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miskamm [114]
3 years ago
10

If 16 is added to one-third of a number, the result is three times the number. What is the number?

Mathematics
1 answer:
AnnZ [28]3 years ago
4 0
First set up the equation based on the description.

\frac{1}{3} x + 16 = 3x

Use subtraction to get the "x"s on one side of the equation. You can next subtract <span>\frac{1}{3} x from both sides.

16 = </span>\frac{8}{3}<span> x

Now you can multiply both sides of the equation by </span>\frac{3}{8}<span>  to solve for x

x = 6</span>
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A sequence can be generated by using an=4a(n-1)
WITCHER [35]
This problem is half understanding the question and half just plugging in numbers.

Understanding the Question:
So its saying that n = whole number bigger than one, making n = 2, 3, 4, 5, etc.

Now try plugging any number n into the a_n = 4a_{n-1} equation. Let's use 2 to make it simple. If you plug in 2, you get:
a_2 = 4a_{2-1}\\&#10;a_2 = 4a_1
Remember that the subscripts (the small numbers in the corner) are simply the term number. a_1 is term 1, a_2 is term 2, etc. The equation is saying that "term 2 = 4 times term 1."

If you keep plugging in random numbers for n, you'll see that the equation basically says, "a term = 4 times the term right before it." That makes it easy to plug and chug to get our answer.

Plugging and Chugging
Now we understand the question is asking for the first 4 terms, and each term is 4 times the last term. You're told that term 1, a_1 = 6. That makes the next four terms:

Term 2
a_2 = 4a_{2-1}\\&#10; a_2 = 4a_1\\&#10; a_2 = 4(6)\\&#10; a_2 = 24

Term 3
a_3 = 4a_{3-1}\\ a_3 = 4a_2\\ a_3 = 4(24)\\ a_3 = 96

Term 4
a_4 = 4a_{4-1}\\ a_4 = 4a_3\\ a_4 = 4(96)\\ a_4 = 384

Your first 4 terms are 4, 24, 96, and 384.

--------

Answer: A) F

6 0
3 years ago
Please answer question plz!!!!!
Neporo4naja [7]

Answer:

V = 214.32

Step-by-step explanation:

Remark

You have to be a little careful with this question. The temptation is just to take the difference of the heights. That is not correct. The difference has to be multiplied by the base to get the volume.

Formula

V = (h1 - h2)* Base

Givens

h1 = 32.9

h2 = 29.1

Base = 56.4

Solution

V = 56.4 ( 32.9 - 29.2)

V = 56.4 * 3.8

V = 214.32

6 0
3 years ago
13/17 as a decimal rounded to the nearest tenth
erma4kov [3.2K]

Answer:

0.8

Step-by-step explanation:

It's right.

6 0
3 years ago
15. What's the sum of 3/8 and 1/16?<br> 1/6 7/16 4/24 1/4
allsm [11]

Answer:

7/16

Step-by-step explanation:

1. you have to have the same denominator

7 0
3 years ago
Read 2 more answers
Given f(x)=-x+7 and g(x)=f(x+4) write a function for function g
finlep [7]

\begin{array}{llrlll}f(x) = -x +7&~\hspace{10em} &f\left( \boxed{x+4} \right) &=& \boxed{-x+4}+7\\\\&&g(x) &=& -x+11\end{array}

6 0
3 years ago
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