Unit 3 parallel and perpendicular lines Homework 2, please help quickly
1 answer:
Answer:
Step-by-step explanation:
Since, lines l and m are parallel and a transverse is intersecting these lines.
5). (9x + 2)° = 119° [Alternate intrior angles]
9x = 117 ⇒ x = 13
6). (12x - 8)° + 104° = 180°
12x = 180 - 96
x = ⇒ x = 7
7). (5x + 7) = (8x - 71) [Alternate exterior angles]
8x - 5x = 71 + 7
3x = 78
x = 26
8). (4x - 7) = (7x - 61) [Corresponding angles]
7x - 4x = -7 + 61
3x = 54
x = 18
9). (9x + 25) = (13x - 19) [Corresponding angles]
13x - 9x = 25 + 19
4x = 44
x = 11
(13x - 19)° + (17y + 5)° = 180°[Linear pair of angles are supplementary]
(13×11) - 19 + 17y + 5 = 180
129 + 17y = 180
17y = 180 - 129
y = 3
10). (3x - 29) + (8y + 17) = 180 [linear pair of angles are supplementary]
3x + 8y = 180 + 12
3x + 8y = 192 -----(1)
(8y + 17) = (6x - 7) [Alternate exterior angles]
6x - 8y = 24
3x - 4y = 12 -----(2)
Equation (1) - equation (2)
(3x + 8y) - (3x - 4y) = 192 - 12
12y = 180
y = 15
From equation (1),
3x + 8(15) = 192
3x + 120 = 192
x = 24
11). (3x + 49)° = (7x - 23)° [Corresponding angles]
7x - 3x = 49 + 23
4x = 72 ⇒ x = 18
(11y - 1)° = (3x)° [Corresponding angles]
11y = 3×18 + 1
11y = 55 ⇒ y = 5
12). (5x - 38)° = (3x - 4)° [Corresponding angles]
5x - 3x = 38 - 4
2x = 34
x = 17
(7y - 20)° + (5x - 38)° + 90° = 180°
[Sum of interior angles of a triangle = 180°]
7y + 5x - 58 = 90
5x + 7y = 148
5×17 + 7y = 148
85 + 7y = 148
7y = 148 - 85
y =
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Answer:
The numbers associated with the triangle are 5.437 and 6.437 centimeters, respectively.
Step-by-step explanation:
Two numbers are consecutives, when their difference is equal to 1. The area of the triangle is determined by the following formula:
Where is the shortest length of the triangle, measured in centimeters.
And we get the following second-order polynomial:
(1)
If we know that , then the shortest length of the triangle is:
and
Since length is a positive variable, the only possible solution is:
Then, the numbers associated with the triangle are 5.437 and 6.437 centimeters, respectively.
Using the slope concept, it is found that the shuttle traveled 3.2 miles while Marion was watching.
<h3>What is a slope?</h3>The slope is given by the <u>vertical change divided by the horizontal change</u>, and it's also the tangent of the angle of depression.
Initially, the angle of elevation is of 16º, with an elevation of 1 mi, hence:
Then, at the end, the angle will be of 74º, with the elevation remaining constant, hence:
The distance is:
The shuttle traveled 3.2 miles while Marion was watching.
More can be learned about the slope concept at brainly.com/question/18090623