consider the figure below. which of the following lines are parallel? justify your answer.
Answers
Answer:
1. r1 || r2 because of the same side or consecutive interior theorem
2. l1 || l2 because they are corresponding angles
The angle formed between two parallel lines having a common transversal have several common properties
The correct responses are;
1. Lines r₁ and r₂ are parallel
2. Lines, l₁ and l₂ are parallel
lines r₁ and r₂, are parallel
The reason why the given lines are parallel are as follows:
1. The given figures are presented as shown in the attached diagram
From the diagram, we have that the same side interior angles formed by the common transversal l₂ the lines r₁ and r₂ are 63° and 117°, which are supplementary angles (63° + 117° = 180°)
Therefore, lines r₁ and r₂ are parallel given that same side interior angles formed by two parallel lines having the same transversal are supplementary
2. From the attached diagram, we have;
The alternate exterior angles formed between the lines, l₁ and l₂ that have the common transversal r₁ are equal, therefore;
Lines, l₁ and l₂ are parallel, given that the alternate exterior angles formed by two parallel lines having a common transversal are equal
From the diagram, we also have that the other angle of the linear pair angle with the 63° angle is 117°, and the second angle of the linear pair angle is both either corresponding angle and alternate interior angle with the given 117°
Therefore, lines r₁ and r₂, are parallel given that corresponding angles and the alternate interior angles formed between parallel lines having a common transversal are equal
Learn more about the angles formed between parallel lines having a common transversal here:
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Related Questions
What is the value of the rational expression below when xis equal to 4?
Answers
Answer:
answer = 2
The Eighteenth Amendment empowered Congress to enforce the Amendment through legislation;
Step-by-step explanation:
The Eighteenth Amendment empowered Congress to enforce the Amendment through legislation;The Eighteenth Amendment empowered Congress to enforce the Amendment through legislation;The Eighteenth Amendment empowered Congress to enforce the Amendment through legislation;The Eighteenth Amendment empowered Congress to enforce the Amendment through legislation;The Eighteenth Amendment empowered Congress to enforce the Amendment through legislation;
The Eighteenth Amendment empowered Congress to enforce the Amendment through legislation;
PLEASE HELP ME
Answer:
4
Step-by-step explanation:
Which of the following is the radical expression of?
Answers
Answer:
The third answer
Step-by-step explanation:
Remember power over root and the 2 would not be under the root.
Answer:
the third one
Step-by-step explanation:
A group of 8 people are picking up litter along a 4
5
km length of road. Each person is assigned an equal section of the road. How can you divide 4
5
km among 8 people?
Which expression is equivalent to 4
5
÷ 8?
÷ 8
Each person picks up litter from a km length of the road.
Answers
Answer:
Each person picks up litter from a
✔ 1/10
km length of the road.
Which expression is equivalent to 4
5
÷ 8?
✔ 8/10
÷ 8
Step-by-step explanation:
The perimeter of a rectangular garden is 40 it. The length is 2 ft more than the width. Find the length and the width of the garden.
Answers
Answer: Length = 11
Width = 9
Step-by-step explanation:
Let x represent the unknown length.
Let x - 2 represent the unknown width.
The perimeter is equal to 2 times x + (x -2)
Equation:
2 (x + (x - 2)) = 40
x + (x - 2) = 40/2
x + x - 2 = 20
2x - 2 = 20
2x -2 + 2 = 20 + 2
The length is: 2x = 22 -> x = 22/2 -> x = 11
The width is: x - 2 = 9
A national standard requires that public bridges over feet in length must be inspected and rated every 2 years. The rating scale ranges from 0 (poorest rating) to 9 (highest rating). A group of engineers used a probabilistic model to forecast the inspection ratings of all major bridges in a city. For the year 2020, the engineers forecast that % of all major bridges in that city will have ratings of 4 or below. Complete parts a and b. a. Use the forecast to find the probability that in a random sample of major bridges in the city, at least 3 will have an inspection rating of 4 or below in 2020. P(x3) nothing (Round to five decimal places as needed.)
Answers
Answer:
The answer is below
Step-by-step explanation:
A national standard requires that public bridges over 20 feet in length must be inspected and rated every 2 years. The rating scale ranges from 0 (poorest rating) to 9 (highest rating). A group of engineers used a probabilistic model to forecast the inspection ratings of all major bridges in a city. For the year 2020, the engineers forecast that 4%of all major bridges in that city will have ratings of 4 or below.
a. Use the forecast to find the probability that in a random sample of major bridges in the city, at least 3 will have an inspection rating of 4 or below in 2020.
Answer:
This problem is a probability binomial distribution and it can be solved using the formula:
[tex]P(X=x)=C(n,x)p^xq^{n-x}\\\\q=1-p,C(n,x)=\frac{n!}{x!(n-x)!}[/tex]
Hence the solution to the problem is given as:
P(x ≥ 3) = 1 - P(x < 3) = 1 - [ P(x=0) + P(x=1) + P(x = 2)]
Given that p = 4% = 0.04, q = 1 - p = 1 - 0.04 = 0.96, n = 10. Hence:
[tex]P(x=0)=C(10,0)*0.04^{0}*(0.96)^{10-0}=0.6648\\\\P(x=1)=C(10,1)*0.04^{1}*(0.96)^{10-1}=0.277\\\\P(x=2)=C(10,2)*0.04^{2}*(0.96)^{10-2}=0.0519\\\\P(x\geq 3)=1-[0.6648+0.277+0.0519]=0.0063[/tex]
I used 1/3 of a bottle of wax to wax 3/4 of a car. How many cars can I wax with one bottle? Please helppp
Answers
Answer:
2.25 cars are waxed with one bottle
Step-by-step explanation:
1/3 * 3 = 1
3/4 * 3 = 9/4
9/4 = 2.25
bc 3/4 divided by 1/3 equals 9/4 which turns into 2 and 1/4
Find the value of x.
Answers
Answer:
x=21
Step-by-step explanation:
180-126=54
54-12=42
42/2=21
x=21
Write a number that has a 3 that is 10
times the value of the 3 in 7.31
Your answer
Answers
Answer:
3
Step-by-step explanation:
7.31
3 in the tenths place
3 = 3/10 or 0.3
0.3*10=3
explain: 7.31
3 is in 10 place so
3= 3/10 or 0.3 ;)
How do we use the question as the example
Answers
Answer:
what question
Step-by-step explanation:
what is 431x18 estameted? please help fast
Answers
Answer:
7758 :)
Step-by-step explanation:
Answer:
9000
Step-by-step explanation:
need help............
Answers
Answer:
Answer=A
Step-by-step explanation:
(when dividing two powers we subtract the upper power by the bottom one)
[tex]\frac{7^{10} }{7^{3} }[/tex]
=[tex]7^{10-3}[/tex]
[tex]7^{7}[/tex]
What is the range of the function f(x) = 2x+3
Answers
Answer: (-∞,∞)
Step-by-step explanation: The line extends forever in both directions meaning that the endpoints will be negative infinity and infinity.
What was Bear B's average speed in
m/min? No units required for answer.
Answers
Given:
Graph of positions of Bear A and Bear B.
To find:
The average speed of Bear B in m/min.
Solution:
From the graph it is clear that initial point of graph of Bear B is (0,100) and the end point is (60,2800).
The average speed of Bear B is
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
[tex]m=\dfrac{2800-100}{60-0}[/tex]
[tex]m=\dfrac{2700}{60}[/tex]
[tex]m=45[/tex]
Therefore, the average speed of Bear B is 45 m/min.
A ball is dropped from a height of 100 cm. The rebound heights to the nearest centimeter are 60, 36, 22, .... What is the total distance the ball will travel both up an down?
Answers
Answer:
400 cm
Step-by-step explanation:
Given that:
Initial height at which ball was dropped = 100m
Rebound heights to the nearest cm = 60, 36, 22...
First we find the rebound percentage x;
x% * 100m = 60
100x % = 60
x = 60%
Hemce, we need to calculate the rebound velocities which aren't given:
0.6 * 22 = 13.2 = 13cm
0.6 * 13 = 7.8 = 8cm
0.6 * 8 = 4.8 = 5cm
0.6 * 5 = 3cm
0. 6 * 3 = 1.8 = 2 cm
0.6 * 2 = 1.2 = 1cm
The total distance the ball travels UP and DOWN :
(100 + 2(60) + 2(36) + 2(22) + 2(13) + 2(8) + 2(5) + 2(3) + 2(2) + 2(1))
= 400 cm
If someone helps, contact me, and I'll give you 80 points or more if you would like.
Determine which statement is true from the information given. diet sodas = 3 regular sodas = 7
For every 3 regular sodas sold there are 7 diet sodas sold
The ratio of diet sodas to regular sodas sold is 7 : 3
The ratio of regular sodas to diet sodas sold is 7 : 3
For every 7 diet sodas sold there are 3 regular sodas sold
Answers
Answer:
Step-by-step explanation:
d = 3, r = 7
3r = 7d 3(7) = 7(3) 21 = 21 true
d/r = 7/3 3/7 ≠ 7/3 false
r/d = 7/3 7/3 = 7/3 true
7d = 3r 7(3) = 3(7) 21 = 21 true
3 of these statements are true, are you sure you got the question written down correctly?
6. In case of short
circuit............current will flow in
that circuit. *
Answers
Answer:
As suggested in the name itself:
a short circuit makes the circuit 'short' which causes the resistance of the circuit to be close to none
When the resistance is decreased, the amount of current flowing in the circuit increases (ohm's law: R ∝ 1/ I)
Therefore, in case of a short-circuit. More current will flow in the circuit
combine like terms to simplify
1.17 - .07a + (-3.92a)
Answers
Answer:
1.17+3.85
Step-by-step explanation:
1.17-(-3.85a)
There are 16 squares and 20 triangles. What is the simplest ratio of squares to total shapes?
Answers
Answer:
1:6
Step-by-step explanation:
There are 20 triangles and four squares, so we know the first part of the ratio is 4. The total number of shapes is 24, so we get 4:24, and if we simplify, we then get 1:6.
Hope this helps!
There is a total of 16 squares, then the ratio of squares to total shapes is 4:9.
What is an arithmetic operation?The four fundamental operations of arithmetic are addition, subtract, multiply, and division of two or more numbers. Included in them is the study of integers, especially the order of operations, which is important for all other aspects of mathematics, notably algebra, information management, and geometry.
As per the given information provided by the question is,
Total number of squares = 16
Total number of shapes = 16 + 20 = 36
Ratio between squares and total shapes,
= 16 : 36
= 4 : 9.
To know more about arithmetic operation:
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#SPJ2
Who ever answers this I will mark as brainliest
Answers
Answer: uhhhhhh pass
Step-by-step explanation:
Mr. Ortiz is a driving instructor. Of his students, 23 have taken the driver's test and 17 of them have passed
on the first attempt. Mr. Ortiz earns a $300 bonus if 80% of his students pass the test on the first attempt.
How many consecutive students must pass on the first attempt in order for Mr. Ortiz to earn the bonus
Answers
Answer:7
Step-by-step explanation:
Which expression uses the associative property to make it easier to evaluate
14( 1/7• 2/5)
Answers
Step-by-step explanation:
Associative property is a(bc)=(ab)c
14(1/7 * 2/5) = (14* 1/7) 2/5 = 2* 2/5 = 4/5
Answer: (14 x 1/7) 2/5
Step-by-step explanation: yes.
Red has already lost three iphones.He didn't spend a lot of money on his newest cellphone because he knows he will eventually lose that one too.Is it deductive or inductive reasoning?
Answers
Answer:
deductive reasoning
Step-by-step explanation:
This graph shows the solution to which inequality?
(3,-1)
(-3,-3)
Answers
Answer:
its c. y>1/3x-2
Step-by-step explanation:
Just took the quiz
The heart rates in beats per minute for runners who walk briskly on a treadmill for 6 minutes follow a Normal distribution with a mean of 104 and standard deviation of 12.5. What percent of the runners have heart rates above 140?
Answers
Answer:
0.2%
Step-by-step explanation:
We apply the z score formula.
This is given as:
Z score = x - μ/σ
x = Raw score = 140
μ = Population mean = 104
σ = Standard deviation = 12.5
z = 140 - 104/12.5
z = 2.88
Probability value from Z-Table:
P(x<140) = 0.99801
P(x>140) = 1 - P(x<140)
= 1 - 0.99801
= 0.0019884
Approximately = 0.0020
Converting to percent = 0.2%
Therefore, percent of the runners have heart rates above 140 is 0.2%
PLEASE HELP!!! Mates spent $15.00 on protein bars and sports drinks. each bar cost $3.00 and each sports drink cost $1.50. which equation represents the number of protein bars, p, and the number of sports drinks, s, Matea could have bought
Answers
Answer:
15=3s+1.5p
Step-by-step explanation:
can i please get brainliest?
Answer:
15=3s+1.5p
Step-by-step explanation:
15(total money spent)
3s s=amount of bars
1.5p p= amount of sports drinks
IDK WHY IT SAYS IM A COLLEGE PERSON IM NOT BUT UM I NEED HELP WITH THIS PLEASEEEEEE
Answers
Answer:
option 3
Step-by-step explanation:
Answer:
it's option 3 i think
Step-by-step explanation:
HOW CAN WE SOLVE THIS 5-2+17=7 PLEASE HELP IAM CONFUSED
5X+17=7
Answers
Answer:
x = -2Step-by-step explanation:
5X + 17 = 7
subtract 17 each side
5x + 17 - 17 = 7 - 17
divide 5 both sides
5x = -10
simplify
5x/5 = -10/5
x = -2
Compute the estimated regression's prediction for the average score of students given 98, 129, or 159 minutes to complete the exam.
Given 98 minutes, the estimated regression's prediction for the average score of students is 91.94 .
Given 129 minutes, the estimated regression's prediction for the average score of students is 108.37
Given 159 minutes, the estimated regression's prediction for the average score of students is 124.27 (Round your responses to two decimal places.)
Compute the estimated gain in score for a student who is given an additional 32 minutes on the exam.
The estimated gain in score for a student who is given an additional 32 minutes on the exam is (Round your response to two decimal places.)
Answers
Answer:
The estimated gain in score for a student who is given an additional 32 minutes on the exam is 16.96
Step-by-step explanation:
The estimated regression prediction is given by:
[tex]\hat{y}=40+0.53x[/tex]
Where x denotes the time
y denotes the average score
A)
Substitute x = 98
[tex]\hat{y}=40+0.53(98) = 91.94[/tex]
B)
Substitute x = 129
[tex]\hat{y}=40+0.53(129) = 108.37[/tex]
C)
Substitute x = 159
[tex]\hat{y}=40+0.53(159) = 124.27[/tex]
D)the estimated gain in score for a student who is given an additional 32 minutes on the exam.
[tex]\hat{y}=40+0.53(x+32)=40+0.53x+9.57=y+16.96[/tex]
So, the estimated gain in score for a student who is given an additional 32 minutes on the exam is 16.96
Please help me now. I am stuck on this one.
Answers
Answer:
Step-by-step explanation:
Formula: Area=(a+b)/2 * h
72=(16+8)/2*h
72=24/2*h
72=12*h
h=72/12
h=6
It will be nice if you give me brainlies.Good luck!
Evaluate:
54 - 75 + 81 - (-27) + 53
Answers
Answer:
140
Step-by-step explanation:
Answer:
140.
Step-by-step explanation:
PEMDAS.
Since there isn't any problems that aren't adding, we can just do it step by step.
54 - 75.
-21.
Add 81.
60.
Subtract -27.
87.
Add 53.
140.
Brainiest?