456.98-10-14.95-6.07-109.10-30=<span>286.86
So her new </span>checkbook balance is $286.86
![\huge\boxed{x=-6}](https://tex.z-dn.net/?f=%5Chuge%5Cboxed%7Bx%3D-6%7D)
Hey there! Our goal here is to isolate the variable on one side of the equation.
![\begin{aligned}-7(x+6)&=4(x+6)&&\smash{\Big|}&&\textsf{Start with the original equation.}\\-7x+(-7)(6)&=4x+4(6)&&\smash{\Big|}&&\textsf{Distribute.}\\-7x-42&=4x+24&&\smash{\Big|}&&\textsf{Multiply.}\\-7x-4x&=24+42&&\smash{\Big|}&&\textsf{Move the terms.}\\-11x&=66&&\smash{\Big|}&&\textsf{Combine like terms.}\\x&=\boxed{-6}&&\smash{\Big|}&&\textsf{Divide both sides by $-11$.}\end{aligned}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7D-7%28x%2B6%29%26%3D4%28x%2B6%29%26%26%5Csmash%7B%5CBig%7C%7D%26%26%5Ctextsf%7BStart%20with%20the%20original%20equation.%7D%5C%5C-7x%2B%28-7%29%286%29%26%3D4x%2B4%286%29%26%26%5Csmash%7B%5CBig%7C%7D%26%26%5Ctextsf%7BDistribute.%7D%5C%5C-7x-42%26%3D4x%2B24%26%26%5Csmash%7B%5CBig%7C%7D%26%26%5Ctextsf%7BMultiply.%7D%5C%5C-7x-4x%26%3D24%2B42%26%26%5Csmash%7B%5CBig%7C%7D%26%26%5Ctextsf%7BMove%20the%20terms.%7D%5C%5C-11x%26%3D66%26%26%5Csmash%7B%5CBig%7C%7D%26%26%5Ctextsf%7BCombine%20like%20terms.%7D%5C%5Cx%26%3D%5Cboxed%7B-6%7D%26%26%5Csmash%7B%5CBig%7C%7D%26%26%5Ctextsf%7BDivide%20both%20sides%20by%20%24-11%24.%7D%5Cend%7Baligned%7D)
Answer:
3.1%, dependent event
Step-by-step explanation:
We have that vowel are 5, it is from A, E, I, O, U therefore the probability of drawing a vowel is:
5/26
since there are a total of 26 options to choose from. Then, when selecting that, we are left with 25 options and 4 vowels, therefore the probability would be:
4/25
Therefore the final probability is:
5/26 * (4/25) = 0.031
In other words, selecting a vowel and then another (without replacement) the probability is 3.1%
The events are dependent, since the first event affects the second event, since the number of vowels and the number of total options are reduced.
Answer:
Sorry to say this... but neither of them have a solution of (2,1)
Step-by-step explanation:
The top one has a solution of (-2,-1). The one on the bottom has a solution of (-2,1). So... I'm not sure how this can help... but yeah...