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Setler79 [48]
3 years ago
14

Topic - Solving Linear Inequalities.

Mathematics
1 answer:
yaroslaw [1]3 years ago
7 0

Answer:

The minimum balance is 68 liters

Step-by-step explanation:

Let the number of liters of petrol required be x

Given that  One litre of petrol has a mass of 737g, x liters will have a mass

= 0.737x kg

Recall that 1 kg = 1000g

Since the empty fuel tank has a mass of 1050kg

The total mass = 1050 + 0.737x IN kg

For the total mass to exceed 1100kg, then

1050 + 0.737x > 1100

0.737x > 1100 - 1050

0.737x > 50

Divide both sides by 0.737

x > 50/0.737

x > 67.84260516

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An ice cream shop makes $1.25 on each small cone and $2.25 on each large cone. The ice cream shop sells between 60 and 80 small
Sergio [31]

Answer:

  • Let x and y represent the numbers of small and large cones sold daily, respectively
  • 60 ≤ x ≤ 80
  • 120 ≤ y ≤ 150
  • 1.25x +2.25y > 350

Step-by-step explanation:

To answer the question, we need to be able to find the number of each type of cone that needs to be sold. For the purpose, it is convenient to define variables that represent those numbers. We have chosen to use the variables x and y to represent the number of small cones and the number of large cones, respectively ("Let" statement in above answer). One could use "s" and "l" as being more mnemonic, but "l" can be confused with a variety of other symbols, so we like not to use it.

The problem statement puts limits on the numbers of small and large cones sold, so our system of inequalities needs to reflect those limits. (We suspect these are not hard limits, but represent historical data. We doubt the shop would decline to sell more, and we can conceive of conditions under which they might sell fewer.)

The heart of the matter is that the profit from each type of cone must total more than $350 (per day). The problem statement requires the shop make a profit, not just break even, so we use the > symbol for profit, instead of ≥.

___

See above for the "Let" statement and the system of inequalities. (This problem does not require we solve them.)

3 0
3 years ago
WILL GIVE BRAINLIEST AND 20 PTS
exis [7]

Answer:16

Step-by-step explanation:dsbwdb

5 0
3 years ago
solve the system of equations by finding the reduced row-echelon form of the augmented matrix for the system of equations. x-2y+
Alekssandra [29.7K]

Answer:

x = -5, y = -6, z = -3

Step-by-step explanation:

Given the system of three equations:

\left\{\begin{array}{l}x-2y+3z=-2\\6x+2y+2z=-48\\x+4y+3z=-38\end{array}\right.

Write the augmented matrix for the system of equations

\left(\begin{array}{ccccc}1&-2&3&|&-2\\6&2&2&|&-48\\1&4&3&|&-38\end{array}\right)

Find the reduced row-echelon form of the augmented matrix for the system of equations:

\left(\begin{array}{ccccc}1&-2&3&|&-2\\6&2&2&|&-48\\1&4&3&|&-38\end{array}\right)\sim \left(\begin{array}{ccccc}1&-2&3&|&-2\\0&-14&16&|&36\\0&-6&0&|&36\end{array}\right)\sim \left(\begin{array}{ccccc}1&3&-2&|&-2\\0&16&-14&|&36\\0&0&-6&|&36\end{array}\right)

Thus, the system of three equations is

\left\{\begin{array}{r}x+3z-2y=-2\\16z-14y=36\\-6y=36\end{array}\right.

From the last equation:

y=-6

Substitute it into the second equation:

16z-14\cdot (-6)=36\\ \\16z=36-84\\ \\16z=-48\\ \\z=-3

Substitute y = -6 and z = -3 into the first equation:

x+3\cdot (-3)-2\cdot (-6)=-2\\ \\x=-2+9-12\\ \\x=-5

7 0
3 years ago
Evaluate the expression when x= -3.<br> x² – 7x+6
aksik [14]

Answer:

-6

Step-by-step explanation:

3^{2} = -3 × -3

-3 × -3 =  9

7 × -3 =-21

9 - 21 +6 = -6

7 0
3 years ago
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What's the best definition of the word "ratio?"
ololo11 [35]

Answer:

Compare

Step-by-step explanation:

Or relation I believe so...

7 0
3 years ago
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