Answer: 62
Step-by-step explanation:
See picture for more information
D+100+40=180
d=180-100-40=40 (sum of all angles)
e= 100+40= 140 (exterior angle)
180-140=40
C+50+40=180
C=180-50-40= 90 (right angle)
A=50
B=180-90-50= 40
Answers:
u = 18
v = 20
========================================================
Work Shown:
The leg YZ is congruent to the left FH
This means YZ = FH and that leads to u+v-18 = 10u-8v
The hypotenuse ZX is congruent to the hypotenuse HG
This means ZX = HG and we get the equation 14v-14u+32 = v+u+22
----------------------
The system of equations we have so far is
u+v-18 = 10u-8v
14v-14u+32 = v+u+22
Let's get the equations into standard form
Start with the first equation
u+v-18 = 10u-8v
u+v = 10u-8v+18
u+v-10u+8v = 18
-9u+9v = 18
-9(u-v) = 18
u-v = 18/(-9)
u-v = -2
Note how we can solve for the variable u to get
u = v-2
which we'll use later
----------------------
Let's get the other equation into standard form as well
14v-14u+32 = v+u+22
14v-14u-v-u = 22-32
-15u+13v = -10
Now plug in u = v-2 and solve for v
-15u+13v = -10
-15(v-2) + 13v = -10
-15v+30+13v = -10
-2v+30 = -10
-2v = -10-30
-2v = -40
v = -40/(-2)
v = 20
Which means,
u = v-2
u = 20-2
u = 18
Answer:
Step-by-step explanation:
The time intervals are [0.00, 0.10], [0.10, 0.30], and [0.30, 0.60].
The rate of change in each interval is the slope of the line between the endpoints:
m = [f(b) − f(a)] / (b − a)
Filling out the table:
![\left[\begin{array}{ccc}Time (s)&Height (ft)&Rate\ of\ change(ft/s)\\0.00&96.44\\&&\frac{97.60-96.44}{0.10-0.00}=11.6 \\0.10&97.60\\&&\frac{98.57-97.60}{0.30-0.10}=4.85\\0.30&98.57\\&&\frac{98.30-98.57}{0.60-0.30}=-0.90\\0.60&98.30\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7DTime%20%28s%29%26Height%20%28ft%29%26Rate%5C%20of%5C%20change%28ft%2Fs%29%5C%5C0.00%2696.44%5C%5C%26%26%5Cfrac%7B97.60-96.44%7D%7B0.10-0.00%7D%3D11.6%20%5C%5C0.10%2697.60%5C%5C%26%26%5Cfrac%7B98.57-97.60%7D%7B0.30-0.10%7D%3D4.85%5C%5C0.30%2698.57%5C%5C%26%26%5Cfrac%7B98.30-98.57%7D%7B0.60-0.30%7D%3D-0.90%5C%5C0.60%2698.30%5Cend%7Barray%7D%5Cright%5D)
The intervals are already in order from greatest to least. Simply reverse the order to get least to greatest:
[0.30, 0.60]
[0.10, 0.30]
[0.00, 0.10]
