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3 years ago

How do i solve this radical expression? It has to do with factoring i know that.

Mathematics

1 answer:

MAVERICK [17]3 years ago

5 0

Firstly it's not a radical expression.

You can factorize the numerator x²+12x+36 = (x+6)²

Factorize the denominator 12x+72 = 12(x+6)

=(x+6)² / 12(x+6) , simplify. Answer = (x+6)/12

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Dont really understand how to do this

bija089 [108]

Answers:

$t_{10} = -22 \ \text{ and } S_{10} = -85$

========================================================

Explanation:

$t_1 = \text{first term} = 5\\t_2 = \text{first term}-3 = t_1 - 3 = 5-3 = 2$

Note we subtract 3 off the previous term (t1) to get the next term (t2). Each new successive term is found this way

$t_3 = t_2 - 3 = 2-3 = -1\\t_4 = t_3 - 3 = -1-3 = -4$

and so on. This process may take a while to reach $t_{10}$

There's a shortcut. The nth term of any arithmetic sequence is

$t_n = t_1+d(n-1)$

We plug in $t_1 = 5 \text{ and } d = -3$ and simplify

$t_n = t_1+d(n-1)\\t_n = 5+(-3)(n-1)\\t_n = 5-3n+3\\t_n = -3n+8$

Then we can plug in various positive whole numbers for n to find the corresponding $t_n$ value. For example, plug in n = 2

$t_n = -3n+8\\t_2 = -3*2+8\\t_2 = -6+8\\t_2 = 2$

which matches with the second term we found earlier. And,

$tn = -3n+8\\t_{10} = -3*10+8\\t_{10} = -30+8\\t_{10} = \boldsymbol{-22} \ \textbf{ is the tenth term}$

---------------------

The notation $S_{10}$ refers to the sum of the first ten terms $t_1, t_2, \ldots, t_9, t_{10}$

We could use either the long way or the shortcut above to find all $t_1$ through $t_{10}$ . Then add those values up. Or we can take this shortcut below.

$Sn = \text{sum of the first n terms of an arithmetic sequence}\\S_n = (n/2)*(t_1+t_n)\\S_{10} = (10/2)*(t_1+t_{10})\\S_{10} = (10/2)*(5-22)\\S_{10} = 5*(-17)\\\boldsymbol{S_{10} = -85}$

The sum of the first ten terms is -85

-----------------------

As a check for $S_{10}$ , here are the first ten terms:

t1 = 5
t2 = 2
t3 = -1
t4 = -4
t5 = -7
t6 = -10
t7 = -13
t8 = -16
t9 = -19
t10 = -22

Then adding said terms gets us...

5 + 2 + (-1) + (-4) + (-7) + (-10) + (-13) + (-16) + (-19) + (-22) = -85

This confirms that $S_{10} = -85$ is correct.

6 0

2 years ago

hannah is making maffins. The recipe calls for 5/8 cup of milk to make 20 muffins. What is the unit rate for cups of milk per mu

STALIN [3.7K]

Answer:

32 muffins

Step-by-step explanation:

one cup of milk will make 32 muffins

you can set up a proportion of milk/muffins = milk/muffins

let 'x' = number of muffins made from one cup of milk

5/8 ÷ 20 = 1 ÷ x

cross-multiply to get 5x = 20(8)

5x = 160

x = 32

6 0

2 years ago

PLEASE ANSWER ASAP FOR BRAINLEST, REALLY EASY QUESTION!!!!!!!!!!!!!!!!!!!!!!!

Marina86 [1]

The answer is C

survey an equal number of boys and girls

5 0

3 years ago

Read 2 more answers

12. What's the simplified form of x − 1 + 4 + 7x − 3?

Leviafan [203]

The first one is B and the second is D

3 0

4 years ago

Read 2 more answers

Plz Help me

Dafna1 [17]

Answer:

6/0

Step-by-step explanation:

Step 1: Label your x and y's

(0,-11) (0, 5)

x1 y1 x2 y2

Step 2: Plug in your x1, x2, y1, and y2 into the slope formula

The slope formula is y1 -y2/ x1 - x2

-5-(-11)/ 0 = 6/0

Undefined

6 0

3 years ago