Answers
Answer:
1. 58 = 5x-2, 60 = 5x, x = 12
2. 134 = 16x+22, 112 = 16x, x = 7
3. 125 = 7x-1, 126 = 7x, x = 18
4. 133+9x+2 = 180, 9x=45, x=6
5. 8x-77 = 3x+38, 5x = 115, x=23
6. 11x-47 = 6x-2, 5x = 45, x=9
7. 13x-21 = 5x+75, 8x = 96, x=12
8. 5x+3+9x-33 = 180, 14x = 210, x=15
9. 8x-31 = 6x+3, 2x = 34, x=17
5y+35+6(17)+3 = 180, 5y = 40, y = 8
10. 29x-3+15x+7 = 180, 44x = 176, x=4
13y-17+15(4)+7 = 180, 13y = 130, y=10
1. x = 12
2. x = 7
3. x = 18
4. x = 5
5. x = 23
6. x = 9
7. x = 12
8. x = 15
9. x = 17; y = 8
10. x = 4; y = 10
To find the value of each missing variable(s), we would need to apply our knowledge of algebra. However, recall the following rules of angles in parallel lines:
corresponding angles are congruent (i.e. equal to each other)vertically opposite angles are congruent alternate angles are congruent same-side interior angles are supplementary (i.e. sum up to give 180°alternate exterior angles are congruent.Let's solve the given problems as shown below given that line l is parallel to line m:
1. [tex]58 = (5x - 2)[/tex] (corresponding angles)
solve for x
[tex]58 = 5x - 2\\58 + 2 = 5x - 2 +2[/tex] (addition property of equality)
[tex]60 = 5x \\\frac{60}{5} = \frac{5x}{5}[/tex](division property of equality)
[tex]12 = x\\x = 12[/tex]
2. [tex]134 = 16x+22[/tex] (alternate exterior angles)
[tex]\\134 - 22 = 16x +22-22[/tex] (subtraction property of equality)
[tex]134 - 22 = 16x +22-22\\112 = 16x\\\frac{112}{16} = \frac{16x}{16}[/tex](division property of equality)
[tex]7 = x\\x = 7[/tex]
3. [tex]7x - 1 = 125[/tex] (alternate angles)
[tex]7x - 1 + 1 = 125 + 1\\7x = 126\\\frac{7x}{7} = \frac{126}{7} \\x = 18[/tex]
4. [tex](9x+2) + 133 = 180[/tex] (same-side interior angles)
[tex]9x+2 + 133 = 180\\9x + 135 = 180\\9x + 135 - 135 = 180 - 135\\9x = 45\\\frac{9x}{9} = \frac{45}{9} \\x = 5[/tex]
5. [tex]3x+38 = 8x-77[/tex] (alternate exterior angles)
[tex]77 + 38 = 8x - 3x\\115 = 5x\\\frac{115}{5} = \frac{5x}{5} \\23 = x\\x = 23[/tex]
6. [tex]6x-2 = 11x-47[/tex] (corresponding angles)
[tex]6x-2 = 11x-47\\47 - 2 = 11x - 6x\\45 = 5x\\x = 9[/tex]
7. [tex]5x+75 = 13x - 21[/tex] (alternate angles)
[tex]5x+75 = 13x - 21\\21 + 75 = 13x - 5x\\96 = 8x\\12 = x\\x = 12[/tex]
8. [tex](5x+3)+(9x-33)= 180[/tex] (same-side interior angles)
[tex]5x+3+9x-33= 180\\14x - 30 = 180\\14x - 30 + 30 = 180 + 30\\14x = 210\\x = 15[/tex]
9. [tex]8x-31 = 6x+3[/tex] (alternate angles)
[tex]8x - 6x = 31 + 3\\2x = 34\\x = 17[/tex]
Solve for y
[tex](5y + 35) + (6x + 3) = 180[/tex] (same-side interior angles)
[tex]5y + 35 + 6x + 3 = 180\\[/tex]
Plug in the value of x
[tex]5y + 35 + 6(17) + 3 = 180\\5y + 35 + 102 + 3 = 180\\5y + 140 = 180\\5y = 180 - 140\\5y = 40\\y = 8[/tex]
10. [tex](29x-3)+(15x+7) = 180[/tex](supplementary angles)
Solve for y
[tex]13y - 17 = 29x - 3[/tex] (alternate exterior angles)
Plug in the value of x
[tex]13y - 17 = 29(4) - 3\\13y - 17 = 116 - 3\\13y - 17 = 113\\13y = 113 + 17\\13y = 130\\y = 10\\[/tex]
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Related Questions
70% off
original price!
Abdul wants to buy a cat calendar. The original price is $5.30. What is the sale price?
I need this worked out please
Answers
Answer:
the price with the offer is going to be 1.59$
Step-by-step explanation:
[tex] \frac{x}{5.30} = \frac{70}{100} [/tex]
[tex]100(x) = 70(5.30)[/tex]
[tex]100(x) = 371[/tex]
[tex] \frac{100(x)}{100} = \frac{371}{100} [/tex]
[tex]x = 3.71[/tex]
[tex]70\% \: \: \: of \: \: \: 5.30 \: \: \: is \: \: \: 3.71[/tex]
[tex]5.30 - 3.71 = 1.59[/tex]
Question 13) Olivia has read 143 pages of a 220 page novel. What
percentage of the book does she still need to read? *
Answers
Answer:
77%
Step-by-step explanation:
Answer:
The answer to Question 13 is 35%.
Step-by-step explanation:
Subtract 143 from 220, which will give you 77. Then, you take that 77 and search, "77 out of 220" in Google. You should get 35 and just put the percentage symbol. Olivia still needs to read 35% of the 220 page book:).
Aubree drives 15 miles in 20 minutes. If she drove three hours in total at the same rate, how far did she go
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Rewrite 12/20 with the denominator of 100
Explain how to get it
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PLEASE PLEASE HELP ME I REALLY NEED HELP
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Answer:
(a) yes it does
(b) the rate is constant because the rate of change (slope) is the same throughout the function.
(c) The rate, or rate of change, is -1/2.
y1 - y2/x1-x2
4 - 2/3 - 9
2/-6
-1/2
what is it???????????
Answers
Answer:
4/5
Step-by-step explanation:
The rise is 4, and the run is 5. The rise comes first, so the answer is 4/5. The line is positive.
Answer:
slope = 4/5
Step-by-step explanation:
The best way to find the slope with just a line is to pick the most direct points on the graph, meaning points that are not in between numbers but right on the graph lines
y value - y value over x value - x value
Points: (-2,0) and (3,4)
4-0 = 4
3-(-2) = 5
4/5
What is the solution to the system of equations below?
y=-x+6 and y-x-6
O no solution
O infinitely many solutions
O (-18, 12)
O (18, 0)
Answers
Answer:
O (-18, 12)
Step-by-step explanation:
brainiest plz
Given AABC : ADEF, find x.
E
B
x
8
А
С
D
12.
18
10
12
14
27
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Answer:
bx8
Step-by-step explanation:
What is the value of x?
Enter your answer in the box
Answers
Answer:
The letter "x" is often used in algebra to mean a value that is not yet known. It is called a "variable" or sometimes an "unknown". In x + 2 = 7, x is a variable, but we can work out its value if we try! A variable doesn't have to be "x", it could be "y", "w" or any letter, name or symbol.
Step-by-step explanation:
Which sequence of transformations will map figure Q onto figure Q′?
Two congruent quadrilaterals are shown on a coordinate plane; quadrilateral Q with coordinates negative 9 comma 2, negative 6 comma 4, negative 4 comma 4, and negative 2 comma 2; quadrilateral Q prime with coordinates 2 comma 2, 4 comma 4, 6 comma 4, and 9 comma 2.
A) Translation of (x, y + 2), reflection over x = 1, and 180° rotation about the origin
B) Translation of (x, y − 2), reflection over x = 1, and 180° rotation about the origin
C) Translation of (x, y − 2), reflection over y = 1, and 180° rotation about the origin
D) Translation of (x, y + 2), reflection over y = 1, and 180° rotation about the origin
Answers
Answer:
Which sequence of transformations will map figure Q onto figure Q′?
Its D.Translation of (x, y + 2), reflection over y = 1, and 180° rotation about the origin
Step-by-step explanation:
The sequence of transformations that will map figure Q onto figure Q′ : 'Translation of (x, y + 2), reflection over y = 1, and 180° rotation about the origin.'
The correct answer is option (D)
What is translation?"It is a geometric transformation in which the displacement of a figure from one place to another."
What is reflection?"It is a geometric transformation where all the points of an object are reflected on the line of reflection."
What is rotation?"It is a transformation in which the object is rotated about a fixed point."
For given question,
Quadrilateral Q with coordinates (-9, 2) ,(-6, 4) ,(- 4, 4) , and (-2, 2) Quadrilateral Q' with coordinates (2, 2), (4, 4), (6, 4), and (9, 2)
Consider a point (-4, 4) of quadrilateral Q. If we reflect Q over x = 1, then it would push the x coordinate of (-4, 4) to new x value 5 units to the right of x = 1, which is x = 6, and 180 rotation would make x = -6 But x = -6 is not in Q' . So it must be reflection over y = 1.Consider the transformations at option C, First translate to (x, y - 2) So, the translation of (-4,4) becomes (-4, 2), reflection over y = 1 gives (-4, 4), and 180° rotation about origin gives (4, -4) which is not the coordinate of Q'Now, consider the translation of (x, y + 2) So, the translation of (-4, 4) becomes (-4, 6), reflection over y = 1 gives (-4, -4), and 180° rotation about origin gives (4, 4) which is the coordinate of Q'Therefore, the sequence of transformations that will map figure Q onto figure Q′ : 'Translation of (x, y + 2), reflection over y = 1, and 180° rotation about the origin'
The correct answer is option (D)
Learn more about geometric transformations here:
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which of the equations below has a slope of 1/4
Answers
Answer:
uh you didnt put the picture please put the picture i really want to help you:)
Step-by-step explanation:
Answer:
bra
Step-by-step explanation:
Please only answer if you know
Answers
Answer:
A, C
Step-by-step explanation:
A.)
32 / 8 * 5.25 ----> 4 * 5.25 ----> 21
C.)
4 * 12.5 / 2----> 49 / 2 ----> 24.5
Answer:
between 20 & 30?
A & C
Step-by-step explanation:
A) 32 / 8 * 5.25 = 21
B) -18 / 6 * 9 = -27
C) 4 * 12.5 / 2 = 25
D) 12 * 4[tex]\frac{1}{3}[/tex] / -2 = -26
two boats leave a ramp traveling in opposite directions. The second boat is 10 miles per hour faster than the first. After 3 hours they are 150 miles apart. Find the speeds of the boats.
Answers
Answer:
220 mph ; 230 mph
Step-by-step explanation:
Given that :
Speed of First boat = x
Speed of Second boat = y
y = (10 + x) mph
Distance apart after 3 hours = 150 miles
Speed of the boats :
Speed / time = distance
First boat distance = x / 3
Second boat distance = (10+x) /3
x/3 + (10+x)/3 = 150
x + 10 + x = 150 * 3
2x + 10 = 450
2x = 450 - 10
2x = 440
x = 220 mph
Speed of second boat = 220 + 10 = 230 mph
What percent of the rectangle below is shaded (hint think about the fraction or ratio of
shaded to total)?
33%
40%
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25%
Answers
1 yard = 3 feet
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HELP ASAP
Answers
Answer: 20
Step-by-step explanation: 3 feet in 1 yard, there are 6 yards.
6 x 3 = 18 feet plus the 2 extra = 20 feet
Which of the following numbers is irrational?
A) 6.124
B) √7
C) √0.25
D) 0.12¯¯¯¯
Answers
Answer:
B
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
The last answer choice is $0.08 per minute
PLEASE help I'll give 20 points
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Answer:
If it's 16, then it's -4 > x
Step-by-step explanation:
Ignore the inequality sign first and solve 12 = -3x
This would equal -4 = x
Now, when you divide or multiply both sides by a negative, you have to change the inequality sign so you change it from -4 > x to -4 < x
what is y<-x+5 and y≤ 2x-1??
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9514 1404 393
Answer:
see attached
Step-by-step explanation:
The pair of inequalities is graphed in the attachment.
The first inequality graphs as a shaded area below the dashed line y=-x+5.
The second inequality graphs as a shaded area below the solid line y=2x-1.
The solution set is the doubly-shaded area below the point where the lines intersect.
4.4 + [4 × 1/4 + 8.6]
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Answer:
14
Step-by-step explanation:
Please help me with these questions ASAP!!!!!!!!
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Answer:
Step-by-step explanation:
Answer:
For the first picture: m angle t=36 and m angle v=54
For the second picture:m angle P=55 m angle Q=81 and m angle QPR=180
Step-by-step explanation:
For the first picture, you had to do 2x+3x+90=180
We got the 90 from the right triangle.
Then you combine like terms, which was then 5x=90=180
Then, you subtract the 90 from both side, leaving 5x=90
Divide 90 by 5, which gives you x=18
For both the answers, you had to do 2(18) for T and 3(18) for V
The second picture, you did (8y + 1) + (5y + 5)= 136
You combine like terms, which levas you with 13y + 6 = 136
You subtract 6 from both sides, leaving you with 13y= 130
Divide 130 by 13, which is 10 so y=10
You then replace the y for (8y + 1) to 10 and solve
As well as for (5y + 5), you replace the y with 10 and solve
And m angle QRP is 180 because every triangle has a total of 180 degrees
Hope this helped!
what's the common difference in −1,−4,−7,−10
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Answer:
-3
Step-by-step explanation:
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What is the sum of the measures of the exterior angles of this triangle
Answers
Answer:
180°
Step-by-step explanation:
because because that's how much the angle of this triangle is
The sum of the exterior angles is always 360. This applies to any polygon.
note: If you wanted to sum up the interior angles, then the answer would be 180.
I will give brainliest! In the figure, the circle has a center O and has a radius of 10. If the length of arc AB is between 5 and 6, what is one possible integer value of x?
Answers
Answer:
any integer in between 29,30,31,32,33,34 will work.
an angle is equal to five times of its complement then what is its measures
Answers
Answer:
Then the complement of it = 90-x. Given that An angle is equal to 5 times its complement. x = 75. Hence the measure of an angle = 75.
Step-by-step explanation:
zasxedcrfvtgbyhjffgh...
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Answer:
yes?
Step-by-step explanation:
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Answer:
wooo
Step-by-step explanation:
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Answers
The correct answer is 18.
Hope this helps!!
Brainliest?
Will give crown help
Answers
Answer:
n x 5
Step-by-step explanation:
The pattern is to multiply each number by 5 so multiplying n by 5 will get you the expression n x 5.
Hope that helps