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Mathematics

2 answers:

Lostsunrise [7]3 years ago

7 0

Answer:

3; all real numbers except x = 2

Step-by-step explanation:

$\dfrac{f(x)}{g(x)}=\dfrac{3x-6}{x-2}=\dfrac{3(x-2)}{(x-2)}=3 \qquad x\ne 2$

irga5000 [103]3 years ago

5 0

Answer:

Step-by-step explanation:

f(x) can be factored from f(x) = 3x-6 into f(x) = 3(x-2). Divide f by g in a fraction now.

$\frac{f(x)}{g(x)}= \frac{3(x-2)}{x-2} =\frac{3}{1}*\frac{x-2}{x-2} =3$

Since anything divided by itself is 1 then x-2 divided by x-2 is 1 leaving 3 as the answer. This leaves a or b. The answer is b because the division cannot happen if the denominator is 0. So x-2 cannot ever be 0. It's 0 when x=2. The answer is b.

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Identify the slope and y-intercept of the line y=5x/3+1.

Gwar [14]

Answer:

slope: 5x/3 and y-intercept: 1

6 0

3 years ago

Read 2 more answers

A = 1011 + 337 + 337/2 +1011/10 + 337/5 + ... + 1/2021

egoroff_w [7]

The sum of the given series can be found by simplification of the number

of terms in the series.

A is approximately <u>2020.022</u>

Reasons:

The given sequence is presented as follows;

A = 1011 + 337 + 337/2 + 1011/10 + 337/5 + ... + 1/2021

Therefore;

$\displaystyle A = \mathbf{1011 + \frac{1011}{3} + \frac{1011}{6} + \frac{1011}{10} + \frac{1011}{15} + ...+\frac{1}{2021}}$

The n + 1 th term of the sequence, 1, 3, 6, 10, 15, ..., 2021 is given as follows;

$\displaystyle a_{n+1} = \mathbf{\frac{n^2 + 3 \cdot n + 2}{2}}$

Therefore, for the last term we have;

$\displaystyle 2043231= \frac{n^2 + 3 \cdot n + 2}{2}$

2 × 2043231 = n² + 3·n + 2

Which gives;

n² + 3·n + 2 - 2 × 2043231 = n² + 3·n - 4086460 = 0

Which gives, the number of terms, n = 2020

$\displaystyle \frac{A}{2} = \mathbf{ 1011 \cdot \left(\frac{1}{2} +\frac{1}{6} + \frac{1}{12}+...+\frac{1}{4086460} \right)}$

$\displaystyle \frac{A}{2} = 1011 \cdot \left(1 - \frac{1}{2} +\frac{1}{2} - \frac{1}{3} + \frac{1}{3}- \frac{1}{4} +...+\frac{1}{2021}-\frac{1}{2022} \right)$