Unit 3 parallel and perpendicular lines Homework 2, please help quickly
1 answer:
Answer:
Step-by-step explanation:
Given that lines l and m are parallel and there is a transversal cutting through these lines.
5). (9x + 2)° = 119° [by alternate interior angles]
9x = 117 ⇒ x = 13
6). (12x - 8)° + 104° = 180°
12x = 180 - 96
x = ⇒ x = 7
7). (5x + 7) = (8x - 71) [by alternate exterior angles]
8x - 5x = 71 + 7
3x = 78
x = 26
8). (4x - 7) = (7x - 61) [by corresponding angles]
7x - 4x = -7 + 61
3x = 54
x = 18
9). (9x + 25) = (13x - 19) [by corresponding angles]
13x - 9x = 25 + 19
4x = 44
x = 11
(13x - 19)° + (17y + 5)° = 180° [linear pairs of angles sum to supplementary]
(13×11) - 19 + 17y + 5 = 180
129 + 17y = 180
17y = 180 - 129
y = 3
10). (3x - 29) + (8y + 17) = 180 [linear pairs of angles sum to supplementary]
3x + 8y = 180 + 12
3x + 8y = 192 -----(1)
(8y + 17) = (6x - 7) [by alternate exterior angles]
6x - 8y = 24
3x - 4y = 12 -----(2)
From equation (1) subtract equation (2)
(3x + 8y) - (3x - 4y) = 192 - 12
12y = 180
y = 15
Plugging into equation (1),
3x + 8(15) = 192
3x + 120 = 192
x = 24
11). (3x + 49)° = (7x - 23)° [by corresponding angles]
7x - 3x = 49 + 23
4x = 72 ⇒ x = 18
(11y - 1)° = (3x)° [by corresponding angles]
11y = 3×18 + 1
11y = 55 ⇒ y = 5
12). (5x - 38)° = (3x - 4)° [by corresponding angles]
5x - 3x = 38 - 4
2x = 34
x = 17
(7y - 20)° + (5x - 38)° + 90° = 180°
[The angles within a triangle sum to 180°]
7y + 5x - 58 = 90
5x + 7y = 148
5×17 + 7y = 148
85 + 7y = 148
7y = 148 - 85
y =
You might be interested in
Answer:
Detailed solution:
Given:
The problem to solve is:
Convert the equation into the standard quadratic form , where
represent constants.
So, by adding to both sides, we get:
Note that .
The roots of this quadratic are found by applying the quadratic formula given as:
Substitute into the formula and calculate for
.
Hence, the roots are:
Given:
The temperature recorded at 10:00 am is 8 degrees Fahrenheit.
The temperature decreases by 3 degrees Fahrenheit each hour.
To find:
The temperature at 2:00 pm on the same day.
Solution:
Let y represent the temperature after x hours since 10:00 am.
The temperature at 10:00 am serves as the initial temperature.
Thus, the y-intercept of the linear equation is 8.
The temperature reduces by 3 degrees Fahrenheit every hour.
This indicates the slope of the linear equation is -3, with the negative sign indicating a decrease.
The slope-intercept form of a linear function is indicated by
where m is the slope and b is the y-intercept.
Inserting m=-3 and y=8 into the above equation gives us the required values.
From 10:00 am to 2:00 pm spans 4 hours; therefore, substitute x=4 into the above equation.
Consequently, the temperature at 2:00 pm is -4 degrees Fahrenheit.
Answer:
12 pencils per package.
Step-by-step explanation:
Details provided:
Ethan purchased 4 packages of pencils.
Number of Packages = 4
Number of pencils shared with friend = 8 pencils
Pencils remaining = 40 pencils
∴Total Number of Pencils = Pencils given to friend + Pencils remaining =
Total Pencils in each package =