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Step2247 [10]
3 years ago
7

20 POINTS!!!! If eight is added to twice a number and the sum is multiplied by five result is the same as if the number is multi

plied by -8 and four is added to the product. What is the number?
Mathematics
1 answer:
Sauron [17]3 years ago
6 0
<h3><u>The value of x is equal to -2.</u></h3>

5(2x + 8) = -8x + 4

<em><u>Distributive property.</u></em>

10x + 40 = -8x + 4

<em><u>Add 8x to both sides.</u></em>

18x + 40 = 4

<em><u>Subtract 40 from both sides.</u></em>

18x = -36

<em><u>Divide both sides by 18</u></em>

x = -2

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The half-life of caffeine in a healthy adult is 4.8 hours. Jeremiah drinks 18 ounces of caffeinated
statuscvo [17]

We want to see how long will take a healthy adult to reduce the caffeine in his body to a 60%. We will find that the answer is 3.55 hours.

We know that the half-life of caffeine is 4.8 hours, this means that for a given initial quantity of coffee A, after 4.8 hours that quantity reduces to A/2.

So we can define the proportion of coffee that Jeremiah has in his body as:

P(t) = 1*e^{k*t}

Such that:

P(4.8 h) = 0.5 = 1*e^{k*4.8}

Then, if we apply the natural logarithm we get:

Ln(0.5) = Ln(e^{k*4.8})

Ln(0.5) = k*4.8

Ln(0.5)/4.8 = k = -0.144

Then the equation is:

P(t) = 1*e^{-0.144*t}

Now we want to find the time such that the caffeine in his body is the 60% of what he drank that morning, then we must solve:

P(t) = 0.6 =  1*e^{-0.144*t}

Again, we use the natural logarithm:

Ln(0.6) = Ln(e^{-0.144*t})

Ln(0.6) = -0.144*t

Ln(0.6)/-0.144 = t = 3.55

So after 3.55 hours only the 60% of the coffee that he drank that morning will still be in his body.

If you want to learn more, you can read:

brainly.com/question/19599469

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2 years ago
Assuming the pattern continues, what are the next two terms in this
pshichka [43]
D. 53, 107
The pattern is multiplying the previous number by two and then adding one to it.
4 0
3 years ago
Describe a model that represents 3/3 * 4/4
ioda
3/3 = 1
4/4 = 1
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Carol's starting pay for her summer job is $10.25 per hour. Carol earns exactly 3 raises this summer.
zlopas [31]
We know that
1) <span>Carol's starting pay for her summer job is $10.25 per hour
</span><span>Carol earn per hour=$10.25 per hour
</span><span>
2) </span><span>For the first rise, she receives a 50 cent-per-hour raise
10.25+0.50=10.75
</span>Carol earn per hour=$10.75 per hour

3) <span>For the second rise, she receives a 10% raise per hour
10.75*1.10=11.825
</span>Carol earn per hour=$11.825 per hour

4) <span>For the third rise, she receives another 50 cent-per-hour raise
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</span>Carol earn per hour=$12.325 per hour

5) At the start of next summer. She will be given a 5% raise per hour based on her pay at the end of this summer. <span>
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the answer is
$12.94 per hour
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3 years ago
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