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saveliy_v [14]
3 years ago
8

2.5 ( 6 x - 4 ) = 10 + 4 ( 1.5 + 0.5 x )

Mathematics
1 answer:
Makovka662 [10]3 years ago
4 0

Answer:

\bold{x=2}

Step By Step Explanation:

Expand \bold{2.5\left(6x-4\right): \ 15x-10}

Expand \bold{10+4\left(1.5+0.5x\right): \ 2x+16}

\bold{15x-10=2x+16}

Add 10 To Both Sides

\bold{15x-10+10=2x+16+10}

Simplify

\bold{15x=2x+26}

Subtract 2x From Both Sides

\bold{15x-2x=2x+26-2x}

Simplify

\bold{13x=26}

Divide Both Sides By 13

\bold{\frac{13x}{13}=\frac{26}{13}}

Simplify

\bold{x=2}

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A scientist has a sample of bacteria that initially contains 10 million microbes. They observe the sample and finds that the num
sergiy2304 [10]

Answer:

M(t) = 6.7 * 10⁷ (67 million)

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Step-by-step explanation:

1. Write an exponential equation that represents M, the total number of bacterial microbes in millions, as a function of t, the number of minutes the sample has been observed.

For answering this question, we will use the following formula:

M(t) = B₀ * g ^(t/m), where:

•M(t) represents the total number of bacterial microbes in millions.

• B₀ represents the initial population of bacteria in millions.

• g represents the growth factor.

• t represents the total number of minutes we will observe the bacteria growing.

• m represents the time in minutes it takes to the growth factor g to occur.

2. Then, determine how much time, to the nearest minute, will pass until there are 67 million bacterial microbes.

M(t) = B₀ * g ^(t/m)

Replacing with the values we know:

6.7 * 10⁷ = 10⁷ * 2 ^(t/20)

6.7 = 2 ^(t/20) (Dividing by 10⁷ at both sides)

ln 6.7 = ln 2 ^(t/20)

ln 6.7 = t/20 ln 2

ln 6.7/ ln 2 = t/20

t = ln 6.7/ln 2 * 20

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t = 54.88

t ≅ 55 (rounding to the nearest minute)

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2 years ago
<img src="https://tex.z-dn.net/?f=%20%5Cfrac%7B2%7D%7B3%7D%20%20%5Ctimes%20%20%5Cfrac%7B1%7D%7B2%7D%20" id="TexFormula1" title="
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