Please please please help me guys

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

Solve the following system of equations using Substitution: Submit your answer as an ordered pair. 2x−3y=32x-3y=32x−3y=3 x=y+2x=

exis [7]

9514 1404 393

Answer:

(3, 1)

Step-by-step explanation:

We assume you want the solution to the system ...

2x−3y=3
x=y+2

The second equation gives a nice expression for x, so we can use that in the first equation.

2(y+2) -3y = 3 . . . . substitute for x in the first equation

2y +4 -3y = 3 . . . . . eliminate parentheses

-y = -1 . . . . . . . . . . . collect terms, subtract 4

y = 1 . . . . . . . . . . . . multiply by -1

x = 1 +2 = 3 . . . . . . substitute for y in the second equation

The solution is (x, y) = (3, 1).

4 0

3 years ago

Divide 25 by 8 write the quotient with a fraction

ehidna [41]

3 1/8 or 3.125 or 25/8

5 0

3 years ago

Help... Jordan earns five dollars per hour babysitting. Each week he babysits six hours during the week, in four hours on the we

Alekssandra [29.7K]

Answer:

well what would you do to figure it out?

Step-by-step explanation:

3 0

3 years ago

Read 2 more answers

Mila graphs the point A

melamori03 [73]

Answers:
B. <span>The x-coordinate of point A is 5.
</span>E. <span>Point A is on the x-axis.
</span>
Explanation:
Any point drawn on the coordinates has the general notation of (x,y).
The given point is (5,0). This means that:
The x-coordinate of the point is 5
The y-coordinate of the point is 0

Now, let's check the place of this point.
The x-coordinate of the point is 5. This means that we will move 5 points to the right of the origin on the x-axis
The y-coordinate of the point is 0. This means that we will not move along the y-axis which means that the point stays on the x-axis.

Now, comparing the deduced results with the given choices, we will find that the correct choices are B and E

Hope this helps :)

6 0

2 years ago