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.
Answer:
no question
Step-by-step explanation:
Answer:
scalene
Step-by-step explanation:
step 1
Find the value of y
we know that
The sum of the interior angles in a triangle must be equal to 180 degrees
In this problem
m∠A+m∠B+m∠C=180°
substitute the given values

Solve for y




step 2
<em>Find the measure of angle B</em>
m∠B=(y+40)°
substitute the value of y
m∠B=(15+40)=55°
step 3
<em>Find the measure of angle C</em>
m∠C=(3y-10)°
substitute the value of y
m∠C=(3(15)-10)=35°
The three interior angles are different
so
The three sides of the ABC triangle will also be different
therefore
The right triangle ABC is scalene
Answer:
1) (n+5)(n-1)
2) (n-4)(n+3)
3) (v-4)(v-1)
4) (p-4)(p+2)
5)(7x-10)(x+1)
6)(7n-1)(n-9)
Step-by-step explanation:
1) Factors of -5 that add up to 4
2) Factors of --12 that add up to -1
3) Factors of 4 that add up to -5
4) Factors of -5 that add up to 4
5) 7
-3x-10
7
+7x-10x-10
7x(x+1)-10(x+1)
(7x-10)(x+1)
6)7
-64n+9
7
-63n-n+9
7n(n-9)-(n-9)
(7n-1)(n-9)