Answer:
x = 56.25
Step-by-step explanation:
The sides of the rectangle are in the ratio 3:4, so those together with the diagonal of the rectangle make a 3-4-5 right triangle. The sum of these adjacent-side ratio units is 3+4 = 7, so the perimeter in ratio units is 2×7 = 14. The actual perimeter is 42 inches, so each ratio unit must stand for ...
(42 in)/(14 units) = 3 in/unit
The diagonal of the rectangle is the diameter of the circle. Its length is 5 units, or ...
(5 units)×(3 in/unit) = 15 inches.
Then the radius is half the diameter, or 7.5 inches.
The area of a circle is given by ...
A = πr² = π(7.5 in)² = 56.25π in²
The value of x is 56.25.
To justify the yearly membership, you want to pay at least the same amount as a no-membership purchase, otherwise you would be losing money by purchasing a yearly membership. So set the no-membership cost equal to the yearly membership cost and solve.
no-membership costs $2 per day for swimming and $5 per day for aerobic, in other words, $7 per day. So if we let d = number of days, our cost can be calculated by "7d"
a yearly membership costs $200 plus $3 per day, or in other words, "200 + 3d"
Set them equal to each other and solve:
7d = 200 + 3d
4d = 200
d = 50
So you would need to attend the classes for at least 50 days to justify a yearly membership. I hope that helps!
245 divided by 49 = 5 therefore there are 5 seats in each row.
1 quart = 4 cups. So 4 x 4 will give you your answer, which is 16 cups.
Answer:
11. x = 6; y = 6.5
12. x = 2; y = 4
Step-by-step explanation:
In each figure, the hash marks on the lines indicate the parallel lines (marked with red arrows) are equally-spaced. That means the two expressions involving x are equal to each other, and the two expressions involving y are equal to each other.
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11. 2x +1 = x +7
x = 6 . . . . . . . subtract (x+1) from both sides
and
3y -8 = y +5
2y = 13 . . . . add (8-y) to both sides
y = 6.5 . . . . divide by the coefficient of y
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12. x +3 = 3/2x +2
1 = 1/2x . . . . . subtract (x+2)
2 = x . . . . . . . multiply by 2
and
2y -1 = 3y -5
4 = y . . . . . . add (5 -2y)
