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3 years ago

Find the prime factorization for 24

Mathematics

2 answers:

Ad libitum [116K]3 years ago

8 0

should be 2^3*3 because:

24=12*2=3*2*2*2, so 2^3*3

GarryVolchara [31]3 years ago

4 0

The prime factorization for 24 is 2 x 2 x 2 x 3.

With exponents, it is written as 2^3 x 3.

Hope this helped!

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The combined area of a square and a rectangle is 225 square yards. the length of the rectangle is 8 times the width of the recta

snow_lady [41]

Answer:

The rectangle: L = 40 yards. W = 5 yards

The square: The length and width are both 5 yards.

Step-by-step explanation:

Let L and W be the length and width of the rectangle.

Let l and w be the length and width of the square.

Area for each is:

Rectangle: L*W

Square: l*w

We are told that L*W + l*w = 225 yards^2

We are also told that

L = 8W

and that

l = W

Since the sides of a square are all equal, w is also W: w=W

Summarizing and substituting:

L*W + l*w = 225 yards^2

(8W)*W + W*W = 225 yards^2

8W^2 + W^2 = 225 yards^2

9W^2 = 225 yards^2

W^2 = 25

W = 5 feet

---------------------

Therefore, since L = 8W , L = 40 yards. W = 5 yards for the rectangle.

The square: l=W, so l = 5 yards, and thus w=5 yards

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Check:

Do a rectangle of 40' x 5' plus a square of 5' x 5' have a total combined area of 225 yards^2?

40yd x 5yd + 5yd x 5yd = 225 yards^2?

200 yd^2 + 25 yd^2 = 225 yards^2?

YES

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2 years ago

The inequality of the most people that can be seated in the auditorium

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Let x be the number of people that can be seated.

The value of x is some number 0 or greater, such that this number is a whole number (we can't have half a person). This means that $x \ge 0$ which is the same as saying $0 \le x$

The instructions state that we can seat up to 1200 people. This is the max capacity. We can't go over this amount. So we will also have $x \le 1200$ indicating that x can be less than 1200 or equal to 1200.

So putting the two inequalities together, we get $0 \le x \le 1200$

Note: if you haven't learned about compound inequalities yet, then the teacher may only want $x \le 1200$ as the answer.

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NeX [460]

Answer:

C, 6

Step-by-step explanation:

31-13 is 18, 18/3 is 6.

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ASHA 777 [7]

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Step-by-step explanation:

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1. What are foci? 2. What is the first step to take to write the equation of a hyperbola? 3. How do you represent parts of a hyp

Andrei [34K]

Answer: see below

Step-by-step explanation:

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b) what is the center (h, k) of the hyperbola?

c) What is the slope of the asymptotes of the hyperbola?

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(h, k) is the center of the hyperbola
± b/a is the slope of the line of the asymptotes
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3 years ago