The side of a rhombus and the half-diagonals form a right triangle. The length of the other half-diagonal is found from the Pythagorean theorem to be
... d = √((10 cm)² -(6 cm)²) = √(64 cm²) = 8 cm
The length of the other diagonal is 16 cm.
The area is half the product of the diagonal lengths, so is
... area = (1/2)(12 cm)(16 cm) = 96 cm²
<span>2^2 times 2^-5 i think but i am not positive</span>
Answer: 100 i think, but am not sure.
Step-by-step explanation:
The formula for area of a rectangle is A=l*w. Since the area is 84, then you can use the A=l*w formula. 84 = x(x+8) would be the equation to solve for x.
Now, you need to put the equation in standard form. So, x2 + 8x - 84 = 0.
Since you can't solve this quadratic using factoring, you need to complete the square.
To complete the square you need to add 84 to both sides. Now you have x2 + 8x = 84. Take the coefficient for the x term (8) and divide by 2. Now square it. That would be 42, so 16. Now you have x2 +8x +16 = 100.
Factor x2 +8x +16, so (x+4)2 = 100
If you use the square root property, you have x+4 = 10. Therefore, x = 6 (the short side) and 14 is the long side.
Okay, I think I understand this. Our first step is to solve how long the string is after he used some of it to tie the package. I have a feeling we have to subtract 7/8 - 1/5. Find a least common multiple (in this case, it's 40) and our new fractions are 35/40 and 8/45. Subtract:
35/40 - 8/40 = 27/40.
I don't think this can be simplified down any further as they do not have any common factors. So with that in mind, let's divide 27/40 with 5/1 (5/1 is basically 5 wholes but in fraction version)
When dividing fractions, you want to use the KCF technique (my old math teacher taught me this). Keep the first fraction the same (in this case, 27/40), change the sign from multiplication to division, and flip 5/1 to get it's reciprocal, 1/5. The equation will look like this:
27/40 * 1/5 = 27/200
So each piece is about 27/200 m in length (or 0.135 m in length).
If this is wrong, please let me know, but this is what I got out of this question. I hope this helped you :)
Answer:
3
Explanation:
Apply Multiplicative Distribution Law:
{x + y =9
{8x + 24y = 120
Reduce the greatest common factor on both sides of the equation.
{x + y = 9
{x + 3y = 15
Subtract the two equations: x + y - (x +3y) = 9 - 15
Remove paranthesis: x + y - x - 3y = 9 - 15
Cancel the unknown variables: y - 3y = 9 - 15
Combine like terms: -2y=9 - 15
Calculate the sum or difference: -2y = -6
Reduce the greatest common factor on both sides of the equation: y =3
Substitute one unknown quantity into the elimination: x + 3 = 9
Rearrange unknown terms to the left side of the equation: x = 9 - 3
Calculate the sum or difference: x = 6
Write the solution set of equations: {x = 6
{y = 3
Substitute: 6 - 3
Calculate the sum or difference: 3
Answer: 3
