geno3141

x²xy  can be simplified to  x³y

Factor  xy - y²  to get  y(x - y)

Now, the problem is:  x³y / [ y(x - y) ]

You can now cancel the  y  in the numerator by the  y  in the denominator. After cancelling, you are left with:

x³ / (x - y)  

Which is the answer in reduced form.

However, if you meant the problem to be:  (x² - xy) / (xy - y²)

then, after factoring both the numerator and the denominator, the problem becomes:  

   [ x(x - y) ] / [ y(x - y) ]

Now, cancel the two  x - y  factors to get:  x/y

The square root of a number is a number, which when multiplied by itself, will have the original number as that answer.

Since 100 = 10 x 10, 10 is the square root of 100.

(h + 3)(h + 4)

= h(h + 4) + 3(h + 4)

= h² + 4h + 3h + 12

= h² + 7h + 12

The reciprocal of 6/5 is 5/6.

The reciprocal of any common fraction a/b is b/a.

Since tan = y/x and every (x, y) point in quadrant IV has a positive x-value and a negative y-value, tangent values in quadrant IV are negative; therefore, there are no values of t in quadrant IV that have a tangent value of +1/2.

This isn't a compound interest problem; this is a simple interest problem, whose formula is:

Interest = Principal x Rate X Time

The principal is 600; the rate is 3.5%; since the time is unknown, assume 1.

3.5% written as a decimal is 0.035 (divide 3.5 by 100, moving the decimal point two places to the right).

Interest = 600 x 0.035 x 1  =  21.00  

To be compound interest, you would need to find the amount of interest earned after several periods, such as 3.5% per year for 5 years.

Trincent is correct -- here are some steps:

(2/3)(x - 5)  =  (3/4)(4x - 3)

The denominators are 3 and 4, so the lowest common denominator is 12; multiply both sides by 12:

12 · (2/3)(x - 5)  =  12 · (3/4)(4x - 3)

--->   8(x - 5)  =  9(4x - 3)

--->   8x - 40  =  36x - 27

Subtract 8x from both sides:

--->   - 40  =  28 x - 27

Add 27 to both sides:

--->   -13  =  28x

Divide both sides by 28:

--->  x  =  -13/28

I'm afraid that my answer might now have been correct, so I deleted it.

If it is an arithmetic sequence, then if you subtract

   the first term from the second (69 - -31)

   and the second term from the third (169 - 69)

   and the third term from the fourth (269 - 169)

you will get the same answer every time ...

Are the answers to these three subtraction problems the same number?

If so, it's an arithemetic sequence; if they are not all the same answer then it isn't an arithmetic sequence ...

(px + q)(2x + 5)  =  6x² + 11x + r

2px² + 5px + 2qx + 5q  =  6x² + 11x + r

--->   2px² = 6x²  --->   p = 3

--->   5px + 2qx = 11x   --->   5p + 2q = 11

         --->  Since p = 3, 5(3) + 2q = 11

         --->   15 + 2q  =  11

         --->   2q  =  -4

         --->   q  =  -2

--->   5q = r

         --->   Since q = -2, 5(-2) = r

         --->   r  =  -10