Question

can someone help me with math!!??

Answer 1

What is your question? @alleeyyssaa

Answer 2

The number of bacteria (b) in a batch of refrigerated food is given by the function b(t) = 20t2 − 70t + 300, where t is the temperature of the food in degrees Fahrenheit. The function t(h) = 2h + 3 gives the temperature of the food h hours after it is removed from refrigeration. Which expression correctly represents the number of bacteria (b) in the food as a function of the number of hours (h) the food is unrefrigerated?

Answer 3

@AihberKhan

Answer 4

Just replace the t in your b(t) equation with the t(h) equation.

Answer 5

Okay. What you want to do is substitute for \(t\).

\(b(t) = 10t^2 - 70t + 300\)

Then this will be

\(b(h) = 10(2h + 3)² – 70(2h + 3) + 300\)

Answer 6

Lastly, you will just want to simplify. You can do this by expanding and combining the like terms. :) Try it! :)

Answer 7

okay thank you so much!!

Answer 8

so would it look like this?
(20h + 30)^2-140h-210+300
@AihberKhan
@Alphabet_Sam

Answer 9

When you plug it into a square position, you still need to square it.

For example:\[f(x)=4x ^{2}\] \[g(x)=a+b\] If you let x=g(x) you get\[4(a+b)^{2}\] which you have to foil out before you distribute the 4.

Answer 10

ohhh i get what you mean
so i would do (2h+3)(2h+3) first? @Alphabet_Sam

Answer 11

Exactly, then you distribute the coefficient out front (I'm not sure if it's 10 or 20, you wrote 20 originally).

Answer 12

yeah its 20
so i have,
4h^2+6h+6h+9? after foiling

Answer 13

Right, then just distribute the 20 and combine all of your like terms.

Answer 14

so it'd be
20(4h^2+12h+9) - 70(2h+3)+300
40h^2+240+180 - 140h+210+300
40h^2-140h +840?
@Alphabet_Sam

Answer 15

Recheck your first term, I'm sure it was just a careless mistake but 20*4=?

Answer 16

Also, you forgot a h on your second term in the second line.

Answer 17

oh your right its 80h^2+100h+690?

Answer 18

@Alphabet_Sam

Answer 19

Right, nice work :)

Answer 20

thank you!!

Answer 21

do you mind helping with acouple more? @Alphabet_Sam

Answer 22

I'm actually just sitting down to New Year's dinner, but I'm sure someone else can help you if you post them as a new question!

Answer 23

okay thank you!