Answer:
![15x^2 + 8x -12](https://tex.z-dn.net/?f=15x%5E2%20%2B%208x%20-12)
Step-by-step explanation:
(5x+6)(3x-2)
"foil" it out
F: 5x * 3x = 15x^2
O: 5x * -2 = -10x
I: 6*3x = 18x
L: 6 * -2 = -12
Ok so let's start with what we know- the shortest piece is 8 inches so there's one length... then the middle piece is 6 inches longer than the shortest (6+ 8) so the middle piece would be 14 inches long. To find the last piece we can add up the other two pieces we know (14+8) which would be 22 and subtract that from how long the whole sandwich is (59-22) which would be 37 inches long. So in the end he shortest piece would be 8 inches, the middle 14 inches and the longest 37 inches.
Answer:
(a) (5, -3)
Step-by-step explanation:
The "substitution method" for solving a system of equations requires that you write an expression that can be substituted for a variable in one or more of the other equations in the system.
<h3>Expression to substitute</h3>
The given equations are ...
We notice the first equation gives an expression for y. This is exactly what we want to substitute for y in the second equation.
<h3>Substitution</h3>
When the expression (x-8) is substituted for y in the second equation, you get ...
2x +3(x -8) = 1
This simplifies to ...
5x -24 = 1
<h3>Solution</h3>
This 2-step equation can now be solved in the usual way:
5x = 25 . . . . . . add 24 to isolate the variable term
x = 25/5 = 5 . . . . . divide by the coefficient of x
Note that we now know what the correct answer choice is.
Using the expression for y, we find ...
y = x -8 = 5 -8 = -3
The solution is (x, y) = (5, -3).
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The attached graph confirms this solution.
Answer:
The correct answer is 30
Step-by-step explanation:
Given: The x-axis represents the time in hours and the y-axis represents the distance in miles.
The line passes through the points
and ![(4,120)](https://tex.z-dn.net/?f=%284%2C120%29)
To find: The rise-over-run value for the relationship in the graph.
![\begin{aligned}m &=\frac{R i s e}{R u n} \\&=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} \\&=\frac{120-60}{4-2} \\&=\frac{60}{2} \\&=30\end{aligned}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7Dm%20%26%3D%5Cfrac%7BR%20i%20s%20e%7D%7BR%20u%20n%7D%20%5C%5C%26%3D%5Cfrac%7By_%7B2%7D-y_%7B1%7D%7D%7Bx_%7B2%7D-x_%7B1%7D%7D%20%5C%5C%26%3D%5Cfrac%7B120-60%7D%7B4-2%7D%20%5C%5C%26%3D%5Cfrac%7B60%7D%7B2%7D%20%5C%5C%26%3D30%5Cend%7Baligned%7D)
Thus, the rise-over-run value for the relationship represented in the graph is 30.