Let daniel's age = d and let jessica's age = j
let your current age = x and your wife's current age = y
x = 5d (given in question)
∴ x - 5d = 0
x + 21 = 2(d+21) (given in question)
∴ x + 21 = 2d + 42
∴ x - 2d = 21
We can solve these two rearranged equations simultaneously by multiplying the first equation by -1 and adding them. This gives us the following:
3d = 21
∴ d = 7
This means that daniel is currently 7 and (if we substitute d = 7 into one of the equations) you are 35. We use a similar method for your wife's and jessica's current ages.
y = 7j (given in question)
∴ y - 7j = 0
y + 8 = 3(j + 8)
∴y + 8 = 3j + 24
∴ y - 3j = 16
If we use a similar method of elimination we get this:
4j = 16
∴ j = 4
Hence, from this we can concur that daniel is 7 and jessica is 4.
Answer:
∠5 = 95°
Step-by-step explanation:
Where the transversal crosses parallel lines at some angle not a right angle, all of the acute angles are congruent, and all of the obtuse angles are congruent. The acute angles are (obviously) not congruent with the acute angles. Any acute angle is supplementary to any obtuse angle.
Since angles 5 and 6 are a linear pair, the angle relationships of the parallel lines are irrelevant. A linear pair of angles is supplementary.
∠6 = 85° . . . . is given
∠5 is shown as obtuse, so its measure is ...
∠5 = 180° -85° = 95°
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<em>Additional comment</em>
85° angles: 2, 3, 6, 7
95° angles: 1, 4, 5, 8
Any angle from the 85° angle list is <em>not congruent</em> with any angle from the 95° angle list. For example, angles 2 and 5 are not congruent.
Answer:
1/4
Step-by-step explanation:
Hope this helps!
Answer:
[Distance to the Horizon]^2 =Height of the skydiver x Diameter of the Earth
D^2 = 1.4 x 7918
D^2 = 11,085.2
D = Sqrt(11,085.2)
D = ~ 105.28628......miles - Distance to Horizon.
Step-by-step explanation:
Answer:
The most cost effective company will be Painting USA that charge $700 to paint Paul house .
As given
Paul is going to have the exterior of his home painted.
Painting USA charges $75.00 to come out and evaluate the house plus $25.00 per hour of labor.
If it takes 25 hours to paint Paul’s house.
Total amount charge by Painting USA = Painting USA charges for come out and evaluate the house + Cost of per hour of labor × Total hours take to paint Paul house .
Total amount charge by Painting USA = 75 + 25 × 25
= 75 + 625
= $ 700
As given
Upscale Home Painting does not charge to evaluate the house. However, they charge $40.00 per hour.
Total amount charge by Upscale Home Painting = Cost of per hour of labor × Total hours take to paint Paul house
= 40 × 25
= $ 1000
Therefore the most cost effective company will be Painting USA that charge $700 to paint Paul house .
Step-by-step explanation:
