Answer:
Step-by-step explanation:
So we have the equation:
First, separate the second term:
Let u equal 5ˣ. So:
Combine like terms:
Divide both sides by 6:
Substitute back u:
Take the base 5 logarithm of both sides:
The left cancels:
Evaluate the right:
So, our answer is 2.
And we're done!
Answer:
A) 24 ft³
Step-by-step explanation:
The area of the right triangle base is ...
A = (1/2)(3)(4) = 6 ft²
The volume of the triangular prism is the product of the area of its base (6 ft²) and its height (4 ft).
V = Bh = (6 ft²)(4 ft) = 24 ft³ . . . . matches choice A
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<em>Comment on the triangle</em>
You know the 3-4-5 triangle is a right triangle, because you have seen those numbers many times in relation to the Pythagorean theorem. If you don't know that, then you can check to see by using the Pythagorean theorem:
5² = 3² +4²
25 = 9 + 16 . . . . . true; so the triangle is a right triangle
In any event, there are other means for finding the area of the triangle based on the lengths of its sides. You will get the same area result.
Using Heron's formula, s = (a+b+c)/2 = (3+4+5)/2 = 6.
A = √(s(s -a)(s -b)(s -c)) = √(6(3)(2)(1)) = √36 = 6 . . . . area of base triangle
Answer:
<u>-22</u>
Step-by-step explanation:
When you multiply a positive and negative number together, it becomes negative.
Multiplication is repetitive addition.
11(-2) = -11 + -11 = -22
Answer:
The coordinates of B is (-5, 4).
