Answer:
c
Step-by-step explanation:
6x² + 54x + 120 = 0
divide by 6
x² + 9x + 20 = 0
(x² + 5x) + (4x + 20) = 0
x(x + 5) + 4(x + 5) = 0
(x + 4) (x + 5) = 0
x + 4 = 0, x + 5 = 0
x = -4, x = -5
Answer:
(In Interval Notation:
)
Step-by-step explanation:
Given the following binomial:
![5x+3](https://tex.z-dn.net/?f=5x%2B3)
You know that if this binomial is in the interval:
![(-6, -2)](https://tex.z-dn.net/?f=%28-6%2C%20-2%29)
It must be:
![-6](https://tex.z-dn.net/?f=-6%3C5x%2B3%3C-2)
Therefore, in order to find for what values of "x" the binomial
belongs to the given interval, you need to solve the inequality.
Then, you get:
![-6](https://tex.z-dn.net/?f=-6%3C5x%2B3%3C-2%5C%5C%5C%5C-6-3%3C5x%3C-2-3%5C%5C%5C%5C-9%3C5x%3C-5%5C%5C%5C%5C%5Cfrac%7B-9%7D%7B5%7D%3Cx%3C%5Cfrac%7B-5%7D%7B5%7D%5C%5C%5C%5C-1.8%3Cx%3C-1)
Now, you can write this in Interval notation.
Since it is an Open Interval, you must use parentheses. Then, this is:
![(-1.8,-1)](https://tex.z-dn.net/?f=%28-1.8%2C-1%29)
What's a pair of numbers that are addends of -6 but factors of 5? That would would be -5 & -1. Now we can break it up into groups. That will give us (x^2 - 5x)(x - 1). Now do the same for the second one. That will give us (x^2 - 8x)(x - 1x).
Answer:
19, 24
Step-by-step explanation:
the pattern adds one then adds five
+1, +5, +1, +5, on and on
6+1 is 7
7+5 is 12
12+1 is 13
13+5 is 18
18+1 is 19
19+5 is 24
Note: <span>Make the rule of three simple
cartoons __ price $
3 --------------- 4.77
8 --------------- y
Solving: (</span><span>directly proportional)
</span>
![\frac{3}{8} = \frac{4.77}{y}](https://tex.z-dn.net/?f=%20%5Cfrac%7B3%7D%7B8%7D%20%3D%20%5Cfrac%7B4.77%7D%7By%7D%20)
<span>Product of extremes equals product of means
</span>
![3*y = 8*4.77](https://tex.z-dn.net/?f=3%2Ay%20%3D%208%2A4.77)
![3y = 38.16](https://tex.z-dn.net/?f=3y%20%3D%2038.16)
![y = \frac{38.16}{3}](https://tex.z-dn.net/?f=y%20%3D%20%20%5Cfrac%7B38.16%7D%7B3%7D%20)
![\boxed{\boxed{y = 12.72}}\end{array}}\qquad\quad\checkmark](https://tex.z-dn.net/?f=%5Cboxed%7B%5Cboxed%7By%20%3D%2012.72%7D%7D%5Cend%7Barray%7D%7D%5Cqquad%5Cquad%5Ccheckmark)
Answer:
The price of eight cartoons was