The transformation required to obtain the graph of the function f(x) from the graph of the function g(x) is by stretching the function g(x) horizontally by 3.
What is Transformation of Functions?When a function is transformed, the curve that represents the graph either "moves to the left/right/up/down," "it expands or compresses," or "it reflects." By moving, extending, compressing, or reflecting the curve rather than directly graphing the function from scratch, function transformations are particularly useful for graphing the functions.
Given:
[tex]f(x) =[/tex] [tex]cos(\frac{x}{3} )[/tex]
[tex]g(x) = cos x[/tex]
As g(x) is the parent function of f(x)
⇒ [tex]f(x) = g( \frac{x}{3})[/tex]
given function [tex]g(x) = cos x[/tex]
Substituting the value of x as [tex]\frac{x}{3}[/tex]
we get,
⇒ [tex]g(\frac{x}{3} ) = cos (\frac{x}{3} )[/tex]
Therefore, the transformation required to obtain the graph of the function f(x) from the graph of the function g(x) is by stretching the function g(x) horizontally by 3.
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Create an equivalent expression for 9−7 • 95.
−9^2
one over nine raised to the second power
one over nine raised to the power of negative two
9^2
The equivalent expression of 9^-7 * 9^5 is 1/9^2
How to create an equivalent expression?The expression is given as
9^-7 * 9^5
Apply the law of indices.
So, we have
9^-7 * 9^5 = 9^(-7 + 5)
Evaluate the sum
9^-7 * 9^5 = 9^-2
Rewrite as
9^-7 * 9^5 = 1/9^2
Hence, the equivalent expression of 9^-7 * 9^5 is 1/9^2
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A student takes out 2 loans to pay for college. One loan at 9% interest and the other at 12% interest.
The total amount borrowed is $65,000, and the interest after 1 year for both loans is $6,360.
Find the amount of each loan.
The loan amount at 9% interest is $48,000.
The loan amount at 12% interest is $17,000
What are the loan amounts?The first step is to form a system of equations that can be used to determine the required values:
0.09a + 0.12b = $6,360 equation 1
a + b = $65,000 equation 2
Where:
a = amount of the loan at 9% interest
b = amount of the loan at 12% interest
What is each loan amount?Multiply equation 2 by 0.09
0.09a + 0.09b = 5850 equation 3
Subtract equation 3 from equation 2
0.03b = 510
Divide both sides of the equation by 0.03
b = 510 / 0.03
b = $17,000
Subtract 17,000 from 65,000
a = 65,000 - 17,000
a = $48,000
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Write the Write the rational number -3.5
using quotients of the form
. Use the integers below.rational number using quotients of the form . Use the integers below.
The quotient form of given rational number is -7/2.
Given the rational number is -3.5.
Here, we want to write the quotient form of the given rational number.
rational numbers, in arithmetic, a number that can be expressed as the quotient p/q of two integers such that q ≠ 0.
Number 3.5 is a rational number. As we know rational numbers can also be expressed as decimals with repeating digits after the decimal point. The number7/2 is the ratio of two integers that are 7 integers divided by 2 integers and expressed in fraction (as p/q where q is not equal to 0).
Hence, the quotient form of the given rational number -3.5 is -7/2.
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Which linear equation shows a proportional relationship?
y equals negative 2 times x minus one third
y equals one third times x minus 1
y equals five sixths times x
y equals 5 times x plus 3
The proportional relation is the third one.
y = (5/6)*x
Which linear equation shows a proportional relationship?A general linear equation in the point-slope form is written as:
y = a*x + b
Where the a is the slope, and b is the y-intercept.
Particularly, a proportional relation is a linear equation where the y-intercept is equal to zero
y = a*x
And in this case, the slope is also called a constant of proportionality.
Then from the given options, the one that is a proportional relation is:
y = (5/6)*x
Which is the third option, counting from the top.
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What is 333 divided by 666
Answer:
333 ÷ 666 = 0.5
Step-by-step explanation:
Hope it helps!!! :)
Answer: 0.5
Step-by-step explanation:
Melissa bought 36 pine seedlings and 30 juniper seedlings to plant in rows on her tree farm. She wants each row to have the same number of seedlings. She wants only one type of seedling in each row. What is the greatest number of seedlings she can plant in each row? How many rows of each type of tree will there be? Each row will contain rows of juniper seedlings. seedlings.
She can plant maximum of 6 seedlings in each row. There can be 6 rows of pine seedlings and 5 rows of juniper seedlings.
The Highest Common Factor (HCF) of two numbers is the highest possible number that divides both the numbers completely.
Given: 36 pine seedlings and 30 juniper seedlings and Melissa wants each row to have the same number of seedlings with only one type of seedling in each row.
The greatest number of seedlings that can be planted in each row can be calculated by HCF.
HCF of 36 and 30:
36= 2*2*3*3
30=2*3*5
HCF is 2*3=6
Number of rows of pine seedlings= [tex]\frac{36}{6}[/tex]
=6
Number of rows of juniper seedlings= [tex]\frac{30}{6}[/tex]
=5
Hence, she can plant 6 seedlings in a row. There will be 6 rows of pine seedlings and 5 rows of juniper seedlings.
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Which point is an x-intercept of the quadratic function f(x) = (x + 6)(x – 3)?
(0,6)
(0,–6)
(6,0)
(–6,0)
Answer:
( -6 , 0 )
Step-by-step explanation:
the other one would be ( 3 , 0 ) but hope this helps !!
Simplify by reducing the index of th
21/ 15
√X
Answer:
simplify the reducing the index of the
21/15√x
Step-by-step explanation:
Answer:
26
Step-by-step explanation:
The graph of the function f(x) = (x + 2)(x + 6) is shown below.
On a coordinate plane, a parabola opens up. It goes through (negative 6, 0), has a vertex at (negative 4, negative 4), and goes through (negative 2, 0).
Which statement about the function is true?
The function is positive for all real values of x where
x > –4.
The function is negative for all real values of x where
–6 < x < –2.
The function is positive for all real values of x where
x < –6 or x > –3.
The function is negative for all real values of x where
x < –2.
The correct statement regarding the graph of the function f(x) = (x + 2)(x + 6) is given by:
The function is negative for all real values of x where -6 < x < -2.
What is the missing information?The graph of the function f(x) = (x + 2)(x + 6) is missing, and is given at the end of the answer.
When a function is positive and when it is negative?We have to look at the graph of the function relative to the x-axis, as follows:
A function is positive when it is above the x-axis.A function is negative when it is below the x-axis.Hence, for function f(x) = (x + 2)(x + 6), we have that:
It is positive for x < -6 and x > -2.It is negative for -6 < x < -2.Hence the correct statement for the signal of the function is given as follows:
The function is negative for all real values of x where -6 < x < -2.
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Parallelogram+RSTU+is+rotated+180°+clockwise+about+the+origin.+How+many+pairs+of+parallel+sides+ Does the rotated figure have
RSTU ≅ R'S'T'U' and R'S'T'U' is also a parallelogram with two pairs of parallel sides.
Given that, parallelogram RSTU is rotated 180° clockwise about the origin.
We need to find how many pairs of parallel sides the rotated figure has.
What is the rotation of 180°?Rotation of a point through 180°, about the origin when a point M (h, k) is rotated about the origin O through 180° in an anticlockwise or clockwise direction, it takes the new position M' (-h, -k).
The given transformation was performed on parallelogram RSTU = 180° clockwise rotation.
Given that a rotation is a form of rigid transformation, the shape and size of the preimage RSTU will be equal to the shape and size of the image R'S'T'U'.
Therefore, RSTU ≅ R'S'T'U' and R'S'T'U' is also a parallelogram with two pairs of parallel sides.
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Your question is incomplete, probably the complete question/missing part is:
Parallelogram RSTU is rotated 180° clockwise about the origin. How many pairs of parallel sides does the rotated figure have?
How do I simplify this?
Answer:
Hello,
Step-by-step explanation:
[tex]\dfrac{1}{\sqrt{1} +\sqrt{2} } =\dfrac{\sqrt{2} -\sqrt{1}}{(\sqrt{2} +\sqrt{1})*(\sqrt{2} -\sqrt{1}) } =\dfrac{\sqrt{2} -1}{2-1} =\sqrt{2} -1\\\\\dfrac{1}{\sqrt{2} +\sqrt{3} } =\dfrac{\sqrt{3} -\sqrt{2}}{(\sqrt{3} +\sqrt{2})*(\sqrt{3} -\sqrt{2}) } =\dfrac{\sqrt{3} -\sqrt{2}}{3-2} =\sqrt{3} -\sqrt{2}\\\\\\\dfrac{1}{\sqrt{n-1} +\sqrt{n} } =\dfrac{\sqrt{n} -\sqrt{n-1}}{(\sqrt{n} +\sqrt{n-1})*(\sqrt{n} -\sqrt{n-1}) }=\sqrt{n} -\sqrt{n-1}\\\\[/tex]
[tex]\\\dfrac{1}{\sqrt{1} +\sqrt{2} } +\dfrac{1}{\sqrt{2} +\sqrt{3} } +...+\dfrac{1}{\sqrt{n-1} +\sqrt{n} } =\boxed{\sqrt{n} -1}\\[/tex]
Please help me, I need it right now
Answer:
Step-by-step explanation:
instead x in f(x) we put g(x) in it.
f(g(x))= 3(7x-3)+1
=21x - 9 +1= 21x -8
What are the correct answers?
Answer:
It has only one answer which is 'The decimal is non-terminating'
Which one is function?
Answer:
a
Step-by-step explanation:
there are not two points on the same line.
Find the perimeter or circumference and area of each figure if each unit on the
graph measures 1 centimeter. Round answers to the nearest tenth, if necessary.
The perimeter or circumference and area of each figure if each unit on the graph measures 1 centimeter is 18.
The area of a circle is π[tex]r^2[/tex]
The area of a triangle is 1/2×base×height
The area of the rectangle is length×breadth
The perimeter of a circle is 2πr
so, Area of Triangle =1/2×b×h
1/2×4×9=18
A rectangle is a quadrilateral with all angles equal and opposing sides equal and parallel. There are numerous rectangular items all around us. Each rectangle shape has two dimensions: length and breadth. The length of the rectangle is known as the length, while the width is known as the width.
A rectangle is a closed two-dimensional shape with four sides. A rectangle's opposite sides are equal and parallel, and all of its angles are 90°. Examine the rectangle below to observe its form, sides, and angles.
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I need help to answer this question please 3(4x−1)=21
Answer: x=1.75
Step-by-step explanation:
Multiply: 12x-3=21
Subtract: 12x=21
Divide: 21/12= 1.75
Final Answer: X = 1.75
Determine whether the following possible responses should be classified as interval, nominal, ratio or ordinal data The starting salaries of new phd graduates from a statistics program
The starting salaries of new phd graduates from a statistics program illustrates a ratio data.
How to explain the information?The four basic levels of measuring scales—nominal, ordinal, interval, and ratio are used to collect data in the form of multiple-choice questions on surveys and questionnaires.
Each scale serves the same purpose as the preceding scale, and all survey question scales are incremental levels of measurement.
Nominal: the data can only be categorized.
Ordinal: the data can be categorized and ranked.
Interval: the data can be categorized and ranked, and evenly spaced.
Ratio: the data can be categorized, ranked, evenly spaced and has a natural zero.
Therefore, the starting salaries of new phd graduates from a statistics program illustrates a ratio data.
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A ball is accidentally dropped from the top of a tall building. It took 3.0 secs for the ball to hit the ground. The acceleration of gravity is g = 10 m/sec². Find the initial height from which the ball was dropped.
Answer:
[tex]{ \rm{s = ut + \frac{1}{2} {at}^{2} }} \\ \\ { \rm{h = 0 + \frac{1}{2} \times 10 \times {3}^{2} }} \\ \\ { \tt{h = 5 \times 9}} \\ { \tt{h = 45 \: m}}[/tex]
the sum of a number and three is forty-one find the number
Answer:
38
Step-by-step explanation:
38+3=41
thats the answer
brainliest please
(7 x 10^7) divide (2 x 10^5)
Answer:350
Step-by-step explanation:
(7 x 10^7)/(2 x 10^5)=350
70000000/200000=350
The number ends in the hundredths place.
2 is the nearest one when rounding
When the number ends in the hundredths place and 2 is the nearest one when rounding, the number is 4.26.
How to illustrate the information?It should be noted that from the information, the number ends in the hundredths place and 2 is the nearest one when rounding.
Therefore, the number will be:
4.26
Therefore, when the number ends in the hundredths place and 2 is the nearest one when rounding, the number is 4.26
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Drag the numbers to match the rule
The number ends in the hundredths place.
2 is the nearest one when rounding
4,2, 6, decimal (.).
what is the measure of angle COW?
Answer: c: 52
Step-by-step explanation:
the angles are congruent as shown by the hashmarks in the arks so you just need to double it
Answer:
c. 52°
Step-by-step explanation:
Since part of the angle is given (26°) and both parts of the angle are equal. 26° + 26° = 52°
What are the coordinates of the y intercept of the function y=|3x-10|+1
Answer: (0,11)
Step-by-step explanation:
The y-intercept is when x is equal to 0, so we can just plug that into get the y-coordinate.
y = |3x - 10| + 1
y = |-10| + 1
y = 10 + 1
y = 11
the formula for the volume of a rectanglular prism is given by
V=lwh
where V is volume, l is length, w is width, and h is height.
a) solve for L if V=120, w=6, and h=4
l=
b) solve for L in general.
l=
Answer:
Step-by-step explanation:
V=lwh
120=l(6)(4)
120=24I
[tex]\frac{120}{24} =\frac{24I}{24} \\I=5[/tex]
Answer:
V=lwh
120=l(6)(4)
120=24I\begin{gathered}\frac{120}{24} =\frac{24I}{24} \\I=5\end{gathered}
Which function has the following domain and range?
Domian {-12, -7, 0, 4, 12}
Range { 0, 1, 2}
A) {(-12, 12), (0,2)}
B) (0,4), (2,12), (1,-7), (0,-12), (1,0)}
C) {(-12,0), (-7,1), (0,2), (-4,5), (3,-1)}
D) {(4,1), (-7,0), (12,2), (0,0), (-12,1)}
D. The function {(4,1), (-7,0), (-12,2), (0,0), (-12,1)} has the given domain {-12, -7, 0, 4, 12} and range { 0, 1, 2}.
What is domain and range ?The domain is the set of all inputs which has an output or range.The range of a function is the set of all outputs form which the domain is defied.
According to the given question domain and range of a function are given they are { -12, -7, 0, 4, 12 } and { 0, 1, 2 }.
This can be written an an ordered pair as { (-12,0), (-12,1), (-12,2), (-7,0), (-7,1), (-7,2), (0,0), (0,1), (0,2), (4,0), (4,1), (4,2), (12,0), (12,1), (12,2) }.
From the given options we can observe that in option D. which has ordered pairs { (4,1), (-7,0), (-12,2), (0,0), (-12,1) }.
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Multiply these polynomials using the FOIL method and the answer should be a polynomial as well.
[tex]( m^{\frac{1}{3} } + y^{-\frac{1}{2} } )^{2}[/tex]
The answer to the expression is m^2/3 + 2 * m^1/3 * y^(-1/2) + 1/y
What is FOIL?FOIL is a mnemonic for the standard method of multiplying two binomials, hence the method may be referred to as the FOIL method. The word FOIL is an acronym for the four terms of the product: First (“first” terms of each binomial are multiplied together)
given:
(m^1/3 + y^(-1/2))^2
we can write it as
(m^1/3 + y^(-1/2))*(m^1/3 + y^(-1/2))
=m^1/3 * m^1/3 + m^1/3 * y^(-1/2) + y^(-1/2) * y^(-1/2) + y^(-1/2)*m^1/3
=m^2/3 + m^1/3 * y^(-1/2) + 1/y + y^(-1/2)*m^1/3
= m^2/3 + 2 * m^1/3 * y^(-1/2) + 1/y
Hence, the answer to the expression is m^2/3 + 2 * m^1/3 * y^(-1/2) + 1/y
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A bag contains 2 gold marbles, 7 silver marbles, and 21 black marbles. Someone offers to play this game: You randomly select one marble from the bag. If it is gold, you win $4. If it is silver, you win $2. If it is black, you lose $1. What is your expected value if you play this game?
The expected value if i play this game is 1/30 dollars.
What is probability ?Probability is the occurrence of a certain event out of the total events that can happen on a given satiation.
According to the given question A bag contains 2 gold marbles, 7 silver marbles, and 21 black marbles.
No. of sample space N(s) = 2 + 7 + 21 = 30.
No. of gold marbles N(g) = 2.
No. of silver marbles N(sil) = 7.
No. of black marbles N(b) = 21.
We know,
P(g) = N(g)/N(s) = 2/30 = 1/15.
P(sil) = N(sil)/N(s) = 7/30.
P(b) = N(b)/N(s) = 21/30 = 7/10.
Given if it is gold, you win 4dollars. If it is silver, you win 2 dollars. If it is black, you lose 1 dollars.
The expected value if you play this game is
= 4P(g) + 2P(sil) - 1P(b)
= 4(1/15) + 2(7/30) - 1(7/10).
= 4/15 + 14/30 - 7/10.
= (8+14-21)/30.
= 1/30 dollars.
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The account balance of each of three children at the end of a month is shown below:
Kyle has −$2.25
Jason has −$2.00
Sue has as much savings in her account as the amount Kyle owes the bank.
Part A: On a blank paper, draw a number line from −4 to +4. Plot points on the number line to show the account balances of the three children. Label the points using the name of each child. Describe in detail how you created and labeled this number line, and what it looks like in detail. (5 points)
Part B: Determine whether Kyle or Jason owes the bank more. Use absolute values and inequalities to write statements that justify your conclusion. (5 points)
The drawing of the number line representing the bank balances is attached below . Kyle owes the bank more money than Jason.
The number line a physical representation of all real numbers. A number line is basically a graph of all real numbers. A number line is a representation of a graduated straight line that is used to represent real numbers visually. It is assumed that every point on a number line corresponds to a real number, and that every real number corresponds to a point.
On the number line all the values of the bank balances of the 3 siblings are given.
Kyle owes the bank $2.25 , therefore Sue has $2.25 in her bank account.
Now we can see in the number line that -2.25 is to the left of -2.0 ,
therefore we can say that:
|-2.25| > |-2.00|
as the absolute value of the given balance .
But -2.25 < -2.00
Hence Kyle owes more money to the bank as represented on the number line.
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The zeros of a 5-th degree polynomial are 2,i,-2i. Find the remaining zeros.
Answer:
-i,2i
Step-by-step explanation:
zeros(2,i,-2i {5th degree}
then the conjugate zeroes are,
I,2i {conjugate zeros}
so the answer is i, 2i
1.2 x (-5) =
I had -60 but it says the answer was incorrect and I’m not sure what I’m doing wrong. Any explanation on what I’m doing wrong?
Answer: -6, not 60
Step-by-step explanation:
Negative+Positive=Negative
Positive+Positive=Negative
Negative+Negative=Positive
