Answers
Find vertex
f(0)=(0)So
(0,0) is the vertexThe graph shifted 3 units right.
So new translation
g(x)=|x-3|Find y intercept
g(0)=|-3|=3But it's at (0,1) approximately
So compression factor
1/3Now last equation
g(x)=1/3|x-3|Accurate oneTake (-4,2)Find value
g(-4)=|-7|=7So compression factor
2/71/3.5So accurate equation is
1/3.5|x-3|Answer:
[tex]g(x)=\dfrac{2}{7}|x-3|[/tex]
Step-by-step explanation:
Translations
For [tex]a > 0[/tex]
[tex]f(x-a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units right}[/tex]
[tex]y=a\:f(x) \implies f(x) \: \textsf{stretched parallel to the y-axis by a factor of}\:a[/tex]
-----------------------------------------------------------------------------------------
Parent function: [tex]f(x)=|x|[/tex]
The vertex of the parent function is at (0, 0) as [tex]f(0)=|0|=0[/tex]
From inspection of the graph, the vertex of the transformed function is at (3, 0). Therefore, there has been a translation of 3 units right:
[tex]\implies g(x)=f(x-3)=|x-3|[/tex]
(There has not been any vertical translation since the y-value of the vertex of the parent function and the translated function is the same)
From inspection of the graph, we can see that it has been stretched parallel to the y-axis:
[tex]\implies g(x)=a\:f(x-3)=a|x-3|[/tex]
The line goes through points (10, 2) and (-4, 2).
Substituting one of these points to find a:
[tex]\implies a|10-3|=2[/tex]
[tex]\implies 7a=2[/tex]
[tex]\implies a=\dfrac{2}{7}[/tex]
Therefore,
[tex]g(x)=\dfrac{2}{7}|x-3|[/tex]
Related Questions
Express tan j as a fraction in simplest terms
Answers
From the figure, the value of tan j is 13/9
How to determine the value of tan j?The tangent of an angle is calculated using:
tan(j) = opposite/adjacent
From the figure, we have:
opposite = 13
adjacent = 9
So, we have:
tan(j) = 13/9
Hence, the value of tan j is 13/9
Read more about tangent function at:
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What is the surface area of the Right Cylinder below
Diameter AB=22, and height BC=8.
Answers
Hope this helps, so sorry if I am wrong!
Answer:
A ≈ 1313.19
Step-by-step explanation:
By using the formula [tex]A = 2 \pi r h + 2 \pi r^{2}[/tex] we can just fill in the information with what we know, which is Diameter = 22, Radius = Diameter/2 = 11. The height is 8. So in doing so we get [tex]A = 2\pi (11)(8)+2\pi (11)^{2}[/tex], which
equals ≈ [tex]1313.18573[/tex].
A sample of 100 cars driving on a freeway during a morning
commute was drawn, and the number of occupants in each car was recorded. The
results were as follows:
Occupants: 1 2 3 4 5
Number of cars: 76 13 6 3 2
Find the...
a) mean
b) standard deviation
c) median
d) What proportion of cars had more than the mean number of occupants
e) What proportion of cars was the number of occupants more than one
standard deviation greater than the mean?
f) What proportion of cars was the number of occupants within one standard
deviation of the mean?
Answers
Answer:
a) mean = 1.42 occupant/car
b) standard deviation = 0.89 occupants
c) median = 1 occupant
d) The proportion of cars had more than the mean number of occupants is 0.24
e) The proportion of cars with the number of occupants more than one
standard deviation greater than the mean is 0.11
f) The proportion of cars with the number of occupants within one standard
deviation of the mean is 0.89
Step-by-step explanation:
Attached work:
An advertisement for a lawn service claims their fertilizer treatment kills weeds in half the
time. When you read the small print at the bottom of the ad, you see that they asked 20 of their
long-term customers to estimate how long it took until their weeds died out before employing
the lawn service. On average, the customers said it took 4 weeks for all the weeds to die before
the service. The company knows that their fertilizer treatment can kill weeds in 2 weeks. Why
is this advertisement misleading?
Answers
The reason why the advertisement misleading is: Number of size which is 20 is a very sample size to make this conclusion valid.
What is advertisement?Advertisement can be defined as the process of creating awareness about a product so as to increase sales.
Based on the given scenario the advertisement is misleading based on the following reasons:
The sample size which is 20 is a very small sample size to make this conclusion valid. The customers said it will take 4 weeks for all the weeds to die before while the company on the other hand knew that the fertilizer treatment can kill weeds in 2 weeks.Therefore The reason why the advertisement misleading is: Number of size which is 20 is a very sample size to make this conclusion valid.
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Which inequality is graphed on the number line?
Answers
Answer:
Option #4: [tex]4\left(x+8\right)-10\ge 42[/tex]
Step-by-step explanation:
[tex]4\left(x+8\right)-10\ge 42[/tex]
x ≥ 5
Answer:
4th option
Step-by-step explanation:
the inequality shows x ≥ 5
solving the inequalities
- 7(3x - 7) + 21 ≥ 50
- 21x + 49 + 21 ≥ 50
- 21x + 70 ≥ 50 ( subtract 70 from both sides )
- 21x ≥ - 20
divide both sides by - 21 reversing the symbol as a result of dividing by a negative quantity , then
x ≤ [tex]\frac{20}{21}[/tex] ← not the required solution
--------------------------------------------------
- 4(- x + 8) - 10 ≤ 8
4x - 32 - 10 ≤ 8
4x - 42 ≤ 8 ( add 42 to both sides )
4x ≤ 50 ( divide both sides by 4 )
x ≤ 12.5 ← not the required solution
--------------------------------------------------
- 7(3x - 7) + 21x ≥ - 50
- 21x + 49 + 21x ≥ - 50 ( subtract 49 from both sides )
0 ≥ - 99 ← not the required solution
-----------------------------------------------------
4(x + 8) - 10 ≥ 42
4x + 32 - 10 ≥ 42
4x + 22 ≥ 42 ( subtract 22 from both sides )
4x ≥ 20 ( divide both sides by 4 )
x ≥ 5 ← Required solution
Given the equation y= 1/2x + 9, what is the y-intercept?
Answers
Answer:
9
Step-by-step explanation:
Y intercept when x = 0
Y = 9
where m is slope and b is y-intercept
Hence,
Here given equation: y = ½ x + 9
Identify,
slope: ½ and y-intercept: 9
What is the range of possible values for x?
The diagram is not to scale.
a) 12 < x < 48
b) 0 < x < 10
c) 10 < x < 50
d) 10 < x < 43
Answers
Answer:
option A is the answer of given question 12 less than its greater than 48
please help! will give brainliest!
Answers
Arc PL = 62
Arc QPS = 258
Explanation:
17. 5x-19 = 2x+11
18. 16x - 28 = 180.
y =x- 6 intercept with graph
Answers
Answer:
y-intercept, when x = 0, y = -6
x-intercept, when y = 0, x = 6
Step-by-step explanation:
y-intercept, when x = 0, y = -6
x-intercept, when y = 0, x = 6
Which of these statements is true for f(x) = 4.2?
A. The y-intercept is (0,4).
B. It is always decreasing.
O C. The domain is x > 0.
D. The y-intercept is (0,1).
Answers
Answer:
A
Step-by-step explanation:
I think it's A hope that helps
A bike rental company charges a fee per hour. The charge, in dollars, is the same each hour. The ordered pairs (3, 13.50) and (5, 22.50) represent the corresponding hours, x, and cost, y. What is the rate of change of the function expressed as a unit rate?
Answers
If the function is y = 4.5x. Then the rate of change of the function expressed as a unit rate will be 4.5.
What is the linear system?A linear system is one in which the parameter in the equation has a degree of one. It might have one, two, or even more variables.
A bike rental company charges a fee per hour.
The charge, in dollars, is the same each hour.
The ordered pairs (3, 13.50) and (5, 22.50) represent the corresponding hours, x, and cost, y.
Then the linear equation is given as
[tex]\begin{aligned} \rm y - 22.5 &= \rm \dfrac{22.5 - 13.5}{5 - 3} (x- 5)\\\\\rm y - 22.5 &= \rm 4.5x - 22.5\\\\\rm y &= \rm 4.5x \end[/tex]
Then the rate of change of the function expressed as a unit rate will be
[tex]\rm \dfrac{dy}{dx} = \dfrac{d}{dx} (4.5x )\\\\\dfrac{dy}{dx} = 4.5[/tex]
More about the linear system link is given below.
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Two squares have areas of 4 cm?
and
16 cm?. What is the ratio of the side length of
the smaller square to the side length of the
larger square?
Answers
Answer:
1/2
Step-by-step explanation:
First square area = 4cm^2, thus the side length is 2cm
Second square area = 16cm^2, thus the side length is 4cm
This gives a ratio of 2/4, simplifying yields 1/2
find the circumference of the circle 5cm
Answers
Area of the rectangle is 126 sqaure meters. Length of the rectangle is 4 more than 2 times its width. Find length and width of the rectangle
Answers
Answer:
Length of the rectangle = 18 mWidth of the rectangle = 7 mStep-by-step explanation:
Given:
Area of the Rectangle = 126 m²Length of the rectangle is 4 more than 2 times its width.To Find:
Length and widthSolution:
Let's assume :
Width of the rectangle = xLength of the recangle = 2x + 4We know that,
[tex]\: \: \dashrightarrow\sf \: \: \: Length \times Width = Area_{(Rectangle)} \\ \\ [/tex]
On Substituting the required values, we get:
[tex] \\ \: \: \dashrightarrow\sf \: \: \:(2x+ 4)(x) = 126 \\ \\ \\ \: \: \dashrightarrow\sf \: \: \:2 {x}^{2} + 4x = 126 \\ \\ \\ \: \: \dashrightarrow\sf \: \: \:2 {x}^{2} + 4x - 126 =0 \\ \\ \\ \: \: \dashrightarrow\sf \: \: \:2( {x}^{2} + 2x - 63) = 0 \\ \\ \\ \: \: \dashrightarrow\sf \: \: \: {x}^{2} + 2x - 63 = 0 \\ \\ \\ \: \: \dashrightarrow\sf \: \: \: {x}^{2} - 7x + 9x - 63 = 0 \\ \\ \\ \: \: \dashrightarrow\sf \: \: \:x(x - 7) + 9(x - 7) \\ \\ \\ \: \: \dashrightarrow\sf \: \: \:(x - 7)(x + 9) = 0 \\ \\ \\ \: \: \dashrightarrow\sf \: \: \: \purple {x = 7 \: or \: - 9} \\ \\ [/tex]
Length of the side of the rectangle can't be negative. So, x = 7
Hence,
Width of the rectangle = x = 7 mLength of the rectangle = 2x + 4 = 2(7) + 4 = 18 mAnswer:
length = 18 m
width = 7 m
Step-by-step explanation:
Finding the length and width of rectangleLet the width of the rectangle = w m
Length = ( 2w + 4) m
Area of rectangle = 126 square meters
length * width = 126
(2w + 4) * w = 126
2w² + 4w = 126
2w² + 4w - 126 = 0
Divide the entire equation by 2
w² + 2w - 63 = 0
Sum = 2
Product = -63
Factors = 9 , (-7) { 9 +(-7) = 2 & 9*(-7) = -63}
w² + 9w - 7w - 63 = 0 {rewrite the middle term using the factors}
w( w + 9) - 7(w + 9) =0
(w +9)(w - 7) = 0
{Ignore w +9 = 0, as measurement will not come in negative}
w - 7 = 0
w = 7
length = 2w + 4
= 2*7 + 4
= 14 + 4
= 18
length = 18 m width = 7 mY’all what is it 87 divided by 3
Answers
Answer:
29
Step-by-step explanation:
87 / 3 = 29
If you can use a calculator it shouldn't be on brainly...
Answer:
Algebraic Expressions
This calculator builds algebraic expressions based on word representations of numbers using the four operators and the words that represent them(increased,product,decreased,divided,times) Also known as Mathematical phrases
Factorials
Calculates the following factorial items:
* A factorial of one number such as n!
* A factorial of a numerator divided by a factorial of a denominator such as n!m!/a!b!
* Double Factorials such as n!!
* Stirlings Approximation for n!
Step-by-step explanation:
Ty pa follow narin po brainly and thank you for the points
1, 8, 5, 4, 1, 8, 5, 4 mean media mode
Answers
Answer:
see below
Step-by-step explanation:
mean: 4.5
median: 1,1,4,4,5,5,8,8
mode: 4.5
The solid below is made from cubes.
Find Its volume.
Answers
Answer: The answer is 30 inches.
Answer:
36
Step-by-step explantion:
1 x 1 = 1 so each cube is 1 square inch
2 x 6= 12
12 x 3 = 36
If f{x)=-4(x-6)+15,what is f(3)?
A -3 B3 C27 D51
Answers
Answer:
C. f(3)=27
Step-by-step explanation:
f(3)=-4(3-6)+15
f(3)=-4(-3)+15
f(3)=12+15
f(3)=27
Step-by-Step Explanation:
=> f(x) = -4(x - 6) + 15
Therefore, f(3) means x = 3.
Substituting the value of ‘x’ :-
=> -4(x - 6) + 15
= -4(3 - 6) + 15
= -4 * 3 + -4 * -6 + 15 (Opening brackets)
= -12 + 24 + 15
= 12 + 15
= 27
Therefore, f(3) = 27
A wiring job requires 5,127 feet of cable. If the cable comes in 250-foot coils, how many coils of cable are required?
Answers
Answer:
20.58 (21)
Step-by-step explanation:
5127/250 = 20.58
if the coils are only be imported in full form your gonna need 21
Answer:
21 cables
Step-by-step explanation:
Because the cables come in 250-foot coils, you cannot have a piece of one cable. So, if you take the total amount of cable you need (5,127 feet) and divide it by how long a single cable is (250 feet).
5,127 divided by 250 is 20.508, but you cannot have a piece of one cable. So, you round up to the nearest whole number, 21.
figure these question out
Answers
Answer:
5) 3x = 135° and x = 45°
6) (8x + 5) = 61° and (3x + 8) = 29°
Step-by-step explanation:
5) supplementary of two angles whose sum is 180°
3x + x = 180 → 4x = 180
4x / 4 = 180 / 4
x = 45
3x = 3(45)
135°
6) complimentary of two angles whose sum is 90°
(8x + 5) + (3x + 8) = 90 → 11x + 13 = 90
11x + 13 - 13 = 90 - 13
11x = 77
11x / 11 = 77 / 11
x = 7
(8x + 5) = 8(7) + 5
56 + 5 = 61
(3x + 8) = 3(7) + 8
21 + 8 = 29
The ratio of a green apple to red apple is 2:3. There are 78 red apples, what is the total number of apples in the store?
Answers
Answer:
The total is 130 apples.
Step-by-step explanation:
If the ratio of green to red apples is 2:3 and there is a total of 78 red apples, we can divide 78/3 which is 26. Since this is 1/3 of 78 we can multiply that by 2 to get 52 which is 2/3 of 78 which is the total amount of green apples. We dont stop here however. The question askes for the total amount of apples so we att 52 and 78 to get 130 which is the total amount of apples.
78/3 = 26
26*2 = 52
52+78 = 130
This is a program for development that lists what an athlete hopes to do in order to meet their goals.
A. Feedback
B. Action Plan
C. none of these
D. Area for improvement
Answers
Answer:
B. Action PlanStep-by-step explanation:
#hope it helps!
Answered by ReyvREYV111
Factor the polynomial
Answers
Answer:
(3x + 5)(9x^2 - 15x + 25)
Step-by-step explanation:
27x^3 + 125
= (3x)^3 + 5^3
= (3x + 5) ((3x)^2 - (3x)(5) + 5^2)
= (3x + 5)(9x^2 - 15x + 25)
FYI: a³ + b³ = (a + b)(a² – ab + b²)
Answer:
(3x + 5)(9x² - 15x + 25)
Step-by-step explanation:
This is given in the form : a³ + b³
Identity :
a³ + b³ = (a + b)(a² - ab + b²)Solving :
27x³ + 125(3x)³ + (5)³(3x + 5)(9x² - 15x + 25)find the value of z
Answers
Check the picture below.
[tex]2x+15~~ = ~~\cfrac{(10x+20)-80}{2}\implies 4x+30=10x-60 \\\\\\ 4x+90=10x\implies 90=6x\implies \cfrac{90}{6}=x\implies \boxed{15=x} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{the whole circle is}}{z + 80 + (10x+20)}~~ = ~~\stackrel{degrees}{360}\implies z+80+[10(15)+20]~~ = ~~360 \\\\\\ z+250=360\implies \blacktriangleright~~ z=110 ~~\blacktriangleleft[/tex]
If the value of x is 15 degrees. Then the measure of the arc z will be 110 degrees.
What is a circle?It is the centre of an equidistant point drawn from the centre. The radius of a circle is the distance between the centre and the circumference.
The diagram is shown below.
[tex]\rm 2x + 15 = \dfrac{10x + 20 - 80 }{2}[/tex]
Then the value of x will be
4x + 30 = 10x - 60
6x = 90
x = 15
Then the value of (10x + 20) will be
(10x + 20) = 10 × 15 + 20
(10x + 20) = 150 + 20
(10x + 20) = 170
Then the measure of the arc z will be
z + 170 + 80 = 360
z = 110
More about the circle link is given below.
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1. A rectangle has a length of 5cm and a height of 4cm.
a. Find the area of the rectangle
b. Find the perimeter of the rectangle.
c. A scale factor of .5 is used to reduce the rectangle. What is the new area?
d. A scaled factor of 2 is used to increase the triangle. What is the new area?
Answers
Answer:
a
20cm squared
b
18cm
c
5cm
d
80cm
Step-by-step explanation:
a
Area is height multiplied by length in a regular quadrilateral
b
Perimeter is calculated by adding all the sides together
c
0.5 is effectively halving, so instead of 4 multiplied by 5 it is 2 multiplied by 2.5
d
2 is effectively doubling, so instead of 4 multiplied by 5 it is 8 multiplied by 10
Answer:
20 cm²18 cm5 cm²80 cm²Step-by-step explanation:
Q1(a)
Area = length x heightArea = 5 x 4Area = 20 cm²Q1(b)
Perimeter = 2(length + height)Perimeter = 2(5 + 4) = 2(9)Perimeter = 18 cmQ1(c)
New dimensions are : 5/2 = 2.5 and 4/2 = 2New Area = 2.5 x 2New Area = 5 cm²Q1(d)
New dimensions are : 2 x 5 = 10 and 2 x 4 = 8New Area = 10 x 8New Area = 80 cm²Expand:
[tex]f(z) = \frac{1}{z(z - 2)} [/tex]
for ;
[tex] |z| > 2[/tex]
Answers
Expand f(z) into partial fractions:
[tex]\dfrac1{z(z-2)} = \dfrac12 \left(\dfrac1{z-2} - \dfrac1z\right)[/tex]
Recall that for |z| < 1, we have the power series
[tex]\displaystyle \frac1{1-z} = \sum_{n=0}^\infty z^n[/tex]
Then for |z| > 2, or |1/(z/2)| = |2/z| < 1, we have
[tex]\displaystyle \frac1{z-2} = \frac1z \frac1{1 - \frac2z} = \frac1z \sum_{n=0}^\infty \left(\frac 2z\right)^n = \sum_{n=0}^\infty \frac{2^n}{z^{n+1}}[/tex]
So the series expansion of f(z) for |z| > 2 is
[tex]\displaystyle f(z) = \frac12 \left(\sum_{n=0}^\infty \frac{2^n}{z^{n+1}} - \frac1z\right)[/tex]
[tex]\displaystyle f(z) = \frac12 \sum_{n=1}^\infty \frac{2^n}{z^{n+1}}[/tex]
[tex]\displaystyle f(z) = \sum_{n=1}^\infty \frac{2^{n-1}}{z^{n+1}}[/tex]
[tex]\displaystyle \boxed{f(z) = \frac14 \sum_{n=2}^\infty \frac{2^n}{z^n} = \frac1{z^2} + \frac2{z^3} + \frac4{z^4} + \cdots}[/tex]
Can anyone help I’ve been struggling
Answers
explanation- 33^2 + 56^2 = 4225
square root of 4225 is 56
Joshua wants to buy a pair
of jeans for $45.00. The tax
rate is 3.4%. If Joshua has
$50, does he have enough
money to pay for the jeans?
Justify your answer.
Answers
Answer:
yes
Step-by-step explanation:
3.4% = .034
.034 x 45 = 1.53
1.53$ + 45$ = 46.53$
46.53$ > 50
yes, he dose have enough money
The perimeter of a rectangle is 72 cm one side is 3 times the length of the other form an equation and solve for the length and width
Answers
Answer:
2(length) +2(width)=perimeter
2(3(width))+2(width)=72
8×width=72
width=9
length=3×9=27
area=27×9
247=area
Step-by-step explanation:
what is a greatest common denominator?
Answers
Answer:
GCF
Step-by-step explanation:
sorry if you dont understand