Solve the Quadratic Equation by factoring. 3r^2-16r-7=5

1 answer:

3 0

So first set one side to zero

subtract 5 from both sides
3r^2-16r-12=0
factor

to find the factor in
ax^2+bx+c form when a>1
multiply a and c together
find what 2 numbers add up to b and multiply to ac so

a=3
b=-16
c=-12

ac=3 times -12=-36
factors that add up to -16
2 and -18 is the answer since 2 times -18=-36 and 2-18=-16 so

split the middle number up
3r^2-16r-12=0
3r^2-18r+2r-12=0
group
(3r^2-18r)+(2r-12)=0
factor out common factors
(3r)(r-6)+(2)(r-6)=0
reverse distribute (ab+ac=a(b+c) so
(3r+2)(r-6)=0

set each to zero
r-6=0
add 6
r=6

3r+2=0
subtract 2
3r=-2
divide 3
r=-2/3

r=6 or -2/3

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4 0

1 year ago

Use a daily production cost C for x units. A manufacturer of gas grills has daily production costs of C = 400 – 5x + 0.125x2, wh

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The function given is a quadratic function, so the graph will be a parabola. It'll look similar to the photo attached. The minimum cost will be at the vertex of the parabola because that is its lowest point! To find the x-value of the vertex (which is what the question is looking for), use the vertex formula: x = -b/2a. The variable b is the coefficient of the x term in the function, and the variable a is the coefficient of the x² term. In this case, a = 0.125 and b = -5.
x = -(-5)/2(0.125)
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So, 20 gas grills should be produced each day to maintain minimum costs. Hope that helps! :)