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IRINA_888 [86]
3 years ago
8

Parallel lines are cut by a transversal such that the alternate interior angles have measures of 3x + 17 and x + 53 degrees. The

value of x is:
A. 9
B. 18
C. 35
D. 71
Mathematics
1 answer:
Dvinal [7]3 years ago
8 0
Alternate interior angles are congruent...they are equal. So lets set them equal and solve for x

3x + 17 = x + 53
3x - x = 53 - 17
2x = 36
x = 36/2
x = 18

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6.
Rudik [331]

Answer:

  (a)  169.1 m

Step-by-step explanation:

The diagram shows you the distance (x) will be shorter than 170 m, but almost that length. The only reasonable answer choice is ...

  169.1 m

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The relevant trig relation is ...

  Cos = Adjacent/Hypotenuse

The leg of the right triangle adjacent to the marked angle is x, and the hypotenuse is 170 m. Putting these values into the equation, you have ...

  cos(6°) = x/(170 m)

  x = (170 m)cos(6°) ≈ (170 m)(0.994522) ≈ 169.069 m

The horizontal distance covered is about 169.1 meters.

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<em>Additional comment</em>

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5 0
2 years ago
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Inessa05 [86]
1 way : 10d + 2d

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4 0
3 years ago
What is the area of a rectangle that is 1 1 4 1 4 1 ​ 1, start fraction, 1, divided by, 4, end fraction meters long and 3 4 4 3
hjlf

Answer:

4 11/16 m²

Step-by-step explanation:

The formula for the area of a rectangle = Length × Width

From the question:

Length = 1 1/4 m

Width = 3 3/4m

Area of the rectangle =

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Area of the rectangle = 4 11/16 m²

7 0
3 years ago
solve this system of linear equations. Separate the X- and Y- values with a comma. -9x+2y=-16 19x+3y=41​
Serjik [45]

Answer:

(2, 1)

Step-by-step explanation:

The best way to do this to avoid tedious fractions is to use the addition method (sometimes called the elimination method).  We will work to eliminate one of the variables.  Since the y values are smaller, let's work to get rid of those.  That means we have to have a positive and a negative of the same number so they cancel each other out.  We have a 2y and a 3y.  The LCM of those numbers is 6, so we will multiply the first equation by a 3 and the second one by a 2.  BUT they have to cancel out, so one of those multipliers will have to be negative.  I made the 2 negative.  Multiplying in the 3 and the -2:

3(-9x + 2y = -16)--> -27x + 6y = -48

-2(19x + 3y = 41)--> -38x - 6y = -82

Now you can see that the 6y and the -6y cancel each other out, leaving us to do the addition of what's left:

-65x = -130 so

x = 2

Now we will go back to either one of the original equations and sub in a 2 for x to solve for y:

19(2) + 3y = 41 so

38 + 3y = 41 and

3y = 3.  Therefore,

y = 1

The solution set then is (2, 1)

6 0
3 years ago
Read 2 more answers
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sveta [45]

Answer:

the answer is 11 1/2.

Step-by-step explanation:

I used a calculator

8 0
3 years ago
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