Answer:
The slope of the line is 1 , because the slope of another line parrallel to it is 1 and we know the when two lines are parralel the slope are equal
One gallon costs $1.88. To find the cost of seven gallons, you would multiply this price by seven.
1.88 x 7 = $13.16, which is answer D
Answer:
Here we will use algebra to find three consecutive integers whose sum is 300. We start by assigning X to the first integer. Since they are consecutive, it means that the 2nd number will be X + 1 and the 3rd number will be X + 2 and they should all add up to 300. Therefore, you can write the equation as follows:
(X) + (X + 1) + (X + 2) = 300
To solve for X, you first add the integers together and the X variables together. Then you subtract three from each side, followed by dividing by 3 on each side. Here is the work to show our math:
X + X + 1 + X + 2 = 300
3X + 3 = 300
3X + 3 - 3 = 300 - 3
3X = 297
3X/3 = 297/3
X = 99
Which means that the first number is 99, the second number is 99 + 1 and the third number is 99 + 2. Therefore, three consecutive integers that add up to 300 are 99, 100, and 101.
99 + 100 + 101 = 300
We know our answer is correct because 99 + 100 + 101 equals 300 as displayed above.
Step-by-step explanation:
Answer:
-58
Step-by-step explanation:
The real is the numbers and the imaginary is the x variable
Answer:
The solutions are
and
.
Step-by-step explanation:
We have the following equation:
.
The first step to solve this problem is using
![2) y = x^{2}](https://tex.z-dn.net/?f=2%29%20y%20%3D%20x%5E%7B2%7D)
We replace in the equation 1, find the values of y, and then we replace in equation 2) to find the values of x.
To solve the equations, it is important to know how we find the roots of a second order polynomial.
Given a second order polynomial expressed by the following equation:
![ax^{2} + bx + c, a\neq0](https://tex.z-dn.net/?f=ax%5E%7B2%7D%20%2B%20bx%20%2B%20c%2C%20a%5Cneq0)
This polynomial has roots
such that
, given by the following formulas:
![x_{1} = \frac{-b + \sqrt{\bigtriangleup}}{2*a}](https://tex.z-dn.net/?f=x_%7B1%7D%20%3D%20%5Cfrac%7B-b%20%2B%20%5Csqrt%7B%5Cbigtriangleup%7D%7D%7B2%2Aa%7D)
![x_{2} = \frac{-b - \sqrt{\bigtriangleup}}{2*a}](https://tex.z-dn.net/?f=x_%7B2%7D%20%3D%20%5Cfrac%7B-b%20-%20%5Csqrt%7B%5Cbigtriangleup%7D%7D%7B2%2Aa%7D)
![\bigtriangleup = b^{2} - 4ac](https://tex.z-dn.net/?f=%5Cbigtriangleup%20%3D%20b%5E%7B2%7D%20-%204ac)
In this problem, we have
![x^{4} - 3x^{2} - 4 = 0](https://tex.z-dn.net/?f=x%5E%7B4%7D%20-%203x%5E%7B2%7D%20-%204%20%3D%200)
![y = x^{2}](https://tex.z-dn.net/?f=y%20%3D%20x%5E%7B2%7D)
So
![y^{2} - 3y - 4 = 0](https://tex.z-dn.net/?f=y%5E%7B2%7D%20-%203y%20-%204%20%3D%200)
So: ![a = 1, b = -3, c = -4](https://tex.z-dn.net/?f=a%20%3D%201%2C%20b%20%3D%20-3%2C%20c%20%3D%20-4)
![\bigtriangleup = b^{2} - 4ac = (-3)^{2} -4(1)(-4) = 25](https://tex.z-dn.net/?f=%5Cbigtriangleup%20%3D%20b%5E%7B2%7D%20-%204ac%20%3D%20%28-3%29%5E%7B2%7D%20-4%281%29%28-4%29%20%3D%2025)
![y_{1} = \frac{-b + \sqrt{\bigtriangleup}}{2*a} = \frac{3 + \sqrt{25}}{2} = 4](https://tex.z-dn.net/?f=y_%7B1%7D%20%3D%20%5Cfrac%7B-b%20%2B%20%5Csqrt%7B%5Cbigtriangleup%7D%7D%7B2%2Aa%7D%20%3D%20%5Cfrac%7B3%20%2B%20%5Csqrt%7B25%7D%7D%7B2%7D%20%3D%204)
![y_{2} = \frac{-b - \sqrt{\bigtriangleup}}{2*a} = \frac{3 - \sqrt{25}}{2} = -1](https://tex.z-dn.net/?f=y_%7B2%7D%20%3D%20%5Cfrac%7B-b%20-%20%5Csqrt%7B%5Cbigtriangleup%7D%7D%7B2%2Aa%7D%20%3D%20%5Cfrac%7B3%20-%20%5Csqrt%7B25%7D%7D%7B2%7D%20%3D%20-1)
The values of y are ![y_{1} = 4, y_{2} = -1](https://tex.z-dn.net/?f=y_%7B1%7D%20%3D%204%2C%20y_%7B2%7D%20%3D%20-1)
We also have that:
![y = x^{2}](https://tex.z-dn.net/?f=y%20%3D%20x%5E%7B2%7D)
So
![4 = x^{2}](https://tex.z-dn.net/?f=4%20%3D%20x%5E%7B2%7D)
![x = \pm \sqrt{4}](https://tex.z-dn.net/?f=x%20%3D%20%5Cpm%20%5Csqrt%7B4%7D)
![x = \pm 2](https://tex.z-dn.net/?f=x%20%3D%20%5Cpm%202)
And
![-1 = x^{2}](https://tex.z-dn.net/?f=-1%20%3D%20x%5E%7B2%7D)
There is no real solution for this. So our only solutions are
and
.