We know that
volume of <span>a rectangular prism =B*h------> equation 1
where
B is the area of the base
h is the height
volume of </span><span>a rectangular pyramid=(1/3)*B*h-----> equation 2
where
</span>B is the area of the base
h is the height
<span>
substitute equation 1 in equation 2
</span>volume of a rectangular pyramid=(1/3)*volume of a rectangular prism
<span>
the answer part a) is
</span>volume of a rectangular pyramid=(1/3)*volume of a rectangular prism
<span>
Part b) </span><span>If the pyramid was full of water, how much of the prism would it fill up?
</span>
the answer part b) is
<span>If the pyramid was filled with water, the prism would only fill 1/3 of its volume
Part c) </span><span>Name another pair of three-dimensional objects that have a relationship similar to this
cones and cylinders
</span>volume of a cylinder =B*h------> equation 1
where
B is the area of the base
h is the height <span>
</span>volume of a cone=(1/3)*B*h-----> equation 2
where
B is the area of the base
h is the height
substitute equation 1 in equation 2
volume of a cone=(1/3)*volume of a cylinder
Answer:
The product results in: 
, which agrees with answer A of the given choices.
Step-by-step explanation:
We need to apply distributive property for the product of two expressions each consisting of two terms, and also use the properties of products of radicals of the same root:
and now, we extract as many factors we can from the roots to reduce them:
Answer: x = 6 plus-or-minus 3 StartRoot 10
Step-by-step explanation:
The given quadratic equation is expressed as
x² - 12x + 36 = 90
Rearranging the equation so that it takes the the standard form of
ax² + bx + c, it becomes
x² - 12x + 36 - 90 = 0
x² - 12x - 54 = 0
The general formula for solving quadratic equations is expressed as
x = [- b ± √(b² - 4ac)]/2a
From the equation given,
a = 1
b = - 12
c = - 54
Therefore,
x = [- - 12 ± √(- 12² - 4 × 1 × - 54)]/2 × 1
x = [12 ± √(144 + 216)]/2
x = [12 ± √360]/2
x = (12 ± 6√10)/2
x = 6 + 3√10
Answer:
It is a perfect square trinomial.
Step-by-step explanation:
The square of a binomial can be solved like this:
We have the expression:
Then, we consider a and b as:
The solution would be:
