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german
3 years ago
5

8 and 21 over 40 in decimal and by step plzzzzzz thank u ill rate it

Mathematics
1 answer:
kaheart [24]3 years ago
3 0
There is a simple and easy method through which 8,21/40 can be changed into a decimal. First, divide 21 by 41. Due to the fact that 40 cannot go into 21, you will have to add a decimal, so you are left with 21.0. Next, you have to consider, how many times can 40 go into 210 or 21.0. The answer is 5. Next, multiply 40 by 5 to get the answer of 200. following this, subtract 200 from 210, which means you have ten left over. You then need to add another 0, which means you are left with 100. 40 can go into 100 twice, which means 20 is then left over. If you then add another 0 to 20, the answer will be 200.40, which goes into 200 5 times. you are then left with 8.525, your answer.
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Answers:
11. B) Acute
12. D) BA = QP
13. C) 36
15. C) BC = ST
16. Hypontenuse is roughly 23.6 millimeters
17. C) 17 ft
------------------------------------------------
Work Shown

Problem 11)
T+U+V = 180
38+U+72 = 180
38+72+U = 180
110+U = 180
110+U-110 = 180-110
U = 70
All three angles (38, 72, 70) are less than 90 degrees. This triangle is acute
-----------------
Problem 12)
If triangle ABC = triangle PQR, then the corresponding parts must be congruent. So,
AB = PQ
BC = QR
AC = PR
angle A = angle P
angle B = angle Q
angle C = angle R
The only choice that fits with the equations mentioned above is choice D, which is why it's the answer
Keep in mind BA is the same as AB. The order doesn't matter
-----------------
Problem 13)
FP is twice as long as PY
FP = 2*PY
FY = FP+PY
FY = 2*PY+PY
FY = 3*PY
Because FP = 24, we can find PY
FP = 2*PY
24 = 2*PY
PY = 12
Which is then used to find FY
FY = 3*PY
FY = 3*12
FY = 36
-----------------
Problem 15)
HL stands for "hypotenuse leg". We already have a pair of congruent legs which is RS = AB, given by the tick marks. We just need a pair of hypotenuses. In this case, BC and ST are the hypotenuse of the triangles. So if we knew BC = ST, then we'd have enough for HL to be used. 
-----------------
Problem 16)
a^2 + b^2 = c^2
14^2 + 19^2 = c^2
557 = c^2
c^2 = 557
c = sqrt(557) <<--- "sqrt" stands for "square root"
c = 23.60084
c = 23.6
The hypotenuse is roughly 23.6 millimeters long
-----------------
Problem 17)
Let a,b,c be the sides of the triangle. The given sides are a=6 and b=17. The unknown side is c. We don't know the exact value of c, but we can figure out how small and how large it can get.
It turns out that c is restricted through this compound inequality
b-a < c < b+a
Plug in the given values and simplify
b-a < c < b+a
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So the third side can be between 11 and 23, but not equal to either endpoint. The only choice that fits this inequality is 17, so that's why the answer is C.
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