Answers
Using translation concepts, the graph of f(x) is given at the end of the answer.
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s definition or in it’s domain. Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis.
The parent absolute value function is given by:
f(x) = |x|
Which has the graph in the format of a V centered at the origin.
The translated function is given by:
g(x) = -1/2|x + 4| + 2.
The translations are as follows:
Reflection over the x-axis, due to the multiplication by the negative number, thus the V is pointing down now.Vertical compression by a factor of 2, due to the division by 2.Shift left of 4 units, as x -> x + 4.Shift up of 2 units, as y -> y + 2.Due to the last two translations, the graph is now centered at (-4,2) and is given at the end of the answer.
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Related Questions
HELP PLSS
The graph shows the corruption ratings for the world's least corrupt and most corrupt countries. The ratings are on a scale from 0 to 10, where higher scores represent less corruption.
a. Write a set of four ordered pairs in which each of the least corrupt countries corresponds to a corruption rating. Each ordered pair should be in the form (country, corruption rating).
Answers
The ordered pairs in which each of the least corrupt countries corresponds to a corruption rating will be {(A,9.7),(B,9.6),(C,9.6),(D,9.1)}.
What is an ordered pair?It should be noted that an ordered pair is the pair of two numbers or variables that are written inside brackets and are separated by a comma.
An example, (1, 2) is an ordered pair. It should be noted it can represent a point. In this case, the pair should be in the form of:
(Country, corruption rating)
(A, 9.7)
(B, 9.6)
(C, 9.6)
(D, 9.1)
Therefore, this will be {(A,9.7),(B,9.6),(C,9.6),(D,9.1)}.
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Maria bought 5 tickets for $20 each. Each ticket had a $2 fee. Write an expression that shows how much Maria paid for the tickets.
Answers
The algebraic expression which shows how much Maria paid for the tickets including the additional fee is y = 20(5) + 2(5)
Algebraic expression to show how much Maria paid for the ticketsNumber of tickets Maria bought = 5Cost of each tickets = $20Additional fee per tickets = $2let
Total amount Maria paid for the tickets = yTotal amount Maria paid for the tickets = Cost of each tickets(Number of tickets Maria bought) + Additional fee per tickets(Number of tickets Maria bought)
y = 20(5) + 2(5)
y = 100 + 10
y = $110
Therefore, the algebraic expression which shows how much Maria paid for the tickets including the additional fee is y = 20(5) + 2(5)
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pleaseee helpppp meeeee this is due sooonnnn
Answers
what is the least whole number that rounds to 230000 when rounded to the nearest ten thousand?
Answers
The least whole number that can be rounded to 230,000 is 225,000.
What is the least whole number?The ten thousand number (10,000) is usually the fifth digit in a number when counting from the right to the left. For example, in 132,456, 3 is the ten thousand number.
To round off to the nearest ten thousand, if the thousand digit is equal to or greater than 5 (i.e. 5,6, 7, 8, 9), 1 is added to the ten thousand digit and other numbers less than the ten thousand digit becomes 0. For example, when 234,612 is rounded to the nearest ten thousand, the number becomes 235,000.
If the thousand digit is less than 5 (i.e. 0, 1, 2, 3, 4), there is no change in the ten thousand digit other numbers less than the ten thousand digit becomes 0. For example, when 234,412 is rounded to the nearest ten thousand, the number becomes 234,000.
The numbers that can be rounded off to 230,000 are: 225,000, 226,000, 227,000, 228,000, 229,000, 230,000, 231,000, 232,000, 233,000, 234,000
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Jane is a cleaner the table shows information about the time it will take to clean each four rooms in the house. Jane wants to clean all four rooms in one day she will have breaks for a total time of 45 minutes. Jane is going to start at 7am what time will she finish?
Answers
Answer:
Dat is
45/7
6.43
6.43+4+4
14.43
Answer:
b c
Step-by-step explanation:
have a great day
Pls help only one question :( im stuck!
Answers
Answer:
-√26, 5.15, 5.2, 16/3
Step-by-step explanation:
-√26 = -5.09
16/3 = 5.33
14.0.02943
Scientific notation?
Answers
The scientific notation of the number 140.02943 is 1.4002943 × 10⁻².
What is termed as the scientific notation?Scientific notation is a technique for expressing numbers that are too large or small to be written in basic decimal form. In some contexts, scientific notation is also recognised as standard form, scientific form, or standard index form.The primary reason for the importance of scientific notation is that it enables us to transform very large or extremely small numbers into much manageable sizes. It is much simpler to work with these numbers when they are written in scientific notation. Scientific notation is also crucial because it ensures that calculations involving large numbers remain accurate, as it is often easy to lose track of successfully counting extremely large numbers. For instance, someone will most likely be able to work with 10¹⁰ rather than 10,000,000,000.The given number is;
140.02943
Shift the 2 decimal to the left of the decimal; because of this, the resultant number will get multiplied by 10⁻².
= 1.4002943 × 10⁻²
Thus, the number in the scientific notations will be written as; 1.4002943 × 10⁻².
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The correct question is-
Write scientific notation of -
140.02943
HELP PLEASE!! (9,-4);slope=-2/3 write the equation of the line
Answers
Given the point and slope, the equation of the line is in slope-intercept form is y = (-2/3)x + 2
What is the equation of line with the given point and slope?The formula for equation of line is expressed as;
y = mx + b
Where m is slope and b is y-intercept.
Given the data in the question;
Point ( 9, -4 )
x = 9y = -4Slope m = -2/3Since already have the slope, we determine the y-intercept b by substituting the given values into the equation of line formula.
y = mx + b
-4 = (-2/3)9 + b
Solve for b
-4 = -18/3 + b
-4 = -6 + b
b = -4 + 6
b = 2
Now that the values of slope m and y-intercept b is known, plug these into y = mx + b to determine the equation of the line.
y = mx + b
y = (-2/3)x + 2
Given the point and slope, the equation of the line is in slope-intercept form is y = (-2/3)x + 2
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Tina feeds her dog pound of dog food per day. If she
buys a bag containing 9 pounds of dog food, how many
days will it last?
Answers
Answer:
If Tina buys a bag containing 9 pounds of dog food, it will last for 9 days.
Step-by-step explanation:
Give Brainliest if I helped!
Suppose that grade point averages of undergraduate students at one university have a bell-shaped distribution with a mean of 2.55 and a standard deviation of 0.43. Using the empirical rule, what percentage of the students have grade point averages that are between 2.12 and 2.98 ?
Answers
Using the Empirical Rule, 68% of the students have grade point averages that are between 2.12 and 2.98.
What does the Empirical Rule state?It states that, for a normally distributed random variable:
Approximately 68% of the measures are within 1 standard deviation of the mean.Approximately 95% of the measures are within 2 standard deviations of the mean.Approximately 99.7% of the measures are within 3 standard deviations of the mean.For this problem, we have that:
2.55 - 0.43 = 2.12.2.55 + 0.43 = 2.98.Hence 68% of the students have grade point averages that are between 2.12 and 2.98.
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Austin has two magnets. The shaded parts of the magnets represent the poles.
What will happen if she brings the dark side of magnet P closer to the dark side of magnet Q?
A They will repel each other.They will repel each other.
B Poles of the magnets will change.Poles of the magnets will change.
C Both the magnets will break.Both the magnets will break.
D They will attract each other.
Answers
Answer:
D They will attract each other
7. Using the test of divisibility rule, determine which of the following numbers are divisible by 11.
(a) 1001935
(b) 154451
(c) 4313101
(d) 213596
Please Explain in paper
Answers
The number that is divisible by 11 is 154451
Which of the numbers are divisible by 11?The divisor is given as
Divisor = 11
Using the test of divisibility rule, numbers are divisible by 11 are palindrome numbers
This means that the numbers remain the same when reversed
From the list of options, 154451 is a palindrome
Hence, the number that is divisible by 11 is 154451
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A certain star is 3.9 x 10^2 light years from the Earth. One light year is about 5.9 x 10^12 miles. How far from the earth (in miles) is the star?
Answers
Answer: The star is 2 quadrillion( 1 followed by 15 zeroes) and 301 trillion( 1 followed by 12 zeroes) miles away from Earth. To shorten this into scientific notation(the format used to write large numbers) is: 2.301 x 10^15.
Step-by-step explanation: First, find the exact value of the units of measurement, which in this case is light years. To do so, your best choice would be to separate the equation given for light years. (Note: the line through the middle is just to separate two very similar series of steps.)
1. 5.9 x 10^12 into 5.9 x (10^12)
2. 10^12 = 1,000,000,000,000. 10^12 is the same as adding 11 zeroes since it is multiplying by tens, not 12 zeroes since there is already a zero on the ten. This number is one-trillion(we will shorten this number to 1T).
3. 5.9 x 1T = 5.9 T. Don't get nervous of the big numbers, this is the same as doing 5.9 x 1 and then adding a name afterwards. Now that we have our number, we must remember the question is asking for miles, so keep in mind this large number is the miles.
4. 5.9T --> 5.9 | T Take off the T from 5.9T for now to make this problem a little simpler for this next part.(Note: the | is a separator)
------------------------------------------------------------------------------------------------------------- 5. 3.9 x 10^2 into 3.9 x (10^2)
6. 10^2 = 100. 10^2 is the same as multiplying adding one zero to the ten. This number is one-hundred.
7. 3.9 x 100 = 390. Please remember that this step is to find the number of light years away from the Earth.
8. 390 x 5.9 = 2301. This is the number of lightyears times the number of miles without the zeroes. The next step is to add the zeroes which brings the number into trillions.
9. 2301 | T --> 2301T. Next is to simplify this number, since every zero after 3 makes the number into a different name, this number is now has 15 zeroes. This number(one-quadrillion) will be shortened to Qu.
10-ish. 2301T = 2.301Qu. This is the name of a number with 15-17 zeroes.
10. 2.301Qu = 2.301 x 10^15. This is just turning the number into scientific notation.
Done!
Grandparents want to make a gift of $100,000 for their grandchild’s 20th birthday. How much would have to be invested on the day of their grandchild’s birth if their investment could earn: (a) 10.5% compounded continuously? (b) 11% compounded continuously? (c) Describe the effect that this slight change in the interest rate makes over the 20 years of this investment
Answers
Answer:
20
Step-by-step explanation:
20 yenara they hain aahe aahe
my answer is 20 i guess........
need help with question 2 pleasee
Answers
Answer:
A: 24
B: 3
C: -1
D: 12
Step-by-step explanation:
Line A: y = 1/2x + 2
Line B: y = -1/2x + 7
Line C: y = 2x + 4
Line D: y = 1/2x + 5/4
Which lines are perpendicular?
Answers
When the multiplication of two slopes of two lines is equal to -1, they are perpendicular to each other.
-1/2*2=-1
Therefore line B & C are perpendicular.
(-2 3/5)(3)(-0.5) what does this equal?
Answers
Answer:
3.9
Step-by-step explanation:
im not sure :<
Answer:
9/25 = 0.36 = nine twenty-fiths
Step-by-step explanation:
Estimate approximately how many people were born on a Sunday. Give a step-by-step process for your estimate and show all calculations. State any assumptions clearly.
Answers
Answer:
Step-by-step explanation:
World Population = 7,750,000,000
7,750,000,000 / 7 (for amount of days in a week) = 1,100,00,000 people born on Sunday (roughly)
Determine which equation is false based on the solution set.
S:{5}
A: 6 = 2y − 4
B: 4(b + 5) = 40
C: one fifth times x plus 16 equals 17
D: −32 = 2(3p − 6)
Answers
3=y-4
7=y
6/2=3
4+3=7
Answer:
d) -32 = 2(3p - 6) is false.
Step-by-step explanation:
A) 6 = 2y - 4
→ 6 = 2(5) - 4
→ 6 = 10 - 4
→ [ 6 = 6 ]
So, the equation is true.
B) 4(b + 5) = 40
→ 4(5 + 5) = 40
→ 4(10) = 40
→ [ 40 = 40 ]
So, the equation is true.
C) (1/5)x + 16 = 17
→ (5/5) + 16 = 17
→ 1 + 16 = 17
→ [ 17 = 17 ]
So, the equation is true.
D) -32 = 2(3p - 6)
→ -32 = 2(15 - 6)
→ -32 = 2 × 9
→ [ -32 ≠ 18 ]
So, the equation is false.
Which expressions are equivalent to -9? Select all that are correct
Answers
The expressions that are equivalent to -9 are -(9) and -|9|
What are rational expressions?Rational expressions are expressions that are represented by the quotient of two polynomials or radicals. This means that, a rational expression is represented by a fraction whose numerator and denominator are polynomials or radicals
How to determine the expression?The expression is given as
-9
According to the identity law of algebra, we have the following equation
-x = -(x)
This means that
-9 = -(9)
Also, we have
-9 = -|9|
Hence, the expressions that are equivalent to -9 are -(9) and -|9|
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A rectangle has a height of b^3+b^2b
3
+b
2
b, cubed, plus, b, squared and a width of b^2+7b+4b
2
+7b+4b, squared, plus, 7, b, plus, 4.
Answers
The area of the rectangle is equal to b² · (b + 1) · (b + 0.628) · (b + 6.372).
What is the area of the rectangle?
The area of the rectangle is equal to the product of the height and the width, each of them represented by polynomials. In this question we must apply algebraic handling to simplify the product of the two polynomials:
A = h · w (1)
Where:
h - Heightw - WidthIf we know that h = b³ + b² and w = b² + 7 · b + 4, then the area of the rectangle is:
A = (b³ + b²) · (b² + 7 · b + 4)
A = b² · (b + 1) · (b + 0.628) · (b + 6.372)
The area of the rectangle is equal to b² · (b + 1) · (b + 0.628) · (b + 6.372).
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The perimeter of an equilateral triangle is 15 inches more than the perimeter of a square, and the side of the triangle is 7 inches longer than the side of the square.
Answers
The length of the equilateral triangle side is 13 inches while that of the square is 6 inches.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let x represent the side of the equilateral triangle and y represent the side of the square. Hence:
For the perimeter:
3x = 4y + 15
3x - 4y = 15 (1)
Also:
x = y + 7
x - y = 7 (2)
From the equations:
y = 6, x = 13
The length of the equilateral triangle side is 13 inches while that of the square is 6 inches.
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Rosa works 30 hours per week making $15.75 per hour. After her paycheck has 28% deducted for Taxes (federal, state, and social security), Rosa takes 10% of her take home pay and puts it into a savings account. How much money does she then have available from her paycheck to spend each week?
Answers
At a dogs shelter a 24 pound bag of dog food will feed 36 dogs a day how many dogs would you expect to feed with a 16 pound bag of dog food
Answers
Answer:
24 dogs
Step-by-step explanation:
36 divided by 24= 1.5
1.5 times 16=24
so 24 dogs :)
Can someone please help me? I’m confused. I’ll give brainliest :)
Answers
6u+18+9u=-12 simplify
Answers
Answer:
u = -2
Step-by-step explanation:
Group
[tex]6u+9u+18=-12[/tex]
Add similar elements in the equation
[tex]15u+18=-12[/tex]
Subtract 18 from all sides
[tex]15u+18-18=-12-18[/tex]
Simplify this
[tex]15u=-30[/tex]
Divide all sides by 15
[tex]\frac{15u}{15}=\frac{-30}{15}[/tex]
Divide 15 by 15, removing u
[tex]\frac{15}{15} = u[/tex]
Transform [tex]\frac{-30}{15}[/tex] by using the fraction rule.
[tex]-\frac{30}{15}[/tex]
Divide 30 by 15.
[tex]\frac{30}{15} = 2[/tex]
Thus,
u = -2
Help pls this is kinda urgent thank you
Answers
The coordinates of the midpoints of the segment with the endpoints are (-1, 0.5)
How to determine the coordinates of the midpoints of the segment with the endpoints?The endpoints of the segment are given as
J = (-6, 3)
K = (4, -2)
The coordinates of the midpoints of the segment with the endpoints are calculated as
Midpoint = 1/2 * (J + K)
So, we have
Midpoint = 1/2 * (-6 + 4, 3 - 2)
Evaluate the sum and the difference
So, we have
Midpoint = 1/2 * (-2, 1)
Evaluate the product
So, we have
Midpoint = (-1, 0.5)
Hence, the coordinates of the midpoints of the segment with the endpoints are (-1, 0.5)
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Carla is riding her tricycle in a race. We only know that 20 seconds after the race began, she was 55 meters from the starting line, and 30 seconds after the race began, she was 85 meters from the starting line. Find the equation of the line describing Carla’s motion during the race, where y represents her distance from the starting line in meters, and x represents the time since the race began in seconds.
Answers
The equation of a line describing Carla's motion during the race is y = 3x - 5.
What is slope?The slope is defined as the rate of change of the y-axis with respect to the x-axis.
As we are representing y as distance in meters and x as time in seconds we can form two co-ordinates for the distance Carla covered, They are
(20,55) and (30,85).
Now to form an equation of a line we have to first determine the slope(m) and y-intercept (b).
We know slope(m) = (y₂-y₁)/(x₂-x₁).
∴ Slope(m) = (85 - 55)/(30 -20).
= 30/10.
= 3.
Now, The equation of this line can be written as slope intercept form as y = mx + b.
55 = 3(20) + b.
b = -5.
So, y = 3x - 5 is our required equation of this situation represented by a line.
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the 3rd term of a linear sequence is 17. the 45th term is 269. determine the formula for the nth term.
Answers
Step-by-step explanation:
a linear or arithmetic sequence has a start value as first term, and then every following term is created by adding the same constant to the previous term.
a1 = a
a2 = a1 + c = a + c
a3 = a2 + c = a + c + c = a + 2c
a4 = a3 + c = a + c + c + c = a + 3c
...
as we can easily see
an = an-1 + c = a + (n-1)c
in our case
a3 = 17 = a + 2c
a = 17 - 2c
a45 = 269 = a + 44c = 17 - 2c + 44c = 17 + 42c
252 = 42c
c = 6
a = 17 - 2c = 17 - 2×6 = 17 - 12 = 5
so,
an = 5 + (n-1)×6
On a sunny day, you and your friend were taking a long walk. You got tired and stopped near a telephone pole for a little rest, but your nervous
friend couldn't stand still. He paced out your shadow and discovered it was 5 meters long even though you are really only 1.5 meters tall. He
paced the long shadow of the telephone pole and found that it was 35 meters long. How high is the telephone pole in meters? Enter your answer
with one digit to the right of the decimal point.
Answers
The telephone pole will stands 10.5 meters tall.
Given shadow of you = 5 meters
The true height is 1.5 meters.
We must determine the telephone pole's height because its lengthy shadow is 35 meters long.
Assume that x is the height of the telephone pole..
Now we can write this as
height of shadow/ actual height
5 / 1.5 = 35 / x
By cross multiplication we get
5 * x = 35 * 1.5
We get it by dividing '5' by both sides
x = 35 * 1.5 / 5
x = 10.5 meters
Therefore ,The telephone pole is 10.5 meters tall.
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