Write an equation that represents the line.<br> Use exact numbers.

Determine the number of solutions for the system of equations. 1. { y=2/5x^2, y=x-2. 2. {y=3x^2, y-3x=-2

umka2103 [35]

A system of two equations can be classified as follows: If the slopes are the same but the y-intercepts are different, the system has no solution. If the slopes are different, the system has one solution. If the slopes are the same and the y-intercepts are the same, the system has infinitely many solutions.

4 0

3 years ago

30 POINTS

nydimaria [60]

Answer:

Lies it’s only 15 points):

Step-by-step explanation:

4 0

3 years ago

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Rosalie is organizing a circus performance to raise money for a charity. She is trying to decide how much to charge for tickets.

Ray Of Light [21]

Answer:

she should charge $7.395 per ticket in order to make the most money.

Step-by-step explanation:

From the given information:

If Rosalie charges $5 then 1175 people will attend the circus performance

If Rosalie charges $7 then 935 people will attend the circus performance

Let x be the cost and y to be the number of people that will attend the performance . Then, we will have two points which are;

(5, 1175) and (7, 935)

The slope(m) of this points = $\dfrac{\Delta y}{\Delta x}$

= $\dfrac{y_2-y_1}{x_2-x_1}$

$=\dfrac{935-1175}{7-5}$

Slope (m) = $\dfrac{-240}{2}$

Slope (m) = -120

However; we can now have the linear equation:

$y-y_1 = m(x-x_1)$

$y-1175= -120(x-5)$

$y-1175= -120x+600$

$y= -120x+600+1175$

$y= -120x+1775$

The linear function is : y = -120x + 1775

Now; the total amount of money she can now earn is:

f(x) = xy

f(x) = x(-120x + 1775)

f(x) = -120x² + 1775x

The above expression is a quadratic equation; Using the quadratic formula; we have:

$=\dfrac{-b \pm \sqrt{b^2-4ac}}{2a}$

where; a = -120 ; b = +1775 and c = 0

$=\dfrac{-(1775) \pm \sqrt{(1775)^2-4(-120)(0)}}{2(-120)}$

$=\dfrac{-(1775) + \sqrt{(1775)^2-4(-120)(0)}}{2(-120)} \ \ \ \ \ OR \ \ \ \ \dfrac{-(1775) -\sqrt{(1775)^2-4(-120)(0)}}{2(-120)}$

$=\dfrac{-(1775) + \sqrt{(1775)^2}}{(-240)} \ \ \ \ \ OR \ \ \ \ \dfrac{-(1775) -\sqrt{(1775)^2}}{(-240)}$

$=\dfrac{-(1775) + (1775)}{(-240)} \ \ \ \ \ OR \ \ \ \ \dfrac{-(1775) - (1775)}{(-240)}$

$=\dfrac{0}{(-240)} \ \ \ \ \ OR \ \ \ \ \dfrac{-3550}{(-240)}$

= 0 OR 14.79

Since; we are considering the value greater than zero

x = 14.79

maximum value of x = 14.79/2 = 7.395

Thus ; she should charge $7.395 per ticket in order to make the most money.

6 0

3 years ago

I need help on 1 and 2

Naily [24]

Answer:

1. ∠1 and ∠3. ∠1 and ∠2.

2. ∠6 and ∠5. ∠6 and ∠4

Step-by-step explanation:

Adjacent angles are two angles that have a common vertex but do not overlap. The ones above are the pairs of adjacent angles that share a common vertex, but do not overlap.

8 0

3 years ago

How to find the area of a circle<br>

Keith_Richards [23]

Answer:

Area = π r^2.

Step-by-step explanation:

Given the radius r of a circle, the area = π r^2.

So for example the area of a circle of radius 2 = π 2^2

= 4π.

8 0

4 years ago

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Write an equation that represents the line. Use exact numbers.