ANSWER
EXPLANATION
If ABCD is a parallelogram, then
line AB is parallel to line DC .
This means that,
and
are alternating angles.
Alternate angles are congruent.
This implies that,
We group like terms to obtain,
This simplifies to,
Also, if ABCD is a parallelogram then,
BC is parallel to AD. This means that,
We group like terms to get,
This simplifies to,
We divide both side by 4 to get,
Answer:
If we are to make x small rugs, each of which takes 2 hours to dye, then the total time taken to dye the small rugs is 2x. Similarly for the y large rugs which each take 3 hours to dye, the total time for dyeing the large rugs is 3y. Therefore the total for all sizes of rugs is 2x + 3y. Finally, we have a maximum of 60 available hours for the dyeing, so the total time cannot exceed 60, and the final inequality is
2x + 3y < 60
Step-by-step explanation:
Answer:
Total number of coins Nancy and bill have = 6x - 5
Step-by-step explanation:
Nancy and bill collect coins. Nancy has x coins. Bill has 5 coins fewer than five times the number of coins Nancy has. Write and simplify an expression for the total number of coins Nancy and bill have . Simplify your answer .
Let
Number of Nancy's coins = x
Number of Bill's coins = 5x - 5
Total number of coins Nancy and bill have = Number of Nancy's coins + Number of Bill's coins
= x + (5x - 5)
= x + 5x - 5
= 6x - 5
Total number of coins Nancy and bill have = 6x - 5
Answer:
ai) 73000 gal/yr
aii) $730 per year
b) 1000 days
Step-by-step explanation:
ai) The water usage per day is ...
(4 showers/day)(10 min/shower)(5 gal/min) = 200 gal/day
Then the usage per year is ...
(200 gal/day)(365 days/yr) = 73,000 gal/yr
__
aii) The cost of electricity is the cost of heating half the water usage, so is ...
(0.20 kWh/gal)(1/2)(73,000 gal/yr)($0.10/kWh) = $730/yr
__
b) The current daily cost of electricity for heating water is ...
($730/yr)/(365 days/yr) = $2/day
If the cost is cut in half, it will be $1 per day. That means the savings is $1 per day, so it will take 1000 days to recover the $1000 initial cost. (Effectively, the average cost for the first 1000 days is the same as if the water heater had not been replaced.)
Answer:
OR
x=\frac{3}{4} ±i\frac{\sqrt{39}}{4}\\
Step-by-step explanation:
