Describe the transformations made on this function:(stretch/compression, reflect, left/right, up/down)
Answers
The function we have is:
[tex]f(x)=\frac{1}{2}(x-7)^3+6[/tex]Since this is a cubic function, we start with the parent cubic function (the simplest form of the cubic function):
[tex]f(x)=x^3[/tex]And compare it to the given function.
The first thing we can note is that there was a subtraction of 7 to the value of x:
[tex]x\longrightarrow x-7[/tex]When we add a number to the x value, the graph moves to the left, and when we subtract a number to the x value, the graph moves to the right.
So the first transformation is moving to the right 7 units.
Next, we have that there was +6 added to the expression --> When you add a number to the function, the graph moves up, and when you subtract a number to the function, the graph moves down.
In this case, since we added a constant value of 6, the graph is translated 6 units up.
The second transformation is moving up 6 units.
Finally, let's analyze the effect that the 1/2 has on the function.
We can compress or stretch the graph of a function by multiplying the x by a constant (a number). If the number of between 0 and 1, there is a stretch, and if the number is greater than 1 there is compression.
In this case, the number next to the x is:
[tex]\frac{1}{2}=0.5[/tex]Since the number is between 0 and 1 there is a stretch of the function.
In summary:
Answer:
Translation of 7 units to the right
Translation of 6 units up
Stretch of the function of 0.5
Related Questions
Choose the description(s) of how I could graph the equation y = − 7 x + 1 . Choose all that apply. Hint: Push the negative either to the top or bottom of the fraction to help you graph.
Answers
We are given the following equation in slope-intercept form.
[tex]y=-7x+1[/tex]The general form of slope-intercept form is given by
[tex]y=mx+b[/tex]So, we see that
slope = m = -7
y-intercept = b = 1
The Slope can be written as
[tex]m=\frac{\text{rise}}{\text{run}}=\frac{7}{-1}=-7[/tex]Also, the y-intercept is the point at which the line crosses the y-axis.
So all those options that say to start on the x-axis are incorrect.
We start at 1 on the y-axis and plot that point.
Then from there, we go up (rise) 7 units and to the left (run) 1 unit.
Go up means positive and go left means negative so the slope becomes -7.
Then plot that point and draw the line connecting the points.
Therefore, there is only one correct answer and that is
Start at 1 on the y-axis. Plot that point. Then from there, go up seven units and left one. Plot that point. Then draw the line connecting the points.
its and left one. Plot that point. Then draw the line connecting the points.
its and left one. Plot that point. Then draw the line connecting the points.
its and left one. Plot that point. Then draw the line connectinits and left one. Plot that point. Then draw the line connectinits and left one. Plot that point. Then draw the line connectinStart at 1 on the y-axis. Plot that point. Then from there, go up seven unG
The total income for the Mr. Jones’s apartment building can be represented by the equation 2R minus C minus 2P, where r is the amount of rent paid by each tenant, C is the cost of the cable bill, P is the cost of the phone bill. If the rent is $700, the cable bill is $100 in the phone bill is $50, what is the total income for Mr. Johnson?
Answers
total income= 2R-C-2P
R= omoun tof rent paid by each tenant = $700
C= cable bill = $100
P = Phone bill = $50
Replace the values:
Total income = 2(700)-100-2(50)
total income= 1,400-100-100 = 1,400-200= $1,200
Total income =$1,200
The safe load, L, of a wooden beam of width w, height h, and length l, supported at both ends, varies directly as the product of the width and the square of the height, and inversely as the length. A wooden beam 4 inches wide, 8 inches high, and 216 inches long can hold a load of 5050 pounds. What load would a beam 2 inches wide, 5 inches high, and 144 inches long, of the same material, support? Round your answer to the nearest integer if necessary.
Answers
We have the following, L, of the beam varies as the product of the width and the square of the height:
[tex]L\propto w\cdot h^2[/tex]And varies inversely as the lenght of the wooden beam:
[tex]L\propto\frac{w\cdot h^2}{l}[/tex]therefore:
[tex]L=k\cdot\frac{w\cdot h^2}{l}[/tex]where k is the proportionality constant
w = 4, h=8, l = 216 and L = 5050
[tex]\begin{gathered} 5050=k\cdot\frac{4\cdot8^2}{216} \\ k=\frac{5050\cdot216}{256} \\ k=4260.93 \end{gathered}[/tex]now, if w = 2, h = 5, l = 144:
[tex]\begin{gathered} L=4260.93\cdot\frac{2\cdot5^2}{144} \\ L=1479.5 \end{gathered}[/tex]Write - 4 - 2y= - x in standard form.
Answers
Answer:
[tex]-x\text{ + 2y = -4}[/tex]Explanation:
Here, we want to write the given equation in standard form
The equation of a line in standard form is as follows:
[tex]Ax\text{ + By = C}[/tex]What we have to do now is to bring the x and y terms together
We can have this as follows:
[tex]-x\text{ + 2y = -4}[/tex]-4 - 2y = -x
We want to leave -4 alone on the left
That means we have to transfer -2y that is there with it
To transfer -2y over the equality sign , its sign changes
-4 = +2y - x
But +2y can be written as 2y only
Finally by re-arrangement:
-x + 2y = -4
A bottle rocket is launched straight up. Its height in feet (y) above theground x seconds after launch is modeled by the quadratic function: y =-16x2 + 116x + 7.What was the maximum height of the rocket?
Answers
1) Looking at the function y= -16x² + 116x + 7
The maximum height is the vertex described by the parabola. The Vertex follows that formula:
[tex]\begin{gathered} V=(\frac{-b}{2a},\frac{-\Delta}{4a}) \\ \end{gathered}[/tex]2) Since the question wants only the height, let's keep with the y-coordinate of the Vertex. Let's call it Yv
[tex]Y_V=\frac{-(116^2-4(-16)(7))}{4(-16)}\Rightarrow\frac{-(13904)}{-64}=\text{ 217.25}[/tex]So the maximum height of that rocket is 217.25 feet above the ground.
Sparks garden is in the shape of a trapezoid and the dimensions are shown belowa gardener needs to spread fertilizer over the flower beds each bag of fertilizer he uses covers 125 square meters and he can only buy full bags how many bags of fertilizer will he need to cover the entire garden
Answers
To be able to determine the bags of fertilizer that the gardener will need, let's first determine the area of the garden.
Since the shape of the garden is a trapezoid, we will be using the following formula:
[tex]\text{ Area = }\frac{1}{2}H(B_1+B_2)[/tex]We get,
[tex]\text{ Area = }\frac{1}{2}H(B_1+B_2)[/tex][tex]\text{ = }\frac{1}{2}(50)(70\text{ + 40)}[/tex][tex]\text{ = }\frac{1}{2}(50)(110\text{) = }\frac{50\text{ x 110}}{2}[/tex][tex]\text{ = }\frac{5,500}{2}[/tex][tex]\text{ Area = }2,75m^2[/tex]Let's determine how many bags of fertilizer will be used.
[tex]\text{ No. of Bags of Fertilizer = }\frac{\text{ Area of Garden}}{\text{ Area that a Bag of Fertilizer can cover}}[/tex]We get,
[tex]\text{ = }\frac{2,750(m^2)}{125\frac{(m^2)}{\text{bag}}}[/tex][tex]\text{ No. of Bags of Fertilizer = }22\text{ Bags}[/tex]Therefore, the gardener will be needing 22 Bags of Fertilizer.
The equation of a circle is (x-2)²+(y-6)²=25. What is the radius of the circle?
Answers
Consider that the general equation of a circle is given by:
[tex](x-h)^2+(y-k)^2=r^2[/tex]where (h,k) is the center of the circle and r is the radius.
Then, by comparing the given equation with the general equation, you can notice that:
25 = r^2 => r = 5
Hence, the radius of the circle is 5
At a sale, a table is being sold for 24% of the regular price. The sale price is $110.40.What is the regular price?
Answers
Let x be the regular price. We are told that the sale price corresponds to the 24% of the regular price. That is, if we calculate the 24% of x, we would get the sale price, which is 110.40. Recall that to calculate the 24% of x, we simply multiply x by 24 and divide it by 100. So this expression would be
[tex]x\cdot\frac{24}{100}[/tex]We know that this quantity should be 110.40 so we have the following equation
[tex]x\cdot\frac{24}{100}=110.40[/tex]So, if we multiply both sides by 100, we get
[tex]24\cdot x\text{ =11040}[/tex]Now, we divide both sides by 24, so we get
[tex]x=\frac{11040}{24}=460[/tex]So the original price of the table was 460.
In which quadrant will the image lie if AB is reflected in the c-axis?
Answers
The quadrants on a xy frame are numbered as below:
The image is originally in the Quadrant I, if we reflect it in the x-axis, then it'll be placed on the fourth quadrant. So the answer is D Quadrant IV.
I NEED HELP FINDING THIS ANSWER ASAP PLEASE AND THANK YOU
Answers
The coordinates of triangle after being reflected across y-axis: X"(-2, -5), Y"(-2, -2), Z"(-1, -4)
Given that the coordinates of triangle X(4, -5), Y(4, -2), Z(5, -4)
ΔXYZ is reflected across the line x = 3 and then reflects the image across the y-axis.
We need to find the coordinates of triangle after mentioned geometric transformation.
i) when ΔXYZ is reflected across the line x = 3
the coordinates of ΔX'Y'Z' are:
X'(2, -5), Y'(2, -2), Z'(1, -4)
The green triangle in the following graph.
ii) when ΔX'Y'Z' is reflected across the y-axis
the coordinates of ΔX"Y"Z" are:
X"(-2, -5), Y"(-2, -2), Z"(-1, -4)
The orange triangle in the following graph.
Therefore, the coordinates of triangle after being reflected across y-axis: X"(-2, -5), Y"(-2, -2), Z"(-1, -4)
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on a map. 1 inch equals 10.1 miles . if two cities are 3.5 inches apart on the map, how far are they actually apart?
Answers
Since each inch equals 10.1 miles, mutliply 3.5 times 10.1 to find how far are two cities that are 3.5 inches apart on the map:
[tex]3.5\times10.1=35.35[/tex]Therefore, they are 35.35 miles apart.
If a shape is dilated by a scale factor of 5, what is the resulting area?A.) The new area is 4Times the originalB.) The new area is 25times the originalC.) The new area isone-fourth theoriginalD.) The new area is 5times the original
Answers
If a shape is dilated by a scale factor of 5, the new dimensions would have increased by a factor of 5 on all sides. This means the new area is 25 times the original
The correct answer is option B
How to slove these problems2 7/8 - 15/161 1/5 x 2 1/32 1/5 ./. 4
Answers
The Solution:
Given the following:
[tex]\begin{gathered} 2\frac{7}{8}-\frac{15}{16} \\ \\ 1\frac{1}{5}\times2\frac{1}{3} \\ \\ \frac{2\frac{1}{5}}{4} \end{gathered}[/tex]We are asked to evaluate each of them.
Step 1:
we shall convert each fraction into an improper fraction.
[tex]\frac{23}{8}-\frac{15}{16}[/tex][tex]\frac{46-15}{16}=\frac{31}{16}=1\frac{15}{16}[/tex][tex]\begin{gathered} 1\frac{1}{5}\times2\frac{1}{3} \\ \\ \frac{6}{5}\times\frac{7}{3}=\frac{2\times7}{5}=\frac{14}{5}=2\frac{4}{5} \end{gathered}[/tex][tex]\frac{2\frac{1}{5}}{4}=\frac{\frac{11}{5}}{4}=\frac{11}{5}\times\frac{1}{4}=\frac{11}{20}[/tex]Question 1 of 10‚Q(t) = Q¸e¯ktThe functionmay be used to model radioactive decay. Qrepresents the quantity remaining after tyears; k is the decay constant. Thedecay constant for plutonium-240 is k = 0.00011. What is the half-life, inyears?OA. 6,301 yearsOB. 1,512,321 yearsC. 0.076 yearsOD. 3,150 years
Answers
The half-life is 6300 years.
From the question, we have
t_1/2 = 0.693/k
where,
t_1/2 = half-life
k = decay constant = 0.00011
substituting the value, we get
⇒t_1/2 = 0.693/0.00011
⇒t_1/2 = 6300 years
Half Life Period:
One of the main terms used in physics to describe the radioactive decay of a specific sample or element over a predetermined amount of time is half-life, also known as half-life period. When studying the subject, nuclear physics students will frequently run into the phrase. The term "exponential decay" is also frequently used to refer to both exponential and non-exponential decay, which are both common forms of decay processes. In fields other than physics, the word is used to describe the biological half-life of specific substances in the human body or in medications.
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marisol has 4/12 cups of flour. A biscuit recipe she wants try requries 3/4 cup of flour for a single batch of biscuits. How many batch s of biscuits can Marisol make
Answers
The number of biscuit batches that Marisol can make from the given task content is; 4 / 9 batches.
What is the number of biscuit batches that can be made from the 4/12 cups of flour?It follows from the task content that the number of batches of biscuit that can be made from the given 4/12 batches of biscuit be determined.
By proportion, since it is given that the one biscuit recipe requires 3/4 cups of flour, it consequently can be inferred that;
In 4/12 cups of flour, the number of batches she can make is;
= 4/12 ÷ 3/4
= 4/12 × 4/3
= 16 / 36
= 4 / 9 batches of biscuits.
Ultimately, the number of batches of biscuits she can make is; 4 / 9 batches of biscuits.
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The table shows a survey of 100 people selected at random at an airport. Find the experimental probability that a person selected at random is going to city B.City A - 26City B - 36City C - 18City D - 18City E - 2
Answers
Given:
The table shows a survey of 100 people selected at random at an airport
We will find the probability that a person selected at random is going to city B
As shown: City B - 36
So, the probability will be as follows:
[tex]probability=\frac{36}{100}=0.36[/tex]So, the answer will be probability = 0.36
I just need answers. No need longer to explain.Solve a
Answers
We need to find the period of the sinusoidal function in this case we have the next form
[tex]y=A\sin \frac{2\pi}{T}(x+a)+b[/tex]First, we need to find the amplitude in this case
[tex]A=\frac{5+1}{2}=\frac{6}{2}=3[/tex]The amplitude is 3
Then we need to find the period
[tex]T=\frac{2\pi}{3}[/tex]and the the displacement b is 2
Then for a we have
[tex]a=\frac{5}{12}\pi[/tex]Therefore we have
[tex]y=3\sin 3(x-\frac{5\pi}{12})+2[/tex]ANSWER
[tex]y=3\sin 3(x-\frac{5\pi}{12})+2[/tex]Nick knows that a + b < 0. Which statement is true?
Answers
I'll inform that to the tech team
Meanwhile I'll help here, ok?
I asked if this part of the question was right: a + b < 0
what is the simplest form for the ratio of 24:48 and how
Answers
For 24 / 48 simplest form find the maximum common divisor ( m.c.d)
In this special case ( but this not common) 24 divides exactly 48
so then 24/24 = 1. And 48/24= 2.
then the simplest form is 24/48= 1/2
What is the probability of landing on a number less than 3 and then landing on a divisor of Write your answer as a percentage
Answers
The number less than 3 are {1,2}.
The total possible outcome is 4.
Determine the probability for number less than 3.
[tex]\begin{gathered} P(A)=\frac{2}{4} \\ =\frac{1}{2} \end{gathered}[/tex]The number divisor of 20 are {1,2,4}.
Determine the probability for landing on a number divisor of 20.
[tex]P(B)=\frac{3}{4}[/tex]The probability for number less than 3 and number divisor of 20 are independent events. So,
[tex]\begin{gathered} P(AandB)=P(A)\cdot P(B) \\ =\frac{1}{2}\cdot\frac{3}{4} \\ =\frac{3}{8} \end{gathered}[/tex]Determine the probability in percentage by multiply the fraction with 100.
[tex]\begin{gathered} P(AandB)=\frac{3}{8}\cdot100 \\ =37.5 \end{gathered}[/tex]So answer is 37.5 %.
Use words to describe each algebraic expression. 3. 6c4. X-15. t/26. 3t - 4
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3. 6c
It multiplication between six and c.
Six times a number c.
4.
x-1
Its a subtraction.
A number minus one.
5.
t/2
A number divided by two.
6.
3t-4
Three times a number minus 4
describe the appearance of the graph
Answers
the equation is a line because the variable is of the first degree, this is because x is raised to 1.
a first degree equation is a line and the slope is the coefficient of the variable, on this case the slope is -4, then the slope get down because the slope is negative
so the right option is fourth
Consider the following three systems of linear equations.(Please list what option it is.
Answers
We transform System A into System B by converting equation A2 into equation B2. We transform System B into System C by converting equation B2 into equation C2.
We are given three systems of linear equations. The first system of linear equations is A1 : -2x + 7y = -5 and A2 : 4x - 3y = -23. The second system of linear equations is B1 : -2x + 7y = -5 and B2 : 11y = -33. The third system of linear equations is C1 : -2x + 7y = -5 and C2 : y = -3. To convert the system A to system B, we transform the equation A2 to equation B2. To convert the system B to system C, we transform the equation B2 to equation C2.
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Matt needs to find the volume of this rectangular pyramid. What answer should he arrive to?
Answers
Given:
• Length of the pyramid, l = 17 units
,• Width of the pyramid, w = 7 units
,• Height of the pyramid, h = 13 units
Let's find the volume of the given rectangular pyramid.
To find the volume, apply the formula:
[tex]V=\frac{l*w*h}{3}[/tex]Where:
l is the length = 17 units
w is the width = 7 units
h is the height = 13 units
Thus, we have:
[tex]\begin{gathered} V=\frac{17*7*13}{3} \\ \\ V=\frac{1547}{3} \\ \\ V=515.67\text{ cubic units} \end{gathered}[/tex]Therefore, the volume of the rectangular pyramid is 515.67 cubic units.
Matt's answer should be 515.67 cubic units.
ANSWER:
515.67 cubic units.
Morris borrowed $9,000 from a credit union at 13% simple interest for 42 months. What were his money installment payments (to the nearest whole cent)?$311.79 per month$307.89 per month$297.58 per month$377.12 per monthNone of these choices are correct.
Answers
Now the total interest for 42 months will be:-
[tex]\begin{gathered} S\mathrm{}I\mathrm{}=\frac{9000\times13\times7}{200} \\ =\frac{90\times13\times7}{2} \\ =45\times13\times17 \\ =4095 \end{gathered}[/tex]So the total amount he has to pay after 42 months will be = 9000+4095
= $13095
So
[tex]\begin{gathered} 42\text{ months = \$13095} \\ 1\text{ month =}\frac{13095}{42} \\ =311.79 \end{gathered}[/tex]So his monthly installment will be $ 311.79
So $ 311.79 is the correct option.
From a 12 foot roll of rubber hose, a person cuts lengths of 2 3/8 feet, 2 1/2 feet, and 3 1/4 feet. How much hose is left on the roll?
Answers
Sum the lengths that the person cuts:
To sum mixed numbers:
[tex]2\frac{3}{8}ft+2\frac{1}{2}ft+3\frac{1}{4}ft=[/tex]1. Add the whole numbers:
[tex]2ft+2ft+3ft=7ft[/tex]2. Add fractions
[tex]\begin{gathered} \frac{3}{8}ft+\frac{1}{2}ft+\frac{1}{4}ft \\ \\ \text{Write all as fractions with denominator 8:} \\ \\ \frac{3}{8}ft+\frac{4}{8}ft+\frac{2}{8}ft=\frac{3ft+4ft+2ft}{8}=\frac{9}{8}ft \\ \\ \\ \end{gathered}[/tex]Then, the person cuts 7 9/8 ft, substract it from the initial 12 ft roll of rubber hose:
[tex]\begin{gathered} \text{Write the mixed number as a fraction:} \\ 7\frac{9}{8}ft=7ft+\frac{9}{8}ft=\frac{56ft+9ft}{8}=\frac{65}{8}ft \\ \\ \text{Substract the fraction above from 12ft}\colon \\ \\ 12ft-\frac{65}{8}ft=\frac{96ft-65ft}{8}=\frac{31}{8}ft \\ \\ \text{Write the result as a mixed number:} \\ \\ \frac{31}{8}ft=\frac{24}{8}ft+\frac{7}{8}ft=3\frac{7}{8}ft \end{gathered}[/tex]Then, 3 7/8 ft of hose are left on the rollAn electric company calculates a person's monthly bill from the number of kilowatt-hours (kWh), x, used. The function b(x) = { x < 200 0.10x, 0.15(x – 200) + 20, x > 200 determines the bill. How much is the bill for a person who uses 800 kWh in a month? O A. $90 O B. $110 O C. $60 O D. $80
Answers
Since x = 800kWh which is greater than 200, we use the function
b(x) = 0.15(x - 200) + 20
b(800) = 0.15(800 - 200) + 20
=0.15(600) + 20
= 90 + 20
=$110
option B is the correct answer
So in my class i am studying RatioThe question is:There are 7 red pens for every 10 pencils in the borrow bin So would the answer be Part to partPart to whole or Whole to part
Answers
Answer:
The ratio of red pens to pencils is 7/10
The ratio of pencils to red pens is 10/7
Step-by-step explanation:
Ratio:
The ratio of a to b is a/b
The ratio of b to a is b/a
In this question:
7 red pens
10 pencils
The ratio of red pens to pencils is 7/10
The ratio of pencils to red pens is 10/7
Write an equation for a function that has a graph with the given characteristics.The shape of y= 1/x shifted down 4 units.
Answers
Given:
y = 1/x
Required:
equation for a function that shifted down 4 units
Solution:
y' = 1/x - 4
Answer:
y' = 1/x - 4
4) B) determine the scope of each of the following lines assume the dots are on integer coordinates
Answers
Given the following question:
Part B:
Point A: (-8, -2) = (x1, y1)
Point B: (3, 2) = (x2, y2)
Formula for slope:
[tex]m=\frac{y2-y1}{x2-x1}[/tex][tex]\begin{gathered} m=\frac{y2-y1}{x2-x1} \\ m=\frac{2--2}{3--8}=\frac{4}{11} \\ m=\frac{4}{11} \end{gathered}[/tex]