1. A family is building a circular fountain in the backyard. The yard is rectangular and measures 14x by 19x and the fountain is going to be circular with a radius of 6x. Once the fountain is built, what will be the area of the remaining yard.
A. 230πx^2
B. 230x^2
C. 266x^2 – 6πx^2
D. 2x^2(133 – 18π)
2. A sports team is building a new stadium on a rectangular lot of land. The ot measures 8x by 12x and the field will be 3x by 6x. How much land will be left for the bleachers, restrooms, and other parts of the stadium?
A. 78x^2
B. 114x^2
C. 96x^2
D. 30x^2
3. Simplify the product using the distributive property.
(3p + 2) (5p - 1)
A. 15p^2 – 7p + 2
B. 15p^2 – 13 + 2
C. 15p^2 + 7p – 2
D. 15p^2 + 13p – 2
4. Simplify using a table.
(5w + 2) (8w + 5)
A. 40w^2 + 41w - 10
B. 40w^2 + 41w + 10
C. 40w^2 – 41w - 10
D. 40w^2 – 41w + 10
C
B
C
B
1. D - 2x^2(133-18pi)
2. A - 78x^2
3. C - 15p^2-13p+2
4. B - 40w^2 + 41w + 10
Which set is correct? •~•?
Hannah is correct
1. To find the area of the remaining yard, we need to subtract the area of the circular fountain from the total area of the rectangular yard.
The total area of the rectangular yard is given by the formula: Area = length * width
In this case, the length of the yard is 14x and the width is 19x. So the total area of the yard is: Area = 14x * 19x = 266x^2
The area of a circle is given by the formula: Area = π * radius^2
In this case, the radius of the fountain is 6x. So the area of the fountain is: Area = π * (6x)^2 = 36πx^2
To find the area of the remaining yard, we subtract the area of the fountain from the total area of the yard: Remaining Area = Total Area - Fountain Area = 266x^2 - 36πx^2
Therefore, the answer is C. 266x^2 – 36πx^2
2. To find the land left for the bleachers, restrooms, and other parts of the stadium, we need to subtract the area of the field from the total area of the rectangular lot.
The total area of the rectangular lot is given by the formula: Area = length * width
In this case, the length of the lot is 8x and the width is 12x. So the total area of the lot is: Area = 8x * 12x = 96x^2
The area of the field is given by the formula: Area = length * width
In this case, the length of the field is 3x and the width is 6x. So the area of the field is: Area = 3x * 6x = 18x^2
To find the land left for the bleachers, restrooms, and other parts of the stadium, we subtract the area of the field from the total area of the lot: Remaining Land = Total Area - Field Area = 96x^2 - 18x^2
Therefore, the answer is C. 96x^2
3. To simplify the product using the distributive property, we need to multiply each term in the first expression by each term in the second expression and then combine like terms.
(3p + 2) (5p - 1) = 3p * 5p + 3p * (-1) + 2 * 5p + 2 * (-1) = 15p^2 - 3p + 10p - 2
Combining like terms, we get: 15p^2 + 7p - 2
Therefore, the answer is C. 15p^2 + 7p - 2
4. To multiply using a table, we create a table with the two expressions and multiply corresponding terms.
We have:
| 5w + 2 | 8w + 5
-------------------------
5w | 25w^2 + 10w | 40w^2 + 25w
2 | 10w + 4 | 16w + 10
Now, we add the terms in each row and column:
25w^2 + 40w^2 + 10w + 16w + 10w + 25w + 4 + 10 = 65w^2 + 51w + 14
Therefore, the answer is A. 65w^2 + 51w + 14
1. A - wrong
2. C - wrong
3. B - wrong
4. A - wrong
How did you get your answers?
Where you just guessing?
No, why would I guess......
I am so sorry, I forgot.
1. A
2. C
3. B
4. A
I don't see any choices or any work
Surely you don't expect somebody to just go ahead and do this assignment for you , do you?
e.g. what steps would you take to answer the first one?