parallel lines, transversal, and algebra really need help

Parallel Lines, Transversal, And Algebra Really Need Help

Answers

Answer 1

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

Answer 2

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]

Learn more about parallel lines here:

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Related Questions

81-1 1/5 x < 55
please help i need help fast

Answers

Step-by-step explanation:

81 - 1.2x < 55

81 < 55 + 1.2x (add 1.2x to both sides)

1.2x > 26 (subtract 55 from both sides)

x > 21 2/3.

Rob was driving his car slowly and then increased its speed by 40.5 miles per hour to reach a top speed of 60 miles per hour. What was his car's initial speed?​

Answers

Answer:

19.5

Step-by-step explanation:

60 - 40.5 = 19.5.

Round 7.284 to the nearest thousandth.

Answers

Answer:

7.28

Step-by-step explanation.

4 is rounded down to 80 and if you just take away the 0 in 80 its 8.

Answer:

it already is

Step-by-step explanation:

.2 is the tenth .28 is the hundredth and .284 id the thousandth. there arent any more decimals after that thousandth so you cant round up or down

Factor the following by completing the square w^4-22w^2+9

Answers

Answer:

(w² - 4w - 3) (w² + 4w - 3)

Step-by-step explanation:

w² + 4w³ - 3w² -4w³ - 16w² + 12w-3w² - 12w + 9

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Answer:

Would be the approx 17.55 or 12p

Step-by-step explanation:

Mark me brainliest because you promised it and have a splended day ( ^ :

The slope is 2/1 or just 2 and usually the slope is also known as rate of change so the answer should be 2

Which line has a slope of 1/2 and passed through (2,-4)

Answers

The Answer is: “D” step by step explanation:

Micah bought a couch for $450. If he had to pay 7% sales tax, how much total did he pay for the couch?

Answers

Answer:

$481.50

Step-by-step explanation:

(7/100)*(450)=31.50

31.50+450=481.50

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simplify ​

Answers

Answer:

x^5/2 - 2x

Step-by-step explanation:

Cancel terms that are in both the numerator and denominator

2

Combine multiplied terms into a single fraction

3

Combine exponents

Answer: x^5/2 - 2x

Step-by-step

what is the difference between the 11th square number and the 4th square number?

Answers

Answer:1 squared 1

2 squared 4

3 squared 9

4 squared 16

5 squared 25

6 squared 36

7 squared 49

8 squared 64

9 squared 81

10 squared 100

11 squared 121

12 squared 144

13 squared 169

14 squared 196

15 squared 225

16 squared 256

17 squared 289

18 squared 324

19 squared 361

20 squared 400

Step-by-step explanation:

dude just search it up

Answer:

105

Step-by-step explanation:

The 11 th square number is 11² = 121

The 4 th square number is 4² = 16

Their difference is 121 - 16 = 105

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Answers

Answer:

B

Step-by-step explanation:

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Answers

Answer:

No, the figures are not similar.

Step-by-step explanation:

In order for the figures to be similar, in object B, the line labeled as 20 would need to be 10.

Complete the equation of the line through (2, 1) and (5, -8). Use exact numbers. y =​

Answers

Answer:

Step-by-step explanation:

given: (2,1) & (5-8)

first find the slope,

m= (Y2-Y1) / (X2-X1)    

m=(-8-1)/(5-2)

m=(-9)/(3)

m=-3

we have y=-3x+b

use any point to sub in x and y

1=-3(2)+b

1+6=b

b=7               therefore, y=-3x+7 is the equation

Answer:

y = - 3x + 7

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (2, 1) and (x₂, y₂ ) = (5, - 8)

m = [tex]\frac{-8-1}{5-2}[/tex] = [tex]\frac{-9}{3}[/tex] = - 3 , then

y = - 3x + c ← is the partial equation

To find c substitute either of the 2 points into the partial equation

Using (2, 1 ), then

1 = - 6 + c ⇒ c = 1 + 6 = 7

y = - 3x + 7 ← equation of line

what is an equation for the line that passes through the points (-2,3), and (2,1)

Answers

Answer:

yes

Step-by-step explanation:

no

Help me and I’ll give brainliest to u

Answers

Answer:

7p

Step-by-step explanation:

Since it is 7 dollars per person, and p stands for person, the admission fee would be 7p.

Thank you, I hope you learned from this answer! If it did help, please mark this as brainliest! Thank you!

If a circle has a diameter of 30 meters, which expression gives its area in
square meters?
A. 30•n
B. 30^2•n
C. 15^2•n
D. 15•n

Answers

Answer:

C. 15²π

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to Right

Geometry

Diameter: d = 2rArea of a Circle: A = πr²

Step-by-step explanation:

Step 1: Define

d = 30 m

Step 2: Find Area

Substitute [D]:                    30 m = 2rIsolate r:                             15 m = rRewrite:                              r = 15 mSubstitute [AC]:                 A = π(15 m)²Rearrange:                        A = 15²π

Solve for x given the lines are parallel.
(7x - 8)
62°

Answers

Answer:

The answer is 0 ✌

Step-by-step explanation:

70 - 8 =62°

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Answers

You have to combine your liked terms first

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Find x:
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Answers

Answer:

cotx - cot2ⁿx

Step-by-step explanation:

Note: finding the sum not x

First rewrite the first term as:

1/sin2x = sinx / (sinxsin2x)  = sin(2x-x) / (sinxsin2x)  =(sin2xcosx - cosxsinx) / (sinxsin2x) = (sin2xcosx)/(sinxsin2x) - (cos2xsinx)/(sinxsin2x) = cosx/sinx - cos2x/sin2x = cotx - cot2x

Now the sum is:

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Answers

Answer: D

Step-by-step explanation:

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Answers

Answer:

Triangle RST is an equilateral triangle.

Step-by-step explanation:

All three sides of the triangle are of equal length, therefore, because an isosceles triangle is when 2 sides of the triangle are the same length, a scalene triangle being when all sides are of different lengths, and a right triangle having a right angle (a 90 degree angle), this only leaves equilateral, all three sides being the same length, like in the triangle shown.

helpp meee pleaseeee​

Answers

Answer:

I think its b:/ srry if I'm wrong

identification method

Find the sale price of the item. Round to two decimal places if necessary. Original price: $238.13 Markdown: 70% The sale price is $

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Answer:

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Step-by-step explanation:

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Angela has 5 fewer quarters than twice the number of her dimes. If d represents
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Answers

Answer:

2d-5=Q ?

Step-by-step explanation:

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Answers

Answer:

x= 2/7

Step-by-step explanation:

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Answer:

Step-by-step explanation:

x=7/2

If a relation has more numbers in its range than in its domain, what has to be true?

Answers

Answer:

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Answer:

D

Step-by-step explanation:

A man drops a stone from a bridge. How high is the bridge if the stone hits the water 4 seconds later

Answers

Answer: 4 feet

Step-by-step explanation:

Check For Understanding
CELL PHONES A Cell phone company is going to build three new towers in a nearby city. The city council has
released s map that shows where the towers will be built. On the map, the distance between towers A and B is 2
centimeters, the distance between towers B and C 3 centimeters, and the distance between towers A and C is 4
centimeters. A technician needs to visit the stes of the three towers, and he has outlined his travel route between
them on a map. The polygon formed by his travel route on the map will be similar to the polygon formed by the
technicians he drives to the three towers. If the actual distance between tower Band tower C is 600 meters, how
for was the technican have to travel to visit all three cell phone towers?

Answers

Answer:

Distance between A ----> B : 2 cm

B ---> C: 3 cm : 600 meters

A----> C: 4 cm

3:600 meters scaled

So its 200 meters per every 1 cm!

From A to B : 400 meters

From B to C : 600 meters

Frok C to A: 800 meters

Therefore we sum 400+600+800= 1800 meters

i need help 10 points

Answers

Answer:

B

Step-by-step explanation:

x intercepts is (- 1/2,0)

y intercepts is (0,2)

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