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2 years ago

Simplify the expression. 1/3r + 1/4 + 2/3r + 3/4

Mathematics

2 answers:

Alina [70]2 years ago

5 0

Answer:

r + 1

Step-by-step explanation:

Combine like terms. Add the constants together and add the terms with the variable r together. In order to add fractions, keep the common denominator and add only the numerators together. Then, simplify, and divide the numerator by the denominator if the result is a whole number.

This gives the following answer:

$\frac{1}{3} r+\frac{1}{4} +\frac{2}{3} r+\frac{3}{4} \\=\frac{1}{3} r+\frac{2}{3} r+\frac{1}{4} +\frac{3}{4}\\=\frac{3}{3} r+\frac{4}{4} \\=r+1$

expeople1 [14]2 years ago

4 0

Answer:

r+1

Step-by-step explanation:

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anyanavicka [17]

Answer:

$\sum\limits_{n=0}^{\infty} \frac{2}{3^n}\frac{(-1)^n}{5^n} = 15/8$

Step-by-step explanation:

The sum you are trying to understand is this.

$\sum\limits_{n=0}^{\infty} \frac{2}{3^n}\frac{(-1)^n}{5^n}$

Remember that in general when you have a geometric series

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$\sum\limits_{n = 0}^{\infty} a*r^n = \frac{a}{1-r}$ and that equality is true as long as $|r| < 1$ .

Therefore here we have

$\sum\limits_{n=0}^{\infty} \frac{2}{3^n}\frac{(-1)^n}{5^n} = \sum\limits_{n=0}^{\infty} 2* \big(\frac{-1}{3*5} \big)^n = \sum\limits_{n=0}^{\infty} 2* \big(\frac{-1}{15} \big)^n$ and $\big|\frac{-1}{15} \big| = \frac{1}{15} < 1$

Therefore we can use the formula and

$\sum\limits_{n=0}^{\infty} 2* \big(\frac{-1}{15} \big)^n = \frac{2}{1-(-1/15)} = \frac{2}{1+1/15} = 30/16 = 15/8$

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What is the value of x in the equation 6x-5/2 = 2x+6

nataly862011 [7]

Answer:

x= 17/8

Step-by-step explanation:

6x− 5/2=2x+6

Step 1: Simplify both sides of the equation.

6x+−5/2=2x+6

Step 2: Subtract 2x from both sides.

6x+−5/2−2x=2x+6−2x

4x+−5/2=6

Step 3: Add 5/2 to both sides.

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3 years ago

Simplify the expression. 1/3r + 1/4 + 2/3r + 3/4​

Simplify the expression. 1/3r + 1/4 + 2/3r + 3/4