1.) Which domain restrictions apply to the rational expression? 14x-2x / x^2-7x

2.) Sara has 85% so far in math. She wants to increase her grade. So far there have been 1,000 points possible in her class. The expression below represents the percent she’ll have if she earns 100% on her final exam, which is worth x points:
(Picture down below)

3.) Solve for x.
3 / x+2 – 1 / x = 1 / 5x

Question

Nicky156 Nicky156

02-12-2019
Mathematics

contestada

1.) Which domain restrictions apply to the rational expression? 14x-2x / x^2-7x

2.) Sara has 85% so far in math. She wants to increase her grade. So far there have been 1,000 points possible in her class. The expression below represents the percent she’ll have if she earns 100% on her final exam, which is worth x points:
(Picture down below)

3.) Solve for x.
3 / x+2 – 1 / x = 1 / 5x

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Answer:

3. [tex]\displaystyle 1\frac{1}{3} = x[/tex]

2C. [tex]\displaystyle III.[/tex]

2B. [tex]\displaystyle I.[/tex]

2A. [tex]\displaystyle II.[/tex]

1. [tex]\displaystyle Set-Builder\:Notation: [x|7, 0 ≠ x] \\ Interval\:Notation: (-∞, 0) ∪ (0, 7) ∪ (7, ∞)[/tex]

Step-by-step explanation:

3. See above.

2C. The keyword is ratio, which signifies division, so you would choose "III.".

2B. The keyword is percent, which signifies multiplication of a ratio by 100, so you would choose "I.".

2A. The keyword is total, which signifies addition, so you would choose "II.".

1. Base this off of the denominator. Knowing that the denominator CANNOT be zero, you will get this:

[tex]\displaystyle x^2 - 7x \\ x[x - 7] = 0; 7, 0 = x \\ \\ Set-Builder\:Notation: [x|7, 0 ≠ x] \\ Interval\:Notation: (-∞, 0) ∪ (0, 7) ∪ (7, ∞)[/tex]

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