Answer:
(x + 9)² = 36
Step-by-step explanation:
Given
x² + 18x + 57 = 12 ( subtract 57 from both sides )
x² + 18x = - 45
To complete the square
add ( half the coefficient of the x- term)² to both sides
x² + 2(9)x + 81 = - 45 + 81
(x + 9)² = 36
This answer is already to the nearest tenth. The 5 is in the tenth's place.
Answer: P(x ≥ 1) = 0.893
Step-by-step explanation:
We would assume a binomial distribution for the outcome of the investment. The formula is expressed as
P(x = r) = nCr × p^r × q^(n - r)
Where
x represent the number of successes.
p represents the probability of success.
q = (1 - r) represents the probability of failure.
n represents the number of trials or sample.
From the information given,
p = 36% = 36/100 = 0.36
q = 1 - p = 1 - 0.36
q = 0.64
n = 5
Therefore,
P(x ≥ 1) = 1 - P(x = 0)
P(x = 0) = 5C0 × 0.36^0 × 0.64^(5 - 0)
P(x = 0) = 1 × 1 × 0.107
P(x = 0) = 0.107
P(x ≥ 1) = 1 - 0.107 = 0.893
Answer:
ASA
ΔFGH ≅ ΔIHG ⇒ answer B
Step-by-step explanation:
* Lets revise the cases of congruence
- SSS ⇒ 3 sides in the 1st Δ ≅ 3 sides in the 2nd Δ
- SAS ⇒ 2 sides and including angle in the 1st Δ ≅ 2 sides and
including angle in the 2nd Δ
- ASA ⇒ 2 angles and the side whose joining them in the 1st Δ
≅ 2 angles and the side whose joining them in the 2nd Δ
- AAS ⇒ 2 angles and one side in the first triangle ≅ 2 angles
and one side in the 2ndΔ
- HL ⇒ hypotenuse leg of the first right angle triangle ≅ hypotenuse
leg of the 2nd right angle Δ
* Lets prove the two triangles FGH and IHG are congruent by on of
the cases above
∵ FG // HI and GH is transversal
∴ m∠FGH = m∠IHG ⇒ alternate angles
- In the two triangles FGH and IHG
∵ m∠FHG = m∠IGH ⇒ given
∵ m∠FGH = m∠IHG ⇒ proved
∵ GH = HG ⇒ common side
∴ ΔFGH ≅ ΔIHG ⇒ ASA
* ASA
ΔFGH ≅ ΔIHG
Answer:
Replace the 4 with a 3 to make the equation true
