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Taking the discriminant, we get c = 49.

how did you find those values??

I got the answer as [-1/2, 1/20]. 

But isn't -20*1/2=-10? That falls into the interval, which we don't want.

There are 42 even divisors of 7!+6!.

The answer is 2.

$20 x [1 + 125%] ==20 x 2.25 ==$45 - marked up price

$45  x  [1 - 0.40] ==$45  x  0.60 ==$27 - the discount price of the coffee table.

It's a pleasure :)

sumfor(n, 1, 1010,  (2*n - 1) - (2*n))== - 1010 + 2021==1011

OR:

2021 + ∑ [ (2n - 1) - (2n), n, 1, 1010] ==1011

The smallest n==30

30^2 == 2^2 * 3^2 * 5^2

Number of divisors==[ (2+1)^3] ==27 divisors

The sum works out to 1001.

The answer is 7/2.

Let P be (x,y)

PA^2 + PB^2 + PC^2

=(x-4)^2+(y+1)^2+(x-6)^2+(y-2)^2+(x+1)^2+(y-2)^2

=3x^2+3y^2-18x-6y+62

=3(x^2+y^2-6x-2y)+62

=3((x-3)^2+(y-1)^2)+32

This shows that if Q=(3,1), PQ^2=(x-3)^2+(y-1)^2

And so PA^2 + PB^2 + PC^2= 3PQ^2+32

k=32

Hope this helped!!!

Yes thank you!

The answer is (1,1349)

I first solved the equation then using an online graphing calculator I put the equation I got from adding the 2 and then found my minimum value. I hoped this helped!!!

20*1.25*0.6 = 15

So the discount price is $15

Look closer when it asks for f(2) that means when x is 2 what is y. Looking closer at the x-axis at 2 if u go up then the line touches at 4 for the y-axis when x is 2 so the answer is (2,4)

The rock hits the surface when the height is 0, or when 

t^2-8t-10=0

Use the quadratic formula: t = -1.099 and 9.099. Time can't be negative, so the answer is t = 9.099.

What is the meaning of .. long in the tooth  

It means old.  Used to describe an animal.  The expression derives from the tendency of an animal's gums to contract as it ages.  The teeth aren't actually longer, it's just that more of them is showing.  

_.

answer is 44 degrees and or 136 degrees

Simplify the polynomial first.

\(\quad 9x^2 + 6x + 8x - 5x^2 + \underline{\phantom{\text{aaaaa}}}\\ = 4x^2 + 14x + \underline{\phantom{\text{aaaaa}}}\\\)

Note that (a + b)^2 = a^2 + 2ab + b^2. What happens if we take a = 2x?

(2x + b)^2 = 4x^2 + 4bx + b^2

There we matched the first term of the polynomial. The rest is just finding the value of b that makes the second term match, and then the answer is just b^2.

Hint: Consider the coefficient. What b would make 4b = 14?

\(\operatorname{Domain}(f) = \{x \in \mathbb R:-2 < x < 2\}\\ correctly\\ Domain\ f(x) = \mathbb R\ |\ -2 \leq x \leq 2\)

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