Answer:
Step-by-step explanation:
<u>Mean of four numbers a, b, c, and d is 8:</u>
- (a + b + c + d)/4 = 8
- ⇒ a + b + c + d = 32
<u>Mean of seven numbers x, y, z, a, b, c and d is 12:</u>
- (x + y + z + a + b + c + d)/7 = 12
<u>Substitute the sum of 4 numbers:</u>
- x + y + z + 32 = 7*12
- x + y + z = 84 - 32
- x + y + z = 52
<u>Mean of x, y and z is:</u>
The angle immediately below x makes up the third angle of the isosceles triangle whose base angles are 55°. That third angle and x are "vertical" angles, hence equal. The value of x can be found from the sum of angles of a triangle:
x + 55° + 55° = 180°
x = 70°
The appropriate choice is the 2nd one:
70°
Answer:
There are 6 dimes and 9 quarters.
Step-by-step explanation:
Represent the number of dimes and the number of quarters by d and q.
Then d + q = 15, or q = 15 - d.
Also, ($0.25)q + ($0.10)d = $2.85, or 5q + 2d = 57.
Substituding 15 - d for q, we get 5(15 - d) + 2d = 57, or
75 - 5d + 2d = 57, or
75 - 3d = 57, or
3d = 18. Thus, there are 6 dimes. Since q = 15 - d, q = 15 - 6 = 9.
There are 6 dimes and 9 quarters.
Answer: In mathematics, the method of equating the coefficients is a way of solving a functional equation of two expressions such as polynomials for a number of unknown parameters. It relies on the fact that two expressions are identical precisely when corresponding coefficients are equal for each different type of term.
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