Answer:
Juan has 32 dimes, 16 nickels and 8 quarters in his coin bank.
Step-by-step explanation:
Since in Juan's coin bank there are nickels (n), dimes (d), and quarters (q), and the number of quarters is one-quarter the number of dimes, and the number of nickels is twice the number of quarters, While the total value of the coins is $ 6.00, to find the number of each type of coin the following calculations must be performed:
Q = 1/4 D
N = 2Q = 1/2 D
D = D
20D + 10N + 5Q = X
20 x 0.10 + 10 x 0.05 + 5 x 0.25 = X
2 + 0.50 + 1.25 = X
3.75 = X
24D + 12N + 6Q = X
24 x 0.10 + 12 x 0.05 + 6 x 0.25 = X
2.40 + 0.60 + 1.50 = X
4.50 = X
32D + 16N + 8Q = X
32 x 0.10 + 16 x 0.05 + 8 x 0.25 = X
3.20 + 0.80 + 2 = X
6 = X
So, Juan has 32 dimes, 16 nickels and 8 quarters in his coin bank.
Answer:
19 1-point shots and 32 2-point shots
Step-by-step explanation:
Let x be the amount of 1-point shots they made and y be the amount of 2-point shots they made then...
x+y=51
x+2y=83
We can solve this equation using elimination. In this case, we can eliminate x be subtracting the two equations.
-y=-32
Divide both sides by -1
y=32
Plug this back into the equation to solve for x
x+32=51
Subtract 32 from both sides
x=19
They scored 19 1-point shots and 32 2-point shots.
Answer:
Step-by-step explanation:
Cot is the inverse of tan. Therefore, the ratios are also inverses. The same goes for csc, which is the inverse of sin.
The tan ∠B = 
so the cot ∠B = 
so the first statement is false.
The sin ∠C = 
so the csc ∠C = 
so the second statement is false.
The tan ∠C = so the cot ∠C = so the third statement is false.
The sin ∠B = 
so the csc ∠B = 
which reduces to 
so the last statement is true!
