Here's the info for f(x): We are going to find the slope of the line and then write the equation for the line using one of the given points. The coordinate points we are given are (0, 0) and (2, 4). Using the slope formula:

gives us a slope equation of:

and the slope is 2. Using the point (0, 0) to write the equation of the line for f(x) looks like this in the slope-intercept form of the equation:

where m is the sloppe of 2 that we found and

and

are the coordinates of one of the points. It doesn't matter which one you choose; you will get the same answer whether you use (0, 0) or (2, 4): y-0=2(x-0) Distributing that 2 into the parenthesis and simplifying gives you the equation of y = 2x, or in our function notation, f(x) = 2x. Since f(x) is the first part of g(x), so far for g(x) we have that g(x) = 2x + k. Now we will do the same thing for g(x) that we did for f(x) as far as writing its equation down; we don't need to find the slope cuz the slope of g(x) is the function f(x). The equation for g(x), using the point (0, 2) (again, you could have used either point; I just picked (0, 2) cuz the other one has a decimal in it!): y - 2 = 2(x - 0). Distributing that 2 into the parenthesis gives you this: y - 2 = 2x - 0; y = 2x + 2. So 2 is your k value!
Answer:

Step-by-step explanation:
∠ABD is the sum of the angles ∠ABC and ∠CBD. In other words:

Substitute in known values:

And subtract. Hence:

In conclusion, ∠ABC measures 34°.
For this case we must solve the following system of equations:

We clear x of both equations:

We match:

We find the value of "x":

Thus, the solution of the system is:

Answer:

Answer:
19 cm
Step-by-step explanation:
Given :
Volume, V = 205 to the √3 = 205^√3
Height, h = 8.9
radius, r
Volume of cylinder:
V = πr²h
205 to the square root of 3 10094.275
company is designing a new cylindrical water bottle. The volume of the bottle will be 205 cm to the square root of 3 cm. The height of the water bottle is 8.9 cm. What is the radius of the water bottle?
10094.275 = π * r² * 8.9
10094.275 = 3.14 * 8.9 * r²
10094.275 = 27.946r²
r² = 10094.275 / 27.946
r² = 361.20643
r = √361.20643
r = 19 cm