Answer:
37 dimes and 10 nickels
Step-by-step explanation:
let d = # dimes
let n = # nickels
we can set up a system of equations:
n + d = 47
.05n + .10d = 4.2
if we solve the first equation for 'n' we get:
n = 47-d
now we can substitute this in for 'n' in the second equation:
.05(47-d) + .10d = 4.2
2.35 - .05d + .10d = 4.2
2.35 + .05d = 4.2
subtract 2.35 from each side to get:
.05d = 1.85
d = 1.85÷.05
d = 37
if d+n = 47 and d=37 then n = 10
Check:
.05(10) + .1(37) should equal 4.2
.50 + 3.7 = 4.2 [It Checks Out]
Answer:
Step-by-step explanation:
y=-1
They will recycle 24 pounds of paper on week 6
Question:
Prove that:

Answer:
Proved
Step-by-step explanation:
Given

Required
Prove

Subtract tan(10) from both sides


Factorize the right hand size

Rewrite as:

Divide both sides by 


In trigonometry:

So:
can be expressed as: 
gives


In trigonometry:

So:

Because RHS = LHS
Then:
has been proven
Notice that the terms in parentheses on both sides of the equation are added to 4.
(3x + 4) + 4 = (5x - 4) + 4
So we can set the equation as.
3x + 4 = 5x - 4
Subtract 3x on both sides of equation.
4 = 2x - 4
Add 4 on both sides of equation.
8 = 2x
Divide both sides of equation by 2.
4 = x
4 is the only value that satisfies the statement.