MATHEMATICS MIDDLE SCHOOL

Find the domain:

y= (6+9x)/(6−|x−1|)

Answers

Answer 1

Answer:

Answer:

The domain = {x : x ≠ -5 , 7}

Step-by-step explanation:

- The domain of the function is the values of x which makes the function

defined

- If the function has a denominator then the domain is all the values of x

except the zeroes of the denominator

- Zeroes of the denominator means the values of x when the

denominator = 0

- The function is $y=(6+9x)/((6-Ix-1I))$

- To find the domain of the function find the zeroes of the denominator

∵ The denominator is ⇒ 6 - Ix - 1I

∴ 6 - Ix - 1I = 0

- Subtract 6 from both sides

∴ - Ix - 1I = -6

- Multiply both sides by -1

∴ Ix - 1I = 6

- The absolute value of x - 1 = 6 that means x - 1 = 6 OR x - 1 = -6

∵ x - 1 = 6

- Add 1 to both sides

∴ x = 7

∵ x - 1 = -6

- Add 1 to both sides

∴ x = -5

∴ The zeroes of the denominator are -5 and 7

∵ x = -5 and x = 7 make the denominator = 0

- Any value divided by 0 is undefined

∴ x can be any value except -5 and 7

∴ The domain of the function is all real values of x except -5 and 7

* The domain = {x : x ≠ -5 , 7}

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What is the solution to the equation-4x - 14 = 6?

Answers

Answer:

x=-5

Step-by-step explanation:

-4x - 14 = 6

Add 14 to each side

-4x - 14+14 = 6+14

-4x = 20

Divide each side by -4

-4x/-4 = 20/-4

x = -5

4. Complete. a. Factor: 2x2 – 5x – 3.

b. Subtract: 3x-2/2x^2-5x-3 - 1/x-3

can anyone help me on these problems and explain how you did it please

Thank you
PLEASE HELP

Answers

a. $2 x^(2) -5x-3=2 x^(2) -6x+x-3$ (I'll explain how I split it in a bit)
$=2x(x-3)+1(x-3)$   Look for common factors between the 1st two and then the second two while trying to make sure the variables in the brackets are the same.
Now you only have to write the value in the bracket once and then join the outer factors in their own bracket so your final answer will be $(2 x^(2) +1)(x-3)$

For the first thing I did, I multiplied the first part of the equation by the last part= 2 $x^(2)$ x -3=-6 $x^(2)$ . I then proceeded to find two numbers that can be multiplied to give the result and when added will give the middle part (-5x).
Factors of -6 $x^(2)$ are: -1x and 6x, -2x and 3x, -3x and 2x, -6x and 1x. The only ones that add up -5x are -x and 6x so that was why I used them.

b. 3x-2/2x^2-5x-3 - 1/x-3
$(3x-2)/(2 x^(2) -5x-3)- (1)/(x-3) = (3x-2)/((2x+1)(x-3)) - (1)/(x-3)$
$= (1(3x-2) +1(2x+1))/((2x+1)(x-3))$
   $= (3x+2x-2+1)/((2x+1)(x-3) )$
  = $(x-1)/(2 x^(2) -5x-3)$

amy has 72 Suites in a bag she keeps one fourth of them for herself and share the rest with their friends how many sweets will he get her friends

Answers

So,

If she keeps one-fourth for herself, she will keep:
72 * 0.25 = 18

That leaves the rest for her friends.
72 - 18 = 54

Her friends will get 54 "Suites."

What is 423.408 rounded to the neatest hundredth

Answers

The hundredth is the second decimal place. You know the rounding rules are where you look at the previous place and if it's 5 or above the number place your rounding to goes up. So the answer is 423.41

423.408 = 423.41
0.08 is nearer to 0.1 than 0.001

The figure is made up of two identical squares and has a perimeter of 42 inches. What is the area of one square?

Answers

The area of one square is 49 square inches.

What is a square?

A square is a two-dimensional figure and a four-sided polygon which has it's all sides equal in length and the measure of the angles are 90 degrees. The total interior angle is 360 degrees.

For the given situation,

The figure is made up of two identical squares. So it forms a rectangle.

Let width be x then length be 2x.

Perimeter of rectangle = 42 inches

The formula of perimeter of rectangle is

⇒ $P=2(l+w)$