Question in photo bc i cant type it right lol

<img src="https://tex.z-dn.net/?f=%28x%5E%7B2%7D%20%2Bx-3%29%3A%20%28x%5E%7B2%7D%20-4%29%5Cgeq%201" id="TexFormula1" title="(x^{

Jlenok [28]

Answer:

$x>2$

Step-by-step explanation:

When given the following inequality;

$(x^2+x-3):(x^2-4)\geq1$

Rewrite in a fractional form so that it is easier to work with. Remember, a ratio is another way of expressing a fraction where the first term is the numerator (value over the fraction) and the second is the denominator(value under the fraction);

$\frac{x^2+x-3}{x^2-4}\geq1$

Now bring all of the terms to one side so that the other side is just a zero, use the idea of inverse operations to achieve this:

$\frac{x^2+x-3}{x^2-4}-1\geq0$

Convert the (1) to have the like denominator as the other term on the left side. Keep in mind, any term over itself is equal to (1);

$\frac{x^2+x-3}{x^2-4}-\frac{x^2-4}{x^2-4}\geq0$

Perform the operation on the other side distribute the negative sign and combine like terms;

$\frac{(x^2+x-3)-(x^2-4)}{x^2-4}\geq0\\\\\frac{x^2+x-3-x^2+4}{x^2-4}\geq0\\\\\frac{x+1}{x^2-4}\geq0$

Factor the equation so that one can find the intervales where the inequality is true;

$\frac{x+1}{(x-2)(x+2)}\geq0$

Solve to find the intervales when the equation is true. These intervales are the spaces between the zeros. The zeros of the inequality can be found using the zero product property (which states that any number times zero equals zero), these zeros are as follows;

$-1, 2, -2$

Therefore the intervales are the following, remember, the denominator cannot be zero, therefore some zeros are not included in the domain

$x\leq-2\\-2$

Substitute a value in these intervales to find out if the inequality is positive or negative, if it is positive then the interval is a solution, if it is negative then it is not a solution. This is because the inequality is greater than or equal to zero;

$x\leq-2$ -> negative

$-2$ -> neagtive

$-1\leq x$ -> neagtive

$x>2$ -> positive

Therefore, the solution to the inequality is the following;

$x>2$

6 0

2 years ago

A rectangle flower bed is 9 feet wide and 12 feet long .what is the length of the diagonal?

BigorU [14]

Answer:

15 feet

Step-by-step explanation:

The question talks about;

A rectangular flower bed whose dimensions are 12 ft by 9 ft

We are required to determine the length of the diagonal

To answer the question, we need to know the following;

All the angles in a rectangle are right angles
A diagonal divides a rectangle into two right-angled triangles
The dimensions of the rectangle acts as the legs of right angled triangle.

Therefore;

Using Pythagoras theorem;

a² + b² = c²

Where, c is the hypotenuse (in this case the diagonal)

a and b are the shorter sides of the right-angled triangle

Therefore;

c² = 12² + 9²

c² = 144 + 81

= 225

c = √225

= 15

Therefore, the length of the diagonal is 15 feet

5 0

3 years ago

Of the 120 rooms in a hotel, 55% are single bed rooms, 30% are double bed rooms and the rest are deluxe rooms. How many deluxe r

Nat2105 [25]

Hey there !

Check the attachment.
Hope it helps you :)

6 0

3 years ago

I need help with #11 and #12 how do I do this?

USPshnik [31]

Answer:

11. x = 6; y = 6.5

12. x = 2; y = 4

Step-by-step explanation:

In each figure, the hash marks on the lines indicate the parallel lines (marked with red arrows) are equally-spaced. That means the two expressions involving x are equal to each other, and the two expressions involving y are equal to each other.

__

11. 2x +1 = x +7

x = 6 . . . . . . . subtract (x+1) from both sides

and

3y -8 = y +5

2y = 13 . . . . add (8-y) to both sides

y = 6.5 . . . . divide by the coefficient of y

__

12. x +3 = 3/2x +2

1 = 1/2x . . . . . subtract (x+2)

2 = x . . . . . . . multiply by 2

and

2y -1 = 3y -5

4 = y . . . . . . add (5 -2y)

8 0

2 years ago

Read 2 more answers

Evaluate the function.<br> f(x) = 3x² + 5x – 14<br> Find f(-3)<br> Answer:<br> Submit Answer

puteri [66]

3*-3^2+5*-3-14
3*-9+(-15)-14
-27+-15-14
-42-14
-56

7 0

2 years ago