Question

I really need help.

7. The function t(x) = 2x + 4 determines how many cans of tomato sauce a food truck needs to stock, where x is the number of shifts the crew is going to work in the truck. The crew uses c(t(x)) to find the amount of money to spend on tomato sauce. The function c(x) = 3x + 1. Solve for how much money must be spent when the crew is going to work 2 shifts.

A. 7
B. 8
C. 18
D. 25

Answer 1

This takes 2 steps:

they tell you
t(x) = 2x + 4 where x is the number of shifts
crew is going to work 2 shifts

first figure out t(2). can you do that ?

Answer 2

t=x+2

Answer 3

or t=4

Answer 4

@phi

Answer 5

almost,
t(x) = 2*x + 4

to figure it out, erase the x and put in a 2

Answer 6

in other words, you used t(x)=x+2 but that is not the equation they gave you.

Answer 7

So, t(2)=2(2)+4

Answer 8

yes, now simplify

Answer 9

t=4

Answer 10

t(2) = 2(2)+4

which means t(2) is 2*2 + 4
what is 2*2 + 4 ?

Answer 11

8

Answer 12

yes

Answer 13

t(2) = 8

we are done with that step

next step.
The crew uses c(t(x)) which means they want to figure out c(8)

Answer 14

t(2) does not mean t*2

when they write
t(x)= 2x + 4

they are saying: 2x+4 is a formula, and to keep things short, we give a NAME to the formula. we call it formula "t"
we put (x) next to the t: t(x) to remind us that the formula uses "x"

Answer 15

c(x) = 3x + 1

is a different formula, which we call formula "c"

we want to use this new formula with x=8

Answer 16

So, for C x=8
C(x)=3x+1
C(8)=3(8)+1
C(8)=24+1
C(8)=25

Answer 17

exactly

Answer 18

Is that the answer. D. 25

Answer 19

to review what we did

The crew uses c(t(x)) to find the amount of money

the c( t(x) )
is a bit complicated, but it means
use formula c with x replaced by t(x)

what does t(x) mean? it means use formula t. what x should we use
luckily they tell us x is the # of shifts, and they want 2 shifts

so we want to figure out t(2), which means use formula t with x replaced by 2

then we use that number in c

Answer 20

yes, 25 is the answer.

Answer 21

that you

Answer 22

yw