Answer:
![x = - 1](https://tex.z-dn.net/?f=x%20%3D%20%20-%201)
![y = - 3](https://tex.z-dn.net/?f=y%20%3D%20%20-%203)
Step-by-step explanation:
![6x - 5y =9 \: \: \: \: \: \: \: \: ...(1)\\ 2x-y=1 \: \: \: \: \: \: \: \: \: \: ...(2)](https://tex.z-dn.net/?f=6x%20-%205y%20%3D9%20%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20...%281%29%5C%5C%202x-y%3D1%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20%20%20%5C%3A%20%20%5C%3A%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20...%282%29)
are given two equation
now,
from equation (1) we get,
![6x - 5y =9 \\ 6x = 5y + 9 \\ x = \frac{5y + 9}{6}](https://tex.z-dn.net/?f=6x%20-%205y%20%3D9%20%5C%5C%206x%20%3D%205y%20%2B%209%20%5C%5C%20x%20%3D%20%20%5Cfrac%7B5y%20%2B%209%7D%7B6%7D%20)
now put the value of x in equation 2
![2( \frac{5y + 9}{6} ) - y = 1 \\ \\ \frac{10y + 18}{6} - y = 1 \\ \\ \frac{10y + 18 - 6y}{6} = 1 \\ \\ 10y + 18 - 6y = 6 \\ 4y = 6 - 18 \\ 4y = - 12 \\ y = - \frac{12}{4} \\ \\ y = - 3](https://tex.z-dn.net/?f=2%28%20%5Cfrac%7B5y%20%2B%209%7D%7B6%7D%20%29%20-%20y%20%3D%201%20%5C%5C%20%20%5C%5C%20%20%5Cfrac%7B10y%20%2B%2018%7D%7B6%7D%20%20-%20y%20%3D%201%20%5C%5C%20%20%5C%5C%20%20%5Cfrac%7B10y%20%2B%2018%20-%206y%7D%7B6%7D%20%20%3D%201%20%5C%5C%20%5C%5C%20%2010y%20%2B%2018%20-%206y%20%3D%206%20%5C%5C%204y%20%3D%206%20-%2018%20%5C%5C%204y%20%3D%20%20-%2012%20%5C%5C%20y%20%3D%20%20%20-%20%5Cfrac%7B12%7D%7B4%7D%20%20%5C%5C%20%20%5C%5C%20y%20%3D%20%20-%203)
now put y = -3 in equation 2
![2x - ( - 3) = 1 \\ 2x + 3 = 1 \\ 2x = 1 - 3 \\ 2x = - 2 \\ x = - \frac{2}{2} \\ x = - 1](https://tex.z-dn.net/?f=2x%20-%20%28%20-%203%29%20%3D%201%20%5C%5C%202x%20%2B%203%20%3D%201%20%5C%5C%202x%20%3D%201%20-%203%20%5C%5C%202x%20%3D%20%20-%202%20%5C%5C%20x%20%3D%20%20-%20%20%5Cfrac%7B2%7D%7B2%7D%20%20%5C%5C%20x%20%3D%20%20-%201)
Answer:
The length of the ramp must be at least 14.71 feet
Step-by-step explanation:
Given
![BC = 2.3ft](https://tex.z-dn.net/?f=BC%20%3D%202.3ft)
![\theta = 9^\circ](https://tex.z-dn.net/?f=%5Ctheta%20%3D%209%5E%5Ccirc)
<em>See attachment for complete figure</em>
Required
Length of the ramp (z)
To do this, we consider sin of angle A (
).
So, we have:
![sin\theta = \frac{Opposite}{Hypotenuse}](https://tex.z-dn.net/?f=sin%5Ctheta%20%3D%20%5Cfrac%7BOpposite%7D%7BHypotenuse%7D)
This gives:
![sin(9)= \frac{2.3}{z}](https://tex.z-dn.net/?f=sin%289%29%3D%20%5Cfrac%7B2.3%7D%7Bz%7D)
Make z the subject
![z= \frac{2.3}{sin(9)}](https://tex.z-dn.net/?f=z%3D%20%5Cfrac%7B2.3%7D%7Bsin%289%29%7D)
![z = \frac{2.3}{0.1564}](https://tex.z-dn.net/?f=z%20%3D%20%5Cfrac%7B2.3%7D%7B0.1564%7D)
![z = 14.71 ft](https://tex.z-dn.net/?f=z%20%3D%2014.71%20ft)
<em>The length of the ramp must be at least 14.71 feet</em>
4 sqrt(400) / 4 sqrt(5)
sqrt(400) =20
4 *20
--------
4 sqrt(5)
the 4's on the top and bottom cancel
20
--------
sqrt(5)
I was taught never to leave a sqrt in the denominator
so you need to multiply by sqrt (5) in the numerator and the denominator
20* sqrt(5)
--------
sqrt(5)* sqrt(5)
20* sqrt(5)
--------
5
= 4 sqrt(5)
Answer:
The answer to your question is $79.38
Step-by-step explanation:
Data
base = 8.1 m
height = 3.5 m
cost = $2.80/ m²
Formula
Area of a parallelogram = base x height
Substitution
Area of a parallelogram = 8.1 x 3.5
= 28.35 m²
Total cost of the carpet
1 m² ------------------- $2.80
28.35 m² --------------- x
x = (28.35 x 2.80) / 1
x = 79.38 m²