Which algebraic rule describes the translation of quadrilateral ABCD to quadrilateral A’B’C’D?
Answers
The algebraic rule that best describes the translation of quadrilateral ABCD to quadrilateral A'B'C'D' is P'(x, y) = (x + 8, y + 7). (Correct answer: A)
How to determine the translation of a quadrilateral on a Cartesian plane
According to the image attached we understand that the quadrilateral ABCD is transformed into quadrilateral A'B'C'D' by applying pure translation. Translations are a kind of rigid transformation, defined as a transformation applied on a geometric locus such that Euclidean distance is conserved at every point of the construction.
Vectorially speaking, translations are described by the following formula:
P'(x, y) = P(x, y) + T(x, y) (1)
Where:
P(x, y) - Original pointP'(x, y) - Resulting pointT(x, y) - Translation vector.By direct comparison, we conclude that the quadrilateral ABCD is translated 8 units in the +x direction and 7 units in the +y direction. Hence, the algebraic rule that describes the translation of quadrilateral ABCD to quadrilateral A'B'C'D' is:
P'(x, y) = (x, y) + (8, 7)
P'(x, y) = (x + 8, y + 7)
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Related Questions
In ΔXYZ, x = 27 cm, y = 79 cm and ∠Z=142°. Find the length of z, to the nearest centimeter.
Answers
The value of side z will be equal to 99.32 cm.
What is trigonometry?The branch of mathematics sets up a relationship between the sides and the angles of the right-angle triangle are termed trigonometry.
Given that:-
In ΔXYZ, x = 27 cm, y = 79 cm and ∠Z=142°
So by applying the formula given below:-
z² = x² + y² - 2xyCos(142)
z² = 79² + 27² - 2 ( 79 x 27 x Cos142 )
z = 99.32 cm
Hence the value of side z will be equal to 99.32 cm.
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For her phone service, Charmaine pays a monthly fee of $15, and she pays an additional $0.05 per minute of use. The least she has been charged in a month is
$66.90.
What are the possible numbers of minutes she has used her phone in a month?
Use m for the number of minutes, and solve your inequality for m.
Answers
Step-by-step explanation:
after subtracting the monthly fee (which she has to pay, even if she does not make a single call) we have
66.9 - 15 = $51.90
for actual phone call minutes.
1 minute is $0.05
so, in the month with the lowest charge she had used
51.9 / 0.05 = 1038 minutes for calls.
since this was the minimum, for all the numbers of minutes m she used in a month we have
m >= 1038 minutes
Use the figure.
10 feet
4 feet
10 feet
7 feet
Find the perimeter of the figure.
Answers
Primeter=10 + 4 +10 +7 = 31 ft
Nathan is considering two different job offers.
He was told by both companies that he would be paid a salary that is in the center of the salaries of the current employees
on his team. The two dot plots represent the annual salaries (in thousands of dollars) of the current employees on the teams
with whom Nathan would be working.
.
10
20 30 40 50
60
70
10
20
70
30 40 50 60
Company B
Company A
mean = 40
mean = 42
median = 35
median = 40
If the mean is used to determine Nathan's salary, he should choose company
If the median is used to determine Nathan's salary, he should choose company
The center of the data for company B is more accurately described by the
because the data is
Answers
1. If the mean is used to determine Nathan's salary, he should choose Company A.
2. If the median is used to determine Nathan's salary, he should choose Company A.
3. The center of the data for Company B is more accurately described by the Median because the data is not uniformly scattered and has extreme values or outliers.
What are the Mean and Median values?The Mean is the average value obtained after adding up a set of values and dividing the result by the number in the set.
The Median represents the middle value in an ordered list from smallest to largest.
Data and Calculations:Salaries Company A Company B
Year 1 10 10
Year 2 20 20
Year 3 30 70
Year 4 40 30
Year 5 50 40
Year 6 60 50
Year 7 70 60
Total 280 280
Mean 40 40
Median 40 35 (30 + 40)/2
Thus, Nathan should choose Company A whether the Mean or the Median is used to determine Nathan's salary.
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Answer: Company B
Company A
Median
Skewed Right
Step-by-step explanation:
If f(x) = 3x +3, which of the following is the inverse of f(x)?
O
A. f-1(x) = 3(x-3)
5
OB. f-1(x) = 3(x+3)
5
O C. f-1(x) = 5(x+3)
3
O D. f-1(x) = 5(x-3)
3
Answers
The inverse function of f(x) = 3x + 3 is f-1(x) = 1/3x - 1
How to determine the inverse?The equation is given as:
f(x) = 3x + 3
Express f(x) as y
y = 3x + 3
Swap the positions of y and x
x = 3y + 3
Make y the subject
3y = x - 3
Divide by 3
y = 1/3x - 1
Replace y with the inverse function
f-1(x) = 1/3x - 1
Hence, the inverse function of f(x) = 3x + 3 is f-1(x) = 1/3x - 1
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According to a 2017 Gallup survey, the percentage of individuals in the United States who are invested in the stock market by age is as shown in the following table.†
Age Range Percent of Individuals
Invested in Stock Market
18 to 29 31
30 to 49 62
50 to 64 62
65+ 54
If 2,000 individuals 18- to 29-years-old are randomly sampled, what is the expected number of 18- to 29-year-olds who invest in the stock market in this sample? What is the standard deviation of the number of 18- to 29-year-olds who invest in the stock market? (Round your answers to two decimal places.)
E(x)=
=
Answers
Answer: 75 people
Step-by-step explanation:
1).
we have percentage of people who invested in 18-29 year category
=31%
we need
n=40 people
this is
30% of x =40
or
0.3x=40
x=40/0.3 =133.33 or 134 people
2).
in 65+ category
percentage =54%
we need
n=40
this is
54% of x =40
or
0.54x=40
or
x=40/0.54 =70.07 or 75 people
A food truck did a daily survey of costumers to dond their food preferences. The data is partially entered in the frequency table. Complete the table to analyze the data and answer the questions:
Answers
HELPP PLEASE!!!
Harry is 5 years older than his sister, and the product of their
ages is 84.
Let h represent Harry's age, then h- 5 represents his
sister's age, and h (h-5) = 84 models the situation.
The equation can also be written as h² - 5h = 84.
Rewrite the equation so that it is in the form polynomial = 0.
Enter the polynomial, in standard form, in the box.
= 0
Answers
Answer:
See below
Step-by-step explanation:
h^2 - 5h = 84
h^2 - 5h - 84 = 0
Please help, having trouble. Show all work if you can :) Photo is attached.
Answers
Answer:
hope it helpssssssss youj
Hi I’m really confused and it’s a new topic
Answers
[tex]\large\boxed{Formula:\frac{sum \: of \: interior \: angles}{n}}[/tex]
n means the number of sides.
Sum of interior angles of a dodecagon is 1800°
Let's substitute the values according to the formula.
[tex]\frac{1800}{12}[/tex]
[tex]\large\boxed{ = 150°}[/tex]
Now, we can find the size of one exterior angle.
[tex]\large\boxed{Formula:\frac{360}{n}}[/tex]
n means the number of sides.
A dodecagon has 12 sides.
Let's substitute the values according to the formula.
[tex]\frac{360}{12}[/tex]
[tex]\large\boxed{ = 30°}[/tex]
Hence, the size of 1 interior angle of a dodecagon is 150° and 1 exterior angle is 30°
PLEASE HELP NEEDS TO BE DONE IN 10 MINUTES!!!
Answers
Answer:
QR = 15 cm
PQ = 20 cm
Step-by-step explanation:
Use the Pythagorean theorem. [tex]a^{2} +b^{2} =c^{2}[/tex]
Find QR first since you know QP are SR.
[tex]a^{2} +b^{2} =c^{2}\\12^{2} +9^{2} =c^{2}\\144+81=c^2 \\225=c^2\\\sqrt{225} = \sqrt{c^2} \\c = 15[/tex]
QR = 15 cm
Now you can find PQ. First find the length of PR by adding PS and SR together.
16 + 9 = 25
[tex]a^{2} +b^{2} =c^{2}\\a^{2} +15^{2} =25^{2}\\a^{2} +225 =625\\a^{2} +225-225 =625-225\\\a^{2} = 400\\\sqrt{a^2} =\sqrt{400} \\a = 20[/tex]
PQ = 20 cm
Convert the degree measure to radian measure. Round to three decimal places.
75°
radians
Answers
The conversion from degree to radian will be 180° = π radian. Then the measure of angle 75° is 1.31 radians.
What is conversion?Conversion means to convert the same thing into different units.
Convert the degree measure to the radian measure.
⇒ 75°
We know the conversion is given as
180° = π radian
1° = π/180°
Then we have
75° = 75° x π/180° radian
75° = 1.30899 radian
75° ≅ 1.31 radian
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One side of a rectangle is 6 meters shorter than four times another side. Find the length of the longer side if we also know that the perimeter of the rectangle is 58 meters
Answers
Answer:
22 meters
Step-by-step explanation:
Let x = width of the rectangle
Let y = length of the rectangle
Equation 1
If the length of the rectangle is 6 meters shorter than four times the width then:
⇒ y = 4x - 6
Equation 2
Perimeter of a rectangle = 2(width + length)
If the perimeter is 58 inches, then:
⇒ 58 = 2(x + y)
Solve by substitution
Substitute Equation 1 into Equation 2 and solve for x:
⇒ 58 = 2(x + 4x - 6)
⇒ 58 = 2(5x - 6)
⇒ 58 = 2 · 5x - 2 · 6
⇒ 58 = 10x - 12
⇒ 58 + 12 = 10x -12 + 12
⇒ 10x = 70
⇒ 10x ÷ 10 = 70 ÷ 10
⇒ x = 7
Substitute found value of x into Equation 1 and solve for y:
⇒ y = 4(7) - 6
⇒ y = 28 - 6
⇒ y = 22
Conclusion
The dimensions of the rectangle are:
width = 7 meterslength = 22 metersTherefore, the length of the longer side is 22 meters
The length of the longer side is 22 meters.
Let, one side of the rectangle is x meters.
According to the problem, the other side is 6 meters shorter than four times this side, which means the length of the second side is (4x - 6) meters.
The perimeter of a rectangle is given by the formula:
Perimeter = 2 * (length + width)
In this case, the perimeter is 58 meters:
58 = 2 * (x + 4x - 6)
Now, let's solve for x:
58 = 2 * (5x - 6)
58 = 10x - 12
Add 12 to both sides:
58 + 12 = 10x
70 = 10x
Now, divide both sides by 10 to isolate x:
x = 70 / 10
x = 7
So, one side of the rectangle is 7 meters.
Now, we can find the length of the longer side:
Length of the longer side = 4x - 6
Length of the longer side = 4 * 7 - 6
Length of the longer side = 28 - 6
Length of the longer side = 22 meters
Therefore, the length of the longer side is 22 meters.
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Use the formula Area = (side)2 to find the area of the square.
3.
2.
1.
7m
5 yd
8 cm
Answers
Answer:
1. 5² is 25 yards
2. 7² is 49m
3. 8² is 64cm
4.draw a square, make one side 6 feet then do 6² which is 36feet
5. do the same thing then write 10 inches on one side and 10² is 100 inches.
6. 7x3= 21 ft
7. 5x4= 20 in.
8. 2x8= 16 yd
Step-by-step explanation:
common sense
2. 49 yard2
3. 64 yard2
D = {f, g, k}
L = {a,f,j}
Find the intersection of D and L.
Find the union of D and I.
Answers
Answer:
Step-by-step explanation:
D∩L={f}
D∪L={a,f,g,j,k}
PLEASE HELP ASAP!!
The table of values represents the function g(x) and the graph shows the function f(x). Which statement about the functions is true?
-all of the x-intercepts of f(x) are common to those of g(x)
-f(x) and g(x) intersect at exactly two points
-the minimum value of f(x) is less than the minimum value of g(x)
-f(x) and g(x) have the same y-intercept
Answers
Using function concepts, it is found that the correct statement is given by:
all of the x-intercepts of f(x) are common to those of g(x).
What are the x-intercepts of the functions?They are the values of x when x = 0, hence:
For g(x), it is of x = -1 and x = 1.For f(x), it is of x = -1.Hence, the first statement is correct, and the x-intercept x = -1 of f(x) is common to the x-intercept x = -1 of g(x).
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AC is the diameter of the circle. Angle AWB is 120 degrees. How big is arc BC
Answers
Answer:
60°
Step-by-step explanation:
Arc BC and Angle BWC are the same number of degrees.
When the vertex of an angle is at the center of a circle, its called a Central Angle. A central angle and the arc it "cuts off" have the same number of degrees.
Angle AWB and Angle BWC lay together on a straight line, so they add up to 180°.
180° - 120° is 60°
Angle BWC is 60° so Arc BC is 60°
River drove for 2 hours on the freeway, then decreased their speed by 20 miles per hour and drove for 2 more hours on a country road. If their total trip was 168 miles, then what was their speed on the freeway?
Answers
Answer:
Step-by-step explanation:
Felipe transferred a balance of $3700 to a new credit card at the beginning of
the year. The card offered an introductory APR of 5.9% for the first 4 months
and a standard APR of 17.2% thereafter. If the card compounds interest
monthly, which of these expressions represents Felipe's balance at the end of
the year? (Assume that Felipe will make no payments or new purchases
during the year, and ignore any possible late payment fees.)
OA. ($3700) (1+0 052)*(1.0172)
B.
(83700)(1+0059) (1+0.172)
OC. ($3700)(1+0 59)*(1.0172)*
0.059
12
OD. $3700)(1+0.059)*(1+0.172)
Answers
The expression that represents Felipe's balance at the end of the year is 3700 x [tex]( 1 + \frac{0.059}{4}) ^{4}[/tex] x [tex](1 + \frac{0.172}{8})^{8}[/tex].
What is the expression that represents the balance?The equation that can be used to determine future value with compounding is:
FV = P (1 + r)^nm
Where:FV = Future value P = Present value R = interest rate m = number of compoundingN = number of years
3700 x [tex]( 1 + \frac{0.059}{4}) ^{4}[/tex] x [tex](1 + \frac{0.172}{8})^{8}[/tex].
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if the equation of a function is a rational experssion the function is a rational
Answers
The statement "If the equation of a function is a rational expression the function is a rational" is true.
What is a rational number?If the value of a numerical expression is terminating then they are the rational number then they are called the rational number and if the value of a numerical expression is non-terminating then they are called an irrational number.
If the equation of a function is a rational expression the function is a rational, the statement is true.
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The weight of 3 cans of juice and 2 energy bars is 33.6 ounces. Four energy bars and two cans of juice weigh 27.2 ounces. How much does one energy bar weigh?
Answers
Answer:
1.8 ounces
Step-by-step explanation:
Let :
⇒ weight of a can of juice = x
⇒ weight of an energy bar = y
=============================================================
Equations formed :
3x + 2y = 33.64y + 2x = 27.2============================================================
Multiply Equation 1 by 2 :
⇒ 2 × (3x + 2y) = 2 × 33.6
⇒ 6x + 4y = 67.2 [Equation 3]
===========================================================
Subtract : Equation 3 - Equation 2
⇒ 6x + 4y - 4y - 2x = 67.2 - 27.2
⇒ 4x = 40
⇒ x = 10
===========================================================
Finding the weight of an energy bar :
⇒ 3(10) + 2y = 33.6
⇒ 2y = 3.6
⇒ y = 1.8 ounces
What is the rational number equivalent to 1.28
Answers
Answer:
1 28/99
Step-by-step explanation:
When a number with 1-2 digits is divided by 99, it gets repeated with two digits. For example, 2/99=0.0202020202...
Another example would be 18/99=0.18181818...
Using this information, we can determine that 1.28282828 repeating would be 1 28/99
Let me know if you have any questions! :)
The functoin f has zeros at -3 and 4 witch graph could represent function f
Answers
Since I don't see the graphs:
⇒ I am going to answer by the general format of what you should see
The function has zeros at -3, 4:
⇒ which means that the function must interest the x-axis at x = -3 and
x = 4
Hope that helps!
⇒look at the image I uploaded which shows a possible answer
The line segment located in the circle below is the circle’s ____________
Pi
Area
Radius
Diameter
Circumference
Answers
Find the missing angle
120 & 30
y = [???]
Answers
Answer:
z = 30
Step-by-step explanation:
All angles of a triangle add up to 180:
z + 120 + 30 = 180
z + 150 = 180
z = 180 - 150
z = 30
Use the formula V = r2h to find the radius of a cylinder with a height of 31 and a volume of 775.
Answers
—> 775=r^*31.
Divide 31 on both sides
—> 25=r^2
Square root both values
5=r
50 pts!!! Please answer without links!
Answers
The value of 'a' in the P(X≤a)=0.6 is 5 because at X =5 we get a probability of 0.7. a = 5 is the answer.
What is probability?It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.
From the graph:
P(X ≤ 1) = 0.05
P(X ≤ 2) = 0.1
P(X ≤ 3) = 0.15
P(X ≤ 4) = 0.2
P(X ≤ 5)= 0.2
Add all the probability:
P = 0.05+0.1+0.15+0.2+0.2 = 0.7
P(X≤a)=0.6 (that means the value of the area under the curve 'a' is 0.6)
So the value of a should be 5
Thus, the value of 'a' in the P(X≤a)=0.6 is 5 because at X =5 we get a probability of 0.7. a = 5 is the answer.
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Answer:
Put 5 in the input
What property states that changing the order of two or more terms does what to the value of the sum
Answers
Answer: Commutative property
change 12' 8" to decimal degree equivalent. express the decimal to the nearest ten-thousandths
Answers
The decimal degree of the angle 12' 8" is 0.2022
How to change the decimal degree?The angle measure is given as:
Angle = 12' 8"
As a general rule;
1 degree = 60 minutes1 minute = 60 secondsWhere:
' represents minutes and " represents seconds.
So, we have:
Angle = 12/60 + 8/(60 * 60)
Evaluate the expression
Angle = 0.2022
Hence, the decimal degree of the angle 12' 8" is 0.2022
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Charles has eight different winter scarves, and he wears three at a time. How many different ways can Charles wear three scarves? 6,720 56 112 336
Answers
Answer:
Ans= 6720 ways
Step-by-step explanation:
From Combination rule from Permutation and Combination, nCr
We use 8^C3 or 8C3,
8x7x6x5x4x3x2x1
-------------------------- =6,720
3x2x1
or
8x7x6x5x4x3! /3!, here the 3! cancels each other out, and we're left with 8x7x6x5x4, which equals 6720.