Option D: 21 in is the base length of the triangular base.
Explanation:
Given that a triangular pyramid with a height of 9 inches has a volume of 63 cubic inches.
The height of the triangular base is 6 inches.
We need to determine the base length of the triangular pyramid.
The base length of the triangular pyramid can be determined using the formula,

Substituting
and
in the above formula, we get,

Simplifying the terms, we get,

Dividing both sides by 3, we have,

Thus, the base length of the triangular pyramid is 21 in
Hence, Option D is the correct answer.
Answer:
-13x+10
Step-by-step explanation:
(4x+5)(x-2)
Multiply each term in the first parenthesis by each term in the second (foil)
Step 1: Expand it by writing out each multiplication. I added a picture showing which order to do it. (go in order of green, red, blue, yellow.) (you can remember this as first, outside, inside, last.)
When you expand it'll look like: 4x⋅x+4x⋅-2-5x-5⋅-2
Step 2: Calculate product
4x⋅x+4x⋅-2-5x-5⋅-2 (for the 4x⋅x it would be written like
)
+4x⋅-2-5x-5⋅-2
+4x⋅-2-5x-5⋅-2 (4x⋅-2 becomes -8x) (multiply 4x times -2)
-8x-5x-5⋅-2
-8x-5x-5⋅-2 (-5⋅-2 becomes +10) (multiply -5 times -2)
-8x-5x+10
Step 3: collect like terms
-8x-5x+10 (-8x-5x becomes -13x) (-8x times -5x)
-13x+10 is the most simplified so it should be your final answer
Answer:
x = 7
x = -5
Step-by-step explanation:
Given
x² - 2x - 35 = 0
Consider the factors of the constant term (- 35) which sum to give the coefficient of the x- term (- 2)
The factors are - 7 and + 5, since
- 7 × 5 = - 35 and - 7 + 5 = - 2, thus
(x - 7)(x + 5) = 0
Equate each factor to zero and solve for x
x + 5 = 0 ⇒ x = - 5
x - 7 = 0 ⇒ x = 7
The value of given expression when m = 3 is 27
<h3><u>Solution:</u></h3>
Given expression is 
We have to evaluate the given expression for m = 3
To find for m is equal to 3, substitute m = 3 in given expression
From given expression,

Plug in m = 3 in above expression
------ eqn 1
We know that,
can be expanded as,

Applying this in eqn 1, we get

Simplify the above expression

Therefore, for m = 3 we get,

Thus value of given expression when m = 3 is found