Answer:
265 quarters ($66.25)
Step-by-step explanation:
10$ in quarters is 250 quarters.
you subtract the 15 from winning (=235), then add 50 for the jackpot (=285). Subtract another 20 for her final plays (=265).
Answer:
x = 25; both labeled angles are 65º
Step-by-step explanation:
To find the value of x, recall that the angles formed by two parallel lines on the same line are equal if they correspond to each other.
In the figure given above, we have two parallel line given. The angle formed by each parallel line is corresponding to the other. Therefore, both angles formed are equal.
Thus,
(3x - 10)° = (x + 40)°
Solve for x
3x - 10 = x + 40
Subtract x from both sides
3x - 10 - x = x + 40 - x
3x - x - 10 = x - x + 40
2x - 10 = 40
Add 10 to both sides
2x - 10 + 10 = 40 + 10
2x = 50
Divide both sides by 2
2x/2 = 50/2
x = 25
*Plug in the value of x to find the measure of each labelled angles:
(3x - 10)° = 3(25) - 10 = 75 - 10 = 65°
(x + 40)° = 25 + 40 = 65°
For this case we have the following inequality:
Subtracting 4 from both sides of the inequality we have:
Dividing between 7 on both sides of the inequality we have:
Thus, the properties used were:
Subtraction property
Division property
Answer:
Subtraction property
Division property
3.1 a) x = 6 / 5 or x = 2, b) x = - 3 / 2 or x = - 1 / 4, c) x = - 3 or x = 2, d) x = 1 or x = - 2.
3.2 a) x = 9 or x = - 3, b) x = 1 or x = - 1 / 4, c) x = - 3 or x = - 5 d) x = 8 or x = - 18
<h3>How to solve algebraic problems by appying absolute value properties</h3>
In this question we have eight expressions involving <em>absolute value</em> expressions, which can be solved by using the following procedure:
3.1 a) |(1 / 2) · x| = 3 - 2 · x
For x ≥ 0:
(1 / 2) · x = 3 - 2 · x
(5 / 2) · x = 3
x = 6 / 5
For x < 0:
- (1 / 2) · x = 3 - 2 · x
(3 / 2) · x = 3
x = 2
b) |x - 1| = 3 · x + 2
For x ≥ 1:
x - 1 = 3 · x + 2
2 · x = - 3
x = - 3 / 2
For x < 1:
- x + 1 = 3 · x + 2
4 · x = - 1
x = - 1 / 4
c) |5 · x| = x - 12
For x ≥ 0:
5 · x = x - 12
4 · x = - 12
x = - 3
For x < 0:
- 5 · x = x - 12
6 · x = 12
x = 2
d) |7 - x| = 5 · x + 1
For x ≤ 7:
7 - x = 5 · x + 1
6 · x = 6
x = 1
For x > 7:
x - 7 = 5 · x + 1
4 · x = - 8
x = - 2
3.2 a) |9 + x| = 2 · x
For x ≥ - 9:
9 + x = 2 · x
x = 9
For x < 9:
- 9 - x = 2 · x
3 · x = - 9
x = - 3
b) |5 · x| - 3 · x = 2
For x ≥ 0:
|5 · x| = 2 + 3 · x
5 · x = 2 + 3 · x
2 · x = 2
x = 1
For x < 0:
- 5 · x = 2 + 3 · x
- 8 · x = 2
x = - 1 / 4
c) |x + 6| - 9 = 2 · x
For x ≥ - 6:
x + 6 - 9 = 2 · x
x - 3 = 2 · x
x = - 3
For x < - 6:
- x - 6 - 9 = 2 · x
- x - 15 = 2 · x
3 · x = - 15
x = - 5
d) |2 · x - 3| + x = 21
For x ≥ 3 / 2:
2 · x - 3 + x = 21
3 · x = 24
x = 8
For x < 3 / 2:
- 2 · x + 3 + x = 21
- x = 18
x = - 18
To learn more on absolute values: brainly.com/question/1301718
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