Josette found 16 coins in her purse. She had 2 more nickels than pennies and 7 fewer quarters than pennies. Josette modeled the
scenario in a table and then wrote the equation p + (p + 2) + (7 – p) = 16.
Is Josette’s equation correct? If not, what was her mistake.
A): Her equation is correct.
B): The variable should have been the number of nickels.
C): Instead of finding the sum, she needed to write an equation to find the difference.
D): The number of quarters was translated incorrectly and should be p – 7.
Is Josette’s equation correct? If not, what was her mistake.
A): Her equation is correct.
B): The variable should have been the number of nickels.
C): Instead of finding the sum, she needed to write an equation to find the difference.
D): The number of quarters was translated incorrectly and should be p – 7.
2 answers:
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Answer:
10.25
Step-by-step explanation:
The slope of AC is given by the slope formula:
m = (y2 -y1)/(x2 -x1)
m = (-4 -1)/(3 -(-1)) = -5/4
Then the slope of CB is the opposite reciprocal, 4/5. The equation of line CB in point-slope form is ...
y -k = m(x -h) . . . . . . line with slope m through point (h, k)
y -(-4) = 4/5(x -3) . . . . line CB
When y = 1 (to match the y-value of A), then ...
1 +4 = 4/5(x -3)
5(5/4) = (x -3) . . . . . multiply by 5/4
6.25 +3 = x = 9.25 . . . . add 3
Point B is (9.25, 1).
The length of the hypotenuse is ...
9.25 -(-1) = 10.25
We have expression that renders the system of inequalities,
Which can be simplified to,
So what we get is something greater than -1 and at the same time greater or equal to 5, so the solution is,
.
Hope this helps.