Polygon EFGH is a scaled copy of polygon ABCD.
Select ALL of the true statements.
(Select all that apply.)
The area of EFGH is twice the area of ABCD.
Segment FG is twice as long as segment CD.
Segment EF is twice as long as segment AB.
The scale factor from EFGH to ABCD is 2.
The length of segment AD is 8 units.
Answers
The following statements are true and correct:
Segment EF is twice as long as segment AB
The length of segment AD is 8 units
How to interpret dilation transformation?
Since quadrilateral ABCD is scaled to form quadrilateral EFGH, both are similar polygon.
Now, it is known that;
scale factor = ratio of any of their corresponding side
Thus;
Scale factor = GH/CD = 12/6 = 2
This means quadrilateral EFGH is twice the size of quadrilateral ABCD.
The shape of the original polygon remains the same while the size increases.
This implies that, all segments of quadrilateral ABCD increases proportionally times 2 to give us corresponding lengths of the segments of quadrilateral EFGH.
Since shape remains the same, their corresponding angles are congruent and the same in measure.
Therefore, the following statements are true and correct:
Segment EF is twice as long as segment AB; because (EF = AB*scale factor = 3*2 = 6)
The length of segment AD is 8 units because (EH = AD*scale factor = 8*2 = 16)
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Related Questions
Translate and solve: 82 less than a is at least −82.
Give your answer in interval notation.
Answers
The interval representing the expression "82 less than a is at least −82." is given by ( -82, 82).
We are given an expression that:
82 is less than a which is at least - 82.
This expression can also be written as:
- 82 < a and a > 82
where a is any variable that can take any value according to the expression.
This can also be written as:
- 82 < a < 82
In interval form, it will be written as:
( -82, 82)
"()" brackets are used as -82 and 82 are not included in the interval.
Therefore, we get that, the interval representing the expression "82 less than a is at least −82." is given by ( -82, 82).
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The mean height of American women in their late twenties is about 64.5 inches and the standard deviation is about 2.5 inches. The mean height of men the same age is about 68.5 inches, with a standard deviation of about 2.7 inches. If the correlation between the heights of married heterosexual men and their wives is about r=0.5, what is the equation of the regression line of the the husbands height on the wife’s height in young couples?
Answers
Answer:
For married couples in their early 20s, the regression equation and the prediction of a husband's heightEquation: Y'=33.67+0.54*X'
Step-by-step explanation:
Given that
r=0.5x'=64.5Sx=2.5y'=68.5Sy=2.7General regression line equation is:
Y'=a+b*X'
Therefore, the slope of the regression line is equal to the linear correlation coefficient times the difference between the standard deviations of y' and x'.
[tex]b = r\times\frac{S_y}{S_x}[/tex]
[tex]b = 0.5\times\frac{2.7}{2.5}[/tex]
b = 0.54
The mean of the lowered by the slope and mean of x is the intercept with axis y.
[tex]a = y'-b\times x'[/tex]
[tex]a = 68.5-0.54\times 64.5[/tex]
[tex]a = 33.67[/tex]
Now, putting the values of a and b in regression equation
So, we get
Y'=a+b*X'
Equation: Y'=33.67+0.54*X'
Answer:
For married couples in their early 20s, the regression equation and the prediction of a husband's heightEquation: Y'=33.67+0.54*X'
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Translate the English phrase into an algebraic expression: the quotient of the sum of a and b and the product of a and b.
Answers
The algebraic expression from the given statement is (a+b)/ab.
Given the statement is the quotient of the sum of a and b and the product of a and b.
In mathematics, an expression is defined as a set of numbers, variables, and operations that are formed according to context-dependent rules.
In the given statement the sum of a and b means a+b.
And the product of a and b means ab.
Now, as it is given in the statement that the quotient of the sum of a and b and the product of a and b can be written as
(a+b)/ab.
Hence, the algebraic expression from the given statement "the quotient of the sum of a and b and the product of a and b" is (a+b)/ab.
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The sum of 8 and three times a number is 41
Answers
Answer:
x=11
Step-by-step explanation:
let number =x
(8+3x)=41
group like terms
3x=41-8
3x=33
divide both side by the coefficient of x
3x/3=33/3
x=11
Bill’s spelling list is 3 words long at the start of the school year. Each month, his teacher adds 8 words to the list.
Let m represent the number of months since school began and w represent the total number of spelling words.
This relationship can also be shown in a table. Complete the equation that represents between m and w.
Answers
Based on the fact that m represents the number of months and w is the total number of spelling words, the equation that represents the relationship between m and w is w = 8m + 3
How to find the equation?The first thing to find is the slope of the relationship. This can be found as:
= ( 51 - 43) / (6 - 5)
= 8 / 1
= 8
The y-intercept is:
w = 8m + c
43 = 8(5) + c
c = 43 - 40
c = 3
The equation to represent the relationship between m and w is:
w = 8m + 3
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Approximate square root 80 by using perfect squares. 80 is between which two perfect squares? What are the square roots of those two perfect squares? What is the approximate value of square root 80?
Answers
By finding square numbers, we will get:
8 < √80 < 9
And we can assume that √80 is closer to 9 than to 8, so a good estimation can be 8.95
How to approximate the square root of 80?
We want to approximate √80, now we need to find two consecutive square numbers such that one is smaller and the other is larger than 80.
We know that:
9*9 = 81
8*8 = 64
Then:
√81 = 9
√64 = 8
So we can see that:
√64 < √80 < √81
Then:
8 < √80 < 9
And we can assume that √80 is closer to 9 than to 8, so a good estimation can be 8.95
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Find the following values for the function
Answers
Answer:
a. -5; b. 4; c. -2.
Step-by-step explanation:
a) f(-3)=3*(-3)+4=-5;
b) f(3)=2*3-2=4;
c) f(0)=2*0-2=-2.
Sixty-five students voted for Jessica. Two times
many students voted for Sierra. How many
students voted
Answers
students voted= 195
Solution :
a word problem is a problem of deciding whether two given expressions are equivalent with respect to a set of rewriting identities. A prototypical example is the word problem for groups, but there are many other instances as well.
Jessica = 65 student
Sierra = 2 (Sixty-five students voted for Jessica.) = 2(65) = 130
Total number of students = NO of students voted for Jessica +NO of students voted for Sierra
= 65+130
= 195
students voted= 195
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Algebra Question Help
Answers
Answer:
[tex]y=\dfrac{7}{3}\left(\dfrac{1}{3}\right)^x[/tex]
Step-by-step explanation:
Given table:
[tex]\begin{array}{|c|c|}\cline{1-2} \phantom{\dfrac{1}{1}} x & y \\\cline{1-2} \phantom{\dfrac{1}{1}} -1 & 7 \\\cline{1-2} \phantom{\dfrac{1}{1}} 0 & \frac{7}{3}\\\cline{1-2} \phantom{\dfrac{1}{1}} 1 & \frac{7}{9}\\\cline{1-2} \phantom{\dfrac{1}{1}} 2 & \frac{7}{27}\\\cline{1-2} \phantom{\dfrac{1}{1}} 3 & \frac{7}{81}\\\cline{1-2}\end{array}[/tex]
Linear function: As x increases by one, y always increases by a constant value. Therefore, the first differences between y-values are the same.Quadratic function: The second differences between y-values are the same.Exponential function: The y-value either increases or decreases by a constant factor.Work out the first differences between the y-values:
[tex]7 \underset{-\frac{14}{3}}{\longrightarrow} \dfrac{7}{3} \underset{-\frac{14}{9}}{\longrightarrow} \dfrac{7}{9} \underset{-\frac{14}{27}}{\longrightarrow} \dfrac{7}{27} \underset{-\frac{14}{81}}{\longrightarrow} \dfrac{7}{81}[/tex]
As the first differences are not the same, it is not a linear function.
Work out the second differences:
[tex]-\dfrac{14}{3} \underset{+\frac{28}{9}}{\longrightarrow} -\dfrac{14}{9} \underset{+\frac{28}{27}}{\longrightarrow} -\dfrac{14}{27} \underset{+\frac{28}{81}}{\longrightarrow} -\dfrac{14}{81}[/tex]
As the second differences are not the same, it is not a quadratic function.
Work out if the second differences have a common ratio:
[tex]\implies \sf \dfrac{28}{27} \div \dfrac{28}{9}=\dfrac{1}{3}[/tex]
[tex]\implies \sf \dfrac{28}{81} \div \dfrac{28}{27}=\dfrac{1}{3}[/tex]
As the second differences have a common ratio of ¹/₃, the function is exponential with base ¹/₃.
General form of an exponential function:
[tex]y=a(b)^x[/tex]
where:
a is the y-intercept.b is the base (growth/decay factor) in decimal form.The y-intercept is the value of y when x = 0.
From inspection of the table, the y-intercept is ⁷/₃.
Therefore:
[tex]a = \dfrac{7}{3}[/tex]
[tex]b = \dfrac{1}{3}[/tex]
Substitute the found values of a and b into the formula to create an exponential function that models the given data:
[tex]\implies y=\dfrac{7}{3}\left(\dfrac{1}{3}\right)^x[/tex]
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The function f(x) = |x| is graphed over the interval [−6, 3].
Which translation of the graph has the domain [−3, 6]?
A. g(x) = |x| + 3
B. g(x) = |x + 3|
C. g(x) = |x| − 3
D. g(x) = |x − 3|
Answers
The translation of the graph that has the domain [−3, 6] is:
B. g(x) = |x + 3|.
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.
In this problem, the parent function is given by:
f(x) = |x|.
The domain changed by [−6, 3] to [-3,6], meaning that 3 units was added to each bound of the domain, hence x -> x + 3 and:
g(x) = |x + 3|.
Which means that option B is correct.
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Find the area of the figure.
Answers
Answer:
10 x 12 x 9 cm^2
= 1080 cm^2
Answer:
105
Step-by-step explanation:
a = 1/2(bh) + 1/2(bh)
a = 1/2(12)(10) + 1/2 (9)(10)
a= 1/2 (120) + 1/2(90)
a = 60 + 45
a = 105
What is the quotient of (−56) ÷ (−4) ÷ 7?What is the quotient of (−56) ÷ (−4) ÷ 7?
Answers
Answer:
98
Step-by-step explanation:
Mr jacobs backyard mesures 150 ft. he wants to fence it to secure his garden, how many meters of fence would he need?
Answers
The number of meters of fence he would need is 45.72 meters
How to determine how many meters of fence would he need?The given parameters are
Length of backyard = 150 ft
As a general rule, we have the following conversion equation
1 foot = 0.3048 meters
So, we have
Length of backyard = 150 * 0.3048 meters
Evaluate the product
So, we have
Length of backyard = 45.72 meters
Hence, the number of meters of fence he would need is 45.72 meters
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Find the value of x. Then find the missing angle measures of the polygon.
x = ?
5x degrees = ?
2x degrees = ?
Answers
Answer:
x = 22.5
2x = 45
5x = 112.5
Step-by-step explanation:
The sum of all internal angles in a triangle is 180 degrees. This can be expressed as the following:
x + 5x + 2x = 180
Combine the like terms:
8x = 180
Divide both sides by 8 to find the value of x:
x = 180/8
Simplify:
x = 22.5
Multiply by 2 to get 2x:
2x = 22.5 * 2
2x = 45
Multiply by 5 to get 5x:
5x = 22.5 * 5
5x = 112.5
Verify the answer is correct by taking all the obtained values and ensuring they sum to 180:
22.5 + 45 + 112.5 = 180
Choose an equivalent expression for two thirds to the fourth power times two thirds raised to the third power comma all raised to the second power.
A. four ninths raised to the fourteenth power
B. four ninths raised to the twenty fourth power
C. two thirds raised to the fourteenth power
D. two thirds raised to the twenty fourth power
Answers
Answer:
C. two-thirds raised to the fourteenth
Step-by-step explanation:
Write an equation in point-slope form of the line
(-7,2); m=2
Answers
Answer: y - 2 = 2(x + 7)
Step-by-step explanation:
Point-slope form is written as y - [tex]y_{1}[/tex] = m(x - [tex]x_{1}[/tex]) where m is the slope and ( [tex]x_{1}[/tex], [tex]y_{1}[/tex]) are points on the line.
y - [tex]y_{1}[/tex] = m(x - [tex]x_{1}[/tex])
y - 2 = 2(x + 7)
I'm looking for a full positive integer for K as my answers.
Answers
The value of full positive integer k such that [tex]O(n^k)[/tex] is the most restrictive polynomial-time upper bound of f(n) are as follows : (A) 9 (B) no integer exists (C)5/3(not an integer) (D)no integer exists (E) [tex]3e^{99}[/tex]
Using the Lower and Upper Bound Theory, it is possible to identify the algorithm with the lowest level of complexity. Let's quickly review what Lower and Upper bounds are before we can understand the theory.
If there are two constants C and N such that U(n) = C*g(n) for n > N, then g(n) is the Upper Bound of A. Let U(n) be the running time of an algorithm A(say). An algorithm's upper bound is displayed using the asymptotic notation Big Oh(O).If there are two constants C and N such that L(n) >= C*g(n) for n > N, then g(n) is the Lower Bound of A. Let L(n) be the running time of an algorithm A(say). The asymptotic notation known as Big Omega displays an algorithm's lower bound.A)[tex]2^{lg(3n+4n+5)}+lg {\spaceh} n \inO(n^k)[/tex]
or, [tex]O(2^{lgn^9}+lgn)\inO(n^k)[/tex] since [tex]3n^9+4n+5=O(n^9)[/tex]
or, [tex]O(2^{lgn^9})\in O(n^k)[/tex] as [tex]2^m+lg m=O(2^m)[/tex]
Applying lg 2 on both sides we get:
[tex]lg_22^{lgn^9}=lg_2n^k[/tex]
solving we get:
k=9 × lg2 × lg n
At n=1/2
k=9
Hence the minimum integer for K is 9.
B) [tex]7lgn+13lg^5n\in O(n^k)[/tex]
Solving for k we get:
k=lgₙ(lg⁵n)
C) [tex]\sqrt[3]{7n^5+2n^3-4}\in O(n^k)[/tex]
Solving by exponent rule we get:
[tex]O(n^{5/3})\in O(n^k)[/tex]
k=5/3
D)[tex]13lg2^{3^n\inO(n^k)}[/tex]
or, [tex]k=lg_n(lg2^{3^n})[/tex]
E)[tex]7^{20!+1} \inO(n^k)[/tex]
As we don't have any term of n on the Left Hand Side, therefore no most restrictive polynomial-time upper bound exist for [tex]O(n^k)[/tex]
[tex]k=e^{99}[/tex]
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3x divided by -8 = -21 divided by 4. The answer is 14. I'm trying =g to figure out why it was not a negative 14
Answers
Answer:
See explanation
Step-by-step explanation:
3x/(-8)=-21/4
-3x/8=-21*8/4
-3x*8/8=-21*8/4 ==> multiply 8 on both sides to get rid of denominator
-3x=-21*2
-3x=-42
3x=42 ==> Multiply by -1 on both sides to get positive values on both sides
x=14
Find two numbers that have a sum of -10 and a product of -56.
Answers
Find the circumference.
Use 3.14 for T.
r = 4 cm
C = ? cm
C =
Answers
Answer:
25.12 cm
Step-by-step explanation:
The circumference of a circle can also be understood as the perimeter of the circle.
Circumference of circle= 2πr= πd
r refers to radius while d refers to diameter
Given that r= 4,
circumference of circle
= 2(π)(4)
= 8π
≈ 8(3.14)
= 25.12 cm
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Need help with number 6
Answers
Applying the definition of bisection, PR = RQ = 28.5 cm.
What is the Definition of Bisection?When a line segment bisects another line segment, it divides the line into two equal segments. This means the two resultant line segments formed have the same length.
The image below shows the bisection of segment PQ by segment ST at point R, which forms two equal segments, PR and RQ.
This means that the length of segments PR and RQ will be equal to each other.
Given that, PQ = 57 centimeters, therefore:
PR = RQ = 1/2(PQ)
PR = RQ = 1/2(57)
PR = RQ = 28.5 cm
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I need solution to this question tutor
Answers
Answer:
x=3 and y=
Step-by-step explanation:
Answer:
x=5 and y any number
Step-by-step explanation:
how do i solve for 6+3+11/4=5
Answers
Answer:
6+3+11/4[tex]\neq[/tex]5
Step-by-step explanation:
Answer:
The answer to the question is 0
7/39
in lowest terms.
Answers
Answer: 7/39
Step-by-step explanation:
Find the GCD (or HCF) of numerator and denominator GCD of 7 and 39 is 1
Divide both the numerator and denominator by the GCD 7 ÷ 1 39 ÷ 1
Reduced fraction: 7 39 Therefore, 7/39 simplified to lowest terms is 7/39.
A control tower observes the flight of an aircraft. At 09:23 the aircraft is 580 km away on a bearing of 043º. At 09:25 the aircraft is 360 km away on a bearing of 016º. What is the speed and the course of the aircraft? (Use a scale of 1 cm to 50 km.)
Answers
The speed and the course of the aircraft is 27465 km/h.
What is an aircraft?A machine or vehicle can fly by obtaining support from the air, and this is how an airplane works. It uses either static lift, dynamic lift provided by an airfoil, or, in certain rare situations, the downward thrust from jet engines to counteract the pull of gravity.
From the figure, let us use cosine formula to calculate the resultant displacement.
B^2 = C^2 + A^2 - 2(A)(C) cosØ
Where C = 580km
A = 360 km
Ø = 153 degree
Substitute all the parameters into the formula
B^2 = 580^2 + 360^2 - 2(360)(580)cos153
B^2 = 466000 - ( - 372084.32 )
B^2 = 466000 + 372084.32
B^2 = 838084.32
Square root both sides
B = 915.5 km
You are told to use a scale of 1 cm to 50 km.
Therefore, B = 915.5/50 = 18.3 cm
The time given are: 09:23 and 09:25.
The time difference = 25 - 23 = 2 minute
Convert minutes to hours
2 minute = 2/60 = 1/30 hours
Speed = distance/time
Speed = 915.5 ÷ 1/30
Speed = 915.5 × 30
Speed = 27465 km/h
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The tables below show some inputs and outputs of functions f and h.
Evaluate
Oh
Answers
The value of the composite functions, (h ° f)(1) = 0.5.
How to Solve Composition of Functions?Given the function, (h ° f)(1), this means h(f(1)) as a composition of functions.
Using the table given for the function, f(x), f(1) = -1.
This means that, to find (h ° f)(1) = h(f(1)), we would find the value of h(x) in the table where x = -1.
Thus, from the table for h(x), when x = -1, h(-1) = 0.5.
Therefore, the value of the composite functions, (h ° f)(1) = 0.5.
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Daslyn has a piece of rope 2.085 meters long and another piece
2.63 meters long. Which piece can she cut to make a piece that is
2.5 meters long? Explain.
Answers
Answer:
the second piece of rope
Step-by-step explanation:
2.63 ≥ 2.5
2.085≤2.5
What is the quotient for 81/-9, -123 divided by -4, -94/-9, and 65 divided by (-5)
Answers
The final answer is -9, -30.75, -13
What is Quotient?
The number resulting from the division of one number by another.
In the given statement is:
What is the quotient for 81/-9
If we divide 81 by -9
The Quotient will be -9
And, come to the next :
-123 divide by -4
The quotient will be -30.75
And, 65 divided by (-5)
The Quotient will be -13
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TJ invested $4000 in a bond at a yearly rate of 2%. He earned $200 in interest. How long was the money invested
Answers
Lines a & m are parallel. Using the diagram below, what is the degree measure of angle 2?
Enter the numerical answer only. Example, if the answer is 12 degrees, only enter 12.
Answers
Answer:
27
Step-by-step explanation:
just subtract 153 from 180