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forsale [732]
3 years ago
9

Suppose C and D represent two different school populations where C > D and C and D must be greater than 0. Whitch of the foll

owing expressions is the largest? Explain why. A. (C+D)^2 B. 2(C+D) C. C^2 + D^2 D. C^2 - D^2
Mathematics
1 answer:
In-s [12.5K]3 years ago
7 0

Answer:

<em>A. (C+D)^2  is the largest expression</em>

Step-by-step explanation:

<u>Squaring Properties </u>

The square of a number N is shown as N^2 and is the product of N by itself, i.e.  

N^2=N*N

If N is positive and less than one, its square is less than N, i.e.

N^2

If N is greater than one, its square is greater than N

N^2>N, \ for\ N>1

We have the following information: C and D represent two different school populations, C > D, and C and D must be positive. We can safely assume C and D are also greater or equal than 1. Let's evaluate the following expressions to find out which is the largest

A. (C+D)^2

Expanding  

(C+D)^2=C^2+2CD+D^2

Is the sum of three positive quantities. This is the largest of all as we'll prove later

B. 2(C+D)

The extreme case is when C=2 and D=1 (recall C>D). It results:

2(C+D)=2(3)=6

The first expression will be

(3)^2=9

Any other combination of C and D will result smaller than the first option

C. C^2 + D^2

By comparing this with the first option, we see there are two equal terms, but A. has one additional term 2CD that makes it greater than C.

D. C^2 - D^2

The expression can be written as

(C+D)(C-D)

Comparing with A.

(C+D)^2=(C+D)(C+D)

The subtracting factor (C-D) makes this product smaller than A which has two adding factors.

Thus A. is the largest expression

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Answer:

12 days

Step-by-step explanation:

Set up an equation with y = mx + b, where m is the rate and b is the y-intercept (starting value)

Let x represent how many days it takes and y represent how many pages he read:

445 = 24x + 157

Solve for x:

288 = 24x

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3 years ago
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(3n-2)(4n+1)<br> how do i solve this by factoring?
Anni [7]

Answer:

12n^2-5n-2

The expression (3n-2)(4n+1) can be factored with the Distributive Property. It cannot be factored with a Least Common Multiple (LCM), for instance, because the terms within each set of parentheses are completely simplified.

Step-by-step explanation:

Part I

.1. (3n-2)(4n+1)\\2. F.O.I.L.: 12n^2+3n-8n-2\\3. Simplify: 12n^2-5n-2\\

Good luck to you!

8 0
3 years ago
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Answer:

0 ≤ x ≤ 70

Step-by-step explanation:

The range is defined by all values in the y-axe that are represented in the graph. In this case, we see the graph goes from 0 to 70, that will be the range.

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The volume of the cylinder above is 2,314.25, and the radius of the base is 8.9 Find the volume of the cone.
olga55 [171]

Answer: 771.41\ units^3

Step-by-step explanation:

The missing figure is attached.

The volume of an oblique cylinders and the volume of  a right cylinder can be found with this formula:

V_{cy}=\pi r^2h

Where "r" is the radius and "h" is the height.

The volume of an oblique cone and the volume of  a right cone can be found with this formula:

V_{co}=\frac{1}{3}\pi r^2h

Where "r" is the radius and "h" is the height.

According to the information given in the exercise, you know that the volume of the cylinder and also the radius of the cylinder and the cone ,are the following:

V_{cy}=2,314.25\ units^3\\\\r=8.9\ units

Therefore, in order to find the volume of the cone, you only need to multiply the volume of the cylinder by \frac{1}{3}.

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V_{co}=\frac{1}{3}(2,314.25\ units^3)\\\\V_{co}=771.41\ units^3

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