Describe each transformation of the parent function y + |x|. Then, graph each function.
33. y = |x| - 4
35. y = -|x + 4| + 3
PLEASE HELP
Answers
The correct transformation include
Transformation 1: Shifted down by 4 unitsTransformation 2: Shifted left by 4 units, reflected across the x-axis and shifted up by 3 unitsHow to determine the transformation of the graph?The equation of the function is given as
y = |x|
The transformed functions are given as
y = |x| - 4
y = -|x + 4| + 3
The transformation 1
Here, we have
y = |x|
y = |x| - 4
This can be represented as
y = f(x) - 4
The description of the above transformation is:
The function y = |x| is shifted down by 4 units
The transformation 2
Here, we have
y = |x|
y = -|x + 4| + 3
This can be represented as
y = -f(x + 4) + 3
The description of the above transformation is as follows
The function y = |x| is shifted left by 4 unitsThe function is then reflected across the x-axisThe function y = |x| is shifted up by 3 unitsNext, we graph the functions where the blue line represents y = |x|, the green line represents y = |x| -4 and the orange line represents y = -|x + 4| + 3
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Related Questions
make a table of values for the equation. Then graph the equation.
Answers
Check the picture below.
there is a jar containing 27 black and 33 gold jelly beans. you will get a chance to draw 10 jelly beans at random from the jar. on each draw, what is probability of drawing a gold jelly bean
Answers
there is a jar containing 27 black and 33 gold jelly beans. you will get a chance to draw 10 jelly beans at random from the jar. on each draw, 0.5 is the probability of drawing a gold jelly bean
How can I find the probability?
The probability of an event can be calculated by probability formula by simply dividing the favorable number of outcomes by the total number of possible outcomes.
there is a jar containing 27 black
and 33 gold jelly beans.
you will get a chance to draw 10 jellybeans at random from the jar.
on each draw, what is probability of drawing a gold jelly bean
Add up the total number of jellybeans, 27 + 33 = 60
Divide the number of gold jellybeans by the total: 33/60 and reduce the fraction to 11/20
=0.55
Hence, there is a jar containing 27 black and 33 gold jelly beans. you will get a chance to draw 10 jelly beans at random from the jar. on each draw, 0.5 is the probability of drawing a gold jelly bean
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Lincoln high school have 75 less than four times as many students as washington high school right in expression to find the number of students at lincoln high school washington high school has w students
Answers
Main Answer:
Number of students in Lincoln high school is [tex]4w-75[/tex]
Explanation:
Number of students in Washington high school = w
Number of students in Lincoln high school = 75 less than four times number of students in Washington high school
Therefore, number of students in Lincoln high school = [tex]4w-75[/tex]
The area of a trapezoid is 31.5cm. If the parallel sides are of lengths 7.3cm and 5.3cm.Calculate te perpendicular distance between them
Answers
The perpendicular distance ( height ) between the parallels sides of the trapezoid is 5cm.
How to calculate the height of a trapezoid?A trapezoid is simply a quadrilateral with at least one pair of parallel sides.
The area of trapezoid is expressed as;
A = h × (a + b)/2
Where a is base a, b is base b and h is height.
Given the data in the question;
Area A = 31.5cm²Base a = 7.3cmBase b = 5.3cmHeight h = ?To determine the height of the trapezoid, plug the given values into the above formula and solve for h.
A = h × (a + b)/2
31.5cm² = h × ( 7.3cm + 5.3cm)/2
31.5cm² = h × ( 12.6cm )/2
31.5cm² = h × 6.3 cm
h = 31.5cm² / 6.3 cm
Height h = 5cm
Therefore, the height of the given trapezoid is 5 centimeters.
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• write each answer in simplest form.
1. 1/6 +2/6
2. 2/5 - 1/5
Answers
Answer:
1. 1/2
2. 1/5
Step-by-step explanation:
I used a calculator!
Answer:
1.3/6 or 1/2
2.1/5
Step-by-step explanation:
Just write that out, thats all the steps there is, 3/6 simplifies to 1/2 because they're equivalent
2/3 x ___ = -1
what’s the blank ?
Answers
By doing multiply of = [tex]\frac{2}{3}[/tex] with =[tex]\frac{-3}{2}[/tex] we get -1 .
What is basic algebra ?Algebra is one of the areas of mathematics where mathematical expressions can be used to represent situations or problems. In order for a mathematical statement to make sense, it must have mathematical operations like addition, subtraction, multiplication, and division as well as variables like x, y, and z. Every branch of mathematics, including calculus, trigonometry, and coordinate geometry, uses algebra. The equation 2x + 4 = 8 is a simple algebraic formula.Mathematical branch known as algebra deals with symbols and arithmetic operations on them. These symbols are referred to be variables since they lack set values. We frequently observe specific values that change in our day-to-day situations. However, there is a continuing need to depict these shifting values. These values are frequently represented in algebra by symbols, which are known as variables, such as x, y, z, p, or q. In order to determine the values, additional arithmetic operations such as addition, subtraction, multiplication, and division are performed on these symbols.
Given that : = [tex]\frac{2}{3}[/tex] x ___ = -1
[tex]\frac{2}{3}[/tex] ×[tex]\frac{-3}{2}[/tex]
=-1
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In the diagram below, AB || CD, AD || BC, DEL CE, m/DCE = 30°
and m/ADE = 59°. Find m/ECB.
Answer: m/ECB
59°
=
You may assume lines that appear straight are straight, but the figure is not otherwise drawn to scale.
||
E
O
B
Submit Answer
30°
attempt 6 out of 10
Answers
Answer:
Angle EDC = 180 - 90 - 30 = 60° (sum of angles in triangle add up to 180°)
Angle ADC + angle DCB = 180° (interior angles, AB//CD)
59 + 60 + 30 + angle ECB = 180
Angle ECB = 180 - 59 - 60 - 30 = 31°
find the value of expression when y=4 2y+2y2
Answers
The value of the expression 2y + 2y² when y = 4 is 40.
Whet is an expression?It should be noted that in Mathematics, an expression simply means the finite combination that is formed according to a specific rule. It should be noted that an expression must have variables that are connected by the operator.
In this case, the expression given in the question is:
2y + 2y².
where y = 4
We have to put y = 4 into the expression. This will be:
2y + 2y².
2(4) + 2(4)²
= 8 + 32
= 40
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Find f(g(x)) and g(f(x)) and determine whether the pair of functions f and g are inverses of each other.
f(x)=6x+5 and g(x)= x-5/6
a. f(g(x))= (Simplify your answer.)
b. g(f(x))= (Simplify your answer.)
Answers
Part a
[tex]f(g(x))=6\left(x-\frac{5}{6})+5=6x-5+5=6x[/tex]
Part b
[tex]g(f(x))=g(6x+5)=(6x+5)-\frac{5}{6}=6x+\frac{25}{6}[/tex]
Therefore, the functions are not inverses of each other since [tex](f(g(x)) \neq x[/tex].
Given the following exponential function, identify whether the change represents growth or decay, and determine the percentage rate of increase or decrease.
y=8800(1.573)^x
y=8800(1.573)
x
Answers
The given exponential function represents the growth in function with a percentage increase as 57.3%.
Given we have the exponential function as :
y=8800(1.573)ˣ
it is in the form of: y=k.aˣ
therefore, if a>2 then the function represents growth.
and if a<1 then the function represents decay.
now, x=1.573
1.573 > 1
so, the function represents change in growth.
therefore, 1.573 - 1
= 0.573
= 57.3%
hence the change in growth of the function is increased by 57.3%.
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If u/8 -4 = 7, what does u equal
Answers
Answer:
88
Step-by-step explanation:
[tex]\frac{u}{8}-4=7 \\ \\ \frac{u}{8}=11 \\ \\ u=88[/tex]
Answer:u=88
Step-by-step explanation:
Which of the following describe 73.222...? Select all that apply.
whole
number
integer
rational
number
Answers
Answer:
rational
number
Step-by-step explanation:
because any decimal number that repeats forever can be written as a fraction and any number that can be written as a fraction is rational
a number is any value that has no variables
a whole number is a positive value that is not a decimal
an integer is also any whole value
You want to cover one wall of your room with neon-color wallpaper that costs $25
for a double roll containing 44 square feet. The wall is 18.5 feet long and 10 feet
high.
a. How much wallpaper will
you need?
b. How much will the wallpaper cost
Answers
B.it will cost 125$
Answer: You will need 185 square feet of wallpaper. It will cost you $125.
Step-by-step explanation:
18.5 x 10= 185
185/44= 4.2
4.2 is a little over 4 so you would need 5. You will have extra.
$25 x 5 rolls= $125
What is the slope of the line parallel to :y=-4/7x+2
Answers
Answer:Two lines are parallel if the have the same slope. To find the slope of the line parallel to the line y=4/7x-2 we need to get the line into slope-intercept form (y = mx + b), but the line is already in that form, so the slope is m = 4/7.
Step-by-step explanation:
The shape of a water tower can partially be modeled by a sphere in which the diameter is 30 feet. A painter needs to calculate the surface area of this part of the water tower to accurately estimate the amount of paint needed for the job. What is the surface area of this portion of the water tower to the nearest square foot? Surface area: square feet
Answers
Answer: i believe the answer is 113.1 square feet
Step-by-step explanation: pi times 30
of 107 athletes surveyed about what sport they play, some play basket ball. Of those who play basketball, 48 play baseball and the remaining 33 who do not play baseball, Write an equation to find the number of athletes surveyed who do not play basketball.
Answers
The equation for the number of athletes who do not play basketball is x = 107 - 81
How to calculate the value?Athletes surveyed = 107 athletes
Athletes who play basketball
Athletes who play baseball = 48 athletes
Athletes who don't play baseball = 33 athletes
Athletes who play basketball will be:
= athletes who play baseball + athletes who don't play baseball
= 48 + 33.
= 81
Total athletes = Athletes who play basketball + Athletes who don't play basketball
107 = 81 + x
x = 107 - 81
x = 26
The value is 26.
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What is the quotient? a-3/7 / 3-1/21
Answers
The quotient of a-3/7 / 3-1/21 is 3/2(a - 3)
The quotient of a-3/7 / 3-a/21 is -3
Determining the quotient of a division operationFrom the question, we are to determine the quotient of the given division operation.
The given division operation is
a - 3/ 7 / 3 -1 / 21
That is,
a - 3/ 7 ÷ 3 -1 / 21
This becomes
a - 3 / 7 × 21 / 3 -1
a - 3 / 7 × 21 / 2
3(a - 3) / 2
= 3/2(a - 3)
If we are to find the quotient of
a - 3/ 7 / 3 -a / 21
This becomes
a - 3/ 7 ÷ 3 - a / 21
a - 3/ 7 × 21 / 3 - a
21(a -3) / 7(3 - a)
3( a - 3) / (3 -a )
Multiply the numerator and the denominator by -1
-1 × 3( a - 3) / -1 × (3 -a )
-3( a - 3) / (-3 + a)
-3( a - 3) / (a - 3)
= -3
Hence, the quotient is -3
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An entry level web developer's annual pay is $56,940 based on 52 weeks per year. Due to the economy, his company is having to cut back on the number of weeks that it employs its web developers. If the firm cuts the work year to 50 weeks but keeps the same rate of pay, how much should the web developer expect his annual pay to decrease? Round your answer to the nearest dollar.
Answers
Based on the first entry level web developer salary paid, and the new work year, the amount the web developer can expect his annual pay to decrease by is $2,190
How to find the decrease in pay?First, find the weekly pay of the web developer in the first salary:
= 56,940 / 52
= $1,095 per week
The new salary of the web developer as a result of the work week becoming 50 weeks is:
= 1,095 x 50
= $54,750
The decrease in this annual pay to the web developer is:
= 56,940 - 54,750
= $2,190
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what is the equation of the least squares regression line that describes the rela- tionship between operating cost per hour and number of passenger seats in the
Answers
The relationship between operating cost per hour and the number of passenger seats is shown by the equation of the least squares regression line, where y=1136+14.673x is the expected operating cost per hour and x is the number of passenger seats.
Why do you use the word "square"?a plane figure in geometry with four equal sides and four right angles of 90 degrees. A square is both an equilateral rectangle and a special kind of parallelogram (an equilateral and equiangular one).
the parallelogram in detail.In Euclidean geometry, a parallelogram is a simple quadrilateral having two sets of parallel sides. The confronting or opposed sides and the opposing angles of a parallelogram are of equal length.
based on the available facts;
y=1136+14.673x
where
x= number of passenger seat
y=predicted operating cost per hour.
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100 people where sampled and their heights were recorded, it was discovered the mean height was 5 feet and 6.3 inches with a standard deviation of 3.75 inches. what is the probability of someone being 5 feet and 4.2 inches tall?
Answers
The probability of someone being 5 feet and 4.2 inched tall is 0.2877
Probability:
Probability means the possibility of occurring the specific even across the total number of event.
Given,
100 people where sampled and their heights were recorded, it was discovered the mean height was 5 feet and 6.3 inches with a standard deviation of 3.75 inches.
Here we need to find the the probability of someone being 5 feet and 4.2 inches tall.
From the given details, we know that,
n = 100
mean (ч) = 5 feet and 6.3 inches
standard deviation (σ) = 3.75 inches
We know that the formula to find the probability is,
P = (x - ч)/σ
But here we have used the different measurement for each. So, the first step is convert them into inches.
So,
5 feet and 6.3 inches = 60 + 6.3 inches = 66.3 inches.
Similarly 5 feet and 4.2 inches = 64.2 inches.
So, the probability is,
P (X < 64.2) = (64.2 - 66.3)/3.75
P (X < 64.2) = -0.56
Based on the standard normal table to conclude that:
P (X < 64.2) = -0.56 = 0.2877
Therefore, the probability of someone being 5 feet and 4.2 inches tall is 0.2877.
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−185%−1.7=I do not know the answer
Answers
Answer: -1.4
Step-by-step explanation: simply subtract negative 185 by 1.7
Show all work to identify the asymptotes and state the end behavior of the function
Answers
The horizontal asymptote of the function is y=36 and vertical asymptote is x = 6 and its end behavior is f(x)→6.
As the independent variable approaches a certain value, the function approaches asymptotes, but does not cross them. They could be angled, vertical, or horizontal.
ascending asymptotes
There will be a vertical asymptote at x=a if the denominator factor of a rational function, (x - a), is not matched by the same factor in the numerator.
horizontal asymptotes:
When x is large, the value of a rational function approaches the ratio of the highest-degree terms in the numerator and denominator.
Given the function is f(x) = 6x/x-36
limx→±∞ 6x/x-36
= limx→±∞ 6/1-36/x
= 6 ⇒ horizontal asymptote: y = 6
Consider denominator = 0 ↔ x-36 = 0 ↔ x=36
limx→₊₂₅ 6x/x-36
= 6×36/0⁺ = ∞ ⇒ vertical asymptote: x = 36
End behavior of f(x):
As x → -∞ or x → ∞, f(x) → 6.
Hence we get the asymptote and the end behavior of the function.
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A trampoline park costs $12 for the first hour and $6 for each additional hour. Flynn pays $30 at the trampoline park. Select the equation that represents the given situation and find the number of additional hours Flynn stays at the trampoline park after the first hour.
Answers
Answer:
Flynn stays at the trampoline park for an additional 3 hours.
Step-by-step explanation:
30 - 12 = 18
18 / 6 = 3
As for the "Select the equation that represents the given situation" I don't know what this really means so I didn't do that. Sorry.
I need help understanding this problem
Answers
The solution to the given inequalities is -7 < x ≤ 6. The graph of the inequality is shown below on a number line.
Solving Inequalities and Graphing Number lineFrom the question, we are to solve the given inequalities
The given inequalities are
-3x - 7 < 14 and -25 ≤ -3x - 7
Solving -3x - 7 < 14
-3x - 7 < 14
Add 3x to both sides of the inequality
-3x + 3x - 7 < 14 + 3x
-7 < 14 + 3x
Subtract 14 from both sides
-7 - 14 < 14 - 14 + 3x
-21 < 3x
Divide through by 3
-21/3 < 3x/3
-7 < x
Solving -25 ≤ -3x - 7
-25 ≤ -3x - 7
Add 3x to both sides
-25 + 3x ≤ -3x + 3x - 7
-25 + 3x ≤ - 7
Add 25 to both sides
-25 + 25 + 3x ≤ - 7 + 25
3x ≤ 18
Divide through by 3
3x/3 ≤ 18/3
x ≤ 6
Thus,
The solutions to the inequalities are
-7 < x and x ≤ 6
That is,
-7 < x ≤ 6
The number line is shown below
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Foster is centering a photo that is 7 1/5 inches wide on a scrapbook page that is 16 inches wide
Answers
The distance that's required to be kept geo either side will be 4.258 inches.
How to calculate the value?From the information, Foster is centering a photo that is 7 1/5 inches wide on a scrapbook page that is 16 inches wide.
It should be noted that 7 1/2 is the same as 7.5. Therefore,we can subtract and this will be:
= 16 - 7.5
= 8.5
Since we know that the scrapbook is 8.5 inches wider,we will divide the width by 2 to get the distance of either side and this will be:
= 8.5 / 2
= 4.25
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Foster is centering a photo that is 7 1/5 inches wide on a scrapbook page that is 16 inches wide. How far from each side go the page did he put the picture?
Simplify
8(x + 3)2/ 2(x + 3)
Answers
Answer:
4(x+
Step-by-step explanation:
8(x+3)^2/2(x+3)
[8(x + 3)(x + 3)]/2(x + 3)
8 ÷ 2 = 4
(x + 3)(x + 3) ÷ (x + 3) = (x + 3). In other words, we cancel one of the numerator factors.
Answer: 4(x + 3).
Answer:
4(x + 3)
or 4x + 12.
Step-by-step explanation:
8(x + 3)^2/ 2(x + 3)
x + 3 is common to both numerator and denominator of the fraction so they simplify to (x + 3)^2 / (x + 3) = (x+3).
the answer is 8 * (x + 3) / 2
= 4(x+ 3).
8 squared plus x squared = 17 squared solve for x
Answers
Answer:
x ≈ 15
Step-by-step explanation:
using Pythagoras' identity in the right triangle
a² + b² = c²
with a = 8, b = x , c = 17
8² + x² = 17²
64 + x² = 289 ( subtract 64 from both sides )
x² = 225 ( take square root of both sides )
[tex]\sqrt{x^2}[/tex] = [tex]\sqrt{225}[/tex]
x = 15
Describe or show how to determine the average rate of change between x = 2 and x = 4 for the function f(x) = 2x3 + 1. Include the average rate of change you found in your answer.
Answers
The average rate of change on the interval [2, 4] is 56
How to find the average rate of change on the given interval?
Here we have the function:
f(x) = 2x^3 + 1
And we want to find the rate of change on the interval [2, 4].
Remember that for a function f(x) the rate of change on an interval [a, b] is.
R = ( f(b) - f(a))/(b - a)
Then in this case, the rate of change is:
R = [ f(4) - f(2)]/[4 - 2] = ( 2*4^3 + 1 - 2*2^3 - 1)/2 = (4^3 - 2^3) = 56
So the rate is 56.
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Find the zeros of the quadratic equation: y = x^2 + 64
Answers
Answer: X=-8
Step-by-step explanation:
(x+8)(x+8)= 0
x=-8
Tickets for the school's jazz concert are $4 for students and $8 for all others. if they sold 40 tickets for opening night for a total of $220, how many students were attendance?
Answers
165
,
000
.
Also, there are a total of
8000
tickets.
Let the number of $
15
tickets be
x
Therefore, the number of $
25
tickets will be
8000
−
x
As, the total amount is $
165
,
000
, we can write that
x
∗
15
+
(
8000
−
x
)
∗
25
=
165
,
000
15
x
+
200
,
000
−
25
x
=
165
,
000
10
x
=
35
,
000
x
=
3
,
500
Number of $
25
tickets =
8000
−
3
,
500
=
4
,
500
Therefore, there are
3
,
500
$
15
ticekts and
4
,
500
$
25
tickets.