Answer:
19
Step-by-step explanation:
When 2 chords intersect then the product of the parts of one chord equal the product of the parts of the other chord, that is
12(x - 7) = 4(x + 3) ← distribute parenthesis on both sides
12x - 84 = 4x + 12 ( subtract 4x from both sides )_
8x - 84 = 12 ( add 84 to both sides )
8x = 96 ( divide both sides by 8 )
x = 12
Thus
12 + x - 7 = 12 + 12 - 7 = 17
4 + x + 3 = 4 + 12 + 3 = 19 ← longer chord
Answer:2/4 more joseph ate
Step-by-step explanation:
Adult tickets cost $10 each and student tickets cost $6 each.
Given:
Kyle's family bought 4 adult tickets and 2 student tickets for $52
Maria's family bought 3 adult tickets and 5 student tickets for 60.
Let us assign x as the adult tickets and y as the students tickets
Kyle's family: 4x + 2y = 52
Maria's family: 3x + 5y = 60
Let us find the value of x using Kyle's equation:
4x + 2y = 52
4x = 52 - 2y
x = (52 - 2y)/4
x = 13 - y/2
Substitute the value of x in Maria's equation to find y.
3x + 5y = 60
3(13 - y/2) + 5y = 60
39 - 3y/2 + 5y = 60
- 3y/2 + 5y = 60 - 39
- 3y/2 + 5y = 21
2(-3y/2 + 5y) = 2(21)
-3y + 10y = 42
7y = 42
7y/7 = 42/7
y = 6
x = 13 - y/2
x = 13 - 6/2
x = 13 - 3
x = 10
To check:
Kyle's Family Maria's Family
4x + 2y = 52 3x + 5y = 60
4(10) + 2(6) = 52 3(10) + 5(6) = 60
40 + 12 = 52 30 + 30 = 60
52 = 52 60 = 60
The measure of ∠7 is 47°. Angle 7 is a vertical angle to angle 5
Suppose the measure of ∠6 is represented represented by (2x - 5), the equation that can be use to solve for x is 42 + 2x = 180
The value of x is 69
<h3>Vertical opposite angles</h3>
Vertically opposite angles are angles that are opposite one another at a specific vertex and are created by two straight intersecting lines.
Vertical opposite angles are congruent. Therefore,
a. ∠5 ≅ ∠7 (vertical angles)
Therefore, angles 5 and 7 are congruent angles.
∠7 = 47°
b. Suppose ∠6 = 2x - 5 . let's find x
Therefore,
∠5 + ∠6 = 180(angle on a straight line)
The equation to solve the above is as follows:
47 + 2x - 5 = 180
42 + 2x = 180
2x = 180 - 42
2x = 138
x = 138 / 2
x = 69
learn more on intersecting lines here: brainly.com/question/24715845
Answer:
horizontal line because it doesn't pass vertical line test
