To find the area of the composite shape, we first need to determine what the shape looks like and then calculate the area.
Let's assume the shape is a rectangle with dimensions 3 and 5, with a semicircle attached to one side of the rectangle (with radius 2) on the 3 side.
The area of the rectangle is length * width = 3 * 5 = 15 square units.
The area of the semicircle is 1/2 * π * radius^2 = 1/2 * π * 2^2 = 2π square units.
Therefore, the total area of the composite shape is 15 + 2π square units.
What is the area of the composite shape?
Numbers are 3 5 6 and 2
11 answers
What is the side length of a triangle's base if the points were (4,2) and (4, 10)?
To find the length of the base of the triangle, we first need to calculate the distance between the two given points. Since the x-coordinates are the same (both 4), the base of the triangle will be the vertical distance between the y-coordinates of the two points.
The formula to calculate the distance between two points in a Cartesian plane is given by the distance formula:
d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
In this case, the two points are (4, 2) and (4, 10). The x-coordinates are the same, so we only need to calculate the difference in the y-coordinates:
d = sqrt((4 - 4)^2 + (10 - 2)^2)
d = sqrt(0^2 + 8^2)
d = sqrt(0 + 64)
d = sqrt(64)
d = 8
Therefore, the base of the triangle, which is the vertical distance between the two points, is 8 units.
The formula to calculate the distance between two points in a Cartesian plane is given by the distance formula:
d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
In this case, the two points are (4, 2) and (4, 10). The x-coordinates are the same, so we only need to calculate the difference in the y-coordinates:
d = sqrt((4 - 4)^2 + (10 - 2)^2)
d = sqrt(0^2 + 8^2)
d = sqrt(0 + 64)
d = sqrt(64)
d = 8
Therefore, the base of the triangle, which is the vertical distance between the two points, is 8 units.
Which expression is equivalent to 40 + 24
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(5 + 3)
8(5 + 3)
8(5 + 0)
64
*
(5 + 3)
8(5 + 3)
8(5 + 0)
64
Equivalent expression to 40 + 24 * (5 + 3) is 64.
To solve the original expression, we first solve the operation inside the parentheses:
5 + 3 = 8
Now, substitute 8 back into the original expression:
40 + 24 * 8
Next, perform the multiplication:
40 + 192
Finally, add 40 and 192:
40 + 192 = 232
Therefore, the equivalent expression to 40 + 24 * (5 + 3) is 232.
To solve the original expression, we first solve the operation inside the parentheses:
5 + 3 = 8
Now, substitute 8 back into the original expression:
40 + 24 * 8
Next, perform the multiplication:
40 + 192
Finally, add 40 and 192:
40 + 192 = 232
Therefore, the equivalent expression to 40 + 24 * (5 + 3) is 232.
Which of the following phrases DOES NOT describes the expression 8x + 4?
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Twice the sum of four times x and four
Four more than eight times x
The sum of eight times x and four
Eight times x increased by 4.
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Twice the sum of four times x and four
Four more than eight times x
The sum of eight times x and four
Eight times x increased by 4.
The phrase that DOES NOT describe the expression 8x + 4 is:
Twice the sum of four times x and four
Explanation:
- The expression 8x + 4 represents "Eight times x increased by 4."
- The expression can be rewritten as: 8 times x + 4.
- The phrase "Four more than eight times x" matches this expression.
- The phrase "The sum of eight times x and four" is also accurate since adding the two terms gives the expression.
- The phrase "Twice the sum of four times x and four" does not accurately describe the expression 8x + 4 as it implies that the sum is being multiplied by 2, rather than just the 8x term.
Twice the sum of four times x and four
Explanation:
- The expression 8x + 4 represents "Eight times x increased by 4."
- The expression can be rewritten as: 8 times x + 4.
- The phrase "Four more than eight times x" matches this expression.
- The phrase "The sum of eight times x and four" is also accurate since adding the two terms gives the expression.
- The phrase "Twice the sum of four times x and four" does not accurately describe the expression 8x + 4 as it implies that the sum is being multiplied by 2, rather than just the 8x term.
Select the three expressions equivalent to 6(y+2).
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2(y+6)+4y
6y+2
6y+12
3y+12+3y
8(y+2) - 2y
6y+8
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2(y+6)+4y
6y+2
6y+12
3y+12+3y
8(y+2) - 2y
6y+8
The three expressions that are equivalent to 6(y+2) are:
1. 6y+12
2. 8(y+2) - 2y
3. 6y+8
Explanation:
Starting from the original expression 6(y+2):
- 6(y+2) = 6y + 12 (Distributive property)
- 6(y+2) = 8(y+2) - 2y (Further simplification by expanding 8(y+2))
- 6(y+2) = 6y + 8 (Simplified version)
These three expressions correctly represent the original expression 6(y+2).
1. 6y+12
2. 8(y+2) - 2y
3. 6y+8
Explanation:
Starting from the original expression 6(y+2):
- 6(y+2) = 6y + 12 (Distributive property)
- 6(y+2) = 8(y+2) - 2y (Further simplification by expanding 8(y+2))
- 6(y+2) = 6y + 8 (Simplified version)
These three expressions correctly represent the original expression 6(y+2).
How many vertices does a rectangular pyramid have?
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4
5
6
8
*
4
5
6
8
A rectangular pyramid has 5 vertices.
Explanation:
A rectangular pyramid is a polyhedron with a rectangular base and four triangular faces that meet at a single point called the apex. The rectangular base of the pyramid has 4 vertices, and the apex adds one additional vertex, resulting in a total of 5 vertices for the rectangular pyramid.
Explanation:
A rectangular pyramid is a polyhedron with a rectangular base and four triangular faces that meet at a single point called the apex. The rectangular base of the pyramid has 4 vertices, and the apex adds one additional vertex, resulting in a total of 5 vertices for the rectangular pyramid.
1 answer