4) An arithmetic sequence has a 7th term of 54 and a 13th term of 94. Find the common difference

Can u guys help me with this problem

netineya [11]

Answer:

$-0.7$ or $-\frac{7}{10}$

Step-by-step explanation:

$-0.75-(-\frac{2}{5})+0.4+(-\frac{3}{4})$

The opposite of $-\frac{2}{5}$ is $\frac{2}{5}$

$-0.75 + \frac{2}{5} +0.4 - \frac{3}{4}$

Convert decimal number −0.75 to fraction $-\frac{75}{100}$ .

Reduce the fraction $-\frac{75}{100}$ to lowest terms by extracting and canceling out 25.

$-\frac{3}{4} + \frac{2}{5}+0.4-\frac{3}{4}$

Least common multiple of 4 and 5 is 20. Convert $-\frac{3}{4}$ and $\frac{2}{5}$ to fractions with denominator 20.

$-\frac{15}{20}+ \frac{8}{20} +0.4 - \frac{3}{4}$

Since $-\frac{15}{20}$ and $\frac{8}{20}$ have the same denominator, add them by adding their numerators.

$\frac{-15 +8}{20} +0.4-\frac{3}{4}$

Add -15 and 8 to get -7

$-\frac{7}{20}+0.4-\frac{3}{4}$

Convert decimal number 0.4 to fraction $\frac{4}{10}$ . Reduce the fraction $\frac{4}{10}$ to lowest terms by extracting and canceling out 2.

$-\frac{7}{20}+\frac{2}{5}-\frac{3}{4}$

Least common multiple of 20 and 5 is 20. Convert $-\frac{7}{20}$ and $\frac{2}{5}$ to fractions with denominator 20.

$-\frac{7}{20}+\frac{8}{20}-\frac{3}{4}$

Since $-\frac{7}{20}$ and $\frac{8}{20}$ have the same denominator, add them by adding their numerators.

$20-7+8-\frac{3}{4}$

Add -7 and 8 to get 1.

$\frac{1}{20}-\frac{3}{4}$

Least common multiple of 20 and 4 is 20. Convert $\frac{1}{20}$ and $\frac{3}{4}$ to fractions with denominator 20.

$\frac{1}{20}-\frac{15}{20}$

Since $\frac{1}{20}$ and $\frac{15}{20}$ have the same denominator, subtract them by subtracting their numerators.

$\frac{1}{20}-15$

Subtract 15 from 1 to get -14.

$20-14$

Reduce the fraction $-\frac{14}{20}$ to lowest terms by extracting and canceling out 2.

$-\frac{7}{10}$ or $-0.7$

Hope this helps! Brainliest would be much appreciated! Have a great day! :)

8 0

2 years ago

Which equation justifies why nine to the one third power equals the cube root of nine?

AVprozaik [17]

Answer:

nine to the one third power all raised to the third power equals nine raised to the one third times three power equals nine

Step-by-step explanation:

we know that

The <u><em>Power of a Power Property</em></u> , states that :To find a power of a power, multiply the exponents

so

$(a^{b})^{c}=a^{b*c}$

In this problem we have

$9^{\frac{1}{3}} =\sqrt[3]{9}$

Remember that

$\sqrt[3]{9}=9^{\frac{1}{3}}$

Raise to the third power

$[9^{\frac{1}{3}}]^3$

Applying the power of power property

$9^{\frac{3}{3}}$

$9^{1}$

$9$

therefore

nine to the one third power all raised to the third power equals nine raised to the one third times three power equals nine

8 0

4 years ago

Read 2 more answers

What is the next three terms to a sequence -1/3125, 1/625, -1/125, 1/25

Natali [406]

Answer:

-1/3125, 1/625, -1/125, 1/25 , -(1÷5) , 1 , -5

Step-by-step explanation:

1÷625÷(-1÷3 125) = -5

-1÷125÷(1÷625) = -5

(1÷25)÷(-1÷125) = -5

Then the common ratio of the geometric sequence is -5 then we keep multiplying by -5 each time to get the next term:

(1÷25)×(-5) = -(1÷5)

-(1÷5)×(-5) = 1

(1)×(-5) = -5

3 0

4 years ago

What is the median of the data set?

Margaret [11]

22 - Median is in the middle

8 0

3 years ago

Read 2 more answers

PLEASE HELP!!! WILL MARK BRAINLIEST!!!

kakasveta [241]

The answer is you need to post a pic in order to give help

5 0

3 years ago

Read 2 more answers