Answer:
<em>7,078,912 cents</em>
Step-by-step explanation:
Given the formula for calculating the value of the account in t years as;
V = Pe^rt
P is the principal initially invested
e is the base of a natural logarithm,
r is the rate of interest
t is the time
Given
P = $51200
r = 5.4% = 0.054
t = 6years
Substitute
V = 51200e^(0.054)(6)
V = 51200e^(0.324)
V = 51200(1.3826)
V = $70,789.12
V = 7,078,912 cents
<em>hence the amount in the account after 6 years to the nearest cent is 7,078,912 cents</em>
Answer:
a) f(x) = (-1/3)x + 8
b) f(x) = (1/3)x + 9
Step-by-step explanation:
f(x) = 1/3x - 8
a) To reflect across the x axis multiply f(x) by -1.
-f(x) = -1 (1/3x - 8)
= (-1/3)x + 8
b) to translate up 17 units add 17 to f(x)
f(x) + 17=
= 1/3x - 8 + 17
= 1/3x + 9
Not sure what you are asking but if you are looking for the next 3 numbers then multiply 5 by 1.5, 7.5 by 1.5, and 11.25 by 1.5
5 * 1.5 = 7.5
7.5 * 1.5 = 11.25
11.25 * 1.5 = 16.875
16.875 * 1.5 = 25.3125
25.3125 * 1.5 = 37.96875
37.96875 * 1.5 = 56.953125
<span>To find the next week in which all three coincide, look for the lowest common multiple of the numbers 2,3, and 6. Two has multiples of (2,4,6,8,10,12), three has (3,6,9,12,15,18), and 6 has (6,12,18,24). The lowest number that is common to all three values is 6, so Clea will attend all three in the same week 6 weeks from now.</span>
140° + ∠5 = 180° <em>same side interior angles </em>⇒ ∠5 = 40°
∠2 ≅ ∠5 <em>vertical angles ⇒ </em>∠2 = 40°
∠8 = 53° <em>alternate interior angles</em>
∠3 ≅ ∠8 <em>vertical angles ⇒ </em>∠3 = 53°
x + ∠2 + ∠3 = 180° <em>triangle sum theorem</em>
x + 40° + 53° = 180°
x + 93° = 180°
x = 87°
Answer: 87°
Note: I just realized that there is an easier way to solve this:
∠9 + 53° + x = 180° <em>triangle sum theorem</em>
140° + ∠9 = 180° <em>supplementary angles </em>⇒ ∠9 = 40°
40° + 53° + x = 180°
x + 93° = 180°
x = 87°
Use whichever solutions makes sense to you.
