Answer:
The Slope of both the lines is the same.
Step-by-step explanation:
Given two co-ordinates (x1, y1) and (x2, y2), the slope of a line can be found using the formula:
For the diagonal line of the first triangle, the coordinates are (0, 0) and (2, 1)
For the diagonal line of the large triangle, the coordinates are (2, 1) and (6, 3)
Answer:
The dimension of the base of the Rectangle Pyramid is Length = 10 and Width = 8/3
Step-by-step explanation:
Given
Rectangle Pyramid
Base Length = 3x + 1
Base Width = x
Height = 12
Volume = 96
Required
Dimension of the base of the pyramid
Given that the volume of the pyramid is ⅓ of the base area * the height.
This is represented mathematical as
Volume = ⅓ * base area * height.
Where
Base area = width * length
Base area = (3x + 1) * x
Base area = 3x² + x.
So,
Volume becomes
Volume = ⅓ * (3x² + x) * 12.
Volume = (3x² + x) * 4
Substitute 96 for volume
96 = (3x² + x) * 4
Divide both sides by 4
96/4 = (3x² + x) * 4/4
24 = 3x² + x
Subtract 24 fr both sides
24 - 24 = 3x² + x - 24
0 = 3x² + x - 24
3x² + x - 24 = 0
Expand
3x² + 9x - 8x - 24 = 0
Factorize
3x(x + 3) - 8(x + 3) = 0
(3x - 8)(x + 3) = 0
3x - 8 = 0 or x + 3 = 0
3x = 8 or x = -3
x = 8/3 or x = -3
Recall that
Length = 3x + 1
Width = x
For any of the above expression, x can't be less than 0; so, x = -3 can't be considered.
Substitute x = 8/3
Length = 3x + 1
Length = 3(8/3) + 1
Length = 8 + 1
Length = 9
Width = x
Width = 8/3
Hence, the dimension of the base of the Rectangle Pyramid is Length = 10 and Width = 8/3
Answer:
The radius of the sphere, to the nearest cm:
cm
Step-by-step explanation:
The surface area of a sphere is given by the formula
A = 4πr²
where r is the radius of the sphere.
Given
- The surface area of sphere A = 5024 cm²
The radius of the sphere can be determined such as
Plug in Surface Area of sphere = 5024, π = 3.14 in the formula
cm
Therefore, the radius of the sphere, to the nearest cm:
cm
Answer:
10 cm
Step-by-step explanation:
1 decimeter is equal to 10⁻¹ meters.
1 meter is equal to 10² centimeters. We can use a conversion fraction to find the centimeters corresponding to 10⁻¹ meters.
10⁻¹ m × (10²cm/1 m) = 10 cm
1 dm = 10⁻¹ m
10⁻¹ m = 10 cm
Due to the transitive property, 1 decimeter is equal to 10 centimeters.
