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3 years ago

Write the next three terms of the arithmetic sequence 1,12,23,34

Mathematics

1 answer:

xz_007 [3.2K]3 years ago

6 0

9514 1404 393

Answer:

45, 56, 67

Step-by-step explanation:

Terms of an arithmetic sequence have a common difference. That is, the next term is found by adding that difference to the previous term.

Here, the difference is 12 -1 = 11, so each term is 11 more that the previous one. The next terms are found by repeatedly adding 11.

34 + 11 = 45

45 + 11 = 56

56 + 11 = 67

The next three terms are 45, 56, 67.

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Combine and Simplify:<br> 48 (1/4x - 1/3y - 2/6x - 3/8y - 2/3<br> WRITE 2 WAYS!

Bezzdna [24]

Answer:

Combining and simplifying $48(\frac{1}{4}x-\frac{1}{3}y-\frac{2}{6}x-\frac{3}{8}y-\frac{2}{3})$ we get $\mathbf{-4x-34y-32}$ or we can write as $\mathbf{48(\frac{-x}{12} -\frac{17y}{24}- \frac{2}{3})}$

Step-by-step explanation:

We need to combine and simplify

$48(\frac{1}{4}x-\frac{1}{3}y-\frac{2}{6}x-\frac{3}{8}y-\frac{2}{3})$

First we will combine like terms and then perform the mathematical operations like addition or subtraction.

<u>Like terms</u>: terms having same variable

$48(\frac{1}{4}x-\frac{2}{6}x-\frac{1}{3}y-\frac{3}{8}y-\frac{2}{3})$

Now we take LCM of like terms

$=48(\frac{1}{4}x-\frac{2}{6}x-\frac{1}{3}y-\frac{3}{8}y-\frac{2}{3})\\=48(\frac{x*3-2x*2}{12} +\frac{-y*8-3y*3}{24}- \frac{2}{3})\\=48(\frac{3x-4x}{12} +\frac{-8y-9y}{24}- \frac{2}{3})\\=48(\frac{-x}{12} +\frac{-17y}{24}- \frac{2}{3})\\=48(\frac{-x}{12} -\frac{17y}{24}- \frac{2}{3})$

Now, we can multiply 48 with terms inside the bracket.

we can simplify the terms if they are both divisible by same number.

$=48(\frac{-x}{12} -\frac{17y}{24}- \frac{2}{3})\\=48(\frac{-x}{12} )-48(\frac{17y}{24})-48(\frac{2}{3}))\\=-4x-34y-32$

So, Combining and simplifying $48(\frac{1}{4}x-\frac{1}{3}y-\frac{2}{6}x-\frac{3}{8}y-\frac{2}{3})$ we get $\mathbf{-4x-34y-32}$ or we can write as $\mathbf{48(\frac{-x}{12} -\frac{17y}{24}- \frac{2}{3})}$

6 0

3 years ago

Show all work to write the expression in simplified rational exponent form:

tatyana61 [14]

Answer:

$x^{\frac{1}{2} } + 48$

Step-by-step explanation:

This is hard to explain, but basically you use exponent rules to switch it to an exponent

$(\sqrt[4]{x^{2} +4} )^{3}$

It's easiest if you calculate $4^{3}$ first

4³ = 4 x 4 x 4 = 48

Then convert the root to a fraction exponent

$\sqrt[4]{x^{2}} = x^{\frac{2}{4}} = x^{\frac{1}{2} }$

Combine them using addition, since addition was in the problem

$x^{\frac{1}{2} } + 48$

I hope this helps!

7 0

1 year ago

Wich is greater 5 divided by 6 or 1 divided by 6 and how did you figure it out?

marysya [2.9K]

Answer:

The answer for this question is 5 divided 6 is greater.

Step-by-step explanation:

because 5 divided 6 is equal to 0.83

and 6 divided by 1 equals to 6

SO the answer is going to be 0.83 which is 5 divided by 6.

GOOD LUCK HOPE YOU GET IT RIGHT

6 0

3 years ago

Read 2 more answers

Peppermint candies per jar

Harlamova29_29 [7]

Leaf #2 because 27 and 23 are closest to 30

4 0

3 years ago

Question 22 Petrolyn motor oil is a combination of natural oil and synthetic oil. It contains 8 liters of natural oil for every

Setler [38]

Answer:

897 liters

Step-by-step explanation:

The motor oil is composed of 8 liters of natural oil and 5 liters of synthetic oil. This means there is a ratio of 8/5. We have 552 liters of natural oil to y liters of synthetic. This is the ratio 552/y. Create a proportion that compares the two ratios.

$\frac{8}{5}=\frac{552}{y}$

Solve by cross multiplying.

8y = 5(552)

8y = 2,760

y= 345

345 liters of synthetic oil.

Together 552+345= 897 liters of motor oil.

4 0

3 years ago