - 7 = 15 - 7
2a = 8
2a/2 = 8/2
a = 4
B) 4m - 6 = 2
4m - 6 + 6 = 2 + 6
4m = 8
4m/4 = 8/4
m = 2
Answer:
a = 4 and m = 2.
a) Find the value of a if the total of a being doubled and added to 7 is 15.
b) Find the value of m if the total of m being multiplied by 4 and being subtracted by 6 is 2.
Step-by-step explanation:
2a + 7 = 15
→ Minus 7 from both sides
2a = 8
→ Divide both sides by 2
a = 4
4m - 6 = 2
→ Add 6 to both sides
4m = 8
→ Divide both sides by 2
m = 2
find the unit rate for this problem
45 tacos for 15 people ______ to is per person
No link please!!!
Answer:
45/15 = 3
Step-by-step explanation:
3 tacos per person
Answer:
3 tacos for 1 person
Step-by-step explanation:
45 tacos / 15 people
Divide the top and bottom by 15
(45/15) / ( 15/15)= 3/1
3 tacos for 1 person
Can somebody help ???
Answer:
2/5, a and b
Step-by-step explanation:
Angel sum theorem ……….
Answer:
y = 42º
Step-by-step explanation:
The unmaked angle of the bottom triangle is 90º
The sum of the angles is 180
y + 90 + 48 = 180
combine like terms
y + 138 = 180
subtract 138 from both sides
y = 42º
what are the similar triangles theorems
Answer:
AA (Angle Angle), SAS (Side Angle Side), SSS (Side Side Side)
Step-by-step explanation:
Please help ME for brainliest.
Answer:
Equation: -1.2y-4.2y=-3.78
Solved: y=0.7
Step-by-step explanation:
-1.2y-4.2y=-3.78
-5.4y=-3.78
y=0.7
I will take you up on your brainliest offer
10+5-7=3y
-10x+5x+5=-15
3x+2x-4x+10
pre algebra 8th grade math
Answer:
1) y=8/3=2 2/3 2) x=4 3) x+10
Step-by-step explanation:
1) 10+5-7=3y
Calculate the sum or difference.
8=3y
Swap the sides of the equation.
3y=8
Divide both sides by 3.
y=8/3=2 2/3
2) -10x+5x+5=-15
Collect like terms.
-5x+5=-15
Move the constant to the right-hand side and change the sign.
-5x=-15-5
Calculate the difference.
-5x=-20
Divide both sides by -5.
x=4
3) 3x+2x-4x+10
Collect like terms.
(3+2-4)x+10
Calculate the sum or difference.
1x+10
When the term has a coefficient of 1, it doesn't have to be written.
x+10
Hope this helps :)
what is the value of 8^-1/3
Answer:
2
Step-by-step explanation:
cube root of 8
The functions f and g are defined as follows.
3
f(x) = 3x - 3 g(x) = 3x' +5
Find f(-6) and g(-3).
Simplify your answers as much as possible.
f(-6) -
X
g(-3) =
pls help ill give brainliest
a
Blue and green dye are mixed in a 7:4 ratio to make 44 litres
of a teal-coloured dye. A further 8 litres of green dye are added
to the mixture. What is the new ratio of blue to green dye in its
simplest form?
Answer:
7:4 is the new ratio.
Step-by-step explanation:
set a proportion; (8+4 = 12)
7 x
-- = --
4 12
12/4 = 3
3 x 7 = 21
x = 21
new ratio: 21:12
simplifies: 7:4 (division of 3)
The new ratio of blue to green dye in its simplest form is 7/6.
Blue and green dye are mixed in a 7:4 ratio to make 44 litres of a teal-coloured dye. A further 8 litres of green dye are added to the mixture. What is the new ratio of blue to green dye in its simplest form to be determined.
The ratio can be defined as the comparison of the fraction of one quantity towards others. e.g.- water in milk.
Calculating the fraction of blue and green in the teal dye,
Blue dye = 7/(4+7) * 44
Blue dye = 7/11 * 44
Blue dye = 28 liters
Similarly,
Green dye = 7/12*44
Green dye = 16
Now
Blue dye = green dye = 28+16 = 44
Now gree dye is increase by 8 liters
new volume fraction of green dye = 16+8
= 24
a fraction of blue dye remains the same,
the ratio of blue dye to new green dye in teal colored.
= 28/24
=7/6
Thus, the new ratio of blue to green dye in its simplest form is 7/6.
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i need it asapp plss
Answer:
#1 is A #2 is C #3 is D #4 is D #5 is D #6 is A
Step-by-step explanation:
I might be wrong for number 5 or the others but hope this works for you.
:)
Can someone help? This is so hard.
y equals 50° since there is a 90° and a 30°
Answer:
cos^-1 (9/15)
Step-by-step explanation:
An investment of $5,690 earns interest at a rate of 4% and is compounded quarterly. What is the
accumulated value of the investment at the end of 7 years?
An item is regularly priced at $35 It is on sale for 40% off the regular price. How much (in dollars) is discounted from the regular price?
Answer:
14 dollars off the original price
Step-by-step explanation:
If
x
=
2
and
y
=
6
, evaluate the following expression:
3
(
3
y
−
4
x
)
At the craft store, Patty bought a bag of yellow and brown marbles. The bag contained 85
marbles, and 60% of them were yellow. How many yellow marbles did Patty receive?
Answer:
51 yellow marbles
Step-by-step explanation:
60% of 85 can be found by multiplying 85 and 0.6 to get 51
Answer:
i got 51 marbles! simple.
Find the value of x in the equation below. 15.4=x-13.9
Answer:
29.3
Step-by-step explanation:
Answer ALL the question. Thank you
1) A toad jumps 8 times. Every time he jumps, he covers the same distance. After 8 jumps, he had traveled 96 steps. How long are his jumps?
2) Roger covers 52 steps in 1 jump and 7 steps. How many steps are equal to on of Roger's jumps?
3)Wartortle takes the same amount of time to get to 96, but he does it differently. Each of his jumps is equal to 8 of the toad's steps. How many jumps does Wartorle make?
4) Ribbbie jumped just as far as MT, 52 steps, but Rabbie did it in 3 jumps and 10 steps. How many steps are equal to one of Ribbie's jumps?
1) The toad's jumps are 12 steps long.
2) One of Roger's jumps equals 45 steps.
3) Wartortle makes 1 jump to cover 96 steps.
4) One of Ribbie's jumps is equal to 14 steps.
1) Given that a toad jumps 8 times, and every time he jumps, he covers the same distance, and after 8 jumps, he had traveled 96 steps, to determine how long are his jumps the following calculation must be performed:
96/8 = X 12 = X So, his jumps are 12 steps long.
2) Given that Roger covers 52 steps in 1 jump and 7 steps, to determine how many steps are equal to one of Roger's jumps, the following calculation must be performed:
52 - 7 = X 45 = X Thus, one of Roger's jumps equals 45 steps.
3) Since Wartortle takes the same amount of time to get to 96, but he does it differently, as each of his jumps is equal to 8 of the toad's steps, to determine how many jumps does Wartorle make the following calculation must be performed :
8 x 12 = X 96 = X 96/96 = 1 Therefore, Wartortle makes 1 jump to cover 96 steps.
4) Given that Ribbie jumped just as far as MT, 52 steps, but Ribbie did it in 3 jumps and 10 steps, to determine how many steps are equal to one of Ribbie's jumps, the following calculation must be performed:
(52 - 10) / 3 = X 42/3 = X 14 = X Therefore, one of Ribbie's jumps is equal to 14 steps.
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Find the least common multiple of: 2v^2y^7 and 11v^4y^8x^3
Answer:
2v6y719x3
Step-by-step explanation:
(1): "x3" was replaced by "x^3". 2 more similar replacement(s).
STEP 1
Equation at the end of step 1
(((2v2 • y711) • v4) • y8) • x3
STEP 2
Final result :
2v6y719x3
Can someone help me please?
Answer:
5.9 x [tex]10^{12}[/tex]
Step-by-step explanation:
( For Brainly )
On which body part a temporal lobe is placed?
The square root of 81 is?
Answer:
On which body part a temporal lobe is placed?
answer-
behind the ears
The square root of 81 is?
answer-
9
Happy late Thanksgiving!!!
Answer:
You too!!
Step-by-step explanation:
A population of values has a normal distribution with μ=5.5 and σ=94.4. You intend to draw a random sample of size n=101.
Find P10, which is the score separating the bottom 10% scores from the top 90% scores. P10 (for single values)
Find P10, which is the mean separating the bottom 10% means from the top 90% means.
P10 (for sample means)
Answer:
P10 = P₁₀ = -115.5
Step-by-step explanation:
Shown in the picture