Answer:
In order: 3, 2, 1, 4, 5
Step-by-step explanation:
Remark
x - 1 is a root.
Proof
x - 1 = 0
x = 1
(1)^3 + 5(1)^2 - 8(1)^2 - 40(1) + 7(1) + 35
1 + 5 - 8 - 40 + 7 + 35
6 + 7 + 35 - 48 = 0
Solution
Divide x - 1 into the original equation.
x^3 + 5x^2 - 8x^2 - 33x + 35
x - 1 || x^3 - 3x^2 - 33x + 35 || x^2 - 2x - 35
<u>x^3 - x^2</u>
-2x^2 - 33x
<u>-2x^2 + 2x</u>
- 35x + 35
<u>-35x + 35</u>
0
x^2 - 2x - 35 factors into (x - 7)(x + 5)
Complete factorization
(x - 1)(x - 7)(x + 5)
1.
Lines a and b are parallel lines.
Line t is a transversal.
Corresponding angles are congruent.
Angle 1 is a corresponding angle to the 107-deg angle, so m<1 = 107.
Angles 1 and 2 are supplementary angles since they are a linear pair.
m<1 + m<2 = 180
m<2 = 180 - 107
m<2 = 73
2.
Lines a and b are parallel lines.
Line t is a transversal.
Corresponding angles are congruent.
Angle 3 is a corresponding angle to the 95-deg angle, so m<3 = 95.
Angles 3 and 4 are supplementary angles since they are a linear pair.
m<3 + m<4 = 180
95 + m<4 = 180
m<4 = 180 - 95
m<4 = 85
3.
Lines a and b are parallel lines.
Line t is a transversal.
Corresponding angles are congruent.
Angle 5 is a corresponding angle to the 49-deg angle, so m<5 = 49.
Angles 5 and 6 are supplementary angles since they are a linear pair.
m<5 + m<6 = 180
49 + m<6 = 180
m<6 = 180 - 49
m<6 = 131
(3c)3 beacause c(3)is multiplies by an numerical number
Answer:
The answer is 4 r 1.
Step-by-step explanation:
We kbow that 9 time 4 will get us 36, so that's what we put in the two boxes below the 37. Then, we subtract 36 from 37 and get 1. The one will go in the box below the 36. This means our answer will be 4 r 1. Hope this helps :)