All categories

2 years ago

Please help me!

Mathematics

1 answer:

nikklg [1K]2 years ago

8 0

Explanation:

The solution set for a system of equation is the set of points where the graphs of the equations intersect.

<h3>general case</h3>

A system will have <em>one solution</em> if there is a <em>single point of intersection</em> of the graphs of the equations.

A system will have <em>no solutions</em> if the graphs have <em>no points of intersection</em>.

A system will have an <em>infinite</em> number of <em>solutions</em> if the graphs <em>intersect at an infinite number of points</em>.

_____

<h3>linear equations</h3>

When the equations are linear equations, their graphs are straight lines. If the lines have different slopes, they must intersect at exactly one point: there will be one solution.

If the lines have the same slope, there are two possibilities:

the lines are parallel -- no solutions
the lines are coincident -- infinite solutions

The attached graph illustrates these cases.

the red and blue lines are the graphs of a system of equations with one solution. Those lines have different slopes
the blue and green lines are the graphs of a system of equations with no solution. Those lines are parallel.
The red and (dotted) purple lines are the graphs of a system of equations with infinite solutions. Those lines are coincident.

You might be interested in

Simplify the square root of 4x^6

Wittaler [7]

Answer:

2x^3

Solution

You simplify to the lowest value possible 4x^6

2x^3

7 0

3 years ago

What is the width (or height) of the parking lot?

Gre4nikov [31]

The width is 146.0315533981 cuz 12033÷82.4 is 146.0315533981

6 0

3 years ago

Determine the equation of each of the following parabolas

Pani-rosa [81]

Step-by-step explanation:

For graphs where the zeros (x-intercepts) are known, use the factored form of a parabola:

y = a (x − b) (x − c)

where (b, 0) and (c, 0) are the zeros. Plug in a third point to find the value of a.

For graphs where the vertex is known, use the vertex form of a parabola:

y = a (x − h)² + k

where (h, k) is the vertex. Plug in a second point to find the value of a.

I'll do the first three problems as examples.

a) The vertex is (0, 5), and one of the zeros is (4, 0). Since the vertex is halfway between the zeros, we also know the other zero is (-4, 0). So we can use either form.

Using factored form:

y = a (x − 4) (x − (-4))

y = a (x − 4) (x + 4)

Plug in the vertex to find the value of a:

5 = a (0 − 4) (0 + 4)

5 = -16a

a = -5/16

Therefore, the equation is:

y = -5/16 (x − 4) (x + 4)

b) The vertex is (0, 0). It is also the only root. So again, we can use either form.

Using vertex form:

y = a (x − 0)² + 0

y = ax²

Plugging in the second point:

9 = a (-3)²

9 = 9a

a = 1

Therefore, the equation is:

y = x²

c) This time, we don't know the coordinates of the vertex, but we do know the roots are (-7, 0) and (0, 0). Using factored form:

y = a (x − 0) (x − (-7))

y = a x (x + 7)

Plugging in the third point:

4 = a (4) (4 + 7)

4 = 44a

a = 1/11

Therefore, the equation is:

y = 1/11 x (x + 7)

7 0

3 years ago

Janice works at the We Are Cells. She earns $650 per week plus a 15% commission on all new cell phone contracts that she sells e

sertanlavr [38]

Answer:

y=650+15x

Step-by-step explanation:

y=mx+b, b is starting amount, m is the multiplier for the x

uwu

7 0

4 years ago

Write the following in exponent form.

ss7ja [257]

1)5^2
2)8^5
3)9^3
4)2^4
5)7^6
6)2.3^2

4 0

3 years ago

Read 2 more answers