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irga5000 [103]
2 years ago
12

mr.ellis has started a vegetable garden.he bought 15 bags of soil and 3 bags of fertilizer for 282.72.he realized he didnt have

enough supplies so he bought another 5 bags of soil and 2 bags of fertilizer for 107.23.what was the cost of each bag of soil and fertilizer?let the cost of each bag of soil =x and the cost of bag of fertilizer = y.
Mathematics
1 answer:
ANTONII [103]2 years ago
8 0

The cost of each bag of soil is $ 16.25 and the cost of each bag of fertilizer is $ 12.99.

<h3>What is the linear system?</h3>

A linear system is one in which the parameter in the equation has a degree of one. It might have one, two, or even more variables.

Mr. Ellis has started a vegetable garden.

He bought 15 bags of soil and 3 bags of fertilizer for 282.72.

He realized he did not have enough supplies so he bought another 5 bags of soil and 2 bags of fertilizer for 107.23.

Let the cost of each bag of soil be x and the cost of a bag of fertilizer be y.

Then we have the linear equations,

15x + 3y = 282.72

5x + 2y = 107.23

On solving the equations 1 and 2, we have

x = 16.25 and y = 12.99

The cost of each bag of soil is $ 16.25 and the cost of each bag of fertilizer is $ 12.99.

More about the linear system link is given below.

brainly.com/question/20379472

#SPJ1

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Which expression is equivalent to |x| &gt; 9
Fynjy0 [20]
D)
x<-9
x>9
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3 0
3 years ago
Which number line represents the solutions to 1-2x1 = 4?
kaheart [24]

Answer:

Third option: x = -2 and x = 2

Step-by-step explanation:

Given:

|-2x|=4

For a modulus function, if |f(x)|=a, then,

f(x)=\pm a

Here, f(x)=-2x, a=4

∴ -2x=\pm 4\\ -2x=-4\textrm{ or } -2x=4\\ x=\frac{-4}{-2}\textrm{ or }x=\frac{4}{-2}\\ x= 2\textrm{ or }x=-2

Therefore, the third option is the correct answer as the graph has x values as -2 and 2

8 0
3 years ago
Solve for x.<br> 7(1x - 3) = 4(x + 5)
alexandr1967 [171]

Answer:

x = 41/3

General Formulas and Concepts:

<u>Pre-Algebra</u>

  • Order of Operations: BPEMDAS
  • Equality Properties

Step-by-step explanation:

<u>Step 1: Define equation</u>

7(1x - 3) = 4(x + 5)

<u>Step 2: Solve for </u><em><u>x</u></em>

  1. Simplify:                                        7(x - 3) = 4(x + 5)
  2. Distribute:                                     7x - 21 = 4x + 20
  3. Subtract 4x on both sides:          3x - 21 = 20
  4. Add 21 on both sides:                  3x = 41
  5. Divide 3 on both sides:                x = 41/3

<u>Step 3: Check</u>

<em>Plug in x to verify it's a solution.</em>

  1. Substitute:                    7(1(41/3) - 3) = 4(41/3 + 5)
  2. Multiply:                        7(41/3 - 3) = 4(41/3 + 5)
  3. Subtract/Add:               7(32/3) = 4(56/3)
  4. Multiply:                        224/3 = 224/3

Here, we see that 224/3 is indeed equivalent to 224/3. ∴ x = 41/3 is a solution to the equation.

And we have our final answer!

6 0
2 years ago
Complete the proof given below.
allochka39001 [22]

Given that the opposite sides of a parallelogram are congruent, a diagonal

of the parallelogram forms two congruent triangles.

The correct options to complete the proof are;

  • <u>Opposite sides of a parallelogram;</u> ABCD is a parallelogram
  • <u>Reflexive property of congruency</u>
  • <u>SSS</u>

Reasons:

The completed two column proof is presented as follows;

Statement  {}                                  Reason

1. ABCD is a parallelogram  {}       1. Given

2. \overline{AB} ≅ \overline{DC} and \overline{BC} ≅ \overline{DA}  {}      2. <u>Opposite sides of a parallelogram</u>

3. \overline{AC} ≅ \overline{CA}    {}                             3. <u>Reflexive property of congruency</u>

4. ΔABC ≅ ΔCDA     {}                   4. <u>SSS</u>

The correct options are therefore;

<u>Opposite sides of a parallelogram;</u> ABCD is a parallelogram

Reflexive property of congruency

SSS;

Reason 2. Opposite sides of a parallelogram, which is based on the

properties of a parallelogram and that ABCD is a parallelogram.

Reason 3. The reflexive property of congruency, states that a side is

congruent to itself.

Reason 4. SSS is an acronym for Side-Side-Side, which is a congruency

postulate that states that if the three sides of one triangle are equal to the

three sides of another triangle, then the two triangles are congruent.

Learn more about parallelograms here:

brainly.com/question/4218263

brainly.com/question/21390857

8 0
3 years ago
(PLEASE HELP) Question is worth 30 points:) The following function represents the production cost F(x) In dollars for x numbers
soldi70 [24.7K]

Answer:

production cost f(x), in dollars, for x number of units produced by company 1:

f(x) = 0.05x^2 − 7x + 300

2) Table that represents the production cost g(x), in dollars, for x number of units produced by company 2:

x        g(x)

0.6     899.58

0.8     899.52

1        899.50

1.2     899.52

1.4     899.58

3) Comparison: do a table for f(x) with the same x-values of the table for g(x).

x            f(x) = 0.05x^2 − 7x + 300    g(x)

0.6         295.818                               899.58

0.8         294.432                               899.52

1            293.05                                 899.50

1.2         291.672                               899.52

1.4          290.298                              899.58

As you can see the values of f(x) are consistently lower than the values of g(x) for the same x-values.

The minimum production cost for company 2 is around 899.50 at x = 1, while the minimum production cost of company 1 is defintely lower (lower than 292.298 for sure, in fact if you find the vertex it is 55).

Answer: Based on the given information, the minimum production cost for company 2 is greater.

Step-by-step explanation:

5 0
3 years ago
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