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Eva8 [605]
3 years ago
12

Decide whether each expression is equivalent to 0.75t-21. 3/4t-21 3/4( t-21) 0.75( t-28) t-0.25t-21. Explain how you know

Mathematics
1 answer:
butalik [34]3 years ago
6 0

Answer: expression 1,3 and 4 are equivalent to 0.75t-21.

Step-by-step explanation:

Expression 1

3/4t-21

= 0.75t - 21

Expression 2

3/4( t-21)

Multiply through by 0.75

= 0.75 ( t - 21 )

= 0.75t - 15.75

Expression 3

0.75( t-28)

Multiply through by 0.75

= 0.75t - 21

Expression 4

t-0.25t-21

let t = 1

1-0.25t - 21

= 0.75t - 21

expression 1,3 and 4 are equivalent to 0.75t-21.

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Tyler went to the supermarket to buy food for a food pantry. He has $36, and can carry up to 20 pounds of food in his backpack.
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Solutions: (2,10), (4,5)

Not solutions: (1,12), (6,10), (12,8), (18,6)

Step-by-step explanation:

Let x be the number of packages of pasta and y be the number of jars of pasta sauce. If pasta costs $1 for a 1-pound package, then x packages of pasta cost $x and weigh x pounds. If pasta sauce costs $3 for a 1.5 pound jar, then y jars cost $3y and weigh 1.5y pounds.

1. Tyler has $36, then

x+3y\le 36.

2. Tyler can carry up to 20 pounds of food in his backpack, then

x+1.5y\le 20.

You get the following system of inequalities:

\left\{\begin{array}{l}x+3y\le 36\\ x+1.5y\le 20\end{array}\right.

Now substitute the coordinates of each point:

<u>(1,12):</u>

\left\{\begin{array}{l}1+3\cdot 12=37> 36\\ 1+1.5\cdot 12=19\le 20\end{array}\right.

False, because first inequality doesn't hold.

<u>(2,10):</u>

\left\{\begin{array}{l}2+3\cdot 10=32\le 36\\ 2+1.5\cdot 10=17\le 20\end{array}\right.

True, both inequalities hold.

<u>(4,5):</u>

\left\{\begin{array}{l}4+3\cdot 5=19\le 36\\ 4+1.5\cdot 5=11.5\le 20\end{array}\right.

True, both inequalities hold.

<u>(6,10):</u>

\left\{\begin{array}{l}6+3\cdot 10=36\le 36\\ 6+1.5\cdot 10=21> 20\end{array}\right.

False, because secondt inequality doesn't hold.

<u>(12,8):</u>

\left\{\begin{array}{l}12+3\cdot 8=36\le 36\\ 12+1.5\cdot 8=24> 20\end{array}\right.

False, because second inequality doesn't hold.

<u>(18,6):</u>

\left\{\begin{array}{l}18+3\cdot 6=36\le 36\\ 18+1.5\cdot 6=27> 20\end{array}\right.

False, because second inequality doesn't hold.

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3 years ago
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