geno3141

Since the figures are similar with a scale factor of 4:3   --->   4/3  =  QR/KL   --->   4/3  =  8/KL

--->   Cross multiply:   4 · KL  =  3 · 8   --->   4 · KL  =  24   --->   KL  =  6

If the figure has straight sides, divide it into triangles and find the areas of all the triangles.

I have to agree with sasefllower ...

I have no idea what n = 6 has to do with the problem ... ignoring that:

∫₀²(x + 1)²dx  =  ∫₀²(x² + 2x + 1)dx  =  [x³/3 + x² + x]₀²  =  [2³/3 + 2² + 2] - [0³/3 + 0² + 0]

   =   8/3 + 4 + 2 - 0 - 0 - 0  =  26/3

For problems like this:  x⁷ · x⁵,  add the exponents to get x¹².

x^a · x^b  =  a^{a + b}

-0.5x² + 5x + 20

Factor out the -0.5 from the first two terms:

-0.5(x² - 10x) + 20

Complete the square:  divide -10 by 2 and square the answer:  (-10 ÷ 2)² = 25

Add 25 inside the parantheses and add 12.5 at the end of the expression, so the value of the expression doesn't change (the reason that you add 12.5 is that you have entered -12.5 within the parantheses: -0.5 x 25 = -12.5):

-0.5(x² - 10x + 25) + 20 + 12.5

-0.5(x - 5)² + 32.5

Now, you can pick out p and q ...

I agree with Anon until the final step.

After calculating 20% or $55.00 and getting $11.00, I believe that you should subtract $11.00 from $55.00 to get the cost to the store of $44.00.

(This assumes that the markup rate is applied to the final price of the item and not to the original cost to the store.)

One way to solve this problem, is to use the method of linear combinations:

4x  -  y  =  3     --->   multiply by -2     --->     -8x + 2y  =  -6

6x - 2y  =  5                                       --->      6x  - 2y  =  5

Add down the columns:                                  -2x          =  -1

Divide by -2:                                                            x  =  -1/-2   --->   x  =  1/2

Replace this value into the first equation:  4x - y  =  3   --->   4(1/2) - y  =  3  

                                                                               --->   2 - y  =  3   --->   -y  =  1   --->   y  =  -1  

Since the perimeter is 4 cm and all the sides of the square have the same length, each side must be 1 cm long.

The area of that square is 1 cm x 1 cm, which is 1 cm².

The locus of points in a plane that are equally distant to two intersecting lines are lines which are the two bisectors of the given lines. (The distance from a point to a line is found by measuring along the perpendicular to the line.)

Since L1 is vertical and L2 are horizontal, the bisectors will be the two lines which have slopes of 45° (m = 1) and 135° (m = -1).

For this problem, you want the line that passes through the intersection point of the two lines (3, 3) with a slope of -1; defined by the equation y = -x + 6.

You can debate whether or not you want the point (3,3) included in the locus (Is a distance of 0 really a distance?); my preference is to include it.