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A    40   =   2^3  *  5

B    54   =     2 *  3^3  

C    60   =   2^2  * 3 *  5

D    90  =    2 * 3^2   * 5

E    96  =    2^5 *  3

F   120  =    2^3 * 3 *  5

G  135  =    3^3 * 5

A  can  be paired  with  D    =   2^4 * 3^2  * 5^2

B  can be paired  with  E  =     2^6  *  3^4

C  can be  paired with  G  =    2^2  *  3^4 * 5^2

F  cannot be  paired

3. f(x) has degree 4 and g(x) has degree 4. Because b is a constant, the maximum degree of \(f(x) + b\cdot g(x)\) can only be 4.

4. f(x) has degree 4 and g(x) has degree 4. By multiplying, you are adding the degrees, so the degree of f(x) * g(x) is 8.

1. \((x-3)(2x^2 + 5x - 7) = (2x^3 + 5x^2 - 7x) -(6x^2 - 15x + 21)\)

\(\boxed{2x^3 - x^2 + 8x - 21}\)

2. \((-3z^2 - 7z + 4)(6z^2 - z + 6) = -18z^4 - 39z^3 + 13z^2 -\boxed{ 46z} + 24\)

The coefficient of z is -46.

x-2    x     and  x+2   are the integers

(x-2) + 2x  + 3 (x+2) = 34

6x + 4 = 34

x = 5                                      3    5   and 7

Numerator    1/4 + 1/9   = 13/36

denominator  1/16 + 1/25 = 41/400

13/36   * 400 / 41  = 5200/1476 = 1 300/369    =   13/x / 41y

1300/369  * 41/13 = x/y =  100/9

take sqrt of both sides     sqrt x  / sqrt y = 10/3

Divide   x+3   into    2x^3 + 6x^2 + 10 x + 30   to find the other factor

= 2x² +10

40% of 70 are sixth graders

.4 (70) = 28 sixth graders

Angle B and angle BMC are two angles of a triangle ..... they cannot equal more than the angles of a triangle = 180   you have them totalling 201.

   Did you type your Q correctly ?

Gretest common factor of 80 and 48 is      16     tarts         each will get   5 rasberries and 3 blueberries

Only one question at a time!

Squares have equal side lengths = l

l * l = area

l^2 = 392

l = sqrt 392 =   14 sqrt 2    units

24 + 24

24 + 8 + 8 + 8

8 + 8 + 8 + 8 + 8 + 8                three ways

The denominator is a bowl shaped parabola (due to the POSITIVE coefficient for x²).... all values of this parabola must be > 0   for the domain to be all real numbers....

    if the denominator touches 0 or turns negative (by crossing 0)     the domain will be limited....

x^2 + 14x + c > 0    the vertex (the low point of the parabola)  of this parabola will occur at   - b/2a = -14/2 = -7

   at this point the parabola must be >0

(-7)^2 + 14 (-7) + c > 0

   c > 49                                  so the smallest integer c would be 50

None of those answers were correct

\(\frac{\sqrt{72}}{\sqrt{10}} = \frac{\sqrt{2} \sqrt{36}}{\sqrt{2} \sqrt{5}} = \frac{6}{\sqrt{5}}\)

\(\frac{6}{\sqrt{5}} \cdot \frac{\sqrt{5}}{\sqrt{5}} = \boxed{\frac{6\sqrt{5}}{5}}\)

Complete the square: \(f(x) = x^2 - 5x + c = (x - \frac{5}{2})^2 + (c - \frac{25}{4})\)

So, \(c - \frac{25}{4} = 1\) which  makes the minimum value of c equal to 29/4.

Let \(\frac{1}{x} = a\) and \(\frac{1}{y} = b..\)

We can rewrite the system like so:

a + b = 3

a - b = 7

Adding, we get a = 5 and b = -2, which means that x = 1/5 and y = -1/2.

x + y = -3/10

Do they have to be different integers?  Because I don't see how 2C can equal 2D if C and D aren't the same. 

No it is not      the inequality say GREATER than 600        600 is NOT greatert than 600

This means that the integer closest to y rounded down is 42.

\(\boxed{y \in [42, 43)}\)

The answer is x^4 - 6x^3 + 6x^2 + 24x - 40.

1 square yap is equal to 49 square inches. There are 12 inches in a foot. How long is a yap in feet?    

1 yap² = 49 in²     therefore 1 yap = 7 in  

so 1 yap is 7/12 of a foot.  

Maybe I'm oversimplifying it too.