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3 years ago

10

Do ALL linear equations have 1 solution? Explain

1 answer:

schepotkina [342]3 years ago

4 0

Answer:

No

Step-by-step explanation:

A system of linear equations usually has a single solution, but sometimes it can have no solution (parallel lines) or infinite solutions (same line). This article reviews all three cases. One solution. A system of linear equations has one solution when the graphs intersect at a point.

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The line $y = 3$ intersects the graph of $y = 4x^2 + x - 1$ at the points $A$ and $B$. The distance between $A$ and $B$ can be w

raketka [301]

Answer:

61

Step-by-step explanation:

Let's find the points $A$ and $B$ .

We know that the $y$ -coordinates of both are $3$ .

So let's first solve:

$3=4x^2+x-1$

Subtract 3 on both sides:

$0=4x^2+x-1-3$

Simplify:

$0=4x^2+x-4$

I'm going to use the quadratic formula, $x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$ , to solve.

We must first compare to the quadratic equation, $ax^2+bx+c=0$ .

$a=4$

$b=1$

$c=-4$

$\frac{-1 \pm \sqrt{1^2-4(4)(-4)}}{2(4)}$

$\frac{-1 \pm \sqrt{1+64}}{8}$

$\frac{-1 \pm \sqrt{65}}{8}$

Since the distance between the points $A$ and $B$ is horizontal. We know this because they share the same $y-coordinate$ .This means we just need to find the positive difference between the $x$ -values we found for the points of $A$ and $B$ .

So that is, the distance between $A$ and $B$ is:

$\frac{-1+\sqrt{65}}{8}-\frac{-1-\sqrt{65}}{8}$

$\frac{-1+\sqrt{65}+1+\sqrt{65}}{8}$

$\frac{2\sqrt{65}}{8}$

$\frac{\sqrt{65}}{4}$

If we compare this to $\frac{\sqrt{m}}{n}$ , we should see that:

$m=65 \text{ and } n=4$ .

So $m-n=65-4=61$ .

5 0

3 years ago

Read 2 more answers

If $7500 is invested at an interest rate of 5% each year, what is the value of the investment in 4 years? Write an exponential f

Vanyuwa [196]

The answer is 9,116.3
7500*(1+0.05)^4

3 0

3 years ago

Which number line illustrates the problem below? x = -1 - (-2) -3

MrRa [10]

The answers to that would be x=-2

8 0

3 years ago

What is an example of what property ?

vodomira [7]

Answer:

Distributive Property

Step-by-step explanation:

7 equals (3+4).

Therefore, 4*7 equals 4*(3+4).

By distributive property, this will equal (4*3) + (4*4)

8 0

3 years ago

Please help me asap! Thank you!

blsea [12.9K]

......bruh okay......

3 0

3 years ago