Answers
Answers in bold:
Problem 4) Shift 6 units left, 1 unit down
Problem 5) Shift 3 units right. Vertically stretch by a factor of 2.
The graphs are below.
==========================================================
Explanation:
In problem 4, the parent function is y = x^2
Replace every x with (x+6) and it will shift the parabola 6 units left. Why left instead of right? It's because the xy axis is moving 6 units to the right. Each old input x is now 6 units larger to get x+6. The xy axis moving 6 units right gives the illusion the curve shifts 6 units left. It's a bit backwards I know.
Luckily the -1 at the end is straight forward and it shifts everything down by 1 unit. This is because we subtract 1 from the y coordinate.
So that's how we get the "6 units left, 1 unit down" translation. No horizontal nor vertical dilations occur.
I recommend using GeoGebra or Desmos or similar to graph out the two equations, to see the comparison.
---------------------------------
For problem 5, the parent function is y = |x|
Replacing every x with x-3 means that the xy grid moves 3 units left. That gives the illusion the V shaped curve is moving 3 units right.
The 2 out front will double each y coordinate. This visually stretches the graph by a factor of 2. It is now twice as tall as it was before. This is equivalent to doing a horizontal compression (since the graph is more skinny now).
Answer:
4. Translated 6 units left and 1 unit down.
5. Translated 3 units right and stretched vertically by a factor of 2.
Step-by-step explanation:
Transformations
[tex]\textsf{For $a > 0$}[/tex]
[tex]f(x+a) \implies f(x) \: \textsf{translated $a$ units left}[/tex]
[tex]f(x-a) \implies f(x) \: \textsf{translated $a$ units right}[/tex]
[tex]f(x)+a \implies f(x) \: \textsf{translated $a$ units up}[/tex]
[tex]f(x)-a \implies f(x) \: \textsf{translated $a$ units down}[/tex]
[tex]a\:f(x) \implies f(x) \: \textsf{stretched parallel to the $y$-axis (vertically) by a factor of $a$}[/tex]
[tex]f(ax) \implies f(x) \: \textsf{stretched parallel to the $x$-axis (horizontally) by a factor of $\dfrac{1}{a}$}[/tex]
[tex]-f(x) \implies f(x) \: \textsf{reflected in the $x$-axis}[/tex]
[tex]f(-x) \implies f(x) \: \textsf{reflected in the $y$-axis}[/tex]
Question 4Parent function:
[tex]f(x)=x^2[/tex]
Translated 6 units left:
Add 6 to the x-variable of the function:
[tex]\implies f(x+6)=(x+6)^2[/tex]
Translated 1 unit down:
Subtract 1 from the function:
[tex]\implies f(x+6)-1=(x+6)^2-1[/tex]
Question 5Parent function:
[tex]f(x)=|x|[/tex]
Translated 3 units right:
Subtract 3 from the x-variable of the function:
[tex]\implies f(x-3)=|x-3|[/tex]
Stretched vertically by a factor of 2:
Multiply the function by 2:
[tex]\implies 2f(x-3)=2|x-3|[/tex]
Related Questions
0.36 converted into a fraction
Answers
Answer:
9/25
Step-by-step explanation:
0.36 = 36/100
36 / 4 = 9
100 / 4 = 25
9/25
Norm's electric bill for December 2013 was $149.32. In 2014 the electric bill was $194.31. Next year Norm expects the bill to be the 2013 amount plus $25.00 more than the difference between 2013 and 2014. What is the new bill expected to be?
Answers
A): 2013 = 149.32
Find difference of: 194.31
2014 = 194.31 149.32
= 44.99
2015 Total Will Be:
B):
149.32 + 25 = 174.32
(2013)
174.32 + 44.99 = 219.31(B) (A)
QUESTION : -137 +854-84+ 506 =
Answers
Answer: 1139
Step-by-step explanation:
-137+854=717
717-84=633
633+506=1139
One bar of candy A and two bars of candy B have 763 calories. Two bars of candy A and one bar of candy B contain 773 calories. Find the caloric
content of each candy bar
Candy bar A contains calories and candy bar B contains
(Simplify your answers.)
calories
Answers
Answer:
A = 261 calories. and B = 251 calories
Step-by-step explanation:
A + 2B = 763
2A + B = 773
---------------------------
-2(A + 2B = 763)
↓
-2A - 4B = - 1526
2A + B = 773
-----------------------------
-3B = - 753
B = 753/3
B = 251
Candy bar B has 251 calories
now let's find A
A + 2B = 763
A + 2 (251) = 763
A + 502 = 763
A = 763 - 502
A = 261
Candy bar A has 261 calories
Steve has 6 3/4 pounds of ground beef to make hamburgers for a party it takes 3/8 of ground beef to make a hamburger how many burgers can Steve make
Answers
The number of burgers Steve can make = 18
In this question, Steve has 6 3/4 pounds of ground beef to make hamburgers for a party.
It takes 3/8 of ground beef to make a hamburger.
We need to find the number of burgers Steve can make.
First we convert the improper fraction 6 3/4 into a proper fraction.
6 3/4 = 27/4
For 1 hamburger 3/8 of ground beef is required.
Let n be the number of burgers Steve can make.
n = (27 / 4) / (3 / 8)
n = 27/4 × 8/3
n = 9 × 2
n = 18
Therefore, the number of burgers Steve can make = 18
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Why is adding two fractions different from multiplying the two fractions?
Answers
Answer:
Step-by-step: The reason we cross multiply fractions is to compare them. Cross multiplying fractions tells us if two fractions are equal or which one is greater. This is especially useful when you are working with larger fractions that you aren't sure how to reduce.
Answer:
adding two fractions is different than multiplying two fractions bc after adding the fractions, you have to simplify them and it is not easy but with multiplying, you multiply from left to right.
Step-by-step explanation:
example: 1/2+3/4
4/8+6/8=10/8=1 1/4
another example: 6/10*4/6=24/60
Find the slope of the regression line.
Shots on goal 22, 25, 28, 29, 33
Points scored 5, 7, 7, 9,8
A -0.561
B 0.283
C. 0.631
D. 0.794
Answers
The length of a rectangle is two more than triple the width. If the perimeter is 84 inches, find the
dimensions.
The width is
The length is
Submit Question
inches.
inches.
Answers
Answer:
The length of rectangle seven more than triple the width. If the perimeter 126 inches, find the dimensions The width inches. The length inches.
If QS bisects PQR, m PQS = (10x-9), and m SQR= (4x+15), find x.
Answers
Given that QS bisects PQR making mPQS the same as the mSQR, the numerical value of x is 4
What is the numerical value of x?A bisector divides a segment or angle into two equal halves.
Given the data in the question;
QS bisects PQRm PQS = (10x-9)m SQR= (4x+15)Value of x = ?Since QS bisects PQR, m PQS is the same as m SQR.
Hence;
m SQR = m PQS
We plug in the values
(4x+15) = (10x-9)
Remove parenthesis and solve for x.
4x + 15 = 10x - 9
15 + 9 = 10x - 4x
24 = 6x
x = 24/6
x = 4
Given that QS bisects PQR making mPQS the same as the mSQR, the numerical value of x is 4
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"divide 9 by p, then multiply 2 by the result" i need the expression for this, thank you
Answers
Answer: The expression would look like this p/9 (2)
Step-by-step explanation: You should make it a fraction by putting the p on top and 9 on bottom and in parentheses you put in the 2!
Hope this helped! :D
Simplify the equation, [tex](x^{4})^{\frac{5}{6} }[/tex], to a simplified radical. Show work
Answers
The simplified radical form of the equation [tex](x^{4})^{\frac{5}{6} }[/tex] is [tex]x^{\frac{10}{3} }[/tex]
The exponentiation is written as [tex]a^{n}[/tex], where a is the base and n is the exponent or power. We say as "a by n". Exponent means the number of times the base is used as a factor.
The expression = [tex](x^{4})^{\frac{5}{6} }[/tex]
Here we have to apply the exponent rule
We know,
The power rules for the exponent [tex](a^{m})^{n}=a^{mn}[/tex]
Here multiply the exponent times the power.
Simplify it
[tex](x^{4})^{\frac{5}{6} }=(x)^{4(\frac{5}{6}) }[/tex]
=[tex]x^{\frac{20}{6} }[/tex]
Divide both 20 and 6 by 2 to make it to simplest form, then the result
=[tex]x^{\frac{10}{3} }[/tex]
Hence, the simplified radical form of the equation [tex](x^{4})^{\frac{5}{6} }[/tex] is [tex]x^{\frac{10}{3} }[/tex]
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Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar.
Write the least common multiple of 7 and 14.
Answers
If the average of 292, 305, 415, and x is 343, what is the value of x?
Answers
1372 - 415 = 957 - 305 = 652 - 292 = 360
x = 360
Baljeet invested $5500 at a simple annual rate of 4.8% for 6 years. What is the total future value of the investment?
State your answer in terms of dollars rounded to the nearest cent, but do not include a $ sign or the word "dollars" with your response.
Answers
Answer:
[tex]a = p(1 + in) \\ = 5500(1 + 0.048 \times 6) \\ = 7084[/tex]
Graph the image of the figure after a dilation with a scale factor of 3 centered at the origin.
Use the polygon tool to graph the dilated figure.
Answers
Answer: (3, 3), (3, 9), (-6, 9), (-6, 3)
Step-by-step explanation:
With a dilation of 3 centered about the origin-
the point (1, 1) would go to (3, 3)
the point (1, 3) would go to (3, 9)
the point (-2, 3) would go to (-6, 9)
the point (-2, 1) would go to (-6, 3)
simply multiply the original coordinates all by 3.
fraction numerator 8 over denominator 2.4 end fraction equals space 9 over x
Answers
Answer:
x = 2.7
Step-by-step explanation:
8/2.4 = 9/x
Cross multiply.
8x = 2.4 × 9
8x = 21.6
8x/8 = 21.6/8
x = 2.7
Of the 30 champions of the National Spelling Bee from 1974 to 2003, 16 are boys. Find the ratio of the number of champions who are girls to the number who are boys.
Answers
Answer:
14/16 or 7/8.
Step-by-step explanation:
We know the total champions is 30. There are 16 boys, so to find the number of girls we can do 30-16. This gives us 14. Now we know that there are 16 boys and 14 girls, and the question is asking for the ratio of champions who are girls to the number who are boys. This means the ratio would simply be 14 to 16, for every 14 girls there are 16 boys. You can simply this ratio to 7 to 8, meaning for every 7 girls there are 8 boys.
if log4^u - log8^v =1 find u in terms of v
Answers
u in terms of v will be represented with the logarithm function as v = u log (- 4 ) - ( log 8) ⁻¹
We are given that:
log 4 ^ u - log 8 ^ v = 1
This can also be written in another way using the logarithm properties. We get that:
u log 4 - v log 8 = 1
Subtract v log 8 from both the sides:
u log 4 = 1 + v log 8
v log 8 = u log 4 - 1
v = ( u log 4 - 1 ) / log 8
v = u log (- 4 ) - ( log 8) ⁻¹
Therefore, we get that, u in terms of v will be represented with the logarithm function as v = u log (- 4 ) - ( log 8) ⁻¹
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On the graph f(x)=cos x and the interval [-2pie,0] for what value of x does the function cross the x-axis?
Answers
The function f(x) = cos x crosses the x-axis at x₁ = - 0.5π and x₂ = - 1.5π.
For what values does the cosine function cross the x-axis?
Cosine function is a function bounded between - 1 and 1 and whose period is 2π, all the values of x such that the cosine function crosses the x-axis is described by the following expression:
cos x = 0 (1)
Then, by inverse trigonometric functions:
x = cos⁻¹ 0
x = 0.5π ± π · i, where i is a non-negative integer.
If we know that i = 1 and i = 2, then the values of x within the interval [- 2π, 0] are, respectively:
x₁ = - 0.5π, x₂ = - 1.5π
The function f(x) = cos x crosses the x-axis at x₁ = - 0.5π and x₂ = - 1.5π.
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Henry will paint 5 birdhouses with 1 quart of paint. How many quarts of paint will Henry use to paint 42 birdhouses?
Answers
Answer:
8
Step-by-step explanation:
because you can't count before 42 so eight
The line graph below shows the number of times Maria drove her car each day of the week.
How many times did Maria drive her car on day 4?
Answers
The number of times Maria drove the car on day 4 is 9 times.
How many times did Maria drive her car on day 4?A line graph is a graph that connects different data points on a graph using a straight line. A line graph is made up of a x-axis and a y-axis. In the line graph given, the number of days is on the x-axis and the number of times the car was driven is on the y-axis. A line graph is used to show quantitative data. Line graphs are used to visualise data.
In order to determine the number of times Maria drove the car on day 4, locate where day 4 is on the x-axis. Then trace 4 upward toward a data point. When the data point is located, trace it to the y-axis. When day 4 is traced to the y-axis, the value gotten is 9.
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Which of the following represents a function?
x -10 -9 0 5
y 19 17 25 19
A value 0 in x corresponds to 7 in y, and 52 in y. A value 1 in x corresponds to 4 in y. A value 2 in x corresponds to 16 in y. A value 3 in x corresponds to 7 in y.
{(0,0), (-4,3), (7,1), (-4,5), (3,2)}
A graph plots the points (negative 3, 4), (negative 3, negative 4), (negative 2, 3), (negative 2, negative 3), (negative 1, 0), (1, 0), (2, 3), (2, negative 3), (3, 4) and (3, negative 4) on the x y coordinate plane.
Answers
x -10 -9 0 5
y 19 17 25 19
✅. Reason: there is only one x for every y value so it will pass the vertical line test
These below are NOT a function
A value 0 in x corresponds to 7 in y, and 52 in y. A value 1 in x corresponds to 4 in y. A value 2 in x corresponds to 16 in y. A value 3 in x corresponds to 7 in y.
❌ no, it has (0, 7) and (0, 52), two same x values
{(0,0), (-4,3), (7,1), (-4,5), (3,2)}
❌no, it has two same x values of -4
A graph plots the points (negative 3, 4), (negative 3, negative 4), (negative 2, 3), (negative 2, negative 3), (negative 1, 0), (1, 0), (2, 3), (2, negative 3), (3, 4) and (3, negative 4) on the x y coordinate plane.
❌ no, it has multiple same x values of -2, -3, 2 and 3.
See attachment showing why the same x value repeated will not be a function because it will not pass the vertical line test
Problem solved!!
Subtract Integers
1. FOOTBALL A team gained 5 yards on
their first play of the game. Then they
lost 6 yards. Find the total change in
yardage.
Answers
total change is -1
The total change in yard is -1
By this question we can get
The football A team gained 5 yard on their first day of the game
Then they lost 6 yards
The total change in yard is
We all know
The formula of find change is
Total-loss
So,
5-6=-1
Gain 5 yards
Lost 6 yards
Total change 5-6=-1 (ans)
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on average max makes 45 out of 60 shots with the basketball, write an equation to represent the average number of shots made out of x attempts
Answers
Answer:
See below
Step-by-step explanation:
Avg shots made = (45/60) x = (3/4 ) x = .75 x
Is it possible to calculate the square root of a negative number?
Answers
Answer: It is impossible to find the square root of negative one, or the square root of any negative number because no number times itself can equal a negative number.
Step-by-step explanation:
Answer:
It is impossible to find the square root of negative one, or the square root of any negative number, because no number times itself can equal a negative number.
Step-by-step explanation:
The square root of a negative number does not exist among the set of Real Numbers.
When problems with negatives under a square root first appeared, mathematicians thought that a solution did not exist. They saw equations such as x2 + 1 = 0, and wondered what the solution n3 really meant.
What is the domain of the graph below.
Answers
Answer:
acbs
Step-by-step explanation:
Sales Application Statins are used to keep cholesterol in check and are a top-selling drug in the U.S. The equation: S = 1.7 x + 5.2 estimates the amount of sales, S , of statin (in billions of dollars) x years after January 1, 1998. Sales of statin on January 1, 2008 was billion dollars. Statin sales reached 25.6 billion dollars in the year .
Answers
Sales of Statin on January 1, 2008 was 22.2 billion dollars; and the year that the Statin sales reached 25.6 billion dollars was in 2010.
How do we calculate sales and the year it occurred?Given:
S = 1.7 x + 5.2 .............................. (1)
Sales of statin on January 1, 2008 can be calculated as follows:
x = 2008 - 1998 = 10
Substituting x = 10 into equation (1), we have:
S = (1.7 * 10) + 5.2
S = 17 + 5.2
S = 22.2
The answer above implies that sales of Statin on January 1, 2008 was 22.2 billion dollars.
The year that the Statin sales reached 25.6 billion dollars can be calculated as follows:
S = 25.6
Substituting S = 25.6 into equation (1) and solving for x, we have:
25.6 = 1.7x + 5.2
25.6 - 5.2 = 1.7x
20.4 = 1.7x
x = 20.4 / 1.7
x = 12
Therefore, we have:
The year Statin sales reached 25.6 billion = 1998 + x = 1998 + 12 = 2010
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The sales of Statin on January 1, 2008 is 22.2 billion dollars and the year statin sales reached 25.6 billion was in 2010
Linear functionsLinear functions are equations that has a leading degree of 1.
Given the expression that represents amount of sales, S , of statin (in billions of dollars) x years after January 1, 1998 as;
S = 1.7 x + 5.2
For the sales of statin on January 1, 2008, this is calculated as
x = 2008 - 1998 = 10years
Substitute x = 10 into the given equation to have;
S = 1.7(10) + 5.2
S = 17 + 5.2
S = 22.2
Therefore the sales of Statin on January 1, 2008 is 22.2 billion dollars.
For the year that the Statin sales reached 25.6 billion dollar;
S(x) = 25.6
Substituting S = 25.6 into the equation
25.6 = 1.7x + 5.2
1.7x = 25.6 - 5.2
1.7x = 20.4
x = 12
Hence the year statin sales reached 25.6 billion was in 2010
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Explain a method to find the area of triangle QRS given that RT is perpendicular QS. Then find the area. Show your work.
Answers
Applying the distance formula to find the base and height of the triangle, the area of the triangle is calculated as: 17.85 units².
How to Find the Area of a Triangle?Area of triangle = 1/2(base)(height).
The base of triangle QRS is QS.
The height of triangle QRS is RT.
Use the distance formula [tex]\sqrt{(y_2 - y_1)^2 + (x_2 - x_1)^2}[/tex] to find the length of QS and RT:
Q(2, 4) = (x1, y1)
S(8, -2) = (x2, y2)
QS = √[(8−2)² + (−2−4)²]
QS = √72
QS ≈ 8.5 units
R(6, 6) = (x1, y1)
T(3, 3) = (x2, y2)
RT = √[(3−6)² + (3−6)²]
RT = √18
RT ≈ 4.2 units
Area of triangle QRS = 1/2(8.5)(4.2)
Area of triangle QRS = 1/2(35.7)
The area of triangle QRS = 17.85 units²
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Find the circumference of the circle with area 1÷4πd² cm²
Answers
Answer:C=3.54
Step-by-step explanation:
Paula pays $19.92 for 2.4 pounds of walnuts. What is the price per pound of walnuts?
Answers
Answer:
8.30
Step-by-step explanation:
19.92 / 2.40 = 8.30
8.30 is the amount per pound.
Answer: 8.30
Step-by-step explanation: We know that Paula Paid 19.92$ for 2.4 pounds
Price of 1 Walnut = 19.92 ÷ 2.4 = 8.30