Mr. Watkins earns $35 an hour at his new job. During a typical month, he works a total of 160 hours. Mrs. Watkins is a homemaker
1 answer:
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Answer:
m∠WXZ = 38°
m∠ZXY = 52°
Step-by-step explanation:
In the question
- ∠WXZ and ∠ZXY are two adjacent angles and formed together ∠WXY
- That means the measure of ∠WXY equal the sum of measures of ∠WXZ and ∠ZXY
∵ ∠WXY is a right angle
→ That means its measure is 90°
∴ m∠WXY = 90°
∵ m∠WXZ + m∠ZXY = m∠WXY
∵ m∠WXZ = (5x + 3)°
∵ m∠ZXY = (8x - 4)°
∵ m∠WXY = 90°
→ Substitute their values in the equation above
∴ (5x + 3) + (8x - 4) = 90
→ Add the like terms in the left side
∵ (5x + 8x) + (3 - 4) = 90
∴ 13x + (-1) = 90
∴ 13x - 1 = 90
→ Add 1 to both sides
∴ 13x - 1 + 1 = 90 + 1
∴ 13x = 91
→ Divide both sides by 13
∴
∴ x = 7
→ To find the measure of each angle substitute x by 7 in their measures
∵ m∠WXZ = 5x + 3
∴ m∠WXZ = 5(7) + 3
∴ m∠WXZ = 35 + 3
∴ m∠WXZ = 38°
∵ m∠ZXY = 8x - 4
∴ m∠ZXY = 8(7) - 4
∴ m∠ZXY = 56 - 4
∴ m∠ZXY = 52°
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This straight line passes through: (0,0), (5,1), (10,2) etc
We can use the slope formula with any two points to find the slope of this line.
The slope formula is .
Let and
Then ,
.
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But we must leave our answer in miles per hour
Hence Carl's speed is miles per hour
After 2 hours, Carl will travel miles.
2. The given line has equation
We write this in slope-intercept form by solving for y.
This is in the form , where
is the slope.
When x=3,
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(0,0) and (20,30).
The slope of this line is
Therefore the rate is $ 15 per ticket.
If the theater sells 150 tickets, the earnings will be: dollars.