Answer:
<h2>1. x = 4</h2><h2>2. x = 20</h2>
Step-by-step explanation:
1.
ΔABC and ΔAJK are similar (AA). Therefore the sides are in proportion:
![\dfrac{AC}{AJ}=\dfrac{AB}{AK}](https://tex.z-dn.net/?f=%5Cdfrac%7BAC%7D%7BAJ%7D%3D%5Cdfrac%7BAB%7D%7BAK%7D)
We have:
AC = 1 + 4 = 5
AJ = 1
AB = 1 + x
AK = 1
Substitute:
![\dfrac{5}{1}=\dfrac{1+x}{1}](https://tex.z-dn.net/?f=%5Cdfrac%7B5%7D%7B1%7D%3D%5Cdfrac%7B1%2Bx%7D%7B1%7D)
<em>subtract 1 from both sides</em>
![4=x\to x=4](https://tex.z-dn.net/?f=4%3Dx%5Cto%20x%3D4)
2.
ΔVUT and ΔVMN are similar (AA). Therefore the sides are in proportion:
![\dfrac{VU}{VM}=\dfrac{VT}{VN}](https://tex.z-dn.net/?f=%5Cdfrac%7BVU%7D%7BVM%7D%3D%5Cdfrac%7BVT%7D%7BVN%7D)
We hve:
VU = x + 8
VM = x
VT = 49
VN = 49 - 14 = 35
Substitute:
<em>cross multiply</em>
<em>use the distributive property a(c + b) = ab + ac</em>
<em>subtract 35x from both sides</em>
<em>divide both sides by 14</em>
![20=x\to x=20](https://tex.z-dn.net/?f=20%3Dx%5Cto%20x%3D20)
Answer:
1 hour = 7/18 of the distance between two ports
Step-by-step explanation:
Given that:
In 3/7 hours distance traveled is 1/6
For finding distance in one hour, divide both sides by 7/3 so that 3/7 would be cancelled out:
3/7 * 7/3 hours = 1/6 * 7/3 distance
By simplifying:
1 hour = 7/18 of the distance between two ports
This means that in one hour 7/18 of the distance is covered between two ports.
i hope it will help you!
Answer:
![opposite\approx 70.02](https://tex.z-dn.net/?f=opposite%5Capprox%2070.02)
Step-by-step explanation:
The triangle in the given problem is a right triangle, as the tower forms a right angle with the ground. This means that one can use the right angle trigonometric ratios to solve this problem. The right angle trigonometric ratios are as follows;
![sin(\theta)=\frac{opposite}{hypotenuse}\\\\cos(\theta)=\frac{adjacent}{hypotenuse}\\\\tan(\theta)=\frac{opposite}{adjacent}](https://tex.z-dn.net/?f=sin%28%5Ctheta%29%3D%5Cfrac%7Bopposite%7D%7Bhypotenuse%7D%5C%5C%5C%5Ccos%28%5Ctheta%29%3D%5Cfrac%7Badjacent%7D%7Bhypotenuse%7D%5C%5C%5C%5Ctan%28%5Ctheta%29%3D%5Cfrac%7Bopposite%7D%7Badjacent%7D)
Please note that the names (
) and (
) are subjective and change depending on the angle one uses in the ratio. However the name (
) refers to the side opposite the right angle, and thus it doesn't change depending on the reference angle.
In this problem, one is given an angle with the measure of (35) degrees, and the length of the side adjacent to this angle. One is asked to find the length of the side opposite the (35) degree angle. To achieve this, one can use the tangent (
) ratio.
![tan(\theta)=\frac{opposite}{adjacent}](https://tex.z-dn.net/?f=tan%28%5Ctheta%29%3D%5Cfrac%7Bopposite%7D%7Badjacent%7D)
Substitute,
![tan(35)=\frac{opposite}{100}](https://tex.z-dn.net/?f=tan%2835%29%3D%5Cfrac%7Bopposite%7D%7B100%7D)
Inverse operations,
![tan(35)=\frac{opposite}{100}](https://tex.z-dn.net/?f=tan%2835%29%3D%5Cfrac%7Bopposite%7D%7B100%7D)
![100(tan(35))=opposite](https://tex.z-dn.net/?f=100%28tan%2835%29%29%3Dopposite)
Simplify,
![100(tan(35))=opposite](https://tex.z-dn.net/?f=100%28tan%2835%29%29%3Dopposite)
![70.02\approx opposite](https://tex.z-dn.net/?f=70.02%5Capprox%20opposite)
Answer: The answer is $4.20
Step-by-step explanation:
Car B because 334 divided by 5= 41 mph