5)
= - i - 2 - 3i
= - 4i - 2
= - 2 (2i + 1)
7)
= - 4 [(2 -2i - i (8 - 4i)]
= - 4 (2 - 2i - 8i + 4i^2)
= - 4 (4i^2 - 10i + 2)
= (- 4) (2) (2i^2 - 5i + 1)
= - 8 (2i^2 - 5i + 1)
9)
= p^2 - 4p - 4p + 16
= p (p - 4) - 4 (p - 4)
= (p - 4) (p - 4)
= (p - 4) ^2
11)
= p^2 - 8p - 8p + 64
= b (b - 8) - 8 (b - 8)
= (b - 8) (b - 8)
= (b - 8)^2
This is a little long, but it gets you there.
- ΔEBH ≅ ΔEBC . . . . HA theorem
- EH ≅ EC . . . . . . . . . CPCTC
- ∠ECH ≅ ∠EHC . . . base angles of isosceles ΔEHC
- ΔAHE ~ ΔDGB ~ ΔACB . . . . AA similarity
- ∠AEH ≅ ∠ABC . . . corresponding angles of similar triangle
- ∠AEH = ∠ECH + ∠EHC = 2∠ECH . . . external angle is equal to the sum of opposite internal angles (of ΔECH)
- ΔDAC ≅ ΔDAG . . . HA theorem
- DC ≅ DG . . . . . . . . . CPCTC
- ∠DCG ≅ ∠DGC . . . base angles of isosceles ΔDGC
- ∠BDG ≅ ∠BAC . . . .corresponding angles of similar triangles
- ∠BDG = ∠DCG + ∠DGC = 2∠DCG . . . external angle is equal to the sum of opposite internal angles (of ΔDCG)
- ∠BAC + ∠ACB + ∠ABC = 180° . . . . sum of angles of a triangle
- (∠BAC)/2 + (∠ACB)/2 + (∠ABC)/2 = 90° . . . . division property of equality (divide equation of 12 by 2)
- ∠DCG + 45° + ∠ECH = 90° . . . . substitute (∠BAC)/2 = (∠BDG)/2 = ∠DCG (from 10 and 11); substitute (∠ABC)/2 = (∠AEH)/2 = ∠ECH (from 5 and 6)
- This equation represents the sum of angles at point C: ∠DCG + ∠HCG + ∠ECH = 90°, ∴ ∠HCG = 45° . . . . subtraction property of equality, transitive property of equality. (Subtract ∠DCG+∠ECH from both equations (14 and 15).)
Answer:
{0,1,2,3,4,5}
Step-by-step explanation:
We are given that
Total number of machine parts=300
Number of defective machine parts=10
Total number of good machine parts=300-10=290
Sample contain parts that do not conform to customer requirement=5
X is a random variable which is the number of parts in a sample of 5 parts that do not conform to customer requirements.
We have to find the correct answer.
The sample contain 5 parts
Therefore, the possible values of random variable X
0,1,2,3,4,5
Hence, the range of X is given by
{0,1,2,3,4,5}
Coefficient of 14x is 14
Coefficientis the number in front of the letter. For example, coeffient of 2b is 2. When there is no number in front of the letter the coefficient is 1.
