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Scilla [17]
3 years ago
14

Which shows all the critical points for the inequality x2-4/x2-5x+6<0

Mathematics
1 answer:
Hoochie [10]3 years ago
7 0

Answer:

x = ±2, 3 are the critical points of the given inequality.

Step-by-step explanation:

The given inequality is \frac{(x^{2}- 4)}{x^{2}-5x+6}

To find the critical points we will equate the numerator and denominator of the inequality to zero.

For numerator,

x^{2}-4=0

(x - 2)(x + 2) = 0

x = ±2

For denominator,

x² - 5x + 6 = 0

x² - 3x -2x + 6 = 0

x(x - 3) -2(x - 3) = 0

(x - 3)(x - 2) = 0

x = 2, 3

Therefore, critical points of the inequality are x = ±2, 3 where the sign of the inequality will change.

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5-4. Solve each of the following equations for the indicated variable. Use your Equation Mat if it is helpful. Write down each o
balu736 [363]
QUESTION 1

The given equation is :

2(y - 3) = 4
We want to solve for y. This means we have to isolate y on one side of the equation while all other constants are also on the other side of the equation,

We first divide both sides by 2 to obtain,

\frac{2(y - 3)}{2} = \frac{4}{2}

We cancel out the common factors to get,

y - 3 = 2

We now group like terms to get,

y = 3 + 2

We simplify to obtain,

y = 5

QUESTION 2

The given equation is

2x + 5y = 10
We want to solve for x. This means that we need to isolate x on one side of the equation, while all other variables and constant are also on the other side of the equation.

This implies that,

2x= 10 - 5y

We now divide through by 2, to obtain,

\frac{2x}{2} = \frac{10}{2} - \frac{5y}{2}

This will now give us,

x = 5 - \frac{5}{2} y

QUESTION 3

The given equation is
6x + 3y = 4y + 11

We want to solve for y. This means that we need to isolate y on one side of the equation, while all other variables and constants are also on the other side of the equation.

We first of all group all the y terms on one side of the equation to obtain,

6x - 11 = 4y - 3y

We simplify to get,

6x - 11 = y

This implies that,

y = 6x - 11

QUESTION 4

The given equation is,

3(2x + 4) = 2 + 6x + 10

We want to solve for x. This means that we need to isolate x on one side of the equation, while all other variables and constant are also on the other side of the equation.

Let us first expand the brackets to get,

6x + 12 = 2 + 6x + 10
This implies that

6x + 12 = 6x + 12

We group like terms to get,

6x - 6x = 12 - 12

We now simplify both sides to get,

0x = 0

We don't want x to vanish, so let us try to divide both sides by zero to get,

x = \frac{0}{0}

This is an indeterminate form, which implies that, x has infinitely many solutions. This means that all the real numbers are solution to the equation.

\therefore \: x \in \: R

QUESTION 5

The given equation is,

y = - 3x + 6

We want to solve for x, so we add the additive inverse of 6, which is -6 to both sides of the equation to get,

y - 6 = - 3x

We rewrite this to obtain,

- 3x = y - 6

We divide through by -3 to get,

\frac{ - 3x}{ - 3} = \frac{y}{ - 3} - \frac{6}{ - 3}

This will give us,

x = - \frac{y}{3} + 2

or

x= 2 - \frac{1}{3} y
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3 years ago
PLEASE HELP!! PICTURE INCLUDED!!
nordsb [41]

1.a

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8 0
3 years ago
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DiKsa [7]

Answer:

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Step-by-step explanation:

Abel = a

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Substitute:

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3 years ago
Isabel is making lemonade for a party with 12 guests. She wants to make equal servings that are at least 2 cups each. She makes
JulsSmile [24]
1 quart = 4 cups
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Fofino [41]

Answer

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