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4 years ago

Check all of the following that are solutions to the system shown below.

1 answer:

5 0

From second equation y = -2-x

Plug this into the first equation:-

- 2 - x = -x^2 - x + 2

x^2 + x - 2 - 2 - x = 0

x^2 - 4 = 0

x^2 = 4

x + +/- 2

Plug these values into x + y = -2 :-
x = 2:-
2 + y = -2

so y = -4

so one solution is (2,-4)

Now try x = -2

- 2 + y = -2

y = 0

so the second solution is ( -2 , 0)

So A and C are correct

You might be interested in

1.) Solve -23.7 + d = -48.57.

Olegator [25]

Answer:

-24.87

Step-by-step explanation:

Step 1: Simplify both sides of the equation.

d−23.7=−48.57

Step 2: Add 23.7 to both sides

d−23.7+23.7=−48.57+23.7

d=-24.87

3 0

3 years ago

20. Joe is standing on top of Marina Towers looking at the Leo Burnett World Headquarters building across the Chicago River. It

Scilla [17]

The height of the Burnett building to the nearest foot be is 444 feet

<h3 /><h3 /><h3>What is angle of elevation and depression?</h3>

The angle from the horizontal to a point or the line of sight is measured with angles of elevation and depression.

when the points is high above the line of sight we have angle of elevation however when the line of sight is below the horizontal we have angle of depression

<u>Given data</u>

distance between the two buildings ( horizontal ) = 880 feet

angle of elevation = 8 degrees

angle of depression = 20 degrees

applying Trigonometry relations

for angle of elevation

tan 8 = h1 / 880

h1 = 123.676 feet

for angle of depression

tan 20 = h2 / 880

h2 = =880 * tan 20

h2 = 320.294

let the height of the Burnett building to the nearest foot be h

h = h1 + h2

h = 123.676 + 320.294

h = 443.97

h = 444 feet

Read more on angle of elevation and depression here: brainly.com/question/15580615

#SPJ1

5 0

2 years ago

For the equation x2 = a, describe the values of a that will result in two real solutions, one real solution, and no real solutio

Tasya [4]

The equation given is $x^{2} =a$ where a is some number.
We can solve for x by taking the square root of both sides.

$x=plusminus \sqrt{a}$

Now let's think through what happens for various values of a.

TWO SOLUTIONS
If a is a positive number the above yields two solutions. Take for example:
$x^{2} =49
 \sqrt{49}=7 or -7$
There will be two solutions (one positive and one negative) as there are two numbers (here -7 and +7) that when multiplied by themselves give 49. That is, $7^{2} =49$ and $(-7)^{2}=49$ . The positive root is called the principal root and the negative root is called the secondary root. This will be the case anytime we take the root of a positive number.

ONE SOLUTION
If a = 0 there is only one solution. That is because $x^{2} =0$ and $x= \sqrt{0}$ . Zero is neither positive nor negative and it has only one root which is 0 itself. So in this case there is only one solution and it is 0.

NO (REAL) SOLUTIONS
If a is negative we would be taking the square root of a negative number. There is no (real) number that when multiplied by itself gives a negative number. Take for example $x^{2} =-49$ which gives us $x= \sqrt{-49}$ . The square root of -49 is not 7 because (7)(7)=49 which is positive. The square root of -49 is not -7 because (-7)(-7)=49 which is also positive. There is no real number that gives -49 when multiplied by itself. I say "real" numbers because there do exist imaginary/complex numbers but because of the way the questions was asked I imagine you may not know about these yet.

7 0

3 years ago

(1 point) Use the graph below to find exact values of the indicated derivatives, or state that they do not exist. If a derivativ

svetlana [45]

Derivatives can be calculated from graphed functions.

The values of the derivatives are:

The given parameter is:

$\mathbf{h(x) = f(g(x))}$

Start by calculating the equations of f(x) and g(x)

<u>Graph f(x)</u>

The slopes of f(x) are: 3/2 and -3/2

So, the equations are:

$\mathbf{f(x) = \frac{3}{2}x,\ 0 \le x \le 2}$

$\mathbf{f(x) = -\frac{3}{2}x,\ x \ge 2}$

<u>Graph g(x)</u>

The slope of g(x) is: -1/2

So, the equation is:

$\mathbf{g(x) = -\frac 12x}$

So, we have:

$\mathbf{h(x) = f(g(x))}$

Where:

$\mathbf{f(x) = \frac{3}{2}x\ 0 \le x \le 2}$ and $\mathbf{g(x) = -\frac 12x}$

$\mathbf{h(x) = f(g(x))}$ becomes

$\mathbf{h(x) = \frac{3}{2}(-\frac{1}{2}x)}$

Open brackets

$\mathbf{h(x) = -\frac{3}{4}x}$

Differentiate

$\mathbf{h'(x) = -\frac{3}{4}}$

So:

$\mathbf{h'(1) = -\frac{3}{4}}$

$\mathbf{h'(2) = -\frac{3}{4}}$

For x = 3, we have:

$\mathbf{h(x) = f(g(x))}$

Where:

$\mathbf{f(x) = -\frac{3}{2}x\ x \ge 2}$ and $\mathbf{g(x) = -\frac 12x}$

$\mathbf{h(x) = f(g(x))}$ becomes

$\mathbf{h(x) = -\frac{3}{2}(-\frac{1}{2}x)}$

$\mathbf{h(x) = \frac{3}{4}x}$

Differentiate

$\mathbf{h'(x) = \frac{3}{4}}$

Substitute 3 for x

$\mathbf{h'(3) = \frac{3}{4}}$

Hence, the values of the derivatives are:

$\mathbf{h'(1) = -\frac{3}{4}}$ , $\mathbf{h'(2) = -\frac{3}{4}}$ and $\mathbf{h'(3) = \frac{3}{4}}$

Read more about graphed functions at:

brainly.com/question/11804653

3 0

3 years ago

Read 2 more answers

The Rachel’s daily expenses for 10 days are in the table.

Annette [7]

The correct answer is $44.20.
If we add up all the tips, the total is $442. If we divide this by the number of days (10), then we find the mean.
442 / 10 = 44.2

4 0

4 years ago