(y2-y1)/(x2-x1)
=(0-1.5)/(-2-0)
=0.5
25 pints are in 7.5 quarts
Answer:
#1
<u>Sum of interior angles is 180:</u>
- y = 180 - (42 + 31) = 107
<u>The law of sines:</u>
- x / sin 107 = 11 / sin 42
- x = 11 sin 107deg / sin 42deg
- x = 15.72
#2
<u>The law of cosines:</u>
- cos 76 = (6² + 17² - x² )/2(6)(17)
- 204*0.24 = 325 - x²
- x² = 325 - 48.96
- x² = 276.04
- x = √276.04
- x = 16.61
#3
<u>Same as above:</u>
- 2*9.4*10*cos 20 = (10² + 9.4² - x²)
- 176.66 = 188.36 - x²
- x² = 188.36 - 176.66
- x² = 11.7
- x = √11.7
- x = 3.42
#4
<u>Sum of interior angles is 180:</u>
<u>The law of sines:</u>
- x / sin 34 = 15 / sin 94
- x = 15 sin 34 / sin 94
- x = 8.41
You don't provide the instructions for this problem, leaving it up to me to guess what you might want.
Note that g(x) should be written as g(x) = (x-2)^2, whereas f(x) = g(x) + 3 (as presented).
If we let g(x) be the input to f(x), we get the "composition" of g and f:
f(x) = g(x) + 3 = (x-2)^2 + 3. You could leave the answer as is or you could expand (x-2)^2: f(x) = x^2 - 4x + 4 + 3 (and so on).
Given:
The given polynomial is
When it divided by (x+1) gives remainder 0 and when divided by (x-2) gives remainder of 45.
To find:
The values of m and n.
Solution:
According to the remainder theorem, if a polynomial P(x) is divided by (x-c), then the remainder is P(c).
Let the given polynomial be P(x).
When it divided by (x+1) gives remainder 0. So, P(-1)=0.
...(i)
When P(x) is divided by (x-2) gives remainder of 45. So, P(2)=0
...(ii)
Multiply 2 on both sides of (i).
...(iii)
Subtract (iii) from (ii).
Putting m=5.5 in (i), we get
Therefore, the values of m and n are 5.5 and -21.5 respectively.
