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3 years ago

Warm Up

Mathematics

1 answer:

katrin [286]3 years ago

6 0

Given the slope m and a point (a,b) of a line, its equation is given by

$y-b=m(x-a)$

In your case, a = -4, b = 7 and m=1/2, so we have

$y-7=\dfrac{1}{2}(x+4) \iff y=\dfrac{x}{2}+2+7\iff y=\dfrac{x}{2}+9$

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What's 2/8 divided by 5/16 simplified in fraction form?

irga5000 [103]

$\frac{2}{8} \div \frac{5}{16} = \frac{2}{8} \times\frac{16}{5} = \frac{1}{4} \times\frac{16}{5} = \frac{4}{5} = 0.8$

3 0

3 years ago

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Chase consumes an energy drink that contains caffeine. After consuming the energy drink, the amount of caffeine in Chase's body

PIT_PIT [208]

Answer:

(a) The 5-hour decay factor is 0.5042.

(b) The 1-hour decay factor is 0.8720.

Step-by-step explanation:

The amount of caffeine in Chase's body decreases exponentially.

The 10-hour decay factor for the number of mg of caffeine is 0.2542.

The 1-hour decay factor is:

$1-hour\ decay\ factor=(0.2542)^{1/10}=0.8720$

(a)

Compute the 5-hour decay factor as follows:

$5-hour\ decay\ factor=(0.8720)^{5}\\=0.504176\\\approx0.5042$

Thus, the 5-hour decay factor is 0.5042.

(b)

The 1-hour decay factor is:

$1-hour\ decay\ factor=(0.2542)^{1/10}=0.8720$

Thus, the 1-hour decay factor is 0.8720.

(c)

The equation to compute the amount of caffeine in Chase's body is:

A = Initial amount × (0.8720)<em>ⁿ</em>

It is provided that initially Chase had 171 mg of caffeine, 1.39 hours after consuming the drink.

Compute the amount of caffeine in Chase's body 2.39 hours after consuming the drink as follows:

$A = Initial\ amount \times (0.8720)^{2.39} \\=[Initial\ amount \times (0.8720)^{1.39}] \times(0.8720)\\=171\times 0.8720\\=149.112$

Thus, the amount of caffeine in Chase's body 2.39 hours after consuming the drink is 149.112 mg.

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3 years ago

Convert the angle theta=7/4pi radians to degrees

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7/4pi multiplied by 180/pi give you about 97 degrees when you calculate it.

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What fraction is equal to 90/4

Ne4ueva [31]

45/2 can't be simplified.

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Daniel works at a nearby electronic store. Makes a commission of 15% on everything he sells. If he sells a laptop for $293.00, h

Yakvenalex [24]

Answer: Daniel made $43.95

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3 years ago