Answer:
True, see proof below.
Step-by-step explanation:
Remember two theorems about continuity:
- If f is differentiable at the point p, then f is continuous at p. This also applies to intervals instead of points.
- (Bolzano) If f is continuous in an interval [a,b] and there exists x,y∈[a,b] such that f(x)<0<f(y), then there exists some c∈[a,b] such that f(c)=0.
If f is differentiable in [0,4], then f is continuous in [0,4] (by 1). Now, f(0)=-1<0 and f(4)=3>0. Thus, we have the inequality f(0)<0<f(4). By Bolzano's theorem, there exists some c∈[0,4] such that f(c)=0.
First replace y with 15.
1/5x-10=30
Then just solve from there.
x=200
Answer: bottom left
4x+2y+15
Step-by-step explanation:
3x + x=4x
5 + 10= 15
2y=2y
4x+2y+15
Answer: The given question is solved :
Step-by-step explanation:
correct solution in imaje
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
