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This is a longer grueling problem: By the zero product property, we have:

x^2 + 16x - 12 = 0    => -16 +- sqrt(256 + 48) over 2, -16 +- 4sqrt(19) over 2, -8 +/- 2sqrt(19)

3x^2 - 9x + 8 = 0      => 9 +- sqrt(81 - 4*8*3), but we see its imaginary, so only consider the above case to be real.

If multiply to greater than 0, by parity, we have:

x^2 + 16x - 12x > 0    =>   x = (-infinity, -8 - 2sqrt(19)) U (-8 + 2sqrt(19), infinity)

and (3x^2 - 9x + 8) > 0 at the same time. => x = (-infinity, infinity)

By negative parities, we have:

x^2 + 16x - 12 < 0         => x = (-8 - 2sqrt(19), -8 + 2sqrt(19))

and 3x^2 - 9x + 8 < 0    => no solutions for x

Now we have to satisfy the original inequality, so we look for the most constricting ranges, obviously (-infinity, infinity) isn't helpful, and we can see that most of our bolded revolve around -8 +/- 2sqrt(19), meaning that those two values are our values of x.

Say the sides of the right triangle were x and y. Originally, the area was xy/2

Now the area is 0.3x * 1.7y / 2 = 0.51xy/2

It decreased by 49%

The solutions are -3, 0, and 2.

Angle CBE = 31 degrees.

QR = 55/2.

Hello, the answer is 217.

it said that it was wrong... thanks for helping, tho. :)

By the Binomial Theorem, the constant term is \(\dbinom{9}{3} \cdot 2^6 \cdot (-1)^3 = -5376\)

this question was already answered before...

"The possible values of k are 2 and 11." - guest

For (a), the answer is U, R, T, S.

-6 * 3 = -1 * 6 * 3

6 * 3 = 6 + 6 + 6 = 12 + 6 = 18

when multiplied by -1, just add the negative to the number because it's reading backwards on the number line 18 times.

-18

you are not wrong, so smart :D

I forgot the first 84 digits since 3rd grade, but I remember 28 or so:

3.14159265358979323846264338327950288149

There are 15 possible ways to color the five squares: Red-Yellow-Blue-Red-Yellow Red-Yellow-Blue-Yellow-Red Red-Blue-Yellow-Red-Yellow Red-Blue-Yellow-Yellow-Red Red-Yellow-Red-Blue-Yellow Red-Yellow-Red-Yellow-Blue Red-Blue-Red-Yellow-Yellow Red-Blue-Red-Yellow-Blue Yellow-Red-Blue-Red-Yellow Yellow-Red-Blue-Yellow-Red Yellow-Blue-Red-Red-Yellow Yellow-Blue-Red-Yellow-Red Blue-Red-Yellow-Red-Yellow Blue-Red-Yellow-Yellow-Red Blue-Yellow-Red-Red-Yellow Blue-Yellow-Red-Yellow-Red

The probability that the distance between the two points is at most 1.5 is 0.5. This is because the maximum distance between two points on a circle of radius 1 is 2, and 1.5 is half of that.

The probability that the first card Grok draws has an even number and is blue is 1/4. The probability that the second card Grok draws has an odd number and is red is also 1/4. Therefore, the probability that the first card Grok draws has an even number and is blue, and the second card Grok draws has an odd number and is red is 1/16.

Marvin can reach his home in 8 different ways. He can go right 4 times and up 6 times, right 3 times and up 7 times, right 2 times and up 8 times, right 1 time and up 9 times, left 1 time and up 9 times, left 2 times and up 8 times, left 3 times and up 7 times, and left 4 times and up 6 times. He cannot go through (2,4) because of the frog.

Let the number of turkey sandwiches sold==T

Then, the number of steak sandwiches sold==925 - T

4T  +  6[925  -  T] ==4524, solve for T

T ==513 turkey sandwiches sold

925  -  513 ==412 steak sandwiches sold

The order is C < B < D < A < E

r^2 + s^2 = 33/8

Angle DAC = 44 degrees.