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masha68 [24]
2 years ago
12

Which value of k would cause the system of linear equations 35 x 14 y = 119 and 5 x 2 y = k to have an infinite number of soluti

ons? 3 7 17 21.
Mathematics
1 answer:
larisa86 [58]2 years ago
3 0

To solve the question we must know about the System of equations.

<h2>System of equation</h2>

<h2>Inconsistent System</h2>

A system of equations to have no real solution, the lines of the equations must be parallel to each other.

<h2>Consistent System</h2><h3>1. Dependent Consistent System</h3>

A system of the equation to be Dependent Consistent System the system must have multiple solutions for which the lines of the equation must be coinciding.

<h3>2. Independent Consistent System</h3>

A system of the equation to be Independent Consistent System the system must have one unique solution for which the lines of the equation must intersect at a particular.

The value of k should be 17 so that the system of equations gives infinite number of solutions.

<h2>Explanation</h2>

Given to us

  • 35x + 14y = 119
  • 5x +2y = k

As we know that for a system of equations to give an infinite number of solutions. the equations of the system must be either same or in ratio.

<h3>In Equation 1</h3>

35x + 14y = 119,

dividing both the sides of the equation by 7,

\dfrac{35x + 14y}{7} = \dfrac{119}{7}\\\\&#10;\dfrac{35x}{7}+\dfrac{14y}{7} = \dfrac{119}{7}\\&#10;5x+2y = 17

As already discussed the system of equations to give infinite number of solutions, the equations must be the same. therefore, comparing both the equations we see that the value of k should be 17.

Hence, the value of k should be 17, so that the system of equations gives infinite number of solutions.

<h3>Verification</h3>

As we can see in the below image on equating the value of k as 17, the line of the system of equations coincides, therefore, the system will have infinite number of solutions.

Learn more about System of Equations:

brainly.com/question/12895249

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Aleonysh [2.5K]

Answer:

The length is 15 yards

Step-by-step explanation:

Given

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Area = 135yd^2

L=3W - 12

Required

Determine the length of the rectangle:

Area is calculated as thus:

Area = L * W

Substitute 3W - 12 for L and 135 for Area

135= (3W - 12) * W

135= 3W^2 - 12W

Reorder:

3W^2 - 12W - 135= 0

Divide through by 3

W^2 - 4W - 45 = 0

Expand:

W^2  - 9W + 5W - 45 = 0

W(W  - 9) + 5(W - 9) = 0

(W + 5)(W-9) = 0

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W = -5 or W = 9

But width can't be negative

So:

W = 9

Recall that: L=3W - 12

L = 3 * 9 - 12

L = 15

<em>Hence, the length 15 yards</em>

4 0
3 years ago
Seventh graders collected some gold sand on a class field trip.
satela [25.4K]

Answer:

Class 7A collected 4.8 ounces of pure gold.

Step-by-step explanation:

<u>Key skills required are: Percentages, Multiplication</u>

<u />

  1. We only need the information about Class 7A. They collected 40 oz that contains 12% gold.
  2. In other words, this means that 12% of that 40 oz gold sand is pure gold.

Here we have to do 12% x 40 to find the number of oz of pure gold. We first have to convert 12% into a decimal. Divide it by a 100 (or move the decimal point 2 places to the left) and you will get 0.12.

<em>Do 0.12 x 40 and you will get 4.8</em>

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Answer:

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Step-by-step explanation:

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Rewrite for clarity.

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Multiply both sides by 2.

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Substitute variable.

5 = 1/2(16) - 3

Multiply 1/2 and 16.

5 = 8 - 3

Subtract 3 from 8.

5 = 5

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