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What are the ordered pairs of the solutions for this system of equations? y = -x2 + 2 y = x

sergiy2304 [10]

Answer:

The solutions of this system of equations are (-2, -2) and (1, 1).

Step-by-step explanation:

Let be the following system of equations:

$y = -x^{2}+2$ (1)

$y = x$ (2)

(2) in (1):

$y = -y^{2}+2$

$y^{2}+y-2 = 0$

This polynomial can be solved analytically by Quadratic Formula:

$y_{1} = 1$ , $y_{2} = -2$

Hence, the solutions of this system of equations are (-2, -2) and (1, 1).

5 0

3 years ago

What is the answer to 4/5+9/11

SCORPION-xisa [38]

Hi there!
When adding fractions we ALWAYS need to make sure the that denominators are the SAME .We need to find a common denominator so that the two fractions are on the same terms. In the end, the denominator stays the same. Let's start:
We are given 2 fractions to add:
$\frac{4}{5} + \frac{9}{11}$

We need to find a LEAST common denominator, start by listing the factors of 5 and 11 since both of these numbers are in the denominator.

Factors of 5: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55
Factors of 11: 11, 22, 33, 44, 55

As we see above, 55 is our LCD (least common denominator)

We can change the denominator of both fractions to 55 since this is our LCD:
 $\frac{4}{55} + \frac{9}{55}$

However, if the denominator changes, the numerator changes as well. We use the following formula to find the numerators:

(Common Denominator ÷ Denominator) x Numerator = Numerator

Lets start by finding the numerator for the first fraction:
4/55

(55 (common denominator) ÷ 5 (original denominator) × 4 (numerator) = 44

The first fraction becomes:

$\frac{44}{55}$

Now let's do the second:

9/55

(55(common denominator) ÷ 11(original denominator))×9(numerator) = 45

Now we have:

$\frac{45}{55}$

Now we have two fractions to add:

$\frac{44}{55} + \frac{45}{55}$

Only add the numerators, the denominators stay the SAME !

44+45=89

Final answer: $\frac{89}{55}$

If you have further questions on this problem, please do not hesitate to comment below! :) Have a nice day!

7 0

3 years ago

Does this graph represent a function? Why or why not?

artcher [175]

Answer:

Yes, this graph represents a function.

Functions can have a maximum of one y-value for every x-value. On a graph, this means it passes the vertical line test.

Step-by-step explanation:

The vertical line test is when a vertical line is passed though the graph. If at any point the vertical line touch more than one point on the graph, the graph is not a function. Vertical line test is also known as VLT.

6 0

3 years ago

Last year mr.peterson had a fence all the way around his garden. he can reuse all of the fence he had around the garden last yea

lakkis [162]

First, you need to find out the perimeter of the fence and how much of the fence he had around his garden last year (leftovers) and subtract them I think.

4 0

3 years ago

What is the area of something that is 2 inches long and 5/6 inches wide

Free_Kalibri [48]

Area = Length x Width

The Length is 2 inches
The Width is 5/6 inches

2 * (5/6) = 10/6

simplify and you get....
5/3

5 0

3 years ago