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If the rectangular frame has width x, and length y, then the perimeter is 2x + 2y = 39. The length (y) is 2.5 more than the width (x), so y = x + 2.5

Then you can substitute it back into the first equation. 2x + 2(x + 2.5) = 39. 4x + 5 = 39. 4x = 34, x = 17/2. y = 8.5 + 2.5 = 11

The width is 8.5 inches, and the height is 11 inches.

Solving the equations, you get x = 18/35 and y = 1/7, so x^2 - y^2 = (18/35)^2 - (1/7)^2 = 299/1225.

But he might be older than your Grandfather !

Carissa isn't a name

The answer is 25.

I just figured out the answer it is 4

Maple produces the following:

0 = 0.972977645*x + 0.000012890360*x^2 - 0.24780681*10^(-8)*x^3 + 6.5559673*ln(x) - 4320.368041;  Using solve in Maple, x is                    

 4342.652916

Whatever temperature scale you are using it looks like the room will be pretty hot!!!
 

The series is based on following pattern : 

$latex \left ( 1 \right )^{2}+1=2$
$latex \left ( 2 \right )^{2}+1=5$
$latex \left ( 5 \right )^{2}+1=26$
$latex \left ( 26 \right )^{2}+1=677$
Therefore, the next number of this series will be 677.

The equation can be written to standard form. 

x/3 + y/4 = 6        =>     4x + 3y = 72         => point-slope form =>     y = -4x/3 + 24

Then since our triangle has base of y = 0 and height of x = 0, we can do some calculations to see the area under the line y = -4x/3 + 24 in Quad 1.

It has y-intercept of 24. x - intercept is 0 = -4x/3 + 24. 0 = -4x + 72. x = 18. So the x-intercept is (18, 0)

Thus the base has length 18, and the height has length 24, the area is 18 * 24 / 2 = 216.

Both sides of the equation have a common denominator, so you can multiply both sides by (a^3 + 7) to get rid of it.

You are left with 1 = -(a^3). Since a is a real number, then the only solution is a = -1.

You can do p + 2p = 3p + 3

Just try and get ap + bp = (a + b)p + c where c is not = 0.

Let the number of children==C
Let the mean height of all children==100 cm

100C==sum of the heights of all kids

[100C + (12*8)] / C ==100 + 6, solve for C

C==16 children

It is 45 not 44. The three sides are 10+10+10 which equals 30. That is our first value and since the sides of the square go up to the diameter of the circle, we get 5+5. Now our sum so far is 40. Now we have a semicircle so we just find the circumference of that to get another 5. The numbers add up to 45.

If its perpendicular, then the slopes of the two lines multiply to negative 1.

y = 3x/2 + b is what we know so far.

Plug in 4, -3

-3 = 6 + b

b = -9

So the equation is y = 3x/2 - 9

This simpifies to 4*p^2*q^8

The number of ways is 1320.

m + n = 44

Let the height of the bottom triangle with the base DC==x
Hypotenuse^2 - x^2 ==2^2
[4 - x]^2 - x^2==4, solve for x
x ==1.5
Area of the bottom triangle ==[2 x 1.5] / 2==1.5 u^2
Since you have 2 similar triangles (bottom + top), therefore their combined area ==2 x 1.5 ==3 u^2
Area of vertical rectangle ==2 x 4 ==8 u^2
Therefore, area of the shaded part==8 - 3 == 5 u^2

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