Answer:
If x varies directly as y, then x=ky. y=5 and x=2.5 are substituted into x=ky to find k.
2.5=5k
k=2.5/5
k=5.
K =5 is substituted in x=ky to find y where x is 10.
x=5y
10=5y
y=10/2
y=2
Answer:
The solution to the equation system given is:
- <u>x = 2</u>
- <u>y = -1</u>
Step-by-step explanation:
First, we must know the equations given:
- 2x + 3y = 1
- 3x + y = 5
Following Crammer's Rule, we have the matrix form:
![\left[\begin{array}{ccc}2&3\\3&1\end{array}\right] =\left[\begin{array}{ccc}x\\y\end{array}\right] = \left[\begin{array}{ccc}1\\5\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D2%263%5C%5C3%261%5Cend%7Barray%7D%5Cright%5D%20%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Dx%5C%5Cy%5Cend%7Barray%7D%5Cright%5D%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%5C%5C5%5Cend%7Barray%7D%5Cright%5D)
Now we solve using the determinants:
![x=\frac{\left[\begin{array}{ccc}1&3\\5&1\end{array}\right]}{\left[\begin{array}{ccc}2&3\\3&1\end{array}\right] } =\frac{(1*1)-(5*3)}{(2*1)-(3*3)} = \frac{1-15}{2-9} =\frac{-14}{-7} = 2](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%263%5C%5C5%261%5Cend%7Barray%7D%5Cright%5D%7D%7B%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D2%263%5C%5C3%261%5Cend%7Barray%7D%5Cright%5D%20%7D%20%3D%5Cfrac%7B%281%2A1%29-%285%2A3%29%7D%7B%282%2A1%29-%283%2A3%29%7D%20%3D%20%5Cfrac%7B1-15%7D%7B2-9%7D%20%3D%5Cfrac%7B-14%7D%7B-7%7D%20%3D%202)
![y=\frac{\left[\begin{array}{ccc}2&1\\3&5\end{array}\right]}{\left[\begin{array}{ccc}2&3\\3&1\end{array}\right] } =\frac{(2*5)-(3*1)}{(2*1)-(3*3)}=\frac{10-3}{2-9} =\frac{7}{-7}=-1](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D2%261%5C%5C3%265%5Cend%7Barray%7D%5Cright%5D%7D%7B%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D2%263%5C%5C3%261%5Cend%7Barray%7D%5Cright%5D%20%7D%20%3D%5Cfrac%7B%282%2A5%29-%283%2A1%29%7D%7B%282%2A1%29-%283%2A3%29%7D%3D%5Cfrac%7B10-3%7D%7B2-9%7D%20%3D%5Cfrac%7B7%7D%7B-7%7D%3D-1)
Now, we can find the answer which is x= 2 and y= -1, we can replace these values in the equation to confirm the results are right, with the first equation:
- 2x + 3y = 1
- 2(2) + 3(-1)= 1
- 4 - 3 = 1
- 1 = 1
And, with the second equation:
- 3x + y = 5
- 3(2) + (-1) = 5
- 6 - 1 = 5
- 5 = 5
Alright, so we know that there are 7 days a week with 24 hours per day.
24x7= 168 hours a week.
Convert the problem to an equation using the percentage formula: P% * X = Y.
Let's take the 40% that is Sleep and use it in the percentage formula with the 168 hours.
40%x168= roughly 67 hours.
Hope this helped!
Answer:
≈ 68.2°
Step-by-step explanation:
tan X= 20/8
tan X= 2.5
x= tan ⁻¹ 2.5
x ≈ 68.2°
Answer:
<h2>84in²</h2>
Step-by-step explanation:
If the first one is 7 inches long, and 6 inches wide, and the second one is also 7 inches long, but is 6x2 inches wide, then what's the area?
6x2=12
So, Picture Frame 2 = 12 inches wide
Formula for finding area = LxW
L = 7
W = 12
7x12=84
So hence, your answer is 84in²
The area of the second frame is 84in²
Thanks!
