Can someone explain how to solve the system of equation x+y=3 by graphing?

Part A: Find a rational number that is between 7.7 and 7.9. Explain why it is rational. (2 points)

8_murik_8 [283]

A rational number is any number that can be written as the ratio between two other numbers i.e. in the form $\frac{a}{b}$

Part A:
An easy choice that makes sense is 7.8, right in the middle. To prove that it's rational we need to write it as a ratio. In this case we have $7.8=\frac{78}{10}$

Part B:
We need a number that can't be written as a ratio (because it neither terminates nor repeats). Some common ones are $\sqrt{2}$ , $e$ , $\phi$ and $\pi$ so it makes sense to try and use those to build our number. In this case $\frac{11\sqrt{2}}{5}\approx7.78$ works nicely.

6 0

3 years ago

Which of the following is not a possible number of solutions when solving a system of equations containing a quadratic and a lin

Kobotan [32]

Answer:

3

Step-by-step explanation:

We have a system with two equations, one equation is a quadratic function and the other equation is a linear function.

To solve this system we have to clear "y" in both equations, and then equal both equations, then we will have a quadratic function and equal it to zero:

$ax^2+bx+c=0, a\neq 0$

Then to resolve a quadratic equation we apply Bhaskara's formula:

$x_{1}=\frac{-b+\sqrt{b^2-4ac} }{2a}$

$x_{2}=\frac{-b-\sqrt{b^2-4ac} }{2a}$

It usually has two solutions.

But it could happen that $\sqrt{b^2-4ac}$ then the equation doesn't have real solutions.

Or it could happen that there's only one solution, this happen when the linear equation touches the quadratic equation in one point.

And it's not possible to have more than 2 solutions. Then the answer ir 3.

For example:

In the three graphs the pink one is a quadratic function and the green one is a linear function.

In the first graph we can see that the linear function intersects the quadratic function in two points, then there are two solutions.

In the second graph we can see that the linear function intersects the quadratic function in only one point, then there is one solutions.

In the third graph we can see that the linear function doesn't intersect the quadratic function, then there aren't real solutions.

7 0

3 years ago

Find the equation of the line in slope-intercept form (-1,-1) and (1,0)

ArbitrLikvidat [17]

Answer:

An equation in slope-intercept form of the line will be

$y\:=\frac{1}{2}x-\frac{1}{2}$

Step-by-step explanation:

The slope-intercept form of the line equation

y = mx+b

where m is the slope and b is the y-intercept

Given the points

(-1, -1)

(1, 0)

Finding the slope between (-1,-1) and (1,0)

$\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}$

$\left(x_1,\:y_1\right)=\left(-1,\:-1\right),\:\left(x_2,\:y_2\right)=\left(1,\:0\right)$

$m=\frac{0-\left(-1\right)}{1-\left(-1\right)}$

$m=\frac{1}{2}$

substituting m = 1/2 and (-1, -1) in the slope-intercept form of the line equation to determine the y-intercept

$y = mx+b$

$-1=\frac{1}{2}\left(-1\right)+b$

$-\frac{1}{2}+b=-1$

Add 1/2 to both sides

$-\frac{1}{2}+b+\frac{1}{2}=-1+\frac{1}{2}$

$b=-\frac{1}{2}$

substituting m = 1/2 and b = -1/2 in the slope-intercept form of the line equation

$y = mx+b$

$y\:=\frac{1}{2}x+\left(-\frac{1}{2}\right)$

$y\:=\frac{1}{2}x-\frac{1}{2}$

Therefore, an equation in slope-intercept form of the line will be

$y\:=\frac{1}{2}x-\frac{1}{2}$

3 0

2 years ago

The expression 2x2 + 12x + 10 represents a bird's height, in feet, x seconds after it leaves its nest,

marusya05 [52]

The answer is A. You add the extra 10 feet to however high the bird flew from there

8 0

2 years ago

A coyote is 60 meters away from a chicken and it can run 20 meters per second.

Dafna1 [17]

Answer: It will take it 3 seconds before getting to the chicken

6 0

2 years ago