Alaina bought a square frame for her desk that has an area of 81 square inches. What is the perimeter of the frame? (answer should be a number only)

Answers

Answer 1
Answer:

Given:

Area of a square frame = 81 square inches.

To find:

Perimeter of the frame.

Solution:

Let length of each side of the frame = a inches.

Area of square frame is

Area=a^2

81=a^2

Taking square root on both sides,

\pm√(81)=a

\pm 9=a

Side length cannot be negative. So, a=9 inches.

Perimeter of frame is

Perimeter=4a

Perimeter=4(9)

Perimeter=36

Therefore, the perimeter is 36 inches.

Answer 2
Answer:

Final answer:

The perimeter of the frame is 36 inches.

Explanation:

To find the perimeter of a square, we need to know the length of its sides. Since the area of the frame is given as 81 square inches, we can find the length of one side by taking the square root of the area. The square root of 81 is 9, so each side of the frame measures 9 inches.

Since a square has four equal sides, we can find the perimeter by multiplying the length of one side by 4. Therefore, the perimeter of the frame is 9 inches x 4 = 36 inches.

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A ten-foot-long board is cut into three pieces. The second piece is half as long as the first. The third piece is 4 feet longer than the second. How long is the first piece?

Answers

Let's say the second piece is x ft long
The first piece is 2x ft long
The third piece is x+4 ft long
All of the pieces should add up to 10ft
x+2x+x+4=10
4x= 6
x=1.5ft
The first piece is 2x ft long=3 ft long

What is the positive solution of x2 – 36 = 5x?

Answers

Answer:

The positive solution is x=9

Step-by-step explanation:

Given the equation

x^2-36=5x

we have to find the positive solution of above equation.

Equation: x^2-5x-36=0

By splitting middle-term method

x^2-5x-36=0

x^2-9x+4x-36=0

x(x-9)+4(x-9)=0

(x+4)(x-9)=0

x+4=0, x-9=0

The solution is x=-4 and x=9

Hence, the positive solution is x=9

The range of the function f(x) = x + 5 is {7, 9}. What is the function’s domain?

Answers

f(x) = x + 5

R = {7; 9}

therefore

x + 5 = 7 nd x + 5 = 9
x = 2 and x = 4

Answer: {2; 4}

PLS HELP ASAP Consider a standard deck of 52 playing cards with 4 suits. If A is the event of drawing a 6 from the deck, and B is the event of drawing a black playing card from the deck, what is the intersection of A and B? (Remember that the black cards are spades and clubs.) A) drawing a 6, a club, or a spade B) drawing the 6 of hearts or the 6 of diamonds C) drawing a 6, a heart, or a diamond D) drawing the 6 of clubs or the 6 of spades

Answers

Answer:

Correct answer is option D) drawing the 6 of clubs or the 6 of spades

Step-by-step explanation:

Given that:

A standard deck of 52 playing cards with 4 suits.

A be the event of drawing a card with 6 from the deck.

B be the event of drawing a black card from the deck.

So, event A will have 4 possibilities i.e. {6 of club, 6 of spade, 6 of diamond, 6 of heart}

And event B will have 26 possibilities {Any card (including 6) from club or spade}

Intersection of two sets is defined as the common elements in the two sets.

As per the explanation of the sets and elements in the sets given above:

If we take intersection it will be:

{6 of club or 6 of spade}

Hence, Correct answer is option D) drawing the 6 of clubs or the 6 of spades

Final answer:

The intersection of events A and B is represented by drawing the 6 of clubs or the 6 of spades (D) .

Explanation:

The intersection of events A (drawing a 6) and B (drawing a black playing card) refers to the cards that satisfy both criteria. In this case, event A consists of the card 6 from any suit, while event B consists of the black cards (spades and clubs) from any value. To determine the intersection, we need to find the cards that are both a 6 and black.

Looking at the options given, option D) drawing the 6 of clubs or the 6 of spades represents the cards that satisfy both events. The 6 of clubs and the 6 of spades are black cards and also have a value of 6. Therefore, the intersection of events A and B is represented by option D).

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Wendy is arranging books on the bookshelves in the school library. The total number of books she arranges is given by the equation b = 12r, where b is the total number of books and r is the number of rows. Each row contains the same number of books.If Wendy arranged 16 rows, she arranged a total of
books.

Answers

Given:
b = 12r 
where:
b =  represents the total number of books
12 = number of books per row
r = number of rows

If Wendy arranged 16 rows, she arranged a total of ___ books.

b = 12r
b = 12(16)
b = 192 total number of books arranged.
you would do 16x12 which is 192

Find the absolute value of the complex number -3 - 6i.a.
6.07
c.
6.7
b.
6.17
d.
6.71


Please select the best answe

Answers

Answer: 6.71


Explanation:


1) The absolute value of a complex number a + bi is √ [ (a)² + (b)²]

2) The given number - 3 - 6i is equivalent to (-3) + (-6)i, so you see that a = -3 and b = - 6.

3) Therefore, the absolute value is √ [ (-3)² + (-6)² ] = √ [ 9 + 36] = √(45) ≈ 6.708 ≈ 6.71