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3 years ago

How many Solutions are in the equation 3n(2n-8)=24-6n

Mathematics

1 answer:

neonofarm [45]3 years ago

6 0

Answer:

two (n = 4, and n = -1)

Step-by-step explanation:

Let's solve it as follows:

First, we can divide out the common factor of 3 from each side, to get:

n(2n-8) = 8 -2n

Next, we expand, and move all the terms over to the right hand side (so that we have 0 on the LHS - as this is how we will want to solve the quadratic equation):

2n^2 - 8n - 8 +2n = 0

2n^2 - 6n - 8 = 0.

We also see we can further simplify by dividing out the factor of 2, to get:

n^2 -3n -4. = 0

Next, as this is a quadratic, the usual next step is to factorise, to get:

(n-4)(n+1) = 0

So we see that n = 4 and n = -1 are the two solutions.

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Middle school Math!!!

liraira [26]

<h2>Answers:</h2>

Question 1: The equations share the same slope, but different y-intercepts.

Question 2: Option B (y = 2x + 1)

<h2>Explanations:</h2><h3>For Question 1:</h3>

Both equations are written in slope intercept form.

$y = mx+b\\\\\text{m - slope}\\\text{b - y-intercept}$

The equations we have are:

$\left \{ {{y=2x} \atop {y=2x-7}} \right.$

Both equations share the same slope of 2. However, they have different y-intercepts.

y = 2x can be written as y = 2x + 0.

Usually if you only have the slope in your equation then the y-intercept is the origin, or (0, 0).

The second equation's y-intercept is -7. It takes 'b's place.

<h3>For Question 2: </h3>

We are given a graph and we need to find a equation.

According to the graph, the line passes at (0, 1). 1 is the y - intercept.

Since y = 2x + 1 is the only option with 1 as the y - intercept, it should be the correct answer.

I'll do the slope as well to verify our answer.

I will use the points (-1, -1) and (1, 3).

$m=\frac{3-(-1)}{1-(-1)}=\frac{4}{2} =\boxed{2}$

The correct answer should be $y = 2x+1$ .

Hope this helps you.

6 0

3 years ago

HELPPPPPPPPP WITH THESE GRAPH! YOU'LL GET BRAINLIEST IF YOU'RE CORRECT! ALSO... THERE'S 20 POINTS!

lara [203]

<u>Given</u>:

Four coordinates lying on the 3rd quadrant of the Cartesian plane are as follows: $\:$

C' = (–6, –5)
D' = (–6, –3)
E' = (–4, –3)
F' = (–4, –5)

<u>Translation</u>:

Since you've been asked to translate the coordinates of the vertices 2 units right and 8 units up, you'll need to add 2 to its x-coordinate and 8 to its y-coordinate.

C'(–6, –5)

ㅤㅤ= C'(–6 + 2, –5 + 8)

ㅤㅤ= C'(–4, 3)

D'(–6, –3)

ㅤㅤ= D'(–6 + 2, –3 + 8)

ㅤㅤ= D'(–4, 5)

E'(–4, –3)

ㅤㅤ= E'(–4 + 2, –3 + 8)

ㅤㅤ= E'(–2, 5)

F'(–4, –5)

ㅤㅤ= F'(–4 + 2, –5 + 8)

ㅤㅤ= F'(–2, 3)