You can write three equations in the numbers of nickels (n), dime (d), and quarters (q).
n + d + q = 23 . . . . . . . there are 23 coins total
0n +d -q = 2 . . . . . . . . .there are 2 more dimes than quarters
5n +10d +25q = 250 . .the total value is $2.50
The collection includes 11 nickels, 7 dimes, and 5 quarters.
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I used the matrix function of my calculator to solve these equations. You can find q by subtracting from the last equation five times the sum of the first two equations.
(5n +10d +25q) -5((n +d +q) +(d -q)) = (250) -5(23 +2)
25q = 125 . . . . . . . simplify
q = 5
From the second equation,
d = q +2 = 7
And from the first,
n = 23 -5 -7 = 11
Answer:
answer is A
Step-by-step explanation:
Answer:
y+4=-(2/5)(x-5) ----> equation of the line into point slope form
y=-(2/5)x-2 ----> equation of the line into slope intercept form
2x+5y=-10 ----> equation of the line in standard form
Step-by-step explanation:
step 1
Find the slope of the given line
we have
5x-2y=-6
isolate the variable y
2y=5x+6
y=2.5x+3
The slope m of the given line is m=2.5
step 2
Find the slope of the line perpendicular to the given line
We know that
If two lines are perpendicular, then their slopes are inverse reciprocal each other
so
m1=5/2
the inverse reciprocal is
m2=-2/5
step 3
Find the equation of the line into point slope form
y-y1=m(x-x1)
we have
m=-2/5
point (5,-4)
substitute
y+4=-(2/5)(x-5) ----> equation of the line into point slope form
y=-(2/5)x+2-4
y=-(2/5)x-2 ----> equation of the line into slope intercept form
Multiply by 5 both sides
5y=-2x-10
2x+5y=-10 ----> equation of the line in standard form
