Answer:
Remember that the Pythagorean's theorem says that:
For a triangle rectangle with hypotenuse H and catheti A and B:
H^2 = A^2 + B^2
Here we also need to remember that the area of a square of side length L is:
area = L^2
Now let's solve this.
First, we start with two squares, one of side length a and the other of side length b.
Such that the complete area in the first image is:
area = a^2 + b^2
Now we draw two triangle rectangles with catheti a and b, and with hypotenuse c.
in step 3, we rotate those triangles in order to make a larger square, with side length c, with an area equal to:
area = c^2
Notice that we never added more shapes, so the area of the image did not change in all this process, then the initial area must be equal to the final area:
a^2 + b^2 = area = c^2
a^2 + b^2 = c^2
And remember that a and b are the catheti of the triangles, and c is the hypotenuse, then this is the Pythagorean's theorem.
Answer:
x = -36
Step-by-step explanation:
Step 1: Write equation
x/16 - (x + 2)/8 = 2
Step 2: Solve for <em>x</em>
- <u>Multiply both sides by 16:</u> x - 2(x + 2) = 32
- <u>Distribute -2:</u> x - 2x - 4 = 32
- <u>Combine like terms:</u> -x - 4 = 32
- <u>Add 4 to both sides:</u> -x = 36
- <u>Divide both sides by -1:</u> x = -36
Step 3: Check
<em>Plug in x to verify it's a solution.</em>
-36/16 - (-36 + 2)/8 = 2
-9/4 - -34/8 = 2
-9/4 + 17/4 = 2
8/4 = 2
2 = 2
Although the square root of 2 times the square root of 14 does equal the square root of 28, it is not simplified to the fullest extent. To simplify separate the square root of 28 into two factors, but make sure one is a perfect square. We can separate into 4 and 7, and since the square root of 4 is 2, we are left with 2* the square root of 7
2 1/5+4 1/10
=11/5+41/10
=(11/5)*2+41/10
=22/10+41/10
=63/10
6 3/10
answer A.6 3/10
Answer:
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