Answer:
- Maria–Ava: 15.7 feet
- Lucas–Maria: 10.1 feet
- angle at Maria: 50°
Step-by-step explanation:
The cosine and tangent functions are useful here. The relevant relations are ...
Cos = Adjacent/Hypotenuse
Tan = Opposite/Adjacent
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The distance from Maria to Ava (ma) is the hypotenuse of the triangle, so we have ...
cos(40°) = 12/ma
ma = 12/cos(40°) ≈ 12/0.76604 ≈ 15.7 . . . feet
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The distance from Lucas to Maria (ml) is the side opposite the given angle, so we have ...
tan(40°) = ml/12
ml = 12·tan(40°) ≈ 12·0.83910 ≈ 10.1 . . . feet
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The angle formed at Maria's position is the complement of the other acute angle in the right triangle:
M = 90° -40° = 50°
In summary, ...
- Maria–Ava: 15.7 feet
- Lucas–Maria: 10.1 feet
- angle at Maria: 50°
FOIL method : F = First , O = Outer , I = Inner, L = Last
(6x-6)(x+6)
First: 6x * x = 6x^2
Outer: 6x * 6 = 36x
Inner: -6 * x = -6x
Last: -6 *6 = -36
Put these in order and we get : 6x^2 + 36x -6x -36
Answer: do you mean gram or gallon??
Step-by-step explanation: if gallon then a gallon is more than 1 oz. If it is gram then 1 oz is more
Answer:
Step-by-step explanation:
Since we are talking about compounded annual interest, we can use the Exponential Growth Formula to calculate the answer for this question.
Where:
- y is the total amount after a given time
- a is the initial amount
- r is the interest rate in decimal form
- t is the amount of time
First we need to calculate the total after 2 years with a 9% interest.
So after 2 years there will be £1,188.10 in the account. Now we can add £3000 to that and use the new value as the initial amount, and calculate the new total in 5 years.
So now we can subtract the £4000 purchase from the amount currently in the account, and calculate one more year of interest with the new initial amount.
So at the end you would have £2,662.86 in the account one year after the purchase.
Answer:
the area of the shape is 8cm