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11111nata11111 [884]
3 years ago
9

Which radical expressions are equivalent to the exponential expression below ? Check all that apply . (13 + 8) ^ (1/2) A. (13 +

8) ^ 2 sqrt(21) . sqrt(13 + 8) E. 10.5
Mathematics
1 answer:
Fantom [35]3 years ago
8 0

Answer:

(B)\sqrt{21}\\(C)\sqrt{13+8}

Step-by-step explanation:

Given the expression (13 + 8) ^{1/2}

Using law of indices: a^{1/2}=\sqrt{a}

(13 + 8) ^{1/2}=\sqrt{13+8}

Also:13+8=21

Therefore:

(13 + 8) ^{1/2}=21^{1/2}\\=\sqrt{21}

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Write an equation for a line parallel to the line y=1/3x-4 through (3,-2)
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3 years ago
Solve the equations PLEASEE<br><br> -1=3x-2<br><br> -3x=9<br><br> -10=-5x
Ilia_Sergeevich [38]

Answers are in bold:

-1=3x-2

add 2 to both sides

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1=3x

divide both sides by 3

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1/3=x

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-3x÷-3=9÷-3

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I hope this is good enough:

6 0
3 years ago
1. In an auditorium, there are 21 seats in the first row and 26 seats in the second row. The number of seats in a row continues
kondor19780726 [428]
1. Let s_n be the number of seats in the n-th row. The number seats in the n-th row relative to the number of seats in the (n-1)-th row is given by the recursive rule

s_n=s_{n-1}+5


Since s_1=21, we have

s_2=s_1+5
s_3=s_2+5=s_1+2\cdot5
s_4=s_3+5=s_1+3\cdot5
\cdots
s_n=s_{n-1}+5=\cdots=s_1+(n-1)\cdot5

So the explicit rule for the sequence s_n is

s_n=21+5(n-1)\implies s_n=5n+16

In the 15th row, the number of seats is


s_{15}=5(15)+16=91

2. Let p_n be the amount of profit in the n-th year. If the profits increase by 6% each year, we would have

p_2=p_1+0.06p_1=1.06p_1
p_3=1.06p_2=1.06^2p_1
p_4=1.06p_3=1.06^3p_1
\cdots
p_n=1.06p_{n-1}=\cdots=1.06^{n-1}p_1

with p_1=40,000.

The second part of the question is somewhat vague - are we supposed to find the profits in the 20th year alone? the total profits in the first 20 years? I'll assume the first case, in which we would have a profit of


p_{20}=1.06^{19}\cdot40,000\approx121,024

3. Now let p_n denote the number of pushups done in the n-th week. Since 3\cdot4=12, 12\cdot4=48, and 48\cdot4=192, it looks like we can expect the number of pushups to quadruple per week. So,

p_n=4p_{n-1}

starting with p_1=3.

We can apply the same reason as in (2) to find the explicit rule for the sequence, which you'd find to be

p_n=4^{n-1}p_1\implies p_n=4^{n-1}\cdot3
6 0
3 years ago
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