Answer:
f ◦ g is the composition function that has f composed with g. ... Find (f ◦ g)(x) for f and g below. f(x)=3x + 4. (6) g(x) = x2 +. 1 x. (7).
Step-by-step explanation:
Is this how you solve this (finding the inverse)
There are a couple ways to go about this.
By definition of inverse function, if [tex]j^{-1}[/tex] exists, then
[tex]j\left(j^{-1}(x)\right) = x[/tex]
All this means is that if you provide some input [tex]x[/tex], plug it into [tex]j^{-1}(x)[/tex], then plug that into [tex]j(x)[/tex], you end up recovering the original input [tex]x[/tex] that you started with.
We can also do this in the opposite direction, so
[tex]j^{-1}(j(x)) = x[/tex]
So now if [tex]j(x)[/tex] is invertible, then
[tex]j(x) = -\dfrac23 x - 9 \implies j\left(j^{-1}(x)\right) = -\dfrac23 j^{-1}(x) - 9 = x[/tex]
Solve for [tex]j^{-1}[/tex].
[tex]-\dfrac23 j^{-1}(x) - 9 = x[/tex]
[tex]\dfrac23 j^{-1}(x) = -x - 9[/tex]
[tex]j^{-1}(x) = -\dfrac32 (x+9)[/tex]
[tex]\boxed{j^{-1}(x) = -\dfrac32 x - \dfrac{27}2}[/tex]
Another way to do it is by algebraically substituting [tex]x[/tex] within the definition of [tex]j(x)[/tex]
Starting with the given definition
[tex]j(x) = -\dfrac23 x - 9[/tex]
we replace [tex]x[/tex] with some new expression in a new variable [tex]y[/tex] that makes the right side reduce to just [tex]y[/tex]. To demonstrate, if we multiply [tex]-\frac23 x[/tex] by [tex]-\frac32[/tex], we end up with a coefficient of 1. So let [tex]x=-\frac32 y[/tex]. Then
[tex]j\left(-\dfrac32 y\right) = -\dfrac23 \left(-\dfrac32 y\right) - 9 = y - 9[/tex]
As you can see, this doesn't completely reduce to [tex]y[/tex], so we're not done. To adjust for this, we just add 9 to [tex]y[/tex], so our ultimate substitution is [tex]x=-\frac32(y+9)[/tex]. Then
[tex]j\left(-\dfrac32 (y+9)\right) = -\dfrac23 \left(-\dfrac32 (y+9)\right) - 9 = (y+9) - 9 = y[/tex]
Now applying [tex]j^{-1}[/tex] to both sides,
[tex]j^{-1}\left(j\left(-\dfrac32 (y+9)\right)\right) = j^{-1}(y)[/tex]
[tex]\implies \boxed{j^{-1}(y) = -\dfrac32 y - \dfrac{27}2}[/tex]
(we can freely swap out [tex]y[/tex] for [tex]x[/tex] at this point)
Yet another way, since the function here is quite simple, we can just think about the action of [tex]j[/tex] on a given number [tex]x[/tex] - multiply it by -2/3, and subtract 9.
[tex]x \mapsto -\dfrac23 x \mapsto -\dfrac23x - 9 = j(x)[/tex]
The inverse operation undoes this, so given some number [tex]j(x)[/tex], we recover [tex]x[/tex] by adding the additive inverse of -9, or 9, then multiplying the whole result by the multiplicative inverse of -2/3, or -3/2.
[tex]j(x) \mapsto j(x) + 9 \mapsto -\dfrac32(j(x) + 9) \mapsto -\dfrac32 j(x) - \dfrac{27}2 = x[/tex]
You seem to be using some version of this method. You made the mistake of thinking the "multiply by -3/2" step applies only to [tex]j(x)[/tex], and not [tex]j(x) + 9[/tex].
What percent is represented by the diagram below?
Alternative text
A. 13%
B. 65%
C. 130%
D. 650%
Answer:
I think it's will be C
Step-by-step explanation:
C I psomes
Answer: C 130%
Step-by-step explanation:
seventy-four thousand,
ninety-nine
Answer:
I think you're looking for 74,099
for each integer $n$ greater than $1$, let $f(n)$ be the number of solutions of the equation $\sin x
The value [tex]\displaystyle \sum^{2007}_{n = 2} F(n)[/tex] is 2016532.
What is an integer?The collection of positive and negative integers is known as an integer. Integers, like whole numbers, do not include the fractional portion. Integers can therefore be defined as numbers that can be positive, negative, or zero but not as fractions. On integers, we can carry out all arithmetic operations, including addition, subtraction, multiplication, and division. Integer examples include 1, 2, 5, 8, -9, -12, etc. "Z" stands for an integer. The Latin term "Integer," which implies entire or intact, is where the word "integer" first appeared. Zero, positive numbers, and negative numbers make up the particular set of numbers known as integers.
Integer examples include: -1, -12, 6, and 15.
Zero is not an integer that can be positive or negative. There is no (+ or -) sign on zero, making it a neutral number.
F(2) = 3
We learn that for the majority of the graphs by examining different graphs.
F(n) = n+1
3+4+5+5+7+8+9+9+··········+2008
= (1+2+3+4+5+·····+2008)-3-501
= [tex]\frac{(2008) \times( 2009)}{2} -504[/tex]
= 2016532
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Jordan knits a square blanket that has an area of 1,500 square inches. What is the approximate length of each side of the blanket?
O 16 inches
O 27 inches
O 39 inches
O 42 inches
PLS HELPPPPPP MEEE!!
What is the slope of line m?
Answer:-1/2
Step-by-step explanation:rise 1 run back 2
this is pain need help and to be explained
Answer:
Equation is 0.5 gal × (0.1) + x gal × (0.35) = (0.5 + x) × (0.15)
0.125 gallons of the 35% acid solution Eli should add.
Step-by-step explanation:
Given: Eli wants to combine 0.5 gallon of a 10% acid solution with some 35% acid solution to make a 15% acid solution.
To find: Equation can you use to determine how many gallons of the 35% acid solution Eli should add?
Solution:
Let x be the gallons of the 35% acid solution.
According to question,
For 0.5 gallon of a 10% acid solution = 0.5×0.1
For x gallon of a 35% acid solution = x×0.35
For (0.5+x) gallon of a 15% acid solution = 0.5 + x × 0.15
The equation form is
0.5 gal × (0.1) + x gal × (0.35) = (0.5+x) × (0.15)
Solving the above equation,
0.05 + 0.35x = 0.075 + 0.15x
0.2x = 0.025
x = 0.025/0.2
x= 0.125
Therefore, 0.125 gallons of the 35% acid solution Eli should add.
Therefore, 0.125 gallons of the 35% acid solution Eli should add.The equation is 0.5 gal × (0.1) + x gal × (0.35) = (0.5 + x) × (0.15)
Suppose that the relationship between price, P, and quantity, Q, is given by the equation Q = 140-4P.
Which of the following equations correctly represents solving Q = 140-4P for P?
OP=140-Q
OP=35-4Q
OP=140-4Q
OP=140+Q
OP=35-10
Answer:
In 1864, Sherman succeeded Grant as the Union commander in the Western Theater. He led the capture of the strategic city of Atlanta, a military success that contributed to the re-election of President Abraham Lincoln.
Step-by-step explanation:
What is the area, in square meters, of the Polygon?
16,608 square cm
2760 Square meters
2091.6 square inches
12,480 square inches
Answer:The answer would be the second one since he question is saying square meters.
Step-by-step explanation:Please give brainliest if right.
Which choice correctly explains the expression?
5 × 9
Responses
5 groups with 9 items per group
5 groups with 9 items per group
5 groups with 5 items per group
5 groups with 5 items per group
9 groups with 9 items per group
9 groups with 9 items per group
Skip to navigation
Answer:
The first choice
Step-by-step explanation:
Since we're looking at 5 × 9, we'd need to group them into 5 groups of 9, or 9 groups of 5. In this case, the first choice is the correct answer.
Mark the other guy with brainliest
Hana has some blue paint. She wants to lighten the shade, so she mixes in 1 cup of white paint. The color is still too dark, so Hana keeps mixing in 1 cup of white paint at a time. After adding 4 cups, she decides the color is too light.
A. Explain in words how much paint Hana should have added initially to get the shade she wants.
Enter your answer.
B. Model With Mathematics Represent your answer to part A with one or more inequalities.
Enter your answer.
C. Hana decides that she likes the shades of blue that appear in between adding 1 cup and 4 cups of white paint. How can you represent the number of cups of white paint that yield the shades Hana prefers?
Enter your answer.
Answer:
e, so she mixes in 1 cup of white paint. The color is still too dark, so Hana keeps mixing in 1 cup of white paint at a time. After adding 4 cups, she decides the color is too light.
A. Explain in words how much paint Hana should have added initially to get the shade she wants.
Enter your answer.
B. Mod
Step-by-step explanation:
One diagonal of a rhombus is three times as long as the other diagonal. If the area of the rhombus is 54 square millimeters, what are the lengths of the diagonals?
Answer:
Assume one diagonal of 2x and other of x inches. and sides of length =L inches.
Area of rhombus = 2*2x*x/2=2x^2 = 81 x=9/sqrt.2 and 2x=9*sqrt 2.
Diagonals are x=6.365 inch 2x=12.73 inch check area =12.73*6.365= 81.026 sq.inch.
Step-by-step explanation:
Gabriel started training with the track team five weeks ago. During the first week, he ran 0.5 mile at each practice. The next three weeks he ran 0.75 mile, 1 mile, and 1.25 miles at each practice. If he continues this pattern, how many miles will he be running at each practice during the 7 th week?
If Gabriel continues the pattern of running that he has done on the past four weeks, the miles he will run on the 7th week is 2 miles.
How many miles will Gabriel run?Gabriel's pattern of running is such that he increases the number of miles by 0.25 miles every week.
This is why he ran 0.5 miles, and then 0.75 miles and then 1 mile.
If he keeps going like this, one the 7th week, he will run:
5th week = 1.5 miles
6th week = 1.75 miles
7th week = 2 miles
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The highest elevation in the world is 29,029 feet and the lowest is -35,994 feet. What is
the difference between the two?
Answer:
Question: Mt. Everest, the highest elevation in Asia, is 29,028 feet above sea level. The Dead Sea, the lowest elevation, is 1,312 feet below sea level.
Marshall pours 1/2 gallon of lemonade into 8 glasses. He pours the same amount of lemonade into each glass. How much lemonade, in gallons, does Marshall pour into each glass?
When working on homework, Jen spends 5 minutes reading for every 10 minutes spent on writing, Andy spends 2 minutes reading for every 5 minutes of writing, and Noor spends 10 minutes reading for every 15 minutes of writing.
When working on homework, Jen spends 5 minutes reading for every 10 minutes spent on writing, Andy spends 2 minutes reading for every 5 minutes of writing, and Noor spends 10 minutes reading for every 15 minutes of writing .
Many teachers and parents believe that homework helps students build study skills and review concepts learned in class. Others see homework as disruptive and unnecessary, leading to burnout and turning kids off to school. Decades of research show that the issue is more nuanced and complex than most people think: Homework is beneficial, but only to a degree. Students in high school gain the most, while younger kids benefit much less.
The National PTA and the National Education Association support the “10-minute homework guideline”—a nightly 10 minutes of homework per grade level. https://brainly.com/question/28529831 #SPJ9
7. Rob wants to purchase a $5,000 drum set. The music store offers him a 2-year installment agreement requiring $800 down and monthly payments of $202.50. Rob has
a poor credit rating.
a. What is his interest on this installment agreement?
The interest on this installment agreement that Rob pays is $660.00
What the loan?In short, the loan is an amount that the bank or financial institution makes available to you for a certain period. Basically, every time you apply for credit, whether it's a loan or even a credit card, you're taking out a type of loan.
The amount borrowed to purchase the drum set is the cost price of $5000 minus the down payment of $800
amount borrowed=$5000-$800amount borrowed=$4,200total monthly payments= $202.50*24total monthly payments=$4,860.00 interest on this installment agreement=$4860-$4200 interest on this installment agreement=$660.00Find out more about loan on: brainly.com/question/2865739
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Question 2 (Essay Worth 10 points)
(03.03)
How does the graph of f(x) = (x + 2)4 + 6 compare to the parent function g(x) = x4?
I really need help, I might get a grade detention
Answer:
Step-by-step explanatio
from up to down
12
30
10
is |-10| greater than
|6|?
Answer:
Yes
Step-by-step explanation:
The value of |-10| is,
→ |-10| = 10
The value of |6| is,
→ |6| = 6
Now the greater value is,
→ 10 > 6
→ |-10| > |6|
Yeah, |-10| greater than |6|.
Answer:
No, it's not
Step-by-step explanation:
Hope it helps you
PLS RATE AS BRAINLIEST ANSWER
Write a declaration for a variable hits that can hold the number of times a baseball player has hit the ball in a baseball game.
A declaration of a hits variable that can store how many times a baseball player has hit the ball during a game of baseball int hits;
How do you declare a variable value?
A programme declares a variable whenever it states that it requires one. Place declaration statements for our brief programmes in-between the main method's two curly braces. The variable's name and data type are provided in the declaration. It could also provide a specific value that has to be entered into the variable.
When a variable is given a value for the first time, it is said to be initialized. The symbol = stands in for the assignment operator. Instead of writing int I and then 9, you can establish a variable for addition and then give it a value in the same line by writing int I = 9.
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Hannah can spend up to $40 on snacks and drinks at the movie theater. A snack costs $5 and a drink costs $3.50.
Use for the number of snacks
Use for the number of drinks
Which inequality represents this situation?
Answer:
5s + 3.50d < 40
Step-by-step explanation:
if you were to total up the costs of a snack and drink together you'll end up with $8.50
-multiply $8.50 until you reach $40 mark
i.e 8.50×2(means 2 of each item) = $17
8.50×3 = $25.5
8.50×4 = $34
8.50×5= $42.5
-if you look at it, the calculation for 5, the pricing is now over the budget therefore the answer is then 5s + 3.50d < 40 because she can only spend up to $34 at most
state the domain and range of the following function: {(-3,4),(0,6),(2,-2),(1,-3),(6,-7),(3,2)} domain: {-7,-3,-2,2,4,6} range: {-3,0,1,2,3,6} domain: {0,1,2,3,4,6} range: {-7,-3,-2} domain: {-3,0,1,2,3,6} range: {-7,-3,-2,2,4,6} domain: {-7,-3,-2} range: {0,1,2,3,4,6}
The domain and range of the given function are: domain: {-7,-3,-2,2,4,6} range: {-3,0,1,2,3,6}. (Option A).
What is domain and range?The terms Domain and Range describe the input values and the function's output values, respectively.In terms of coordinates, domain is the x-coordinate and range is the y-coordinate of a function.Now,
In the given function {(-3,4),(0,6),(2,-2),(1,-3),(6,-7),(3,2)},
the x- coordinates are: {-3, 0, 2, 1, 6, 3} and the y-coordinates are: {4, 6, -2, -3, -7, 2}.Thus, According to the definition of domain and range,
the domain is {-3, 0, 2, 1, 6, 3} and the range is {4, 6, -2, -3, -7, 2}.Hence, Option A is correct, i.e., the domain and range of the given function are: domain: {-7,-3,-2,2,4,6} range: {-3,0,1,2,3,6}.
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Suppose that 24 inches of wire costs 72 cents. At the same rate, how much (in cents) will 49 inches of wire cost?
Answer:
147 cents
Step-by-step explanation:
If 24 inches of wire cost 72 cents then each inch cost 3 cents. 49*3=147
find the LCM of 2 and 3
Answer:
6
Step-by-step explanation:
If you multiply both together once that will be the lowest it gets
Answer: 6
Step-by-step explanation: compare the multiplication tables ig
What is the remainder when 17^77 is divided by 35?
The remainder when 17^(77) is divided by 35 is 12
How can the remainder of dividing a large number be found?The number being divided = 17^(77)
The number by which 17^(77) is divided = 35
Using a graphing calculator as follows, we have;
Enter the value 17^(77) in the calculatorEnter the value 35 in the calculatorPress the divide by '÷' buttonUse the 'Display as proper fraction' button on the calculator, to display the result as proper fraction, [tex] a \frac{b}{c} [/tex]Use the left arrow button to move to the fraction part of the result displayed as proper fraction The remainder is the numerator of the fraction part of the proper fraction, which is 12[tex] \frac{17^{77}}{35} = V+ \frac{12}{35} [/tex]
Where V is a very large number quotient
From the above fraction, we have;
17⁷⁷ ÷ 35 = V + 12/35Expressing the above result using long division gives;
__V___ (Quotient)
35 (17⁷⁷)
____
12 (Remainder)
The remainder is therefore; 12Learn more about long division in maths here:
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Which expression is equivalent to (a^8)^4
Answer:
Brainliest pls
Step-by-step explanation:
a^32
simplify each expression 9(7k-2)+6k
Answer:
= 69k - 18
Step-by-step explanation:
9(7k-2) + 6k
= (9*7k + 9*-2) + 6k
= (63k - 18) + 6k
= 63k + 6k - 18
= 69k - 18
Congruence: Mastery Test
4
Select the correct answer.
pair 1
pair 3
Which pairs of polygons are congruent?
OA pairs 1, 2, and 3
OB. pairs 1, 2, 3, and 4
OC. pairs 2 and 3
OD. pairs 1 and 3
ANYONE GOT THE AWNSERRRRR???
From the given polygons, the pairs of polygons that are congruent are D. pairs 1 and 3.
What are congruent polygons?When two or more polygons are said to be congruent, it means that they have the same shape and that the lengths of their sides are the same.
The orientation of the shape is irrelevant if the above requirements are met.
The pair of polygons in Pair 1 are congruent because they have the same shape and are the same length. The same is true of the polygons in pair 3.
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verbal expression for 7 to the third power
The answer is " 7 to the power 3rd ".
We translate the algebraic expression 7³ into a verbal expression. The given expression has a base number of 7 raised to the power of 3 . This means is that 7 is multiplied by itself 3 times. So we should write " 7 to the power 3rd "
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