Answer:
see explanation
Step-by-step explanation:
Given
10 = 7 - m ( subtract 3 from both sides )
3 = - m ( multiply both sides by - 1 )
- 3 = m , or
m = - 3
As a check
Substitute m = - 3 into the right side of the equation and if equal to the left side then it is the solution
7 - m = 7 - (- 3) = 7 + 3 = 10 = left side
Thus m = - 3 is the solution to the equation
Answer:
- a) 16.4 m, 101°
- b) 6.22 m, 51 m²
Step-by-step explanation:
<u>Find the measure of angle Q:</u>
- 50° + (180° - 130°) = 100°
a) <u>Find PR using the law of cosines:</u>
- PR = √(8² + 13² - 28*13*cos 100°) = 16.4 m (rounded)
<u>Find ∠P using law of sines:</u>
- 16.4/sin 100° = 13/ sin P
- m∠P = arcsin (13 sin 100° / 16.4) = 51° (rounded)
<u>The bearing of R from P is:</u>
b)
<u>Find the measure of h, the distance from Q to PR:</u>
- h/ PQ = sin P
- h = PQ sin P
- h = 8 sin 51° = 6.22 m
<u>Find the area of ΔPQR:</u>
- A = 1/2PR*h
- A = 1/2(16.4)(6.22) = 51 m²
Answer:
12 units²
Step-by-step explanation:
a=longer base
b = shorter base
h = height
Area=(a+b)*h/2
Area = (10+2)*2/2=12 units²
Find the number of distinguishable permutations of the letters m, i, s, s, i, s, s, i, p, p, i.
Tatiana [17]
Solution:
we have been asked to find the number of distinguishable permutations of the letters m, i, s, s, i, s, s, i, p, p, i.
Here we can see
m appears 1 time.
i appears 4 times.
S appears 4 times.
p appears 2 times.
Total number of letters are 11.
we will divide the permutation of total number of letters by the permutation of the number of each kind of letters.
The number of distinguishable permutations
Hence the number of distinguishable permutations