HELP TO ASAP Compare the graph of f(x) with the graph of k(x) = 5(x-6)².
OA. The graph of k(x) is horizontally stretched by a factor of 5 and
shifted 6 units right.
OB. The graph of k(x) is vertically stretched by a factor of 5 and shifted
6 units right.
OC. The graph of k(x) is horizontally stretched by a factor of 5 and
shifted 6 units left.
Answers
Parent function
y=x²Now look the transformations
y=(x-6)²x is changed and shifted 6 units right
Then
y=5(x-6)²Horizontally Streched with a factor of 5
Answer:
B) The graph of k(x) is vertically stretched by a factor of 5 and shifted 6 units right.
Step-by-step explanation:
Translations
For a > 0
[tex]f(x+a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units left}[/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 (vertically) by a factor of}\:a[/tex]
[tex]y=f(ax) \implies f(x) \: \textsf{stretched parallel to the x-axis (horizontally) by a factor of} \: \dfrac{1}{a}[/tex]
Given functions:
[tex]f(x) = x^2[/tex]
[tex]k(x) = 5(x - 6)^2[/tex]
Parent function: [tex]f(x) = x^2[/tex]
Translated 6 units right: [tex]f(x-6)=(x-6)^2[/tex]
Then stretched vertically by a factor of 5: [tex]5f(x-6)=5(x-6)^2[/tex]
[tex]\implies 5f(x-6)=5(x-6)^2=k(x)[/tex]
Therefore, the graph of k(x) is vertically stretched by a factor of 5 and shifted 6 units right.
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Related Questions
PLEASE HELPP!!!!!
Question 9 of 13
Which of the following scatterplots represents the data shown below?
(1,31), (2,8), (3, 38), (4, 14), (5, 22), (6, 31), (7, 27), (8, 47),
(9,34), (10,3), (11, 33), (12, 35)
Answers
The attached graph below can represent the scatter plot of the points. the correct option is B.
How to find the function which was used to make graph?A graph contains data of which input maps to which output.
Analysis of this leads to the relations which were used to make it.
Given:
(1,31), (2,8), (3, 38), (4, 14), (5, 22), (6, 31), (7, 27), (8, 47), (9,34), (10,3), (11, 33), (12, 35)
The above points would be plotted using the following scale such as:
x: axis -> 1 interval = 10 units
y: axis -> 1 interval = 10 units
The attached graph below can represent the scatter plot of the points. the correct option is B.
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Which expression is equivalent to One-fifth (150 x minus 80 y + 50 minus 50 x minus 25 y + 20)?
20 x minus 21 y + 14
20 x + 11 y + 14
20 x minus 11 y + 6
20 x + 21 y + 6
Answers
Answer:
150 x - 80 y + 50 - 50 x - 25 y + 20
Arranging like terms
150 x - 50 x -25 y - 80y + 50 + 20
100x - 105 y + 70
5 ( 20x - 21y + 14)Answer:
20x - 21y + 14
Explanation:
[tex]\rightarrow \sf \dfrac{1}{5} (150x - 80y + 50 - 50x - 25y + 20)[/tex]
collect like terms
[tex]\rightarrow \sf \dfrac{1}{5} (150x-50x - 80y -25y + 50 + 20)[/tex]
add/subtract like terms
[tex]\rightarrow \sf \dfrac{1}{5} (100x - 105y+70)[/tex]
distribute inside parenthesis
[tex]\rightarrow \sf \dfrac{1}{5} (100x) + \dfrac{1}{5}( - 105y) + \dfrac{1}{5}(70)[/tex]
simplify the following
[tex]\rightarrow \sf 20x -21y + 14[/tex]
Select The correct answer.
Segment AB Is tangent to the circle at point B. Which equation describes the relationship between the tangent and secant line segments?
B
D
OA
(AD)² = (AC) (AB)
OB. (AB)2 = (AC)(CD)
OC. (AB)2 = (AC)(AD)
OD. AB=(AC + AD)
Answers
According to the tangent-secant theorem, the relationship of the tangent and secant in the given circle is: C. AB² = (AC)(AD).
What is the Tangent-Secant Theorem?The secant tangent theorem defines the relationship between the lengths of the secant and the tangent line segments when they meet outside a circle.
Based on the tangent-secant theorem, using the image given, the equation that describes the relationship of the tangent and secant in the given circle is:
C. AB² = (AC)(AD)
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Answer: C
Step-by-step explanation:
got it right on my test!!
The equation for the pH of a substance is pH = -log[H*], where H+ is the concentration of hydrogen ions. A basic
solution has a pH of 11.2. An acidic solution has a pH of 2.4. What is the approximate difference in the concentratic
of hydrogen ions between the two solutions?
1.6x10-9
O4.0x10-3
O 6.7x10-1
O 1.6x10¹11
Answers
The approximate difference in the concentration of hydrogen ions between the two solutions is 4.0×10⁻³
What is pH value?The pH of a solution is a measurement of the concentration of hydrogen ions in the solution, as well as its acidity or alkalinity. Normally, the pH scale ranges from 0 to 14.
pH value for basic solution = 11.2
pH value for acidic solution = 2.4
Concentration for a basic solution:
[tex]\rm = 10^{-11.2}[/tex]
[tex]= 6.309\times10^{-12}[/tex]
Concentration for an acidic solution:
[tex]\rm = 10^{-2.4}[/tex]
[tex]= 3.981\times10^{-3}[/tex]
Difference between the concentration:
[tex]= 3.981\times10^{-3}- 6.309\times10^{-12}[/tex]
[tex]= 3.98\times10^{-3}[/tex]
[tex]= 4\times10^{-3}[/tex]
Thus, the approximate difference in the concentration of hydrogen ions between the two solutions is 4.0×10⁻³
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Is AABCDEF? If so, identify the similarity postulate or theorem that
applies.
A
B
16 105⁰
36
с
D
4
LLI
E
9
-105⁰
F
OA. Similar - AA
OB. Similar - SSS
OC. Similar - SAS
OD. Cannot be determined
4
Answers
Answer:
C
Step-by-step explanation:
C is the correct answer as both triangles have a similar angle of 105⁰ and both side lengths of triangle ABC are being divided by 4 to have the same two side lengths as triangle DEF
The triangles ΔABC and ΔDEF are similar triangles by SAS theorem
What are similar triangles?If two triangles' corresponding angles are congruent and their corresponding sides are proportional, they are said to be similar triangles. In other words, similar triangles have the same shape but may or may not be the same size. The triangles are congruent if their corresponding sides are also of identical length.
Corresponding sides of similar triangles are in the same ratio. The ratio of area of similar triangles is the same as the ratio of the square of any pair of their corresponding sides
Given data ,
Let the first triangle be ΔABC
The measure of side AB = 16
The measure of side AC = 36
And , the measure of ∠ABC = 105°
Let the first triangle be ΔDEF
The measure of side DE = 16
The measure of side DF = 36
And , the measure of ∠DEF = 105°
Now , the ratio of sides of the triangles is given by
AB / DE = AC / DF
4/16 = 9/36
1/4 = 1/4
So , corresponding sides of similar triangles are in the same ratio
And , the measure of angles = 105°
Therefore , by SAS , Two sides are equal and the angle between the two sides is equal (SAS: side, angle, side)
Hence , they are similar triangles
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A carpenter wants to cut an 84 inches long board into two-pieces such that one piece is twice as long as the other piece. Set up an equation and find the length of each piece.
Answers
Answer:
small piece = 28 inches
large piece = 56 inches
Step-by-step explanation:
The carpenter has one piece of wood 84 inches long. He wants to cut that piece of wood into two pieces. One piece will be 2 times as long as the other. Let's let x = the small piece of wood
2x + x = 84
In this equation, the longer piece is 2 times the shorter piece and the shorter piece is added, which equals 84 inches. Lets solve:
2x + x = 84
3x = 84
3x/3 = 84/3
x = 28
This means that the shorter piece is 28 inches. To find the longer piece, multiply 28 by 2 because the longer piece is twice the shorter piece. Therefore the longer piece is
28 × 2 = 56
Finally, we figured out that the short piece is 28 inches and the longer piece is 56 inches
We can double check this by doing 56 + 28 and making sure it equals 84
Word Problem 3 Priscilla works 43 hours a week for eight weeks. If she makes $14.73 per hour, how much money did she make in the eight weeks? Operation(s): Math sentence(s): Solution: Word Problem 3 Priscilla works 43 hours a week for eight weeks . If she makes $ 14.73 per hour , how much money did she make in the eight weeks ? Operation ( s ) : Math sentence ( s ) : Solution :
Answers
Answer:
$5067,12
Step-by-step explanation:
14,73*43*8
The required money Priscilla will earn in 8 weeks is $5067.12.
As mentioned in the question, Priscilla works 43 hours a week for eight weeks. If she makes $14.73 per hour,
What is simplification?The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
Let the amount earned be x,
According to the condition,
x = 8 × 43 × 14.73
x = $5067.12.
Thus, the required money Priscilla will earn in 8 weeks is $5067.12.
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What is the value of x?
E
(2x)°
xº
D
Answers
Answer:
30°
Step-by-step explanation:
Since ED = FD, the ∠DEF = ∠EFD
Since ∠DEF = 2x, ∠EFD is also equal to 2x
The sum of the 3 angles of a triangle is 180°
So x + 2x + 2x = 180
6x = 180
x = 30
Where does billy bob johns
Answers
Answer:
in ur moms house
Step-by-step explanation:
Answer:
he doesn't
Step-by-step explanation:
help pls i jusiot jiojfgnio43nfginfmowenfviowngognior3
Answers
Answer:
i dont know
Step-by-step explanation:
sorry please be a bit more clear on what help you would like
how do you simplify
−(12st3+34s3t+t2−1)
Answers
Answer:
-34s^3t - 12st^3 - t^2 + 1
Step-by-step explanation:
hope this helps
Find the area of a 150° sector of a circle whose radius is 3.
Answers
Answer: [tex]\frac{15\pi}{4}[/tex]
Step-by-step explanation:
[tex]A=\pi(3^{2})\left(\frac{150}{360} \right)=\boxed{\frac{15\pi}{4}}[/tex]
Another day, another math problem 3
Answers
Answer:
[tex]2\sqrt{x+1}-3\\domain:[-1, \infty)[/tex]
Step-by-step explanation:
[tex]g(h(x)) = 2(\sqrt{x+1})-3\\g(h(x)) = 2\sqrt{x+1} - 3\\[/tex]
the function is only defined when (x+1) >= 0 (since square root) so the domain is when x >= -1
Work out the lengths of sides a and b.
Give your answers to 1 decimal place.
triangle a is a right angled triangle with a height | of 8cm base of 5cm and missing hypotenuse
triangle b is a right angled triangle with a height | of 12cm and a hypotenuse of 17cm with a missing base
Answers
The length of the missing sides of triangles A and B are 9.43 cm and 12.04 cm respectively.
Pythagoras theoremTriangle A:
Height = 8cmBase = 5cmHypotenuse = x cmHypotenuse² = height ² + base²
x² = 8² + 5²
= 64 + 25
x² = 89
x = √89
x = 9.43 cm
Triangle B:
Height = 12cmBase = x cmHypotenuse = 17 cmHypotenuse² = height ² + base²
17² = 12² + x²
17² - 12² = x²
289 - 144 = x²
145 = x²
x = √145
x = 12.04 cm
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Which statements are true? Select three options O The line x = O is perpendicular to the line y = -3 O All lines that are parallel to the y-axis are vertical lines. O All lines that are perpendicular to the x-axis have a slope of O. O The equation of the line parallel to the x-axis that passes through the point (2, -6) is x = 2. O The equation of the line perpendicular to the y-axis that passes through the point (-5, 1) is y = 1
Answers
The statements which are true among the answer choices are;
The line x = O is perpendicular to the line y = -3.All lines that are parallel to the y-axis are vertical lines. Which statements among the answer choices are true?In the concept of straight line graphs (linear graphs) the statements are evaluated as follows;
The line x = O is perpendicular to the line y = -3. - This is true because the former is a vertical line while the latter is horizontal.All lines that are parallel to the y-axis are vertical lines. - True, because the y-axis itself is a vertical line.All lines that are perpendicular to the x-axis have a slope of O. - False, because all lines perpendicular to the X axis are vertical lines and have do not have slope 0.The equation of the line parallel to the x-axis that passes through the point (2, -6) is x = 2. - False, because a line parallel to the x-axis is defined by y.The equation of the line perpendicular to the y-axis that passes through the point (-5, 1) is y = 1. - True.Read more on parallel and perpendicular lines;
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A comedy club's nightly revenue from the sale of x tickets is given by R = 15x and its
nightly costs are given by C= 1.25x + 495. How many tickets need to be sold each night
to break even? In other words, when will revenue equal costs?
Answers
Considering the given equations for the revenue and the cost, it is found that 36 tickets have to be sold each night to break even.
What is the break-even point?The break-even point is when the revenue and the costs are equal.
In this problem, the equations are given as follows:
R(x) = 15x.C(x) = 1.25x + 495.At the break-even point:
R(x) = C(x)
15x = 1.25x + 495
13.75x = 495
x = 495/13.75
x = 36.
36 tickets have to be sold each night to break even.
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Simplify the root below
\frac{a}{b} \sqrt[]{ \frac{405}{324} }
Answers
Answer:
(√5)/2
Step-by-step explanation:
To simplify the root, we remove perfect squares.
__
Factors that are the same in numerator and denominator cancel. A square under the radical can have its root brought out of the radical.
[tex]\sqrt{\dfrac{405}{324}}=\sqrt{\dfrac{9^2\cdot5}{9^2\cdot2^2}}=\boxed{\dfrac{\sqrt{5}}{2}}[/tex]
Analyze the diagram below and complete the instructions. Find the value of x and the value of y
Answers
The value of the variable x and y will be 15 and 5√3. Then the correct option is D.
The complete question is attached below.
What is trigonometry?The connection between the lengths and angles of a triangular shape is the subject of trigonometry.
The right triangle is shown.
Then the value of x will be
x = 10√3 × sin 60°
x = 15
Then the value of y will be
y = 10√3 × cos 60°
y = 5√3
Then the correct option is D.
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This is from Khan academy I have to attach a PNG if you can help me solve it! Thank you!
Answers
Step-by-step explanation:
[tex]29 {}^{ \frac{x}{2} } [/tex]
[tex]((29) {}^{ \frac{1}{2} } ) {}^{x} [/tex]
The answer is A
Describe the change in the graph of the parabola f(x) when it transforms into g(x) =
The parabola g(x) will open in the opposite direction of f(x), and the parabola will be narrower than f(x).
The parabola g(x) will open in the same direction of f(x), and the parabola will be narrower than f(x).
The parabola g(x) will open in the opposite direction of f(x), and the parabola will be wider than f(x).
The parabola g(x) will open in the same direction of f(x), and the parabola will be wider than f(x).
Answers
Answer:
(d) The parabola g(x) will open in the same direction of f(x), and the parabola will be wider than f(x).
Step-by-step explanation:
We assume you intend ...
f(x) = equation of a parabola
g(x) = 2/3·f(x)
Multiplying a function by a factor of 2/3 will cause it to be compressed vertically to 2/3 of its original height. When the function is a parabola, this has the effect of making it appear wider than before the compression.
__
The compression factor is positive, so points on the graph remain on the same side of the x-axis. The direction in which the graph opens is not changed.
The attachment shows parabolas that open upward and downward, along with the transformed version.
Answer:
D.) The parabola g(x) will open in the same direction of f(x), and the parabola will be wider than f(x).
Step-by-step explanation:
I got it right on the test :)
stay hydrated.
which of the following expresses the coordinates of the foci of the conic section shown below? (x-2)^2/4+(y+5)^2/9
Answers
Step-by-step explanation:
[tex] \frac{(x - 2) {}^{2} }{4} + \frac{(y + 5) {}^{2} }{9} = 1[/tex]
This is the equation of the ellipse. Since the denominator is greater for the y values, we have a vertical ellipse. Remember a>b, so a
The formula for the foci of the vertical ellipse is
(h,k+c) and (h,k-c).
where c is
Our center (h,k) is (2, -5)
[tex] {c}^{2} = {a}^{2} - {b}^{2} [/tex]
Here a^2 is 9, b^2 is 4.
[tex] {c}^{2} = 9 - 4[/tex]
[tex] {c}^{2} = 5[/tex]
[tex]c = \sqrt{5} [/tex]
So our foci is
[tex](2, - 5 + \sqrt{5} )[/tex]
and
[tex](2, - 5 - \sqrt{5} )[/tex]
Find the value of: (4/5)^1 A. 4/5 B. 1 C. 0 D. 16/25
Answers
Answer:
A. 4/5
Step-by-step explanation:
Answer:
4/5 (option a)
Step-by-step explanation:
by following the exponent rule of [tex]a^1 = a[/tex], we know that
[tex](\frac{4}{5} )^1[/tex] = [tex]\frac{4}{5}[/tex]
So, the value of
[tex]\frac{4}{5}^{1}[/tex] is 4/5
statement that is assumed to be true without proof is . A statement that has been shown to be true by vigorous application of logic is . is a statement that is believed to be true but hasn't been proven.
Answers
An axiom is a statement that is assumed to be true without proof.
What are the types of statements?In logic, a statement could be shown to be valid or true by the use of premises that lead to a sound conclusion.
The following terms can be used to describe the statements;
Axiom - a statement that is assumed to be true without proofTheorem - a statement that has been shown to be true by vigorous application of logicHypothesis - a statement that is believed to be true but hasn't been proven.Learn more about mathematical statements:https://brainly.com/question/17029275?
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Answer:
The answer is axiom, theorem, and then conjecture
Step-by-step explanation:
What are the roots for the quadratic equation below?
3x^2+9x-2=0
Answers
Answer:
[tex]\sf{$a)$} \ x=\dfrac{-9\pm\sqrt{105}}{6}[/tex]
Step-by-step explanation:
Quadratic formula: [tex]x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
Quadratic equation: ax² + bx + c = 0, where a ≠ 0
Given: 3x² + 9x - 2 = 0
⇒ a = 3, b = 9, c = -2
Substitute the given values into the formula and simplify:
[tex]x=\dfrac{-9\pm\sqrt{9^2-4(3)(-2)}}{2(3)}\\\\x=\dfrac{-9\pm\sqrt{81+24}}{6}\\\\x=\dfrac{-9\pm\sqrt{105}}{6}[/tex]
Therefore, the correct answer is A.
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Simplify
[tex]\left(\frac{123}{321}\right)\left(\frac{456}{654}\right)\left(\frac{789}{987}\right) \left(\frac{123}{321}\right)^{-1}\left(\frac{456}{654}\right)^{-1}\left(\frac{789}{987}\right)^{-1}[/tex]
Answers
Answer:
1
Step-by-step explanation:
using the rule of exponents
[tex](\frac{a}{b}) ^{-1}[/tex] = [tex]\frac{b}{a}[/tex] , then
[tex]\frac{123}{321}[/tex] × [tex]\frac{456}{654}[/tex] × [tex]\frac{789}{987}[/tex] × [tex]\frac{321}{123}[/tex] × [tex]\frac{654}{456}[/tex] × [tex]\frac{987}{789}[/tex]
[ [tex]\frac{123}{321}[/tex] × [tex]\frac{321}{123}[/tex] = 1 , [tex]\frac{456}{654}[/tex] × [tex]\frac{654}{456}[/tex] = 1 , [tex]\frac{789}{987}[/tex] × [tex]\frac{987}{789}[/tex] = 1 ]
= 1 × 1 × 1
= 1
3xy - ² + 4x for x = -2, y = - and = 6?
Answers
Answer:
See below
Step-by-step explanation:
Not sure what you are asking....do you want to know what y is when x = -2 and the equation = 6 ?
3 xy^2 + 4x = 6 or is that 3 xy^(-2) + 4x = 6
Could use some serious editing of your question if you are able ....
indicate whether the statement is true of false.
please provide a explanation
A linear system with three variables and three equations has a unique solution.
Answers
The statement is false, as the system can have no solutions or infinite solutions.
Is the statement true or false?
The statement says that a system of linear equations with 3 variables and 3 equations has one solution.
If the variables are x, y, and z, then the system can be written as:
[tex]a_1*x + b_1*y + c_1*z = d_1\\\\a_2*x + b_2*y + c_2*z = d_2\\\\a_3*x + b_3*y + c_3*z = d_3[/tex]
Now, the statement is clearly false. Suppose that we have:
[tex]a_1 = a_2 = a_3\\b_1 = b_2 = b_3\\c_1 = c_2 = c_3\\\\d_1 \neq d_2 \neq d_3[/tex]
Then we have 3 parallel equations. Parallel equations never do intercept, then this system has no solutions.
Then there are systems of 3 variables with 3 equations where there are no solutions, so the statement is false.
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Can anyone Help I have 25 questions, 2hr 40mins remaining,
Answers
Combining the like-terms, the result of the addition of polynomials f(x) and g(x) is given by:
[tex]f(x) + g(x) = 21x^3 + \frac{5}{4}x^{\frac{1}{2}} + 19x^{-\frac{1}{4}} + 8x^{-4}[/tex]
How do we add polynomials?We add polynomials combining the like-terms, that is, adding terms with the same exponent.
In this problem, the polynomials are:
[tex]f(x) = 3x^{\frac{1}{2}} + 7x^{-\frac{1}{4}} + 8x^{-4}[/tex][tex]g(x) = -\frac{7}{4}x^{\frac{1}{2}} + 12x^{-\frac{1}{4}} - 21x^3[/tex]Combining the like terms, the addition is given by:
[tex]f(x) + g(x) = \left(3 - \frac{7}{4}\right)x^{\frac{1}{2}} + (7 + 12)x^{-\frac{1}{4}} + 8x^{-4} + 21x^3[/tex]
[tex]f(x) + g(x) = 21x^3 + \frac{5}{4}x^{\frac{1}{2}} + 19x^{-\frac{1}{4}} + 8x^{-4}[/tex]
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A 13 -ft ladder is leaning against a house when its base starts to slide away. By the time the base is 12 ft from the house, the base is moving away at the rate of 15 ft/sec.
a. What is the rate of change of the height of the top of the ladder?
b. At what rate is the area of the triangle formed by the ladder, wall, and ground changing then?
c. At what rate is the angle between the ladder and the ground changing then?
Answers
If y=4 when x=12, find y when x=-24
Answers
The value of y is -8 if the x -24 and y varies directly with x, and If y = 4 when x = 12.
What is a proportional relationship?It is defined as the relationship between two variables when the first variable increases, the second variable also increases according to the constant factor.
The question is incomplete.
The complete question is:
If y varies directly with x, and If y = 4 when x = 12, how do you find y when x = -24?
y ∝ x (given)
y = kx
k is the constant of proportionality.
4 = 12k (y = 4, and x = 12)
k = 1/3
y = x/3
Plug x = -24
y = -24/3
y = -8
Thus, the value of y is -8 if the x -24 and y varies directly with x, and If y = 4 when x = 12.
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