Answer:
50 nickels, 20 quarters.
Step-by-step explanation:
System of equations (q = # of quarters, n = # of nickels):
<em>q + n = 70, 0.25q + 0.05n = 7.50</em>
the first equation can be changed to q = 70 - n, so we are able to <em>substitute q with 70 - n</em>.
So, it will look like <em>0.25*70 - 0.25n + 0.05n = 7.50</em>. This can be simplified to <em>0.2n = 10</em>, which means that n = 50.
Knowing that we can solve <em>q + 50 = 70</em>, which means that q = 20.
Answer:
x=6,y= 7
Step-by-step explanation:
-6x +7y= 13
-6x+8y=20
-y = -7
divide through by -1
y =7
sub y= 7 in equation 1
then x= 6
Answer:
V = kr²h
Step-by-step explanation:
Given that V varies jointly with r² and h, then the equation relating them is
V = kr²h ← k is the constant of variation
Note that joint variation involves the product of the joint quantities
Answer:
(x, y) = (2, 4) or (-1, 1)
Step-by-step explanation:
y = x^2
y = x + 2
=> x^2 = x + 2
Transfer all terms to the left, we have:
=> x^2 - x - 2 = 0
Perform some modifications, we have:
=> x^2 + x - 2x - 2 = 0
Let's group the left-side terms up.
=> x(x + 1) - 2(x + 1) = 0
=> (x - 2)(x + 1) = 0
=> x = 2 => y = x + 2 = 2 + 2 = 4
=> x = -1 => y = x + 2 = -1 + 2 = 1
=> Solution is (x, y) = (2, 4) or (-1, 1)
Hope this helps!
