There exists a linear function f(x) such that f(6) = 8, f(2)=20, and f(a) = 16. What is the value of 2a?

Mathematics

1 answer:

atroni [7]3 years ago

3 0

Answer:

a = 10/3.

Step-by-step explanation:

We write the linear function as follows:

f(x) = mx + b where m is the slope and b is the y-intercept.

f(6) = 6m + b = 8

f(2) = 2m + b = 20 Subtracting these 2 equations:

4m = -12

m = -3.

and -3 * 2 + b = 20 so:

b = 20 + 6 = 26.

So we have the linear function:

f(x) = -3 x + 26

f(a) = 16 = -3 a + 26

-3 a = 16-26

a = -10 * -3 = 10/3.

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Answer:

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Step-by-step explanation:

Amount of Acetaminophen prescribed is 15 mg/kg. This means for every 1 kg of the child's weight, 15 mg of Acetaminophen will be administered to the child.

Weight of the child = 9.6 kg

Since, for each 1 kg the amount of Acetaminophen is 15 mg, the amount of Acetaminophen needed for 9.6 kg will be = 9.6 x 15 = 144 mg

Therefore, the child must be administered 144 mg of Acetaminophen in total.

The strength of Acetaminophen is 160mg / 5 mL. This means 5 mL of an injection contains 160 mg of Acetaminophen. But since, the child needs 144 mg, we need to calculate in mL, the volume of injection needed for 144 mg of Acetaminophen.

160 mg of Acetaminophen is present in an injection of volume = 5mL

1 mg of Acetaminophen is present in an injection of volume = $\frac{5}{160}$ mL