Answers
The ASA and AAS theorems are used in the proof as explained below for each given statements.
How to Write a Proof?A proof is a logical argument that demonstrates the truth of a mathematical statement.
The proof that can be used to prove each given statements are demonstrated below.
14. Proof for ∆UVY ≅ ∆XVW:
Statement Reason
1. V is the midpoint of YW. 1. Given
2. UY || XW 2. Given
3. YV ≅ WV. 3. Def. of midpoint
4. <UYV ≅ <XWV. 4. Alternate <s theorem
5. <UVY ≅ <XVW 5. Vertical<s theorem
6. ∆UVY ≅ ∆XVW 6. ASA
15. Proof for ∆MSP ≅ ∆RQP:
Statement Reason
1. MS ≅ RQ 1. Given
2. MS || RQ 2. Given
3. <MSP ≅ <RQP. 3. Alternate <s theorem
5. <MPS ≅ <QPR 4. Vertical<s theorem
6. ∆MSP ≅ ∆RQP 6. AAS
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Related Questions
Please solve this linear equation
7x-3y=-5
3x+2y=11
Answers
The value of x and y in the equation are 1 and 4 respectively
What is Simultaneous equation?Simultaneous equations are two or more algebraic equations that share variables e.g. x and y . They are called simultaneous equations because the equations are solved at the same time. For example, below are some simultaneous equations: 2x + 4y = 14 , 4x − 4y = 4.
7x-3y=-5 equation 1
3x+2y=11 equation 2
using elimination method, we multiply the coefficient of x by both equations
21x- 9y = -15 equation 3
21x +14y = 77 equation 4
subtract equation 3 from 4
23y = 92
y = 92/23
y = 4
substitute 4 for y in equation 1
7x -3(4) = -5
7x -12 = -5
7x = -5+12
7x = 7
x= 7/7= 1
therefore the value of x and y are 1 and 4 respectively
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Lucy says the hypotenuse is 15 Annie says its 117. Timo says it rounds to 11.
Explain who is right. PROVE your answer using Pythagoras visually or numerically.
Answers
Answer: Timo is correct; the hypotenuse rounds to 11
Work Shown:
[tex]a^2+b^2 = c^2\\\\c = \sqrt{a^2+b^2}\\\\c = \sqrt{6^2+9^2}\\\\c = \sqrt{36+81}\\\\c = \sqrt{117}\\\\c \approx 10.81665\\\\c \approx 11\\\\[/tex]
This confirms Timo is correct.
It appears Lucy mistakenly added the side lengths 6 and 9 to get 6+9 = 15, which is not the correct way to get the hypotenuse.
Annie mentioning the 117 seems to suggest that she might have forgotten about the square root, since we got [tex]\sqrt{117}[/tex] earlier in the steps shown above.
If Annie said [tex]\text{The hypotenuse is } \sqrt{117} \text{ units long}[/tex], then she would be correct. Though it's probably better to go with the decimal form (rounding however you want) to get a better sense of how long the hypotenuse is.
gravel is being dumped from a conveyor belt at a rate of 10 cubic feet per minute. it forms a pile in the shape of a right circular cone whose base diameter and height are always equal. how fast is the height of the pile increasing when the pile is 25 feet high?
Answers
Below is the answer
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Lawrence worked 12 days for a total of 112.8 hours. How many hours did he average per day?
Answers
Answer:
112.8 hours / 12 days
112.8/12 = average of 9.4 hours per day
Sheng drives at a constant speed for 0.2
hours to get to the train station. He then boards a train that takes him 35
miles to downtown. His whole trip is 42
miles long.
How can Sheng determine his driving speed?
Answers
The train travels an average 12 miles/hr
We always need to be working in the same units, so lets convert the trains speed to minutes since the time traveled is in minutes.
12 miles / 60 min = 0.2 miles/min
which part of the expression -2(3 +4) is the sum of two terms
Answers
The part containing the sum of two terms in the given expression can be found to be as (3 + 4) and (6 + 8) respectively.
What is an Algebraic expression?An algebraic expression can be obtained by doing mathematical operations on the variable and constant terms.
The variable part of an algebraic expression can never be added or subtracted from the constant part.
here, we have,
The given expression is 2(3 + 4).
It can be rewritten as follows,
2(3 + 4)
=2 × 3 + 2 × 4
=6 + 8
or, 2 × 7
Thus, in order to find the expression for sum of two terms in the given expression, there can be two possible ways, the first is (3 + 4) and the other is (6 + 8).
Hence, the sum of two terms in the given expression is found to be as (3 + 4) and (6 + 8) respectively.
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the area of a rectangle field is 7350m to the second power. if the length of the field is 98m, what is its width
Answers
Answer:
Step-by-step explanation:
The formula of the area of a triangle is equal to Length multiply by Width[A = L * W]
Therefore:7350m[tex]x^{2}[/tex] = 98 * W.7350m[tex]x^{2}[/tex] = 98W.7350m[tex]x^{2}[/tex]/98 = 98W/98.Thus: 7350 divided by 98 is 75 which is the width.W=75m .True or false
The following graph represents a maximum:
f(x)=3x^2+2
Answers
Answer:
False
Step-by-step explanation:
Answer come only two
on two tosses of a coin, what is the probability of head on 1st toss or head on 2nd toss (assume all outcomes are equally likely)
Answers
As an alternative, we could contend that the probability of the first coin coming up heads or tails is 1/2, the probability of the second coin coming up heads or tails is 1/2, and so on for the third and fourth coins.
This would reduce the probability of any given sequence of heads and tails to (1/2)x(1/2)x(1/2)x(1/2)=(1/16).
The curve achieves its greatest value for N=2 heads, which is the case where the outcome is most likely. This is exactly what you would anticipate: if each coin has an equal chance of landing heads or tails, then in four flips, half of the results should be heads, making N = 4x(1/2) = 2 the most likely result.
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Katy wants to wrap a present that is 15cm wide, 18cm deep and 4cm high. How much wrapping paper will she need to use?
Answers
If Katy wants to wrap a present that is 15cm wide, 18cm deep and 4cm high , then amount of wrapping paper that she need to use is 804 cm² .
Katy is wrapping a gift ,
the dimensions of the box that needs to be wrapped is ⇒
length(l) is = 15cm , width(w) is = 18cm and height(h) is = 4cm .
the present is in shape of cuboid ,
we know that Total Surface Area of cuboid is = 2(lw + wh + hl) ;
substituting values of length , width and height ,
we get ;
Area is = 2(15×18 + 18×4 + 4×15)
= 2( 270 + 72 + 60)
= 2( 402 )
= 804 cm² .
Therefore , Katy will need 804 cm² of wrapping paper to wrap the gift .
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Mandy owns a car dealership in which her employees earn commission for each car they sell in addition to a weekly salary. One employee sells 5 cars and makes $1,700 that week. A second employee sells 6 cars and makes $1,940 that week.
Answers
The equation in slope-intercept form as required is; y = 240x + 500
What is partial variation?This is when the value of the dependent variable depends partly on the value of the independent variable and partly on an initial value that is not 0
According to the statements in the task content;
One employee sells 5 cars and makes $1,700 that week.
A second employee sells 6 cars and makes $1,940 that week.
Hence, it follows from partial variation that;
1700 = 5a + b
1940 = 6a + b
Hence, by solving simultaneously, it follows that;
a = 240
b = 500
Hence, the equation in slope-intercept form as required is; y = 240x + 500
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The dot plots below show the number of students present in Mr. King's first and second period classes each day in April.
2 dot plots showing the number of students present in Mr. King's first and second period. X axis is labelled number of students present.
The mean absolute deviation for each class period is 1.4. The difference between the mode number of students present for each class period is how many times the mean absolute deviation?
A.
6
B.
5
C.
7
D.
4
Answers
The mode of each data-set is given by the input that has the most dots in the dot plot.
After obtaining the mode, the difference is obtained subtracting the mode from the MAD of 1.4 for each data-set.
How to obtain the modes and the difference?A dot plot shows the number of times that each observation appears in the data-set.
The mode of a data-set is the observation that appears the most times in the data-set, hence it will be given by the observation with the most dots in the dot plot.
The mean absolute deviation is of 1.4, then for each data-set the mode is subtracted by 1.4.
Missing InformationThe problem is incomplete, hence the answer was given in general terms.
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5) Which number is 10 times less than 45.3?
a) 453.0
b) 45.30
c) 4.53
d) 0.453
Answers
Answer: 4.53
Step-by-step explanation:
10 times less than 45.3 means that you will be looking for an answer that is the solution to 45.3 / 10, which equals 4.53.
You have a recipe that indicates to use 7 parts of sugar for every 6 parts of milk. You use 28 cups of sugar. How much milk do you need?
Answers
7/6 = 28/x
To solve for x, you can cross-multiply:
7 * x = 6 * 28
Simplifying:
x = 6*28/7
x = 24
So, you would need 24 cups of milk.
Answer:
28 cups of sugar / 7 parts of sugar = 4 cups
If 4 cups is 1 part, 6 parts of milk would be 4 x 6
4 x 6
= 24
You would need 24 cups of milk.
The table shows the decrease in the amount of chicken feed in a farmer's barn over a seven-month period. Let x represent the number of months since March. Write a linear regression equation for the data. Explain what does the linear regression equation for the data represents in the problem situation.
Answers
This data's linear regression equation is y = mx + b, where y is the quantity of chicken feed, x is the number of months since March, m is the line's slope (or the rate at which y changes with respect to x), and b is the y-intercept (or the value of y at x = 0).
The pace at which the amount of chicken feed has been decreasing over time is seen by the slope of the line. The beginning quantity of chicken feed in the barn in March is represented by the y-intercept.
Based on the rate of reduction and beginning quantity for each month since March, the linear regression equation may be used to forecast the amount of chicken feed in the barn in the issue situation.
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{96 divide[36 divide 3-(18x2-30)]} divide(31-16+1)
Answers
Note that the answer to the expression {96 ÷ [36÷3-(18 x 2 - 30)]} ÷ (31-16+1) Is: one (1). This problem is solved using PEMDAS.
What is PEMDAS?
PEMDAS is the acronym for parenthesis, exponents, multiplication, division, addition, and subtraction. These operators must be solved exactly in the order given above. Thus:
{96 ÷ [36÷3-(18 x 2 - 30)]} ÷ (31-16+1)
⇒ {96 ÷ [36÷3-(6)]} ÷ (31-16+1)
⇒ {96 ÷ [12-6]} ÷ (31-16+1)
⇒ {96 ÷ 6} ÷ (31-16+1)
⇒ 16 ÷ 16
⇒ 1
Thus, it is correct to state that the answer to the mathematical expression {96 ÷ [36÷3-(18 x 2 - 30)]} ÷ (31-16+1) is 1 or
{96 ÷ [36÷3-(18 x 2 - 30)]} ÷ (31-16+1) = 1
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please look at the attachment
Answers
The points for the inequality are plotted on the graph attached below.
What is inequality?
A linear inequality is one that, if the equals relation were used in place of the inequality, would provide a linear equation. When multiplying or dividing both sides by a negative number, the direction of the inequality is reversed when the problem is solved. The solution set for an inequality is the set of all solutions.
We are given an inequality as y ≤ 6x/5 - 6
Now, in order to plot the points, we need to find x and y
So, let y be 0, then
⇒0 ≤ 6x/5 - 6
⇒6 ≤ 6x/5
⇒6 ≤ 6x/5
⇒5 ≤ x
So, we get first point as (5,0).
Now, let x=0, then
⇒y ≤ 6(0)/5 - 6
⇒y ≤ -6
So, we get second point as (-6,0).
From these two points, the graph is plotted which is shown below.
Hence, the graph for the inequality is plotted.
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70%
60%
50%
40%
30%
20%
10%
0%
Federal Government Funding of Stem Cell Research
55%
58%
52%
Should fund
41% 39%
44%
Should not fund
4%
Total
Men
Women
3% 4%
No opinion
1. There are about 117,000,000 adult American men. About how many of these men
think the federal government should fund stem cell research?
Answers
Based on the given percentages, the number of adult American men who think the federal government should fund stem cell research is 67,860,000.
What is the percentage?The percentage is the ratio of a value in relation to another.
The percentage is determined as the quotient of the numerator divided by the denominator, multiplied by 100.
The percentage of men who approve of stem cell research = 58%
The percentage of men who do not approve of the research = 39%
The percentage of men who have no opinion on the research = 3%
The estimated number of adult American men = 117,000,000
Thus, based on the percentage of men who approve of stem cell research, the number is 67,860,000. (117,000,000 x 58%).
Federal Government Funding of Stem Cell Research
Total Men Women
Should fund 55% 58% 52%
Should not fund 41% 39% 44%
No opinion 4% 3% 4%
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A camera has a listed price of $653.99 before tax. If the sales tax rate is 8.5%, find the total cost of the camera with sales tax included.
Round your answer to the nearest cent, as necessary.
Answers
Answer:
$709.58
Step-by-step explanation:
The total cost is 100% plus the tax rate of 8.5%, it will be 108.5%
To find the cost of the camera with the sales tax included, we take
$653.99 divided by 100, then times 108.5 = $709.58
So, the cost of the camera with sales tax is $709.58
Question 15 of 46
What identity can be used to rewrite the expression 4x² - 9?
A. Difference of Squares
B. Sum of Cubes
C. Difference of Cubes
D. Pythagorean Triples
SUBMIT
Answers
Answer:
A.
Step-by-step explanation:
4x² is a perfect square because it is (2x)²
9 is a perfect square with a value of 3
so if we factor 4x² - 9 we can use the difference of two squares to get:
(2x+3)(2x-3)
An architect is designing a new windmill with four sails. In his sketch, the sails' center of rotation is the origin, (0,0), and the tip of one of the sails, point Upper R,
has coordinates (2,-4).
He wants to make another sketch that shows the windmill after the sails have rotated 180 degrees about their center of rotation. What would be the coordinates of Upper R prime ?
The coordinates of Upper R prime would be ______?
Answers
The coordinates of upper R prime are (-2, 4).
Now, According to the question:
Rotation describes the circular motion of an object around its center. There are different ways things can rotate. Rotation of the Earthre. A very familiar kind of rotation is when a spherical, three-dimensional object turns around an invisible line inside its center.
The sails center of rotation is the origin (0,0)
The top of one sails point R(2, -4).
A 180 degree rotation make you turn (x, y) into (-x, -y),
So, the point turn (2,-4 ), into (-2, 4).
Therefore the coordinates of R are (-2, 4).
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given f(x) = 3x^2 - 9, find f(1)
Answers
Answer:
Answer is in attached photo.
Step-by-step explanation:
SolutionSolution is in attached photo, this question is testing on function substitution. (Substituting an input to get an output.)
in hillsboro, the use of landlines has been declining at a rate of 10% every year. if there are 86,652 landlines this year, how many will there be in 12 years?
Answers
Answer: A decline of 10% per year means that the number of landlines will be multiplied by 0.9 (100% - 10%) every year.
So, in 12 years the number of landlines will be multiplied by 0.9^12 = 0.531441
So, in 12 years there will be 86,652 * 0.531441 = 46,115.69 landlines.
Rounded to the nearest whole number there will be 46,116 landlines in 12 years.
Step-by-step explanation:
Answer: 24,473
Step-by-step explanation: This is the formula for exponential decay:
y=a(1–r)t
In this formula, a is the initial amount, r is the rate of decrease expressed as a decimal, t is the elapsed time, and y is the final amount.
solve
Plug in 86,652 landlines for the initial amount, 0.1 for the rate of decrease, and 12 years for the time elapsed.
y
= a(1–r)t
y
= 86,652(1–0.1)12 Plug in values
y
= 86,652(0.9)12 Subtract
y
= 86,652(0.28242…) Simplify
y
= 24,473.08419… Multiply
Round to the nearest whole number.
24,473.08419… → 24,473
To the nearest whole number, there will be 24,473 landlines.
if you are driving from vegas to los angeles, how fast would you need to drive to make it there in 3.5 hours?
Answers
You need to drive 122.86 km/ h to driving from Vegas to los Angeles in 3.5 hours
What is velocity?It is a physical quantity that indicates the displacement of a mobile per unit of time, it is expressed in units of distance per time, for example (miles/h, km/h).
The formula and procedure we will use to solve this exercise is:
v = x /t
Where:
x = distancet = timev = velocityInformation about the problem:
x = 430 km (distance from Vegas to los Angeles)t = 3.5 hoursv = ?Applying the velocity formula, we get:
v = x /t
v = 430 km / 3.5 h
v = 122.86 km/ h
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x^-4/x^3 times x^-7 in equivalent expression
Answers
x^-4/x^3 times x^-7 in equivalent expression is x⁻¹⁴
What are index forms?The index form of a number can be defined as the number that is written as an exponential expression.
It is also seen as the single number that is raised to another number.
The rules of index forms are;
Multiplying the index forms when they have the same base, add the exponents or powersDividing indices, in dividing, they must have the same base so subtract the powers Brackets with indices. When there is a power outside the parentheses, then multiply the powersFrom the information given, we have that;
x⁻⁴/x³ × x⁷
Since the denominators are of the same base, add the powers
x⁻⁴/x³⁺⁷
Add the values
x⁻⁴/x¹⁰
Now, subtract the powers
x⁻¹⁴
Hence, the value is x⁻¹⁴
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A spinner with repeated colors numbered from 1 to 8 is shown. Sections 1 and 8 are purple. Sections 2 and 3 are yellow. Sections 4, 5, and 6 are blue. Section 7 is orange.
A spinner divided into eight equal colored sections, with one orange, two purple, two yellow, and three blue.
Which statement about probability is true?
The probability of landing on orange is greater than the probability of landing on purple.
The probability of landing on yellow is less than the probability of landing on orange.
The probability of landing on orange is equal to the probability of landing on yellow.
The probability of landing on purple is equal to the probability of landing on yellow.
Answers
The probability of landing on purple is equal to the probability of landing on yellow. Therefore, option D is the correct answer.
What is the probability?Probability can be defined as the ratio of the number of favourable outcomes to the total number of outcomes of an event.
We know that, probability of an event = Number of favourable outcomes/Total number of outcomes
Given that, a spinner divided into eight equal colored sections, with one orange, two purple, two yellow, and three blue.
Here,
Probability of landing on orange is 1/8
Probability of landing on purple is 2/8 =1/4
Probability of landing on yellow is 2/8 =1/4
Probability of landing on blue is 3/8
Therefore, option D is the correct answer.
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What is equal to 4 pencils every 2 students
Answers
Solve the quadratic equation using the square root method:
-108 = (x-11)^2 +13
Answers
Answer:
[tex]\sf x=11+11i\\x=11-11i[/tex]
Step-by-step explanation:
Given quadratic equation:
[tex]\sf -108=(x-11)^2+13[/tex]
Subtract 13 from both sides:
[tex]\implies \sf -108-13=(x-11)^2+13-13[/tex]
[tex]\implies \sf -121=(x-11)^2[/tex]
Switch sides:
[tex]\implies \sf (x-11)^2=-121[/tex]
[tex]\textsf{For $(g(x))^2=f(a)$ the solutions are $g(x)=\pm\sqrt{f(a)}$}[/tex]
[tex]\implies \sf x-11=\pm \sqrt{-121}[/tex]
Rewrite -121 as 11² · -1 :
[tex]\implies \sf x-11=\pm \sqrt{11^2 \cdot-1}[/tex]
[tex]\textsf{Apply radical rule} \quad \sqrt{ab}=\sqrt{a}\sqrt{b}:[/tex]
[tex]\implies \sf x-11=\pm\sqrt{11^2} \sqrt{-1}[/tex]
[tex]\implies \sf x-11=\pm11\sqrt{-1}[/tex]
[tex]\textsf{Apply\;imaginary\;number\;rule}:\quad \sqrt{-1}=i[/tex]
[tex]\implies \sf x-11=\pm11i[/tex]
Add 11 to both sides:
[tex]\implies \sf x=11\pm11i[/tex]
Therefore, the solutions are:
[tex]\implies \sf x=11+11i[/tex]
[tex]\implies \sf x=11-11i[/tex]
from a (western) standard 52-card deck, how many ways are there to draw two cards such that the first card is a spade and the second card is a queen?
Answers
So, there are 52 ways to draw two cards such that the first card is a spade and the second card is a queen.
In a standard 52-card deck, there are 13 cards of each suit: spades, hearts, diamonds, and clubs. Each suit has 4 face cards (Jack, Queen, King, and Ace) and 9 numbered cards (2 through 10).
To find the number of ways to draw two cards such that the first card is a spade and the second card is a queen, we first need to determine the number of spades in the deck, and then the number of queens.
There are 13 spades in a standard 52-card deck, so there are 13 ways to draw a spade as the first card.
There are 4 queens in a standard 52-card deck (one from each suit), so there are 4 ways to draw a queen as the second card.
To find the total number of ways to draw two cards such that the first card is a spade and the second card is a queen, we multiply the number of ways to draw each card: 13 * 4 = 52 ways.
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There are 875 hotel rooms in Edwin's city. During a convention, 16% of the hotel rooms were occupied. How many occupied hotel rooms were there during the convention?
Answers
The number of occupied rooms is 140 rooms
What is percentage?Percentage can be defined as a ratio or number that is expressed as a fraction of the number, 100.
It is denoted the the percent sign, "%"
Percentage is known as a dimensionless number. This means that is it has no unit of measurement.
They can also be represented in fraction or decimal forms, like 0.3%, 0.5%, etc
From the information given, we have that;
875 hotel rooms were avaliable16% of the rooms were occupiedThe number of occupied rooms is;
= 16/100 × 875
Find the fraction
=0. 16 × 875
multiply the values
= 140 rooms
Hence, the value is 140 rooms
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