1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Tasya [4]
3 years ago
10

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.

Pasta costs $1 for a 1-pound package. Pasta sauce costs $3 for a 1.5 pound jar. Let x = the number of packages of pasta and y = the number of jars of pasta sauce. Identify each point as either a solution to the system or not a solution to the system of inequalities. (1, 12) (2, 10) (4, 5) (6, 10) (12, 8) (18, 6) .
Mathematics
1 answer:
sattari [20]3 years ago
7 0

Answer:

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.

You might be interested in
Help ASAP<br><br><br> 22.41 + 8.9
Diano4ka-milaya [45]

Answer:

<em>22.41 + 8.9</em><em>=</em><em> </em><em>31.31</em>

<em>hope this helps</em><em> </em><em><</em><em>3</em>

8 0
2 years ago
there is an unknown number in the sequence counting backward. The number is after 48. The number is before 46. What is the unkno
Ghella [55]
The unknown number is 47.
5 0
3 years ago
Need help quickly test
MissTica
The answer is A - 5.
7 0
3 years ago
What is the equation of the line that passes through (2, -7) and (-1, 2)?
SVETLANKA909090 [29]

Answer:

y = -3x - 1

Step-by-step explanation:

The slope intercept form of the equation of a line is:

y = mx + b

where m is the slope, and b is the y-intercept.

First, we find the slope of the line using the two given points.

m = slope = (y2 - y1)/(x2 - x1) = (2 - (-7))/(-1 - 2) = (2 + 7)/(-3) = 9/(-3) = -3

Now we plug in the slope we found into the equation above.

y = -3x + b

We need to find the value of b, the y-intercept. We use the coordinates of one of the given points for x and y, and we solve for b. Let's use point (2, -7), so x = 2, and y = -7.

y = -3x + b

-7 = -3(2) + b

-7 = -6 + b

Add 6 to both sides.

-1 = b

Now we plug in -1 for b.

y = -3x - 1

4 0
3 years ago
Find the next two term in this sequence​
MariettaO [177]

Answer: 0.5 and 0.25

Step-by-step explanation: You have to divide the number by 2 to get to the next term.

7 0
3 years ago
Read 2 more answers
Other questions:
  • Select all the names for a in the expression.
    6·2 answers
  • The value of y varies directly with x, and y = 12 when x = 16. Find y when x 6.
    15·1 answer
  • What is the equation of a line that is parallel to y=-3x+5 and passes through the point (5,-3).
    13·2 answers
  • Simplify the expression 3(9+4x-5)
    7·1 answer
  • Which statement is true when 3.4 is placed in the blank? 10.2 ÷ ___ = 0.3 20.4 ÷ 6 = ___ 27.2 ÷ ___ = 0.8 30.6 ÷ 0.9 = ___
    8·2 answers
  • Use the diagram to name the following
    6·2 answers
  • A building brick weighs 2.7 kilograms. work out the weight of 840 bricks. give the answer in tonnes
    5·1 answer
  • 3x - 2<br> 2x + 1<br> д<br> B<br> c<br> If x = 5, then the length of BC is
    8·1 answer
  • Atasha jumped 2 1/5 meter in a long jump competition. Arya jumped 1 2/3 meter. Who jumped longer and how many meters?​
    10·1 answer
  • Which equation is represented by the graph below?
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!