Answer:
x = 8
Step-by-step explanation:
A line with "undefined" slope is a vertical line, whose equation is of the form ...
x = constant
In order for the line to go through a point with an x-coordinate of 8, the constant must be 8.
x = 8 . . . . . a vertical line through (8, -3)
The value of x<em> </em>in the polynomial fraction 3/((x-4)•(x-7)) + 6/((x-7)•(x-13)) + 15/((x-13)•(x-28)) - 1/(x-28) = -1/20 is <em>x </em>= 24
<h3>How can the polynomial with fractions be simplified to find<em> </em><em>x</em>?</h3>
The given equation is presented as follows;
![\frac{3}{(x - 4) \cdot (x - 7) } + \frac{6}{(x - 7) \cdot (x - 13) } + +\frac{15}{(x - 13) \cdot (x - 28) } - \frac{1}{(x - 28) } = - \frac{1}{20}](https://tex.z-dn.net/?f=%20%5Cfrac%7B3%7D%7B%28x%20-%204%29%20%5Ccdot%20%28x%20-%207%29%20%7D%20%20%2B%20%5Cfrac%7B6%7D%7B%28x%20-%207%29%20%5Ccdot%20%28x%20-%2013%29%20%20%20%7D%20%20%2B%20%2B%5Cfrac%7B15%7D%7B%28x%20-%2013%29%20%5Ccdot%20%28x%20-%2028%29%20%7D%20-%20%5Cfrac%7B1%7D%7B%28x%20-%2028%29%20%20%7D%20%3D%20%20-%20%20%5Cfrac%7B1%7D%7B20%7D%20)
Factoring the common denominator, we have;
![\frac{3\cdot(x - 13) \cdot(x - 28) + 6 \cdot(x - 4) \cdot(x - 28) + 15 \cdot(x - 4) \cdot(x - 7) - (x - 4) \cdot (x - 7)\cdot(x - 13)}{(x - 4) \cdot (x - 7)\cdot(x - 13) \cdot(x - 28)} + = - \frac{1}{20}](https://tex.z-dn.net/?f=%20%5Cfrac%7B3%5Ccdot%28x%20-%2013%29%20%5Ccdot%28x%20-%2028%29%20%2B%206%20%5Ccdot%28x%20-%204%29%20%5Ccdot%28x%20-%2028%29%20%20%2B%2015%20%5Ccdot%28x%20-%204%29%20%5Ccdot%28x%20-%207%29%20%20-%20%28x%20-%204%29%20%5Ccdot%20%28x%20-%207%29%5Ccdot%28x%20-%2013%29%7D%7B%28x%20-%204%29%20%5Ccdot%20%28x%20-%207%29%5Ccdot%28x%20-%2013%29%20%5Ccdot%28x%20-%2028%29%7D%20%20%20%2B%20%3D%20%20-%20%20%5Cfrac%7B1%7D%7B20%7D%20)
Simplifying the numerator of the right hand side using a graphing calculator, we get;
By expanding and collecting, the terms of the numerator gives;
-(x³ - 48•x + 651•x - 2548)
Given that the terms of the numerator have several factors in common, we get;
-(x³ - 48•x + 651•x - 2548) = -(x-7)•(x-28)•(x-13)
Which gives;
![\frac{-(x - 7) \cdot(x - 28)\cdot (x - 13)}{(x - 4) \cdot (x - 7)\cdot(x - 13) \cdot(x - 28)} + = - \frac{1}{20}](https://tex.z-dn.net/?f=%20%5Cfrac%7B-%28x%20-%207%29%20%5Ccdot%28x%20-%2028%29%5Ccdot%20%28x%20-%2013%29%7D%7B%28x%20-%204%29%20%5Ccdot%20%28x%20-%207%29%5Ccdot%28x%20-%2013%29%20%5Ccdot%28x%20-%2028%29%7D%20%20%20%2B%20%3D%20%20-%20%20%5Cfrac%7B1%7D%7B20%7D%20)
Which gives;
![\frac{-1}{(x - 4)} + = - \frac{1}{20}](https://tex.z-dn.net/?f=%20%5Cfrac%7B-1%7D%7B%28x%20-%204%29%7D%20%20%20%2B%20%3D%20%20-%20%20%5Cfrac%7B1%7D%7B20%7D%20)
x - 4 = 20
Therefore;
Learn more about polynomials with fractions here:
brainly.com/question/12262414
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Let x = the number.
"increased by" tells you we are adding.
"twice a number" tells you 2 times a number.
16 + 2x = - 24
Subtract 16 from both sides so that we have the variable on one sides and the constants on the other.
2x = - 24 - 16
2x = - 40
Divide by 2 to isolate the variable.
x = - 40/2 = - 20
Your solution is - 20.
To check your answer, plug in.
16 + 2(-20) = - 24
16 - 40 = - 24
- 24 = - 24
I'd say the 3rd one. I haven't done this stuff in 2 years ... me forgot. But if it's not right, then the 1st one!
I want you to know you're smart and you can do this! Good luck!
Answer:
1.56%
Step-by-step explanation:
A standard deck of cards has 52 cards, and 13 of these are hearts, as there are 4 suits, and 52/4=13. This means the probability of choosing a heart card from a deck of cards is 1/4, or 25%. Now to find the probability of doing this from 3 decks in a row, we simply cube 1/4 to get 1/64, and in percentage this is ~1.56%.