NO LINKS!!! Part 1:
What is the Transformation of f(x)= x^3:
THIS IS NOT MULTIPLE CHOICE!!!!
1. f(x)= 1/5x^3
2. f(x)= (x-5)^3
3. f(x)= x^3 + 5
Answers
Answer:
1. Vertical shrink by a factor of ¹/₅
2. Right 5
3. Up 5
Step-by-step explanation:
Transformations of Graphs (functions) is the process by which a function is moved or resized to produce a variation of the original (parent) function.
Transformations
For a > 0
[tex]f(x+a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units left}[/tex]
[tex]f(x-a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units right}[/tex]
[tex]f(x)+a \implies f(x) \: \textsf{translated}\:a\:\textsf{units up}[/tex]
[tex]f(x)-a \implies f(x) \: \textsf{translated}\:a\:\textsf{units down}[/tex]
[tex]y=a\:f(x) \implies f(x) \: \textsf{stretched parallel to the y-axis (vertically) by a factor of}\:a[/tex]
[tex]y=f(ax) \implies f(x) \: \textsf{stretched parallel to the x-axis (horizontally) by a factor of} \: \dfrac{1}{a}[/tex]
[tex]y=-f(x) \implies f(x) \: \textsf{reflected in the} \: x \textsf{-axis}[/tex]
[tex]y=f(-x) \implies f(x) \: \textsf{reflected in the} \: y \textsf{-axis}[/tex]
Identify the transformations that take the parent function to the given function.
Question 1
[tex]\textsf{Parent function}: \quad f(x)=x^3[/tex]
[tex]\textsf{Given function}: \quad f(x)=\dfrac{1}{5}x^3[/tex]
Comparing the parent function with the given function, we can see that the parent function has been multiplied by ¹/₅.
Therefore, the transformation is:
[tex]y=\dfrac{1}{5}\:f(x) \implies f(x) \: \textsf{stretched parallel to the y-axis (vertically) by a factor of}\:\dfrac{1}{5}[/tex]
As 0 < a < 1, the transformation visually is a compression in the y-direction, so we can also say: Vertical shrink by a factor of ¹/₅
Question 2
[tex]\textsf{Parent function}: \quad f(x)=x^3[/tex]
[tex]\textsf{Given function}: \quad f(x)=(x-5)^3[/tex]
Comparing the parent function with the given function, we can see that 5 has been subtracted from the x-value of the parent function.
Therefore, the transformation is:
[tex]f(x-5) \implies f(x) \: \textsf{translated}\:5\:\textsf{units right}[/tex]
Question 3
[tex]\textsf{Parent function}: \quad f(x)=x^3[/tex]
[tex]\textsf{Given function}: \quad f(x)=x^3+5[/tex]
Comparing the parent function with the given function, we can see that 5 has been added to the parent function.
Therefore, the transformation is:
[tex]f(x)+5 \implies f(x) \: \textsf{translated}\:5\:\textsf{units up}[/tex]
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Answer:
1) Vertical shrink by a factor of 1/5
2) Right 5
3) Up 5
Explanation:
Given main function: f(x) = x³
1.) f(x) = 1/5 (x³)
Comparing with a(f(x)) which gives vertical stretch or compression.
Here the function f(x) has been shrinked vertically by a factor of 1/5
2.) f(x) = (x - 5)³
Comparing with f(x - c) which gives horizontal translation c units right.
Here the function f(x) has been shifted 5 units to the right.
3.) f(x)= x³ + 5
Comparing it with f(x) + d which gives vertical translation d units up.
Here the function f(x) has been moved 5 units up.
Related Questions
I hate math so I really need help
Answers
Answer:
b. 4.5 cm
a. 42 mm is the answer
You buy tomatoes in 25 pound cases. One portion of salad requires .75 ounces of tomatoes. How many portions can be made with one
case?
Answers
The amount of the portions can be made with one case will be 399.25 ounces.
What is conversion?Conversion means to convert the same thing into different units.
You buy tomatoes in 25 pounds (11.34 kg) cases.
We know that 1 pound (0.45 kg) is equal to 16 ounces (0.45 kg).
Then the number of the ounces in 25 pounds (11.34 kg) will be
⇒ 25 x 16
Multiply the numbers, then the expression will be
⇒ 400 ounces (11.33 kg)
In 25 pounds of tomatoes, there will be 400 ounces.
One portion of salad requires 0.75 ounces (0.02 kg) of tomatoes.
Then the amount of the portions can be made with one case will be
⇒ 400 – 0.75
⇒ 399.25 ounces
Thus, the amount of the portions can be made with one case will be 399.25 ounces.
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For every 6 students who purchase a bag of M&M’s, there are 5 students who purchase a pack of gum. Use M for the number of students purchasing bags of M&M’s and G for the number students purchasing packs of gum, write an equation for this statement.
Answers
Answer:
M/6 = G/5
Step-by-step explanation:
We are given a relation between the numbers of students in two different groups. That relation can be used to write an equation.
Groups who bought M&Ms
If we consider M&M buyers to be 6 in a group, then the number of those groups is ...
M/6
Groups who bought gumSimilarly, the number of groups who bought gum will be ...
G/5
where there are 5 gum-buyers in each group.
EquationThe problem statement tells us that for each group of one kind, there is a matching group of the other kind. That is, the numbers of groups are equal:
M/6 = G/5
If you want to study which science course students liked the most during high school, you should survey... science teacher's, because they know what students like. science majors, because they love science. O the lunch room, because they will consist of all genders and ages and be unbiased about science. graduating seniors, because they have taken a wider variety of science courses. If you want to study which science course students liked the most during high school , you should survey ... science teachers , because they know what students like . science majors , because they love science . O the lunch room , because they will consist of all genders and ages and be unbiased about science . graduating seniors , because they have taken a wider variety of science courses .
Answers
Answer:
the last option
Step-by-step explanation:
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wo competing companies are having sales on projectors. Projector #MD375 has a retail price of $1,200. The Office Spot is advertising #MD375 for 20% off, while Office & Beyond has stated they will match any competitor’s advertised special and take an additional 15% off of the competitor’s advertised price. How much money is saved by purchasing the projector from Office & Beyond instead of the Office Spot?
Answers
The amount of money that is saved by purchasing the projector at Office and beyond is $144.
How much money is saved?The first step is to determine the price of the projector at The Office spot.
Discounted price : (1 - 0.20) x $1200
0.80 x $1200 = $960
The second step is to determine the price of the projector at the Office and Beyond.
Discounted price : (1 - 0.15) x $960 = $816
Difference in price : 960 - 816 = $144
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The surface area of a sphere is 6477 square inches. Which equation can be used to solve for the radius of the
sphere?
64m 4mr
647=2m³
6477= 2m²
64- 4m²
Answers
The expression πr² = 6477 can be used to solve for the radius of the sphere.
What is a sphere?It is defined as three-dimensional geometry when half-circle two-dimensional geometry is revolved around the diameter of the sphere that will form.
[tex]\rm V = \dfrac{4}{3} \pi r^3[/tex]
Area of sphere A = 6477 square inches
A = 4πr²
A = 6477
4πr² = 6477
πr² = 6477
Thus, the expression πr² = 6477 can be used to solve for the radius of the sphere.
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A train travels 65 miles and then stops in a city. Then it travels at a speed of 95 miles per hour before reaching its last stop.
Enter a linear model which represents the total distance traveled, d, by the train, as a function of t, the number of hours
after leaving the city
Answers
Step-by-step explanation:
as speed is always
distance/time
we need to multiply speed by the time traveled to get the distance traveled.
so,
d = 95t + 65
after all, until it reached the city it traveled already 65 miles (we don't know the speed, but it does not matter for the question about the total distance traveled), which we need to add to get the total distance.
he circle graph shows how the annual budget for a company is divided by department. If the amount budgeted for Media and Engineering combined is 31,250,000, what is the total annual budget? Media 4% Support 19% Editorial 6% Engineering 21% Research 32% Sales 18%
Answers
Answer:
let's playthe games questiontag
Simplify:
(12+14) x 8+ (8² +4²) =
Answers
Answer:
288
Step-by-step explanation:
[tex]26 * 8+(2^{6} +2^{4} )\\\\208+(64+16)\\208+80[/tex]
Answer:
288
Step-by-step explanation:
PEMDAS
Parentheses, Exponents, Multiplication, Division, Addition, Subtraction.
Parentheses and Exponents:
(26) x 8+(64+16) (28) x 8+(80)
Multiplication:
26 x 8 + 80 208+80
Addition:
208+80= 288
PLS ANSWER PLS!
Two functions are represented below.
FUNCTION A FUNCTION B
y=35x (looked at linked image)
What is the difference in the rate of change between Function A and Function B? Be sure to include the rate of change of each function in your answer
Answers
The difference in the rate of change of both functions is: 15.
What is the Rate of Change of a Function?Rate of change of a linear function = change in y / change in x.
Function A is given as: y = 35x. The rate of change for function A is 35.
From the graph of function B, using two points, (1, 50) and (2, 100):
Rate of change = (100 - 50)/(2 - 1)
Rate of change = 50.
Therefore, the difference in the rate of change of both functions = 50 - 35 = 15.
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Given segment AC and point B that lies on AC,
find CB if AC = 17, AB = 32 + 3x, and CB=57+6x
CB=
I give brainliest
Answers
The total length of the segment AC is the sum of AB and CB, which gives, CB = 9
How can the length of CB be found?The given parameters are;
AC = 17AB = 32 + 3•xCB = 57 + 6•xRequired: CB
Solution:
AC = AB + CB by segment addition property
Therefore;
AC = 17 = 32 + 3•x + 57 + 6•x = 89 + 9•x
17 = 89 + 9•x
[tex]x = \frac{17 - 89}{9} = - 8[/tex]
CB = 57 + 6•x = 57 + 6 × (-8) = 9
Therefore;
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are 12d +36 and 12(d+3) equivalent
Answers
Answer:
Yes
Step-by-step explanation:
They are equivalent as 12d + 36 is the expanded form of 12(d + 3)
Answer:
Yes,
just factorize 12d+36 and since 12 is common
12(d+3)
When sending a letter, Bobby pays a fixed amount for letters weighing up to an ounce. He then pays a smaller, fixed amount for each additional ounce (or part of an ounce). The cost of sending the letter in cents is modeled by the function y = 30 + 20(x - 1), where x is the weight of the letter in ounces. What does the number 20 describe?
Answers
A function assigns the values. The number 20 describes the cost that Bobby needs to pay for each extra ounce of letters.
What is a Function?A function assigns the value of each element of one set to the other specific element of another set.
In the given function y = 30 + 20(x - 1), the number 20 describes the cost that Bobby needs to pay for each extra ounce of letters.
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(PLEASE HELP FAST!!!) Which expression gives the area of triangle QRS?
Answers
The expression which gives the area of triangle QRS is [tex]\frac{1}{2} (9)(15)sin(20^{o} )[/tex].
We need to find the area of triangle QRS.
How do I find the area of a triangle using trigonometry?The area of a triangle can be expressed using the lengths of two sides and the sine of the included angle. Area of Δ = ½ ab sin C.
Now, the area of the triangle QRS[tex]=\frac{1}{2} (9)(15)sin(20^{o} )[/tex]
Therefore, the expression which gives the area of triangle QRS is [tex]\frac{1}{2} (9)(15)sin(20^{o} )[/tex].
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Study: Factoring Polynomials Completely
What are the possible roots of the polynomial function below? (Check all
that apply.)
F(x) = 2x² + 5x -5
Answers
Answer:
x = 0.76556443 x = -3.26556443
Step-by-step explanation:
You can use the quadratic formula to find the roots.
Use two different methods to find an explain the formula for the area of a trapezoid that has parallel sides of length a and B and height H. Consider these ideas or others: combine two copies of a trapezoid to make a parallelogram. Subdivide the trapezoid into two triangles one with base b and one with base a.
Answers
The two ways that can be used to find the area of a trapezoid include:
A = (a + b) × h/2A = a × hHow to illustrate the information?It should be noted that a trapezoid simply means a four sided shape that has parallel sides.
To find the area of the shape goes thus:
Find the length of each base.
Find the height of the trapezoid.
Substitute the values into the formula: A = (a + b) × h/2
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How can we write an algebraic expression to describe a two digit number whose unit's digit is 5
ess than the ten's digit?
Let's x be ten's digit
Answers
Answer:
required expression = 11x-5
Step-by-step explanation:
We have information about the following things :
Its a two digit numberUnits digit is 5 less than the tens digittens digit is xSince units digit is 5 less than the tens digit, then the unit digit will become
x-5
Now we have these two things:
Tens digit is xUnits digit is x-5Now let us look at some two digit numbers like 29 , 43 and 78
in 29, tens digit is 2 and units digit is 9
29 is formed by multiplying the tens digit by 10 and multiplying the units digit by 1 like this : 29 = (2×10) + (9×1)
Similarly;
43 = (4×10) + (3×1)
78 = (7×10)+(8×1)
Now to get out two digit number from the question, we similarly need to multiply the tens digit with 10 and units digit with 1 and add them like this:
tens digit : x
Units digit : x-5
Hence the number is (x × 10) + [(x-5)×1] = 10x + x-5 = 11x-5
hence the required algebraic expression is 11x-5
The mean of a set of numbers is 500. a. If 10 is added to each of the numbers in the set, then what will be the mean of the new set? The mean of a set of numbers is 500 . a . If 10 is added to each of the numbers in the set , then what will be the mean of the new set ?
Answers
Answer:
510
Step-by-step explanation:
Assume 2 numbers 500,500.. with a mean of 500
so if we add 10 to each of the two numbers, mean will be:
[tex]\frac{510+510}{2}=510[/tex]
Of course you can vary the set and the numbers and still get the same mean
Use your calculator to find the approximate value of e. (Round to 4 decimal places)
Answers
Using a calculator to find the approximate value of e in
F(e)=e^{2e} we have F(e)=229.6516. This is further explained below.
What is maclurin polynomial?Generally, To approximate a function f (x) f (x) f (x) for values of x near to zero, one may use a power series known as a Maclaurin series.
In conclusion, Using your calculator to find the approximate value of e in
F(e)=e^{2e}
We have
F(e)=e^{2e}
F(e)=229.6516
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A sample of size 400 has mean =6.0. Can it be regarded as a sample from a large population with mean 6.25 inches and standard deviation 2.25 inches ? using α=0.05
Answers
The value of Z at the 5% level is not significant if the sample of size 400 has mean is 6.0.
What is the standard deviation?It is defined as the measure of data disbursement, It gives an idea about how much is the data spread out.
[tex]\rm \sigma = \sqrt{\dfrac{ \sum (x_i-X)}{n}[/tex]
σ is the standard deviation
xi is each value from the data set
X is the mean of the data set
n is the number of observations in the data set.
The standard error of the estimated mean:
[tex]\rm = \dfrac{2.5}{\sqrt{400}}[/tex]
= 0.1125
x = 6.0–6.2 = 0.2
[tex]\rm Z = \dfrac{0.2}{0.1125}[/tex]
Z = 1.778
This is not significant at the 5% level.
This would have been significant at the 5% level if the same sample means had been found using a sample size of merely 500.
Thus, the value of Z at the 5% level is not significant if the sample of size 400 has mean is 6.0.
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Suppose you have opened some Nutty Bars to check the company’s claim of an “average” of 8 peanuts per bar. Here is what you found after opening 10 bars: 5, 8, 8, 8, 11, 7, 8, 6, 6, and 6. Which average should the company use to support their claim?
Answers
The company should use the median to support their claims.
Which measure of average should the company use?Measures of average commonly used are mean and median.
Mean is the sum of the numbers divided by the total number
Mean : (5 + 6 + 6 + 6 + 7 + 8 + 8 + 8 + 8 + 11) / 10 = 7.3
Median is the number at the center of the dataset when it is arranged either in ascending or descending order.
Median = 8
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What is the measure of arc ECF in circle G? pls show work, I don't get edge teachers
Answers
The measure of arc ECF in circle G is 98°. The correct option is the second option 98°
Circle GeometryFrom the question, we are to determine the measure of arc ECF
By using the one of the circle theorems
The angle subtended by an arc of a circle is twice the angle it subtends anywhere on the circle's circumference
In the given diagram,
∠F = 1/2 ×104°
∠F = 52°
∠D + ∠E + ∠F = 180° (Sum of angles in a triangle)
∠D + 79° + 52° = 180°
∠D = 180° - 79° - 52°
∠D = 49°
m arc ECF = 2 × m ∠D
m arc ECF = 2 × 49°
m arc ECF = 98°
Hence, the measure of arc ECF in circle G is 98°. The correct option is the second option 98°
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Place the steps for finding f(x) in the correct order.
H
11
K
f(1) = 41 + 7
0·0-0-0-0
Answers
The answer is C
Ik this bc
Someone told me
For finding the inverse of a function you have to write it as an ecuation.
[tex]y = 4x + 7[/tex]
Invert the values of x and y.
[tex]x = 4y + 7[/tex]
Our objetive now in this new equation is to clear y. First, subtract 7 in both sides of the equation.
[tex]x - 7 = 4y[/tex]
Then, divide both sides by 4.
[tex] \frac{x - 7}{4} = y[/tex]
Finally, invert the values of x and y again and put the equation like a function.
[tex] {f}^{ - 1} (x) = \frac{x - 7}{4} [/tex]
This is correct because f(x) = x is the axis of symmetry for both functions (green one).
Volume (to the nearest tenth)
Answers
Answer:
913
Step-by-step explanation:
cylinder:
radius=5.6 height=7
first lets find the volume of the cylinder the formula for the volume of a cylinder is pi times radius squared times height. so after plugging in the height and radius you get 689.64242
cone:
radius=5.6 height=6.8
now the volume of the cone, the formula for the volume of a cone is pi times radius squared times height/3. so after plugging in the height and radius of the cone you get 223.31278
so 689.64242 + 223.31278= 912.9552 and that rounded to the nearest tenth is 913
Given h(f)=-2(f+5)^2+4 find h(-8)
Answers
Answer:
h(-8)= -14
Step-by-step explanation:
[tex]h(-8)=-2(-8+5)^2+4 \\h(-8)=-18+4=-14[/tex]
[tex]\huge\boxed{-14}[/tex]
We have the following equation:
[tex]h(f)=-2(f+5)^2+4[/tex]
Substitute in [tex]-8[/tex] for [tex]f[/tex] and simplify.
[tex]\begin{aligned}h(-8)&=-2(-8+5)^2+4&\textsf{Substitute.}\\&=-2(-3)^2+4&\textsf{Add.}\\&=-2\cdot9+4&\textsf{Simplify the power.}\\&=-18+4&\textsf{Multiply.}\\&=\boxed{-14}&\textsf{Add.}\end{aligned}[/tex]
Problem 10-09 (Algorithmic) Cress Electronic Products manufactures components used in the automotive industry. Cress purchases parts for use in its manufacturing operation from a variety of different suppliers. One particular supplier provides a part where the assumptions of the EOQ model are realistic. The annual demand is 5,300 units, the ordering cost is $70 per order, and the annual holding cost rate is 25%.
Answers
The economic order quantity is 385 and reorder point is 254.
Economic order quantity (EOQ)a. Economic order quantity (EOQ)
EOQ=√2×D×C÷H
Where:
D =Annual Demand
S = Cost of Ordering
H=Holding cost
Hence:
EOQ=√2×5300×70÷.25×20
EOQ=√742,000÷5
EOQ=√148,400
EOQ=385
b. Reorder point
Reorder point=5300/250×12 days
Reorder point=254
c. Reorder point
Reorder point=5300/250×35 days
Reorder point=742
d. Reorder point
Reorder point=742-385
Reorder point=357
Therefore the economic order quantity is 385 and Reorder point is 254.
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The complete question is:
a. If the cost of the part is $20 per unit, what is the economic order quantity?
b. Assume 250 days of operation per year. If the lead time for an order is 12 days, what
is the reorder point?
c. If the lead time for the part is seven weeks (35 days), what is the reorder point?
d. What is the reorder point for part (c) if the reorder point is expressed in terms of the inventory on hand rather than the inventory position?
There's 18 deer and 52 lions if 10 lions eat 17 deer how many deer are left
Answers
Answer:
1 deer
Step-by-step explanation:
18 deer minus 17 eaten leaves 1 deer
Jamie had seven posters, but only 3 could fit on his closet door. How many different ways can he arrange the three posters out of the seven on his door?
A. 52.5
B. 210
C. 1260
D. 5040
Answers
Answer:
210 ways
Step-by-step explanation:
7 P 3 = 210 ways
or 7 C 3 = 35 choices of 3 posters which can bearrranged in 6 different ways 6 * 35 = 210 ways
The product of 12, x and y. Translate the following phrase into an algebraic expression. Do Not simplify.
Answers
The product of 12, x, and y written in an algebraic expression is 12xy.
What are algebraic expressions?Algebraic expressions are mathematical expressions containing variables, coefficients, and their arithmetic operators such as addition, subtraction, multiplication, and division.
An algebraic expression can be used to interpret and solve mathematical word problems.
From the information given:
The algebraic expression can be translated as 12x × y = 12 xy.
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The algebraic expression that can be translated as product of 12, x and y is 12 xy.
What are algebraic expressions?Expressions are used to interpret mathematical problems
From the question given we are to translate the product of 12, x and y.
The product of 12 and x is 12x
The product of 12x and y is 12xy, hence the algebraic expression that can be translated as product of 12, x and y is 12 xy.
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What is another way to summarize this proof?
A. Angles forming a linear pair are congruent.
B. Vertical angles are supplementary.
C. Vertical angles are congruent.
D. Angles forming a linear pair are supplementary.
Answers
Another way to summarize this proof is to say vertical angles are congruent.
Vertical anglesLines are shortest distance between two point and angles are forned from the intersection of two lines.
From the given figure, they are trying to prove that the angles ANR and VNE are equal. Since these angles are formed at the point of intersection, hence another way to summarize this proof is to say vertical angles are congruent.
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