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Roman55 [17]
3 years ago
11

A circle has a diameter of 4 inches. A square has a side length of 4 inches. What is true about the areas of these two figures?

Math item stem image CLEAR CHECK The areas of the two figures are the same. The area of the circle is greater than the area of the square. The area of the square is greater than the area of the circle. More information is needed to solve the problem.
Mathematics
1 answer:
Nuetrik [128]3 years ago
4 0
The area of the square is greater than the circle: the area of the circle is pi(r)^2 while the area of the square is length times width. The area of the circle is about 12.5 while the area of the square is 16.
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The lengths of three sides of a quadrilateral are shown below:
julsineya [31]
Answers: 
Part A: 12y² + 10y – 21
Part B: 4y³ + 6y² + 6y – 5 
Part C: See below.

Explanations: 
Part A: 
For this part, you add Sides 1, 2 and 3 together by combining like terms:
Side 1 = 3y² + 2y – 6
Side 2 = 4y² + 3y – 7
Side 3 = 5y² + 5y – 8
3y² + 2y – 6 + 4y² + 3y – 7 + 5y² + 5y – 8
Combine like terms: 
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Part B: 
You have the total perimeter and the sum of three of the sides, so you just need that fourth side value, which we can call d.
P = 4y³ + 18y² + 16y – 26
Sides 1, 2 & 3 = 12y² + 10y – 21 
Create an algebraic expression: 
12y² + 10y – 21 + d = 4y³ + 18y² + 16y – 26
Solve for d: 
12y² + 10y – 21 + d = 4y³ + 18y² + 16y – 26
– 12y²                                – 12y²
10y – 21 + d = 4y³ + 6y² + 16y – 26 
– 10y                               – 10y
– 21 + d = 4y³ + 6y² + 6y – 26 
+ 21                                + 21 
d = 4y³ + 6y² + 6y – 5 

Part C: 
If closed means that the degree that these polynomials are at stay that way, then yes, this is true in these cases because you will notice that each side had a y², y and no coefficient value except for the fourth one. This didn't change, because you only add and subtract like terms.
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m =  \frac{y1 - y2}{x1 - x2}
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Which is equal to,
m = 3
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