In parallelogram ABCD , diagonals AC¯¯¯¯¯ and BD¯¯¯¯¯ intersect at point E, BE=2x2−x , and DE=x2+6 . What is BD ?
2 answers:
Refer to the diagram shown below.
BE = 2x² - x
DE = x² + 6
The intersecting diagonals bisect one another.
Therefore BE = DE, so that
2x² - x = x² + 6
x² - x - 6 = 0
Factorize.
(x + 2)(x - 3) = 0
x = -2, or x = 3.
When x = -2,
BE = 2(-2)² - (-2) = 10
DE = (-2)² + 6 = 10
Therefore BD = 20
When x = 3;
BE = 2(3²) - 3 = 15
DE = 3² + 6 = 15
Therefore BD = 30
Answer: Either 20 or 30.
BE = 2x² - x
DE = x² + 6
The intersecting diagonals bisect one another.
Therefore BE = DE, so that
2x² - x = x² + 6
x² - x - 6 = 0
Factorize.
(x + 2)(x - 3) = 0
x = -2, or x = 3.
When x = -2,
BE = 2(-2)² - (-2) = 10
DE = (-2)² + 6 = 10
Therefore BD = 20
When x = 3;
BE = 2(3²) - 3 = 15
DE = 3² + 6 = 15
Therefore BD = 30
Answer: Either 20 or 30.
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Answer:
The proportion of the volume of the cone to the volume of the pyramid is: 3.14 times bigger.
Step-by-step explanation:
<u>Given the information of the cone: </u>
- The height: 12 inches
- The radius of the base is : 10/2= 5 inches
=> the volume of the cone
= 1/3π
= 1/3*3.14*
= 314 cubic inches
<u>Given the information of the pyramid: </u>
- the height: 12 inches
- The base is a suqare with a side lengh = 5 inches
=> the volume of the pyramid:
= 1/3*Bh (where B is the area of the base)
= 1/3*5*5*12
= 100 cubic inches
<u>The proportion of the volume of the cone to the volume of the pyramid is: </u>
= 314 /100
= 3.14 times bigger.
Hope it will find you well