What two positive numbers whose difference is 7 and whose product is 294

Step-by-step explanation:

We will use x and y as our positive numbers.  We need to write 2 equations from this information.  The first is that the difference between the numbers is 7:

x - y = 7 is the equation for that.

The second is that the product of the 2 numbers is 294:

xy = 294

Let's begin by solving the first equation for x:

x = 7 + y

Now sub that in for x in the second equation:

(7 + y)y = 294 and

This is a quadratic, so let's put it into standard form, setting it equal to 0:

We have to factor this now to find out what values of y satisfy this equation.

Think: "what 2 number multiply to equal -294 and add to equal 7.  To find these numbers we find all the factors of 294, which are:

1, 294

2, 147

3, 98

6, 49

7, 42

14, 21

It looks like 14 and 21 will work.  If we make the 14 negative, then 21 - 14 = 7.  And if the 14 is negative, then -14 * 21 = -294.  So the signs are correct.  The equation rewritten using those values in place of 7y is:

and we factor by grouping:

Out of the first set of parenthesis we can pull out a y, and from the second set we can pull out a 14:

y(y + 21) - 14(y + 21) = 0

What's common now is the factor (y + 21).  So factor THAT out, and you're left with:

(y + 21)(y - 14) = 0

Set each of these expression equal to 0 and solve for y:

y + 21 = 0 so

y = -21 and

y - 14 = 0 so

y = 14

Since we were told that both of the numbers are positive, then y has to be 14.  

Sub in y = 14 to find x:

x = 7 + 14 so

x = 21

There you go!

area of part 1:

a1=base*height/2=(8+2)*(8-2-2-1)/2=10*3/2=15 ft^2

area of part 2:

a2=length*width=(8+2)*1=10 ft2

area of part 3:

a3=length*width=8*2=16 ft2

total shaded area : a1+a2+a3=41 ft2

total area of the reactangle : a=16*8=128 ft2

total area of the nonshaded region : 128-41=87 ft2

part 1 answer = 8

part 2 answer = 72

step-by-step explanation:

part 1 explanation = add all of the numbers, then divide by how many numbers you have. so, 200/25 = 8.

part 2 explanation = not gonna lie, this is hard to explain, so just google how to do it.