D= # of dimes
q= # of quarters
QUANTITY EQUATION:
d + q= 64
COST EQUATION:
0.10d + 0.25q= $9.25
STEP 1:
multiply quantity equation by -0.10 to be able to eliminate the d term in step 2
(-0.10)(d + q)= (-0.10)(64)
-0.10d - 0.10q= -6.40
STEP 2:
add equation from step 1 to cost equation to eliminate the d term and solve for q
Add
0.10d + 0.25q= $9.25
-0.10d - 0.10q= -6.40
0.15q= 2.85
divide both sides by 0.15
q= 19 quarters
STEP 3:
substitute q value in step 2 into either original equation to find d value
d + q= 64
d + 19= 64
subtract 19 from both sides
d= 45 dimes
CHECK:
0.10d + 0.25q= $9.25
0.10(45) + 0.25(19)= 9.25
4.50 + 4.75= 9.25
9.25= 9.25
ANSWER: There are 45 dimes and 19 quarters.
Hope this helps! :)
Answer:
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The equation of the line is y = 1/6x + 3
<h3>How to determine the equation?</h3>
The equation of the line is given as:
y = -6x - 14
The above equation has a slope of
m = -6
Let the slope of the other line be n.
So, we have:
n =-1/m ---- slope condition for perpendicular lines
So, we have:
n = 1/6
The equation is then calculated as:
y = n(x - x1) + y1
Where
(x1, y1) = (12,5)
This gives
y = 1/6(x - 12) + 5
Expand
y = 1/6x - 2 + 5
Evaluate the sum
y = 1/6x + 3
Hence, the equation of the line is y = 1/6x + 3
Read more about linear equations at:
brainly.com/question/14323743
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Answer:
x=-6,x=3
Step-by-step explanation:
x^2-x-18=-4x
Adding both sides by 4x
x^2+3x-18=0
Factoring
(x+6)(x-3)=0
x=-6,x=3
