Answer: First Option
, ![cos(A)=\frac{12}{37}](https://tex.z-dn.net/?f=cos%28A%29%3D%5Cfrac%7B12%7D%7B37%7D)
Step-by-step explanation:
We know that the sine function is defined as:
![sin(\alpha)=\frac{Opposite}{Hypotenuse}](https://tex.z-dn.net/?f=sin%28%5Calpha%29%3D%5Cfrac%7BOpposite%7D%7BHypotenuse%7D)
In the same way the cosine function is defined as:
![cos(\alpha)=\frac{adjacent}{Hypotenuse}](https://tex.z-dn.net/?f=cos%28%5Calpha%29%3D%5Cfrac%7Badjacent%7D%7BHypotenuse%7D)
Therefore it is fulfilled that:
Opposite: is the length of the side opposite angle
Adjacent: It is the length of the side that contains the angle of 90 ° and angle A
Hypotenuse: It is the length of the side opposite the angle of 90 °
So:
![sin(A)=\frac{35}{37}](https://tex.z-dn.net/?f=sin%28A%29%3D%5Cfrac%7B35%7D%7B37%7D)
![cos(A)=\frac{12}{37}](https://tex.z-dn.net/?f=cos%28A%29%3D%5Cfrac%7B12%7D%7B37%7D)
Answer:
10 quarters, 9 dimes, and 20 nickels.
Step-by-step explanation:
q - 1 = d, 2q = n or q = 1/2n
.25q + .10(q - 1) + .05(2q) = 4.40
.25q + .10q - .10 + .10q = 4.40
.45q - .10 = 4.40
.45q = 4.50
4.5/.45 = 10
He has 10 quarters, 9 dimes, and 20 nickels.
Step-by-step explanation:
1.
![- 2(3x + 7) = 32 - 4x \\ distribute \\ - 2 \times 3x = - 6x \\ - 2 \times 7 = - 14 \\ - 6x - 14 = 32 - 4x \\ add \: 4x \: to \: both \: sides \\ - 6x + 4x = 32 - 4x + 4x \\ - 2x = 32 \\ divide \: by \: - 2 \\ \frac{ - 2x}{ - 2} = \frac{32}{ - 2} \\ \\ x = - 16](https://tex.z-dn.net/?f=%20-%202%283x%20%2B%207%29%20%3D%2032%20-%204x%20%5C%5C%20distribute%20%5C%5C%20%20-%202%20%5Ctimes%203x%20%3D%20%20-%206x%20%5C%5C%20%20-%202%20%5Ctimes%207%20%3D%20%20-%2014%20%5C%5C%20%20-%206x%20-%2014%20%3D%2032%20-%204x%20%5C%5C%20add%20%5C%3A%204x%20%5C%3A%20to%20%5C%3A%20both%20%5C%3A%20sides%20%5C%5C%20%20-%206x%20%2B%204x%20%3D%2032%20-%204x%20%2B%204x%20%5C%5C%20%20-%202x%20%3D%2032%20%5C%5C%20divide%20%5C%3A%20by%20%5C%3A%20%20-%202%20%5C%5C%20%20%20%5Cfrac%7B%20-%202x%7D%7B%20-%202%7D%20%20%3D%20%20%5Cfrac%7B32%7D%7B%20-%202%7D%20%20%5C%5C%20%20%5C%5C%20x%20%3D%20%20-%2016)
2.
![4x + y = 3 \\ y = - 4x + 3 \\ using \: point \: slope \: form \\ y - y1 = m(x - x1) \\ y + 6 = - 4(x + 4) \\ y + 6 = - 4x - 16 \\ y = - 4x - 22](https://tex.z-dn.net/?f=4x%20%2B%20y%20%3D%203%20%5C%5C%20%20y%20%3D%20%20-%204x%20%2B%203%20%5C%5C%20using%20%5C%3A%20point%20%5C%3A%20slope%20%5C%3A%20form%20%5C%5C%20y%20-%20y1%20%3D%20m%28x%20-%20x1%29%20%5C%5C%20y%20%2B%206%20%3D%20%20-%204%28x%20%2B%204%29%20%5C%5C%20y%20%2B%206%20%3D%20%20-%204x%20-%2016%20%5C%5C%20y%20%3D%20%20-%204x%20-%2022)
First equation: Your equation is given.
Second equation: Distribute by multiplying every number in the parentheses by the number outside it.
3rd equation: Combine like terms by adding 4x to both sides.
4th equation: Combine like terms by subtracting 14 from both sides.
5th equation: Divide both sides by -2, the coefficient of x.
Answer:
8 percent or .8
Step-by-step explanation:
Have a great day
The answer to this question is A obviously.