Write the quadratic function in vertex form. y = x^2 - 14x + 53

1 answer:

8 0

Complete the square

y=(x^2-14x)+53
take 1/2 of -14 and square it and add negtive and postive inside arenthasees
y=(x^2-14x+49-49)+53
complete the square
y=(x-7)^2-49+53
y=(x-7)^2+4

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An owner of a key rings manufacturing company found that the profit earned (in thousands of dollars) per day by selling n number

vovikov84 [41]

Answer:

The number of key rings sold on a particular day when the total profit is $5,000 is 4,000 rings.

Step-by-step explanation:

The question is incomplete.

An owner of a key rings manufacturing company found that the profit earned (in thousands of dollars) per day by selling n number of key rings is given by

$P=n^2-2n-3$

where n is the number of key rings in thousands.

Find the number of key rings sold on a particular day when the total profit is $5,000.

We have the profit defined by a quadratic function.

We have to calculate n, for which the profit is $5,000.

$P=n^2-2n-3=5\\\\n^2-2n-8=0$

We have to calculate the roots of the polynomial we use the quadratic equation:

$n=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\n= \frac{-2\pm\sqrt{4-4*1*(-8)}}{2}= \frac{-2\pm\sqrt{4-32}}{2} = \frac{-2\pm\sqrt{36}}{2} =\frac{-2\pm6}{2} \\\\n_1=(-2-6)/2=-8/2=-4\\\\n_2=(-2+6)/2=4/2=2$

n1 is not valid, as the amount of rings sold can not be negative.

Then, the solution is n=4 or 4,000 rings sold.

7 0

3 years ago

Fill in the blanks below.

Crank

The slope for the first one would be:
y2-y1/x2-x1, so replace those with the coordinates and you'll get:
-3-1/-7-(-7) => -4/0 so I guess the slope is zero

the slope for the second one would be:
-3-(-3)/5-(-4)=> 0/9 I think this one would be undefined.
Check to make sure, though!

4 0

3 years ago

Read 2 more answers

Write the expression in complete factored form 4u^2(a-3)+q(a-3)

Sauron [17]

[ Answer ]

$\boxed{\bold{4au^{2} \ - \ 12u^{2} \ + \ aq \ - \ 3q}}$