Answer:
x = 4 + sqrt(5) or x = 4 - sqrt(5)
Step-by-step explanation:
Solve for x:
(x - 4)^2 = 5
Take the square root of both sides:
x - 4 = sqrt(5) or x - 4 = -sqrt(5)
Add 4 to both sides:
x = 4 + sqrt(5) or x - 4 = -sqrt(5)
Add 4 to both sides:
Answer: x = 4 + sqrt(5) or x = 4 - sqrt(5)
Answer:
see below
Step-by-step explanation:
![\frac{1}{x^{2} } + \frac{2}{y}/ \frac{5}{x} -\frac{6}{y^2}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7Bx%5E%7B2%7D%20%7D%20%2B%20%20%5Cfrac%7B2%7D%7By%7D%2F%20%5Cfrac%7B5%7D%7Bx%7D%20-%5Cfrac%7B6%7D%7By%5E2%7D)
find common denominator and add the fractions in numerator and denominator:
1/x² + 2/y = y+2x²/x²y
5/x -6/y² =5y² -6x/xy²
(y+2x²)/x²y / (5y²-6x)/xy² change into multiplication
(y+2x²)/x²y * xy²/(5y²-6x)
simplify
y(y+2x²)/ x(5y²-6x)
Answer:
m = 15/4
Step-by-step explanation:
slope (m) = (y₂ - y₁)/(x₂ - x₁)
Let:
(x₁ , y₁) = (-5 , -10)
(x₂ , y₂) = (-1 , 5)
Plug in the corresponding numbers to the corresponding variables:
m = (5 - (-10))/(-1 - (-5))
m = (5 + 10)/(-1 + 5)
m = (15)/(4)
m = 15/4 is your answer.
~
Answer: 448 dollars
=============================================
Work Shown:
P = 400 is the balance
r = 0.12 is the decimal form of the interest rate
t = 1 is the number of years
Use those values to get the simple interest to be
i = P*r*t
i = 400*0.12*1
i = 48
The amount of interest charged is $48
Add this onto the balance of 400 dollars and the total amount Aaron owes is P+i = 400+48 = 448 dollars.
Answer:
![\displaystyle y=-\frac{1}{2}x+4](https://tex.z-dn.net/?f=%5Cdisplaystyle%20y%3D-%5Cfrac%7B1%7D%7B2%7Dx%2B4)
Step-by-step explanation:
<u>Equation of a Line</u>
We can find the equation of a line by using two sets of data. It can be a pair of ordered pairs, or the slope and a point, or the slope and the y-intercept, or many other combinations of appropriate data.
We are given a line
![y - 12 = 2x -8](https://tex.z-dn.net/?f=y%20-%2012%20%3D%202x%20-8)
And are required to find a line perpendicular to that line. Let's find the slope of the given line. Solving for y
![y = 2x +4](https://tex.z-dn.net/?f=y%20%3D%202x%20%2B4)
The coefficient of the x is the slope
![m=2](https://tex.z-dn.net/?f=m%3D2)
The slope of the perpendicular line is the negative reciprocal of m, thus
![\displaystyle m'=-\frac{1}{2}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20m%27%3D-%5Cfrac%7B1%7D%7B2%7D)
We know the second line passes through (2,3). That is enough information to find the second equation:
![y-y_o=m'(x-x_o)](https://tex.z-dn.net/?f=y-y_o%3Dm%27%28x-x_o%29)
![\displaystyle y-3=-\frac{1}{2}(x-2)](https://tex.z-dn.net/?f=%5Cdisplaystyle%20y-3%3D-%5Cfrac%7B1%7D%7B2%7D%28x-2%29)
Operating
![\displaystyle y=-\frac{1}{2}(x-2)+3](https://tex.z-dn.net/?f=%5Cdisplaystyle%20y%3D-%5Cfrac%7B1%7D%7B2%7D%28x-2%29%2B3)
Simplifying
![\displaystyle y=-\frac{1}{2}x+4](https://tex.z-dn.net/?f=%5Cdisplaystyle%20y%3D-%5Cfrac%7B1%7D%7B2%7Dx%2B4)
That is the equation in slope-intercept form. Intercept: y=4