Answer:
5 km
Step-by-step explanation:
It helps to draw a diagram.
The triangle between Stamford, Newport, and Amanda's house is a right triangle with one leg of length 12 and hypotenuse 13. The Pythagorean theorem can be used to find the remaining leg:
13² = 12² + (distance to Newport)²
169 -144 = (distance to Newport)²
√25 = 5 = distance to Newport
Newport is 5 km from Amanda's house.
_____
It can be useful to remember this right triangle. 5-12-13 right triangles show up in a number of algebra and geometry problems.
Equation: (Not sure if it's the right order...)
468 = 40x + 18(x - 3)
The fee Micheal charges each suscriber is $6
Work:
468 = 40x + 18(x - 3)
468 = 40x + 18x - 54
Mutilpy 18 & x and 18 & 3
468 = 58x - 54
Add 40x amd 18x
468 + 54 = 58x - 54
Add 54 to 468 to have -54 gone in 58x - 54
522 divide by 58 is 9
x = 9
9 - 3 = 6
Answer:
X=-8
Step-by-step explanation:
A number x is multiplied by 4, added to 3, and then divided by x+2, leaving us with 7/2. Or, as an equation:
![\frac{4x + 3}{x + 2} = \frac{7}{2}](https://tex.z-dn.net/?f=%20%5Cfrac%7B4x%20%2B%203%7D%7Bx%20%2B%202%7D%20%20%3D%20%20%5Cfrac%7B7%7D%7B2%7D%20)
Now, let's cross multiply:
![2(4x + 3) = 7(x + 2)](https://tex.z-dn.net/?f=2%284x%20%2B%203%29%20%3D%207%28x%20%2B%202%29)
![8x + 6 = 7x + 14](https://tex.z-dn.net/?f=8x%20%2B%206%20%3D%207x%20%2B%2014)
And solve:
![x + 6 = 14](https://tex.z-dn.net/?f=x%20%2B%206%20%3D%2014)
![x = - 8](https://tex.z-dn.net/?f=x%20%3D%20%20-%208)
For a better understanding of the solution provided here please go through the diagram in the file attached.
As can be seen from the diagram, we need to find the initial horizontal component of the vector that represents the velocity of the ball. Let us represent that initial horizontal component by,
.
Now, since basketball player shoots the ball with an initial velocity,
, of 14.4 ft./sec at an angle of 41.9 degrees with the horizontal, we can find the initial horizontal component by,
using the following formula:
ft./sec
9.20 divides by 4 is 2.3 per quarter pound
There are 9 quarters in 2 1/4
So 9 times 2.3 is 20.7