Answer: QE = 10
Step-by-step explanation: To solve this problem, it's important to understand that the diagonals of a parallelogram bisect each other.
This means that E is the midpoint of diagonal SQ.
So we can setup the equation x² + 9x = 4x + 6.
To solve this polynomial equation, set it equal to zero first.
So we have x² + 5x - 6 = 0 and we get (x + 6)(x - 1) = 0
when we factor the left side of the equation.
So this means that x = -6 or x = 1.
However, -6 will give us a negative length when we plug it in
to find QE so this will not work.
However, plugging 1 in will give us 10 as a length so QE = 10.
Answer:
4 √6
Step-by-step explanation:
We have a few right triangles. We know that a²+b²=c², with c being the side opposite the right angle. Representing the side without a value as z, we have:
m²+z² = (8+4)² = 12²
4²+n²=z²
8²+n²=m²
We have 3 equations with 3 unknown variables, so this should be solvable. One way to find a solution is to put everything in terms of m and go from there. First, we can take n out of the equations entirely, removing one variable. We can do this by solving for it in terms of z and plugging that into the third equation, removing a variable as well as an equation.
4²+n²=z²
subtract 4²=16 from both sides
z²-16 = n²
plug that into the third equation
64 + z² - 16 = m²
48 + z² = m²
subtract 48 from both sides to solve for z²
z² = m² - 48
plug that into the first equation
m² + m² - 48 = 144
2m² - 48 = 144
add 48 to both sides to isolate the m² and its coefficient
192 = 2m²
divide both sides by 2 to isolate the m²
96 = m²
square root both sides to solve for m
√96 = m
we know that 96 = 16 * 6, and 16 = 4², so
m = √96 = √(4²*6) = 4 √6
Formula to convert F to C:
(F -32) x 5/9
F = 63 + 10 = 73
73-32 = 41
41 x 5/9 = 22.77777
Rounded to the nearest degree = 23 C
The correct answer is the first choice
