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3 years ago

13

Help me solve this question please for 10 points

1 answer:

ankoles [38]3 years ago

3 0

Answer: D for the first one and B for the second

Step-by-step explanation:

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Hello, I need help finding the solutions of the equation log base 2 (x+8)+2=2 log base 2 (x)

yuradex [85]

$\bf log_{{ a}}\left( \frac{x}{y}\right)\implies log_{{ a}}(x)-log_{{ a}}(y)
\\\\\\
% Logarithm of exponentials
log_{{ a}}\left( x^{{ b}} \right)\implies {{ b}}\cdot log_{{ a}}(x)
\\\\\\
{{ a}}^{log_{{ a}}x}=x\impliedby \textit{log cancellation rule}\\\\
-----------------------------\\\\$

$\bf log_2(x+8)+2=2log_2(x)\implies log_2(x+8)-2log_2(x)=-2
\\\\\\
log_2\left(\cfrac{x+8}{x^2} \right)=-2\implies 2^{log_2\left(\cfrac{}{}\frac{x+8}{x^2} \right)}=2^{-2}\implies \cfrac{x+8}{x^2}=\cfrac{1}{2^2}
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4x+32=x^2\implies 0=x^2-4x-32
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0=(x+4)(x-8)\implies 
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6 0

3 years ago

Read 2 more answers

Multiple the binomials (x+3)^2

maxonik [38]

Answer:

$=x^2+6x+9$

Step-by-step explanation:

$\left(x+3\right)^2\\\mathrm{Apply\:Perfect\:Square\:Formula}:\quad \left(a+b\right)^2=a^2+2ab+b^2\\a=x,\:\:b=3\\=x^2+2x\cdot \:3+3^2\\\mathrm{Simplify}\:x^2+2x\cdot \:3+3^2:\quad x^2+6x+9\\x^2+2x\cdot \:3+3^2\\\mathrm{Multiply\:the\:num\\bers:}\:2\cdot \:3=6\\=x^2+6x+3^2\\3^2=9\\=x^2+6x+9$

8 0

3 years ago

A box has three balls, one white and two red. We select one ball, put it back in the box, and select a second ball (sampling wit

Dennis_Churaev [7]

Answer:

See explaation

Step-by-step explanation:

Given

Represent the balls with the first letters

$W =1$

$R =2$

Solving (a): P(F) --- White balls twice

The event of F is:

$F = \{(W,W)\}$

So:

$P(F) = P(W) * P(W)$

$P(F) = \frac{n(W)}{n} * \frac{n(W)}{n}$

$P(F) = \frac{1}{3} * \frac{1}{3}$

$P(F) = \frac{1}{9}$

Solving (b): P(G) --- two different colors

The event of G is:

$G = \{(W,R),(R,W)\}$

So:

$P(G) = P(W) * P(R) + P(R) * P(W)$

$P(G) = \frac{n(W)}{n} * \frac{n(R)}{n} + \frac{n(R)}{n} * \frac{n(W)}{n}$

$P(G) = \frac{1}{3} * \frac{2}{3} + \frac{2}{3} * \frac{1}{3}$

$P(G) = \frac{2}{9} + \frac{2}{9}$

$P(G) = \frac{4}{9}$

Solving (c): P(H) --- White picked first

The event of H is:

$H = \{(W,R),(W,W)\}$

So:

$P(H) = P(W) * P(R) + P(W) * P(W)$

$P(H) = \frac{n(W)}{n} * \frac{n(R)}{n} + \frac{n(W)}{n} * \frac{n(W)}{n}$

$P(H) = \frac{1}{3} * \frac{2}{3} + \frac{1}{3} * \frac{1}{3}$

$P(H) = \frac{2}{9} + \frac{1}{9}$

$P(H) = \frac{3}{9}$

$P(H) = \frac{1}{3}$

Solving (d): F and G, mutually exclusive?

We have:

$F = \{(W,W)\}$

$G = \{(W,R),(R,W)\}$

Check for common elements

$n(F\ n\ G) = 0$

<em>Hence, F and G are mutually exclusive</em>

Solving (e): G and G, mutually exclusive?

We have:

$G = \{(W,R),(R,W)\}$

$H = \{(W,R),(W,W)\}$

Check for common elements

$n(G\ n\ H) = 1$

<em>Hence, F and G are not mutually exclusive</em>

7 0

3 years ago

6 is what percent of 8%

kupik [55]

Answer:

75

Step-by-step explanation:

8% of x =6

8x/100=6

x=600/8=75

8 0

3 years ago

Read 2 more answers

3x + x + x + x − 3 − 2 = 7 + x + x In the equation above, what is the value of x?

algol13

Answer:

x=3

Step-by-step explanation:

3x + x + x + x − 3 − 2 = 7 + x + x

Combine like terms

6x -5 = 7+2x

Subtract 2x from each side

6x-2x -5 = 7+2x-2x

4x-5 =7

Add 5 to each side

4x-5+5 = 7+5

4x =12

Divide by 4

4x/4 = 12/4

x = 3

7 0

3 years ago