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3 years ago

Literal equations 2x-3y=8 solve for y

Mathematics

2 answers:

ludmilkaskok [199]3 years ago

7 0

2x - 3y = 8
- 3y = 8 - 2x
y = ( 8 - 2x ) / -3

or

2x - 3y = 8
2x = 8 + 3y
2x - 8 = 3y
(2x - 8) / 3 = y

vichka [17]3 years ago

4 0

2x-3y = 8

Add 3y on both sides

2x = 8 + 3y

Subtract 8 on both sides

3y = 2x - 8

Divide 3 on both sides

$y= \frac{2}{3}x- \frac{8}{3}$

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Determine the number of real solutions of -2x^2+5x-3=0

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Answer:

Two distinct real solutions.

Step-by-step explanation:

Given the equation in the form $ax^2+bx+c=0$ , you need to find the Discriminant with this formula:

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For the equation $-2x^2+5x-3=0$ you can identify that:

$a=-2\\b=5\\c=-3$

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3 years ago

Prove that if r is any rational number, then 3r2 − 2r + 4 is rational. The following properties may be used in your proof. Prope

ziro4ka [17]

Given:

Expression is

$3r^2-2r+4$

To prove:

If r is any rational number, then $3r^2-2r+4$ is rational.

Step-by-step explanation:

Property 1: Every integer is a rational number. It is Theorem 4.3.1.

Property 2: The sum of any two rational numbers is rational. It is Theorem 4.3.2.

Property 3: The product of any two rational numbers is rational. It is Exercise 15 in Section 4.3.

Let r be any rational number.

We have,

$3r^2-2r+4$

It can be written as

$3(r\times r)-2r+4$

Now,

3, -2 and 4 are rational numbers by property 1.

$r^2=r\times r$ is rational by Property 3.

$3r^2\text{ and }-2r$ are rational by Property 3.

$3r^2+(-2r)+4$ is rational by property 2.

So, $3r^2-2r+4$ is rational.

Hence proved.

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3 years ago