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4 years ago

Difference between solutions of linear equations and solutions of linear in equalities

1 answer:

5 0

A linear equation is any equation involving one or two variables whose exponents are one. In the case of one variable, one solution exists for the equation. For example, with 2_x_ = 6, x can only be 3.

One obvious difference between linear equations and inequalities is the solution set. A linear equation of two variables can have more than one solution.

For instance, with x = 2_y_ + 3, (5, 1), then (3, 0) and (1, -1) are all solutions to the equation.

In each pair, x is the first value and y is the second value. However, these solutions fall on the exact line described by y = ½ x – 3/2.

If the inequality were x ? 2_y_ + 3, the same linear solutions just given would exist in addition to (3, -1), (3, -2) and (3, -3), where multiple solutions can exist for the same value of x or the same value of y only for inequalities. The "?" means that it is unknown whether x is greater than or less than 2_y_ + 3. The first number in each pair is the x value and the second is the y value.

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student tickets for the football game cost $12 each and adult ticket cost $20 $1,720 was collected for the 120 ticket sold at la

erik [133]

Answer:

85 student tickets and 35 adult tickets were sold.

Step-by-step explanation:

Howdy!

We know that student tickets cost $12, adult ticket cost $20 and 120 tickets were sold.

So:

$12×A + $20×B = $1,720. Where A and B are the number of student tickets and adult tickets sold, respectively.

Given that 120 tickets were sold in total, we have that:

A + B = 120

So the system of equations to be solved is the following:

$12×A + $20×B = $1,720 (1)

A + B = 120 (2)

Solving for 'A' in equation (2) we get:

A = 120 - B

Substituting this value into equation (1) we get:

$12×(120 - B) + $20×B = $1,720

Solving for 'B' we have:

$12×(120 - B) + $20×B = $1,720

$1,440 - $12×B + $20×B = $1,720

$1,440 + $8×B = $1,720

$8×B = $1,720 - $1,440

$8×B = $280

B = 35 tickets.

Given that B = 35, then A = 120 - 35 = 85 tickets.

So 85 student tickets and 35 adult tickets were sold.

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3 years ago

Read 2 more answers

Using the credit card from question 13, if you have a good credit rating, how much must you pay at the end of the month to get t

Reptile [31]

Where is the credit card?

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3 years ago

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One of the legs of a right triangle is twice as long as the other, and the perimeter of the triangle is 35. Find the

Aloiza [94]

Answer:

6.68, 13.37, 14.95

Step-by-step explanation:

One of the legs is twice as long as the other.

b = 2a

The perimeter is 35.

35 = a + b + c

The triangle is a right triangle.

c² = a² + b²

Three equations, three variables. Start by plugging the first equation into the second and solving for c.

35 = a + 2a + c

c = 35 − 3a

Now plug this and the first equation into the Pythagorean theorem:

(35 − 3a)² = a² + (2a)²

1225 − 210a + 9a² = a² + 4a²

1225 − 210a + 4a² = 0

Solve with quadratic formula:

a = [ -(-210) ± √((-210)² − 4(4)(1225)) ] / 2(4)

a = (210 ± √24500) / 8

a ≈ 6.68 or 45.82

Since the perimeter is 35, a = 6.68. Therefore, the other sides are:

b ≈ 13.37

c ≈ 14.95

8 0

3 years ago

16 is a factor of 24. O A. True O B. False

Alexxx [7]

The answer is b/false I hope this help

5 0

3 years ago

Read 2 more answers

Which statement describes the effect on the parabola f(x)=2x•x-5x+3 when changed to f (x)= 2x•2-5x+1

o-na [289]

Answer:

The parabola is translated down 2 units.

Step-by-step explanation:

You have the parabola f(x) = 2x² – 5x + 3

To change this parabola to f(x) = 2x² - 5x + 1, you must have performed the following calculation:

f(x) = 2x² – 5x + 3 -2= 2x² - 5x + 1 Expresion A

The algebraic expression of the parabola that results from translating the parabola f (x) = ax² horizontally and vertically is g (x) = a(x - p)² + q, translating in the same way as the function.

If p> 0 and q> 0, the parabola shifts p units to the right and q units up.
If p> 0 and q <0, the parabola shifts p units to the right and q units down.
If p <0 and q> 0, the parabola shifts p units to the left and q units up.
If p <0 and q <0, the parabola shifts p units to the left and q units down.

In the expression A it can be observed then that q = -2 and is less than 0. So the displacement is down 2 units.

This can also be seen graphically, in the attached image, where the red parabola corresponds to the function f(x) = 2x² – 5x + 3 and the blue one to the parabola f(x) = 2x² – 5x + 1.

In conclusion, the parabola is translated down 2 units.

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3 years ago