There are 12 coins ; dimes and quarters. The number of dimes is 2 more than the number of quarters. A. $2.25
B. $2.10
C. $2.50
D. $1.95
E. $1.65
F. $1.80
You have 15 coins; dimes and quarters. The number of quarters is twice as many as dimes. Find the total value of the coins.
A. $2
B. $3.25
C. $3.50
D. $2.50
E. $2.25
F. $3

D.  $1.95

F.  $3

Step-by-step explanation:

dimes:  x + 2

quarters:  x

x + 2 + x = 12

2x + 2 = 12

2x = 10

x = 5

dimes:  x + 2 = 5 + 2 = 7

quarters:  x = 5

Total value: (7 * .10) + (5 * .25) = $1.95

dimes:  x

quarters:  2x

x + 2x = 15

3x = 15

x = 5

dimes:  x = 5

quarters:  2x = 2(5) = 10

Total value: (5 * .10) + (10 * .25) = $3

1 number

if we use a graphing calculator, there is only one such number that satisfies the conclusion of the mean value theorem, that is, a number such that

where the right-hand side is the average rate of change of f on the interval [0.5,0.75], which is the slope of the secant line.

in the attached graph, the black line is the secant line which has its slope as the average rate of change of f on [0.5,0.75], while the orange line is the only tangent line to the graph of f in the interval that satisfies the mvt conclusion.