The equation 
is
Some observations:
is defined only as long as 
, or 
- wherever is defined, its value must be non-negative, so that
is never positive - by the definition of absolute value, we have
if 
, and 
if 
. Then
If , the equation becomes
Taking the square of both sides gives
but since the discriminant is 
, there are no real solutions.
If , then
Taking squares gives
and solving by the quadratic formula gives two potential solutions,
which have approximate values of 8.49 and 26.51.
We know for any value of 
that 
. We have 
and 
, so only the first solution 8.49 is valid.
Answer:
x = number of quarters = 25
y = number of dimes = 15
Step-by-step explanation:
Let
x = number of quarters
y = number of dimes
1 dime = $0.10
1 quarter = $0.25
x + y = 40 (1)
0.25x + 0.10y = 7.75 (2)
From (1)
x = 40 - y
Substitute x = 40 - y into (2)
0.25x + 0.10y = 7.75 (2)
0.25(40 - y) + 0.10y = 7.75
10 - 0.25y + 0.10y = 7.75
- 0.25y + 0.10y = 7.75 - 10
-0.15y = -2.25
y = -2.25/-0.15
y = 15
Substitute y = 15 into (1)
x + y = 40 (1)
x + 15 = 40
x = 40 - 15
x = 25
x = number of quarters = 25
y = number of dimes = 15
Total quarters = 25 × $0.25
= $6.25
Total dimes = 15 × $0.10
= $1.5
Answer:116cm2
2(12+11+5+7+3+4+4+12)
Step-by-step explanation:
Answer:
y=0x-1
Step-by-step explanation:
y=0(x)+c
-1=0(7)+c
-1=0+c
C=-1
Greatest proportion = Glass c 12.75%
Glass a is 3/25 = 12% and Glass b is 1/8 = 12.5%
