Answer:
[tex]f^{-1}[/tex](x) = [tex]\frac{1}{3}[/tex] x + 7
Step-by-step explanation:
let y = f(x) and rearrange making x the subject, that is
y = 3(x - 9) + 6 ← distribute and simplify right side
y = 3x - 27 + 6 = 3x - 21 ( add 21 to both sides )
y + 21 = 3x ( divide all terms by 3 )
[tex]\frac{1}{3}[/tex] y + 7 = x
Change y back into terms of x with x = [tex]f^{-1}[/tex](x) , thus
[tex]f^{-1}[/tex](x) = [tex]\frac{1}{3}[/tex] x + 7
"one half of a number is 8 less than the number itself ''
Answer:
16
Step-by-step explanation:
16/8=8
Half of 16 is 8.
8 is 8 less than 16.
Hope this helps.
Answer:
The required number is 12
Need help please! On this math question
Answer:
B 2+-5=-3
Step-by-step explanation:
Johnny is saving money to buy a PS 5. He already has $30 in the bank and gets $10 per week allowance for doing his chores. Write an equation to to find the number of weeks, x, it will take him to have $600.
Answer:
10x + 30 = 600
Step-by-step explanation:
Johnny gets $10 per week, which is $10x for x number of weeks.
He already has $30, so his money becomes 10x + 30.
His goal is to have $600, so our equation becomes 10x + 30 = 600
evaluate to 212 base 3 - 121 base 3 + 222 base 3
Answer:
212 bp^3 (base pairs cubed) - 121 bp^3 (base pairs cubed) + 222 bp^3 (base pairs cubed) = 313 bp^3 (base pairs cubed
Step-by-step explanation:
What does this mean?
~p~9
What are the solutions of 3(x - 4)(2x - 3) = 0? Check all that apply.
-4
-3
-2/3
3/2
3
4
Answer:
3/2 and 4
Step-by-step explanation:
Answer:
3/2 and 4 are the answers. Hope this helps!
john missed 4 problems on the test but did 75% of them correctly. how many problems were there in the test?
Answer:
16
Step-by-step explanation:
por que si por 25 son 4 en 75 son 12
Consider the function f(x) = 10x^2 + 6x - 2 when x=3
Answer:
106
Step-by-step explanation:
Substitute x = 3 into f(x) and evaluate , that is
f(3)
= 10(3)² + 6(3) - 2 = 10(9) + 18 - 2 = 90 + 18 - 2 = 106
Please help me! thank you :)
Answer:
A
Step-by-step explanation:
As the equation has already been factorised, we can find the value of x that results in 0 in each bracket:
x - 3 >= 0
x >= 3
x+2 >= 0
x >= -2
8.7 x 0.45
I keep getting the weonv answer
Answer:
3.915
Step-by-step explanation:
Use a calculator.
8.7 × 0.45 = 3.915
What is the slope of the line x=5
The slope of the line x = 5 is undefined.
What is the slope-intercept form?In Mathematics and Geometry, the slope-intercept form of the equation of a straight line is given by this mathematical equation;
y = mx + b
Where:
m is the slope or rate of change.x and y are the points.b is the y-intercept or initial value.Based on the information provided about this line, a linear equation that models it is given by;
y = mx + b
x = 5
This ultimately implies that, this line is a vertical line and as such, it has no slope or an undefined slope. Therefore, the x-intercept is 5 and the slope is undefined.
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please help me out!!!
the answer is G
Step-by-step explanation:
G is the answer
Step-by-step explanation:
I guess it's G because g might make make an exponents
Rebecca starts this week with $3.00. each day she does her chores her mother gives her $ 1.50 . If y represents the total amount of moeny . Rebecca has after x days . Can someone plz write an expression based on this problom.
Answer:
Amount of money she gets per day -> $1.50
Amount of money she gets after x days -> [tex]1.5x[/tex]
Total amount of money = 3 + 1.5x
Total amount of money = y
[tex]1.5x+3=y[/tex]
PLEASE SOLVE FOR Y: [tex]7y+4=3-2y[/tex]
Answer:
[tex]y = \frac{-1}{9}[/tex]
Step-by-step explanation:
[tex]7y + 4 = 3 - 2y[/tex]
add [tex]2y[/tex] to both sides
[tex]7y + 4 + 2y = 3 -2y + 2y \\9y + 4 = 3[/tex]
add [tex]-4[/tex] to both sides
[tex]9y + 4 -4 = 3 - 4 \\9y = -1[/tex]
divide both sides by [tex]9[/tex]
[tex]\frac{9y}{9} = \frac{-1}{9} \\[/tex]
[tex]y = \frac{-1}{9}[/tex]
The solution to the equation 7y + 4 = 3 - 2y is y = -1/9.
Here, we have,
To solve for y in the equation 7y + 4 = 3 - 2y, we can follow these steps:
Step 1: Combine like terms on both sides of the equation:
7y + 2y = 3 - 4.
Simplifying:
9y = -1.
Step 2: Divide both sides of the equation by 9 to isolate the variable y:
(9y)/9 = (-1)/9.
Simplifying:
y = -1/9.
Therefore, the solution to the equation 7y + 4 = 3 - 2y is y = -1/9.
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Find the range of the data set: 7, 12, 15, 4, 23, 15, 25, 9
Answer: Range = 21
Step-by-step explanation: you subtract the highest number by the lowest number in the set to find your range
aleysius bakes 30 cupcakes to celebrate her birthday. she had her friends over to celebrate and when the party was over there was 7 cupcakes left. how many was taken
Answer: 23 cupcakes
Step-by-step explanation:
Answer:
23 were taken
Step-by-step explanation:
30-7=23
Which of the following polynomial functions is graphed below
Answer:
A, the other person was correct
Step-by-step explanation:
The polynomial functions is graphed below is f(x) = (x+ 4)(x- 2)².
What is Function?a mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable).
There are three components that make up a function: a set of inputs, a set of outputs, and a rule that links the elements of the input set to the elements of the output set so that each input is paired with exactly one output.
We have a graph for polynomial function.
We know that the function of graph have solution where the graph touches or passes the x axis.
Here from the graph at x = -4 and at x= 2 the touches and moves upward.
So, the factors of polynomial are (x+ 4) and (x- 2).
Thus, the polynomial function is f(x) = (x+ 4)(x- 2)².
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A dog rolls over 25 times in 2 minutes. How many times can the dog roll over in 6 minutes? *
Hey there! I'm happy to help!
How many times does 2 minutes go into 6 minutes?
6/2=3
So, the dog rolls over 25 times 3 times!
25(3)=75
Therefore, the dog can roll over 75 times in 6 minutes.
Have a wonderful day! :D
A group of 29 friends gets together to play a sport. First, people must be
divided into teams. Each team has to have exactly 4 players, and no one can
be on more than one team. How many teams can they make? (It is possible
that not everyone can be on a team.)
Answer:
7 teams of 4 but there would be an extra person
Step-by-step explanation:
Find the product. (-10) (-10) (-10)
1000
-1000
10,000
-10,000
the answer is -1000 as -10 cube is -1000
The value of product of (-10)(-10)(-10) is -1000.
What are Arithmetic operations?Arithmetic operations can also be specified by subtracting, dividing, and multiplying built-in functions.
The operator that performs the arithmetic operations are called arithmetic operators.
Operators which let do a basic mathematical calculation
+ Addition operation: Adds values on either side of the operator.
For example 4 + 2 = 6
- Subtraction operation: Subtracts right-hand operand from left-hand operand.
for example 4 -2 = 2
* Multiplication operation: Multiplies values on either side of the operator
For example 4*2 = 8
/ Division operation: Divides left-hand operand by right-hand operand
For example 4/2 = 2
To determine the product of (-10)(-10)(-10)
⇒ (-10)(-10)(-10)
Multiplying the last two terms and (-) signs cancel out each other,
⇒ (-10)(100)
Multiplying the two terms,
⇒ -1000
Hence, the value of product of (-10)(-10)(-10) is -1000.
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A rectangle that is 2 inches by 3 inches has been scaled by a factor of 7
1. What are the side lengths of the scaled copy?
Shorter length?
Answer:
Step-by-step explanation:
14 by 21. 14 shorter length
It takes billy 6 minutes to walk 1.5 km. How long will it take billy to walk 9km?
Answer:
It will take Billy 36 minutes to walk 9km.
Answer:
[tex]\boxed{\tt 36 \ minutes}[/tex]
Step-by-step explanation:
Let's make a proportion using the following setup:
[tex]\frac{minutes}{kilometers} =\frac{minutes}{kilometers} \\[/tex]
We know it takes Billy 6 minutes to walk 1.5 kilometers.
[tex]\frac{6\ minutes}{1.5\ kilometers} =\frac{minutes}{kilometers}[/tex]
We don't know how long it takes him to walk 9 kilometers, so we can say it takes him x minutes to walk 9 kilometers.
[tex]\frac{6\ minutes}{1.5\ kilometers} =\frac{x\ minutes}{9\ kilometers}[/tex]
[tex]\frac{6}{1.5} =\frac{x}{9}[/tex]
Now, solve for x. To do this, isolate x on one side of the proportion. x is being divided by 9. The inverse of division is multiplication. Multiply both sides of the proportion by 9.
[tex]9*\frac{6}{1.5} =\frac{x}{9}*9[/tex]
[tex]9*\frac{6}{1.5} =x[/tex]
[tex]9*4=x[/tex]
[tex]36=x[/tex]
x= 36 minutes
It will take Billy 36 minutes to walk 9 kilometers.
Ruby, her brother, and 3 friends will share the bag of candy she bought. There are 110 candies in the bag. How many will each person get? A. 22 B. 24 C. 26
Answer: A
Step-by-step explanation: since there’s 110 candies divide it between the 3 friends plus ruby and her brother. So divide 110 by 5 and it will be your final answer
Answer:
A. 22
Step-by-step explanation:
First, you don't want to fall into the trap. The question says Ruby, her brother, AND 3 friends. That means you have to add everyone. 3(friends)+2(Ruby and her brother)=5 people. Then you have to divide. 110/5=22.
So, A.22 candies each.
4. The student council sold flowers for the Sweetheart dance as a fundraising
project. They sold 200 flowers that included carnations, roses, and Gerber
daisies. The carnations sold for $1.50 each, the roses sold for $3.75 each, and
the daisies sold for $2.25. Most of the order was carnations and there were
20 fewer roses than daisies. The total flower sales came to $453.00. How
many of each type of flower were ordered and sold.
Answer:
Kindly check explanation
Step-by-step explanation:
Given that :
Total flowers sold = 200
Flowers are :
Carnations, Roses, and Gerber daisies
Carnations = c
Roses = r
Daisies = d
20 fewer roses than daisies ; r = d - 20
Total sales = $453
c = $1.50 each ; r = 3.75 each ; d = 2.25 each
c + d + d - 20 = 200
c + 2d = 220 - - (1)
1.50c + (d - 20)(3.75) + 2.25d = 453
1.50c + 3.75d - 75 + 2.25d = 453
1.50c + 6d = 528 - - - (2)
From (1)
c = 220 - 2d
1.5(220 - 2d) + 6d = 528
330 - 3d + 6d = 528
330 + 3d = 528
3d = 528 - 330
d = 198/3
d = 66
66 × 2.25 = $148.5
c = 220 - 2(66)
c = 88
88 * 1.50 = $132
r = d - 20
r = 66 - 20
r = 46
46 × $3.75 = $172.5
What’s the prime factor** of 630
Answer:
Positive Integer factors of 630 = 2, 3, 6, 18, 5, 90, 7, 630 divided by 2, 3, 3, 5, 7, gives no remainder. They are integers and prime numbers of 630, they are also called composite number.
What is Five more than twice a number?
Write each phrase as a mathematical equation
Answer:
2x+5
Step-by-step explanation:
2 times a number plus 5
A carton holds 1.248 liters of fruit juice. What is this amount rounded to the nearest tenth? Use the number line below
Answer:
1.2 is the answer
Step-by-step explanation:
The rounding off of the number 1.248 to the nearest tenth is 1.2L
What is rounding off numbers?Rounding off numbers is a process used to simplify or approximate a numerical value to a specific degree of precision or to a specified number of decimal places. It involves adjusting a number to a nearby value that is easier to work with or more meaningful in a particular context.
When rounding off, you typically consider a specific digit in the number and look at the digit to the right of it. Depending on the value of that digit, you either increase or keep the original digit unchanged.
In the given problem, to round off the number to the nearest tenth;
1.248L ≈ 1.2L
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How is this A? Or is it wrong? This is polynomials
Answer:
D
Step-by-step explanation:
The volume for a rectangular prism is given by the formula:
[tex]V=lwh[/tex]
The length is 2h, the width is 9-h, and the height is h. So:
[tex]V=2h(h)(9-h)[/tex]
Multiply the first two terms:
[tex]V=2h^2(9-h)[/tex]
Distribute:
[tex]V=18h^2-2h^3[/tex]
Our answer is D.
I hope this helps!
PLZZ ANSWER THIS QUESTION
Answer:
D because a function cannot be on the same line as another function. Same goes with the X-axis but in this case it is the y-axis
Step-by-step explanation:
Find the equation of a line that is perpendicular to the line y = 1/9x +6 and contains the point (-7,0).
Answer:
y = -9x - 42Step-by-step explanation:
Perpendicular lines have negative reciprocal slopes
Given line:
y = 1/9x + 6Perpendicular line is:
y = - 9x + b and passes through the point (-7, 0)0 = -9*(-7) + bb = - 42So the line is:
y = -9x - 42