It is to be noted that the graph of g(x) = (x+2)³ -6 compares to the parent function f(x) = x³ in that g(x) is shifted 2 units to the left and 6 units down. See the explanation below.
What is a parent function?A parent function in mathematics is the simplest function in a family of functions that retains the concept of the whole family.
Here is how the transformation of a function can occur
Any change can occur during the transformation of a function.
Typically, they can be moved horizontally or vertically (by changing inputs or outputs), stretched (by multiplying outputs or inputs), and so on.
If the initial function is y = f(x), and the horizontal axis represents inputs and the vertical axis represents outputs, then:
Horizontal shift (also called phase shift):
Left shift by c units, y=f(x+c) (same output, but c units earlier)Right shift by c units, y=f(x-c)(same output, but c units late)Vertical shift
Up by d units: y = f(x) + dDown by d units: y = f(x) - dStretching:
Vertical stretch by a factor k: y = k × f(x)Horizontal stretch by a factor k: y = f(x/k)A function sets the value of one set's elements to the value of another set's specified element.
Given that the parent function is f(x)=x³, while the transformed function is g(x)=(x+2)³ - 6. Therefore, the transformation of the parent function that results in the transformed function is that g(x) is shifted 2 units to the left and 6 units down.
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The transformation of the parent function results in the transformation which shows g(x) is shifted 2 units to the left and 6 units down.
What is a function?The function is a type of relation, or rule, that maps one input to a specific single output.
A change can be moved horizontally or vertically (by changing inputs or outputs), stretched (by multiplying outputs or inputs), and so on.
If the initial function is y = f(x), and the horizontal axis shows the inputs and the vertical axis shows outputs, then:
Horizontal shift would be Left shift by c units; y=f(x+c) and Right shift by c units; y=f(x-c)
Vertical shift would be Up by d units; y = f(x) + d and Down by d units; y = f(x) - d
Stretching would be as Vertical stretch by a factor k: y = k × f(x)
Horizontal stretch by a factor k: y = f(x/k)
Given that the parent function is; f(x)=x³,
And the transformed function is; g(x)=(x+2)³ - 6.
Hence, the transformation of the parent function results in the transformation which shows g(x) is shifted 2 units to the left and 6 units down.
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Rollaround skate rink charges $5 admission and $3 per hour for a skate rental. Spinaround skate rink charges $8 admission and $1.50 per hour for a skate rental. Write an equation to determine at what point the cost of both roller skating rinks is the same.
Answer:
2 hours
Step-by-step explanation:
Let x be the time, in hours, for which the cost of Rollaround and Spinaround are the same.
Rollaround Cost (Cr): Cr = $5 + $3x
Spinaround Cost (Cs): Cs = $8 + $1.50x
We want to find the value of x that makes Cr = Cs
Cr = Cs
$5 + $3x = $8 + $1.50x
$1.50x = $3
x = 2 hours
====
CHECK:
Cr = $5+$3(2) = $11
Cs = $8+$1.50(2) = $11
At 2 hours, both cost the same.
Which algebraic expression is equivalent to the expression below?
8(3x - 5)
A.
24x - 40
B.
8x - 3
C.
8x - 8
D.
24x + 40
Answer: A
Step-by-step explanation:
Using the distributive property,
[tex]8(3x-5)\\\\=8(3x)-5(8)\\\\=24x-40[/tex]
please help me ty
this needs a step-by-step explanation
Answer:
4x3 which would be 12
Step-by-step explanation:
You write the words as numbers. Check if your answer is the same as the answer you have put for Number 4 and explain the difference
four times three can be numerically written as 4×3 which is equal to 12.
What are some alternative names for arithmetic operations?The addition is also known as the sum, subtraction is also known as the difference, multiplication is also known as the product, and division is also known as the factor.
We know an alternative name for multiplication is times.
Given in the question four times three, this means we have to multiply 4 and 3 which is,
= 4×3.
= 12.
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A triangular cell has a perimeter of 26 m. Side A is 2 m shorter than twice side B, inside C is 3 m longer than side B. What is the length of each side?
Lengths are:
Side A = 4.25
Side B = 6.25
Side C = 9.25
What is perimeter?The perimeter is the length of the shape's perimeter. It is determined by adding up all of the shape's sides. It is linearly stated and one-dimensional. Area, on the other hand, quantifies how much space a shape takes up. It is stated in square units and has two dimensions. The total distance around a shape, or the sum of its side lengths, is the shape's perimeter. Units used to measure perimeter (P) include millimeters (mm), centimeters (cm), and meters (m).
Given Data
A triangular cell has a perimeter of 26 m. Side A is 2 m shorter than twice side B, inside C is 3 m longer than side B
Side A = 2Side B - 2
Side C = Side B + 3m
Perimeter = Sum of all sides
Perimeter = Side A + Side B +Side C
Equating values
26 = 2SideB - 2 + Side B + Side B + 3
26 +2 - 3 = 4 Side B
25 = 4 Side B
Side B = [tex]\frac{25}{4}[/tex]
Side B = 6.25
Side A = 2(2.25) -2
Side A = 4.25
Side C = 6.25 +3
Side C = 9.25
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ASAP!! 4(x + 4) + 2x = 52
Solve for X and include step by step explanation for branliest.
Answer:
x = 6
Step-by-step explanation:
4 ( x + 4 ) + 2x = 52
Use distributive property to open parenthesis and combine like terms
4x + 16 + 2x = 52
6x + 16 = 52
6x = 52 - 16
6x = 36
x = 6
How do the digestive and circulatory systems interact?
Answer:
(1) Digestive System gets nutrients (good) from food and hands it over to the blood and Circulatory System then carries those nutrients where they need to go. (2) Filters out waste from food and pushes it through intestines and out the body (and you know how and where it gets out).
Step-by-step explanation:
Digestive System gets nutrients (good) from food and hands it over to the blood and Circulatory System then carries those nutrients where they need to go. (2) Filters out waste from food and pushes it through intestines and out the body (and you know how and where it gets out).
Find the 7th term in the
sequence
-4, -8,-16, . . .
Answer: -512
Step-by-step explanation:
to answer this problem you need to understand the sequence and hen extrapolate the sequence out until you get to the seventh term (which would be your answer).
looking at -4, -8, -16
First we clearly see that each number is a negative and an even number. going beyond this we see -4 goes into -8 twice and -8 goes into -16 twice (in other words the next number in the sequence is always double the proceeding number). Also, each number is an even factor of four which can help us with double checking at the end!
-4 --> (-4) + (-4) = -8 -8 --> (-8) + (-8) = -16 -16 --> (-16) + (-16) = -32 -32 --> (-32) + (-32) = -64 -64 --> (-64) + (-64) = (-120) + (-8) = -128 -128 --> (-128) + (-128) = (-200) + (-40) + (-16) = -256 -256 --> (-256) + (-256) = (-400)+(-100)+(-12) = -512Can also be seen as:
4 times (-2) = -8 4 times (-4)= -16 4 times (-8) = -32 4 times (-16) = -64 4 times (-32) = -128 4 times (-64) = -256 4 times (-128) = -512Double check by going back and reviewing you math as well as making sure each answer is even and divisible should be divisible by four!
I hope this helps!
P.S.
As this addition is rather tedious you could also times each previous answer by 2 .
example:
-64 times 2 = -128
(previous number in sequence) times 2 = (next number in sequence)
Question 22 (3 points)
Given that you are starting with:
4 + 2x = 10 - 4x
What are the equivalent equations in order to solve.
>
6x = 6
Xx = 1
4 +6x = 10
Answer:
Step-by-step explanation:
4+2x=10-4x
4+6x=10
6x=6
x=1
:]
Please help Determine an expression that would represent the area of the figure shown below:
The expression that represents the area of the figure is: D. x² + 5x + 6.
What is the Area of a Triangle?The area of a triangle can be found using the following formula:
Area of triangle = 1/2 × base × height.
Given the following parameters for the triangular figure shown:
Length of the base of the triangle = 2x + 4
Height of the triangle = x + 3
The area of the triangle = 1/2 × (2x + 4) × (x + 3)
Expand
The area of the triangle = 1/2 [2x(x + 3) + 4(x + 3)]
The area of the triangle = x(x + 3) + 2(x + 3)
The area of the triangle = x² + 3x + 2x + 6
The area of the triangle = x² + 5x + 6
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1/5x=15 what is x equal to?
Answer:
x=75
Step-by-step explanation:
because 1x=15
15x5=75 or 5 x
a river barge travels at an average of 8 mi/h in still water. the barge travels 60 miles up the mississippi river and 60 miles down the river in a total of 16.5 hours. what is the average speed of the current in this section of the mississippi river? round the tenths place.
the average speed of the current in this section of the mississippi river is 5.8
let C = the speed of the current
then B - C = effective speed up river
B+C =effective speed down river
time up + time down = 16.5 hrs
60/B-C+60/B+C= 16.5
taking lcm and solving we get
480+60C +480-60C= 16.5 (64 - C^2)
960= 1056 - 16.5 C^2
16.5 C^2 =96
C^2= 5.82
Hence , the average speed of the current in this section of the mississippi river is 5.8
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Ian's car can go 217 miles on 7 gallons of gas. During a drive last weekend, Ian used 8 gallons of gas. How far did he drive? Use pencil and paper. Explain how the problem changes if you were given the distance Ian drove last weekend instead of how much gas he used.
Answer:
165 miles
Step-by-step explanation:
part 1
231/7=33mpg
33×5 =165 miles
part 2
distance/mpg= gas used
for example: if you were told he went 200 miles,
200/33= 6.06 gallons of gas
Is y=x(1-x)-(1-x^2) a linear, quadratic, or absolute value
The y=x(1-x)-(1-x²) is a linear value that is not absolute.
Simplifying,
y=x(1-x)-(1-x²)
y=x-x²-1+x²
y=x-1
Thus, it is a linear equation with a negative value therefore it is not an absolute value.
Ax+By=C is the general form of a two-variable linear equation. When the equation is written in this manner, it is quite simple to obtain both segments (x and y).
Any polynomial that can be rewritten in the canonical form is a quadratic equation. where x represents an unknown quantity and a, b, and c represent known quantities, with a = 0. This indicates that f(x) = 0 is the root of function f(x) = ax2 + bx + c, which is the answer to the quadratic equation ax2 + bx + c = 0.
The absolute value of a real figure x, denoted by |x|, is the non-negative real value of x, regardless of its sign.
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Solve the rational equation for n
Answer:
n = 29
Step-by-step explanation:
please give brainliest
Answer: 29
Step-by-step explanation:
The answer will be 29 because if you put it all together and do the equation(-646 = 3(-646 = 3(65 - n) 3 over 2. N will equal 29. If you don't understand I recommend looking it up or something.
But yeahhhhhhhhhhhhhh.
I hope it helps?
Assume a profitable economic well produces an average income of $23 million, while the average cost of a dry hole is $1.2 million. How much profit can be expected from a 100-well drilling program?
The most appropriate choice for revenue and profit will be given by-
Profit expected from a 100-well drilling program = $[tex]146.2[/tex]
What is revenue and profit?
Total income generated by sale of goods and service is called revenue.
If [tex]p[/tex] is the cost of producing one unit of a commodity and [tex]q[/tex] is the number of units of the commodity, then the product of [tex]p[/tex] and [tex]q[/tex] gives the revenue.
If the revenue obtained by selling a commodity is more than the cost, difference between revenue and cost gives the profit.
Here,
Number of economic wells = 11
An economic well produces an average income of $23
Revenue obtained = $[tex]$[/tex][tex](23 \times 11)[/tex]
Number of dry wells = [tex]100 - 11[/tex]
= [tex]89[/tex]
Average cost of a dry hole is $1.2 million
Cost of 89 dry holes = $[tex]$[/tex][tex](89 \times 1.2)[/tex]
= $[tex]106.8[/tex]
Profit = Revenue - cost
= $[tex](253-106.8)[/tex]
= $[tex]146.2[/tex]
Profit expected from a 100-well drilling program = $[tex]146.2[/tex]
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Complete Question
The diagram has been attached
Assume a profitable economic well produces an average income of $23 million, while the average cost of a dry hole is $1.2 million. How much profit can be expected from a 100-well drilling program?
80/15 y 6 son equivalentes?
6 y 5 7/8 son equivalentes?
Answer:
80/15 and 6 are equivalent?-no because 80/15=5 5/15 or 5 1/3
6 and 5 7/8 are equivalent? no because it is 1/8 off
Which type of transformation is described by (x,y)
(x,y) → (x-4, y+8)?
(x, y) => (x-4, y+8) is a transformation of 4 units left and 8 units up
How is the transformation described?
From (x, y) to (x-4, y+8) ,
(a) Let us consider x => (x - 4)
Consider x axis and the ' - ' sign
Here a point moves 4 units to the left
(b) Let us consider y => (y + 8)
Consider y axis and the ' + ' sign
Here a point moves 8 units upwards
What is a transformation?
A point, line, or geometric object can be changed in four different ways that are all collectively referred to as transformations. Translation, rotation, reflection, and expansion are the four different types of transformation. The pre-image is the shape of the object as it was originally, and the transformed shape of the object is termed the image. Every point is equally distant from a fixed line in a reflection. Rotation is the act of turning about a central point .Translation is where every point of the shape must translate the same amount and in the same direction. A dilation is a resizing. A form changes size when you adjust it; even so, it retains the same appearance.To learn more about transformation, refer:
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In Rodger's state, unemployment compensation is calculated by finding the total of the quarterly wages of two consecutive quarters and dividing by 26. The weekly unemployment is 65% of that amount. In the quarter including January, February, and March, Rodger made a total of $13,950.80. In the quarter including April, May, and June, he made a total of $14,250.10. Find Rodger's weekly unemployment amount.
Rodger's weekly unemployment amount is $ 705.0225
Given,
The total of the quarterly wages of two consecutive quarters and dividing by 26.
The weekly unemployment is 65% of that amount.
Rodger made a total of $13,950.80.
and, he made a total of $14,250.10
We have to follow the some steps for solving question:
Step 1: Find the total of the quarterly wages of two consecutive quarters.
= $ 13,950.80 + $ 14,250.10
= $28,200.90
Step 2 : Divide the total by 26
= $28,200.90 / 26
= 1,084.65
Step 3 : Find the 65%
= 1,084.65 x 65%
= 1,084.65 x 65/100
= 705.0225
Hence, Rodger's weekly unemployment amount is $ 705.0225
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Answer:
$705.02
got it right
Step-by-step explanation:
10. One contestant on a game show has
1,500 points and another contestant has
-250 points. What is the difference
between the scores of the contestants?
how do i do this question
Answer: So the question is asking you to see what will happen is like attempt 2.
Step-by-step explanation:
So I recommend reading what to do, if you still don't know, you can search it up or maybe even watch a video of how to do it.
I really hope this helps you!
72. At 6:00 a.m., the temperature was 7 degrees below zero Fahrenheit. At noon, the temperature was 10 degrees higher. At 6:00 p.m., the temperature was 5 degrees cooler than it was at noon. What was the
temperature at 6:00 p.m.?
E. -2°
F. -1°
G. 3°
H. 5°
Answer:
E. -2
Step-by-step explanation:
First, find the temperature at 6 am, which was -7 degrees Fahrenheit
Then, add the ten degrees from noon, making the temperature 3 degrees Fahrenheit
lastly, take away the 5 degrees that dropped making it -2 degrees Fahrenheit
Simplify the expression √9x^3/25y^2 and be sure to explain your steps!
The expression √9x³/25y² when simplified gives the result 3x³/25y².
What is the mathematical definition of expression?In mathematics, an expression is a statement made up of terms and operations. The terms can be numbers or variables with coefficients. Addition, subtraction, multiplication, and division are all possible operations.Simplifying an expression is the same as solving a math problem. When you simplify an expression, you are attempting to write it in the simplest feasible manner.The given expression is √9x³/25y².
In the expression, calculate the square root of 9.
As a result, we have the following expression.
⇒ 3x³/25y²
The above expression cannot be simplified any further.
Therefore, the simplified expression is 3x³/25y².
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the graph of F(x) = |x| is shown below. if you horizontally shift this function right 7 units, what is the equation of the new function?
ANSWER:
C. G(x) = |x - 7|
STEP-BY-STEP EXPLANATION:
An absolute value function has the following form:
[tex]y=|x-a|+b[/tex]Where (a, b) is the origin, if we want to move 7 units to the right, we must add 7 units on the x-axis, that is, in a, therefore, the function would be:
[tex]\begin{gathered} G\left(x\right)=\left|x-+7\right| \\ \\ G(x)=\lvert x-7\rvert \end{gathered}[/tex]So the correct answer is C. G(x) = |x - 7|
In your own words, explain the relationship between the graph of a function and the graph of function's derivative.
Answer:
The derivative of a function in a point is the slope of the graph in that point, so the graph of the function's derivative shows the slope of the function at any point. It is useful because we can say if the function is increasing or decreasing using the graph of the function's derivative. Where the derivative is positive, the graph of the function is increasing and when the derivative is negative, the graph of the function is decreasing.
A gym charges for attending exercise classes. Raquel pays $10 to attend
each class because she is a non-member. Since Viola is a member, she pays $15 per
month for a membership fee, but only $5 for each class.
Set the two expressions equal to each other. Solve this equation to determine how
many classes they would each have to attend to have the same cost.
The number of classes that they would each have to attend to have the same cost is 3 classes.
How to calculate the equation?Viola is a member, she pays $15 per month for a membership fee, but only $5 for each class. This will be illustrated as 15 + 5x.
Raquel pays $10 to attend each class because she is a non-member. This will be illustrated as 10x
where x = number of classes
Therefore, the equation will be equated together. This will be:
10x = 15 + 5x
Collect like terms
10x - 5x = 15
5x = 15
Divide
x = 15 / 5 = 3
The number of classes is 3.
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through: (-4,-2), slope 7/4
Answer:
y = 7/4x + 5
Step-by-step explanation:
Point slope form:
y+2 = 7/4(x+4)
y+2 = 7/4x + 7
y = 7/4x + 5
:]
A rectangle concrete patio is 20 FEET long, 12 FEET wide, & 4 INCHES thick. What is the volume in cubic feet, of the concrete?
Answer:960
Step-by-step explanation:
4x12x20=960
Question 2(Multiple Choice Worth 1 points)
(03.01 MC)
Simplify nine square root of two minus three square root of seven plus square root of eight minus square root of twenty eight.
eleven square root of two minus five square root of seven
eleven square root of four minus five square root of fourteen
six square root of five
six square root of nine
Answer:1. eleven square root of two minus five square root of seven.
Step-by-step explanation:
Given-nine square root of two minus three square root of seven plus square root of eight minus square root of twenty eight.
•we can write √8 as 2√2 as 8 =2*2*
•we can write √28 as 2√7 as 28=2*2*
•Now putting these in the given equation we get
•9√2-3√7+2√2-2√7
•11√2-5√7
what is -3.1 x (-2.9)
For the regular octagon, please find the order of rotation and the angle
of rotation. Show all work for full credit.
A regular octagon is a closed figure with equal-length sides and equal-sized interior angles.
Measure of interior angle = 135°
Measure of exterior angle = 45°
What is meant by regular octagon?A regular octagon is a closed figure with equal-length sides and equal-sized interior angles. It possesses rotational symmetry of order 8 and eight lines of reflective symmetry. The Schläfli sign "8" represents a regular octagon. A regular octagon's internal angle at each vertex is 135°. ( radians).
We know that for a regular polygon with n sides the measure of each of the exterior angle = 360/n
Also, the measure of each of the interior angles of the regular polygon with n sides = (n - 2) × 180 / n
We have n = 8 (octagon)
Therefore, the measure of each of the exterior angles is: 360/8 = 45
Measure of each of the interior angles is given by:
(8-2) × 180/8 = 1080/8 = 135
Measure of interior angle = 135°
Measure of exterior angle = 45°
Therefore, the correct answer is option A. 45°, 135°.
The complete question is:
What is the angle of rotation of this regular octagon? What is the measure of an interior angle? A. 45°, 135° B. 22.5°, 135° C. 45°, 108° D. 22.5°, 108°
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