The simplified form of the given expression is -18. The correct option is the third option- -18
<h3>Simplifying an expression</h3>
From the question, we are to simplify
|3-10| - (12 ÷ 4 + 2)²
Simplifying
|3-10| - (12 ÷ 4 + 2)²
|-7| - (3 + 2)²
7 - (5)²
7 - 25
= -18
Hence, the simplified form of the given expression is -18. The correct option is the third option- -18
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Option (A) represents the function and its inverse of a function option (A) is correct.
<h3>What is a function?</h3>
It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
We have a function and inverse of a function shown in the picture.
Checking for option (A):

Taking f(x):

To find the inverse of a function interchange the x and y variables:
f(x) → x
x → g(x)

Solving:
4x = g(x) + 10
g(x) = 4x - 10
Similarly, we can find the inverse of a function.
Thus, option (A) represents the function and its inverse of a function option (A) is correct.
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Answer:
x = (1/2) (-9 ± √73)
Step-by-step explanation:
Using completing the square method
x²+9x+2=0
x²+9x = -2 (complete the square by adding (9/2)² to both sides)
x²+9x + (9/2)² = -2 + (9/2)²
( x + (9/2) )² = -2+ (9/2)²
( x + (9/2) )² = -2+ (81/4)
( x + (9/2) )² = 73/4
x + (9/2) = ± √(73/4)
x + (9/2) = ± √(73) / 2
x = -(9/2) ± √(73) / 2 (factorize out (1/2) )
x = (1/2) (-9 ± √73)
Answer:
L = 18 and w = 16
Step-by-step explanation:
The area of a rectangle is found by A = l*w. Since the length here is 2 more than the width or 2 + w and the width is w, substitute these values and A = 288 to solve for w.

To solve for w, move 288 to the other side by subtraction. Then factor and solve.

Set each factor equal to 0 and solve.
w - 16 = 0 so w = 16
w + 18 = 0 so w = -18
Since w is a side length and length/distance cannot be negative, then w = 16 is the width of the rectangle.
This means the length is 16 + 2 = 18.
Answer:

Step-by-step explanation:
So, we are given:

First, we should immediately rule out 0 as an answer. This is because the if
, the equation would be undefined.

Now, cross multiply.


Divide everything by x (and we can do this safely because we already know x cannot be equal to zero).


We didn't run into any possibilities for extraneous solutions.