m = rise/run = (-10 - (-1))/(-6 - (-3)) = -9/-3 = 3
the slope of the line is equal to 3.
Step 4 because where did she get the 2 there was no two hope this helps hope i am brainliest
Answer:
x = 3 . . . or . . . x = 4
Step-by-step explanation:
The factored form is ...
(x -3)(x -4) = 0
The zero product rule tells you the solutions are the values of x that make the factors be zero:
x = 3
x = 4
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Comment on factoring
When the leading coefficient is 1, the coefficient of the x-term is the sum of the constants in the binomial factors, and the constant term is their product. You can see this by multiplying out the generic case:
(x +a)(x +b) = x^2 +(a+b)x + ab
What this means is that when you're factoring, you're looking for factors of the constant that add up to give the coefficient of the x-term. Here, the x-term is negative and the constant is positive, so both factors will be negative.
12 = -1×-12 = -2×-6 = -3×-4
The sums of these factor pairs are -13, -8, -7. Clearly, the last pair of factors of 12 will be useful to us, since that sum is -7. So, the binomial factors of our equation are ...
(x -3)(x -4) = 0
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If the leading coefficient is not zero, the method of factoring is similar, but slightly different. Numerous videos and web sites discuss the method(s).
Answer:
The solutions for the given system of equations are:
Step-by-step explanation:
Given the equation system:
We obtain the following matrix:
![\left[\begin{array}{cccc}3&1&4&-3\\-1&1&4&17\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccc%7D3%261%264%26-3%5C%5C-1%261%264%2617%5Cend%7Barray%7D%5Cright%5D)
<u>Step 1:</u> Multiply the fisrt row by 1/3.
![\left[\begin{array}{cccc}1&\frac{1}{3} &\frac{4}{3}&-1\\-1&1&4&17\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccc%7D1%26%5Cfrac%7B1%7D%7B3%7D%20%26%5Cfrac%7B4%7D%7B3%7D%26-1%5C%5C-1%261%264%2617%5Cend%7Barray%7D%5Cright%5D)
<u>Step 2:</u> Sum the first row and the second row.
![\left[\begin{array}{cccc}1&\frac{1}{3} &\frac{4}{3}&-1\\0&\frac{4}{3} &\frac{16}{3}&16\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccc%7D1%26%5Cfrac%7B1%7D%7B3%7D%20%26%5Cfrac%7B4%7D%7B3%7D%26-1%5C%5C0%26%5Cfrac%7B4%7D%7B3%7D%20%26%5Cfrac%7B16%7D%7B3%7D%2616%5Cend%7Barray%7D%5Cright%5D)
<u>Step 3:</u> Multiply the second row by 3/4.
![\left[\begin{array}{cccc}1&\frac{1}{3} &\frac{4}{3}&-1\\0&1 &4&12\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccc%7D1%26%5Cfrac%7B1%7D%7B3%7D%20%26%5Cfrac%7B4%7D%7B3%7D%26-1%5C%5C0%261%20%264%2612%5Cend%7Barray%7D%5Cright%5D)
<u>Step 4:</u> Multiply the second row by -1/3 and sum the the first row.
![\left[\begin{array}{cccc}1&0 &0&-5\\0&1 &4&12\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccc%7D1%260%20%260%26-5%5C%5C0%261%20%264%2612%5Cend%7Barray%7D%5Cright%5D)
The result of the reduced matrix is:
This is equal to:
These are the solutions for the system of equations in terms of z, where z can be any number.
