A student taking a Calculus class makes the following statement: ”If f(1) > 0 and f(3) < 0, then there exists a number c, between 1 and 3 such that f(c) = 0.”
Is the statement true? If it’s true, explain why, if it is false, explain why, or give an example that disproves it.

Explanation:

Imagine that f(x) was a road without any gaps. The road can be straight or it can be curved somehow.

Now imagine that a horizontal line is the border between two countries. The country up north is the positive country and the southern country is negative.

f(1) > 0 means we're in the northern country since f(x) is positive here

then f(3) < 0 means we're now in the southern negative country

Somewhere along the road we must have crossed the border at least one time. This must be the case because the road does not have any gaps in it and we cannot teleport. This is what it means to be a continuous function. To draw a continuous curve, you cannot lift your pencil up.

So because f(x) transitions from positive to negative, this means f(x) = 0 at some point at least once. So that's why there exists a c such that f(c) = 0

12

step-by-step explanation:

a triangle's   full angle is 180 degrees so 180 - 156 = 24. 24/2=12

answer:   x*94 +688*6   = 267*100

94x+4128=26700    

94x=22572     /94

x=240.128

step-by-step explanation: mark as brainlest reallly need it thx