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Yuliya22 [10]
2 years ago
13

Solve the system of equations: y= x^2 + 2x - 3 and y=3x+ 3.

Mathematics
1 answer:
Semenov [28]2 years ago
3 0

Answer:

(-2, -3)

(3, 12)

Step-by-step explanation:

To solve this, we're gonna get rid of the y's with substitution

x² + 2x - 3 = 3x + 3

Let's make this equation equal to zero

Subtract 3 from both sides

x² + 2x - 3 = 3x + 3

            - 3         - 3

x² + 2x - 6 = 3x

Subtract 3x from both sides

x² + 2x - 6 = 3x

    - 3x        - 3x

x² - x - 6 = 0

Factor the equation

(x - 3)(x + 2) = 0

This means x can be -2 or 3

Let's solve it with -2 first, plug the new x in y = 3x + 3

y = 3(-2) + 3

y = -6 + 3 = -3

Do the same for x = 3

y = 3(3) + 3

y = 9 + 3 = 12

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denis-greek [22]

Answer:

1. The location of the center of the given circle = The origin (0, 0)

The given points on the circumference of the circle = (1, √3), and (0, -2)

The general form of the equation of a circle, is presented as follows

(x - h)² + (y - k)² = r²

Where;

(h, k) = The coordinates of the center of the circle

r = The radius of the circle

∴ (h, k) = (0, 0)

The radius of the given equation is the distance from the center (0, 0) to either the point (0, -2) or (1, √3)

The distance from the center (0, 0) to the point (0, -2), which are points on the same ordinate,  r = y₂ - y₁

∴ r =  0 - (-2) = 2

r = 2

The equation of the circle is therefore;

(x - 0)² + (y - 0)² = 2²

∴ x² + y² = 2²

2. When x = 1, and y = √3, we have;

(1 - 0)² + (√3 - 0)² = 1 + 3 = 4 = 2²

When x = 0, and y = -2, we have;

(0 - 0)² + ((-2) - 0)² = (-2)² = 4 = 2²

Therefore, the points shown on the circle (1, √3), and (0, -2) satisfy the equation of the circle, x² + y² = 2² and are solutions to the equation of the circle

Step-by-step explanation:

3 0
3 years ago
What is the product of 3/7x2/5
Ivan

Answer:

0.1714285714285714

Step-by-step explanation:

4 0
3 years ago
Howie works at a petting zoo. He fed a piglet 1/5 of a bottle of milk then gave 3/4 of what was left to the calf. How much of th
Lapatulllka [165]

Answer:

\frac{3}{5}th part of the bottle will be drunk by the calf.

Step-by-step explanation:

Part of the bottle fed by the piglet = \frac{1}{5}

Milk left in the bottle = 1 - \frac{1}{5}

                                  = \frac{5-1}{5}

                                  = \frac{4}{5}

Milk drunk by the calf = \frac{3}{4}th of the left part

                                     = \frac{3}{4}\times \frac{4}{5}

                                     = \frac{3}{5}th part of the bottle

Therefore, \frac{3}{5}th part of the bottle will be drunk by the calf.

7 0
3 years ago
A communications company offers a variety of calling card options. Card A has a 30¢ connection fee and then costs 2¢ per minute.
arlik [135]

Answer:

The length of the call that would cost the same with both cards is 5 minutes.

Step-by-step explanation:

Hi there!

The cost with card A can be expressed as follows:

cost A = 30 + 2 · m

Where "m" is the length of the call in minutes.

In the same way, the cost of card B will be:

cost B = 10 + 6 · m

Where "m" is the length of the call in minutes.

We have to find the value of "m" for which the call would cost the same with both cards.

Then:

cost A = cost B

30 + 2 · m = 10 + 6 · m

Subtract 10 and 2 · m to both sides of the equation:

30 - 10 =  6 · m - 2 · m

20 = 4 · m

Divide by 4 both sides of the equation:

20/4 = m

5 = m

The length of the call that would cost the same with both cards is 5 minutes.

Have a nice day!

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