Answer:
f(x)=2x-1
Step-by-step explanation:
The output is f(x). The input is x.
The prompt says to multiply the input by 2, so 2x.
Then subtract 1 to get f(x).
Hope this helps!
Answer is : 6 4/6
in simplest form is : 6 2/3
Answer:
The rate of the plane is 862 miles per hour
Step-by-step explanation:
An airplane travels 6903 kilometers against the wind in 9 hours.
Speed = distance / time
Speed of the airplane while travelling against the wind is
6903/9 = 767 miles per hour
The airplane travelled 8613 kilometers with the wind in the same amount of time. This means that the speed while travelling with the wind will be
8613/9 = 957 miles per hour
Let x = speed of the airplane
Let y = speed of the wind
While travelling against the wind,
x - y = 767 - - - - - -- 1
While travelling with the wind,
x + y = 957 - - - - - - -2
Subtracting equation 2 from equation 1,
-y - y = 767 - 957
-2y = -190
y = -190/-2
y = 95 miles per hour
x = 957 - y
x = 957 - 95
x = 862 miles per hour
Answer:
(x + 1)² = 7
Step-by-step explanation:
Given:
-2x = x² - 6
We'll start by rearranging it to solve for zero:
x² + 2x - 6 = 0
The first term is already a perfect square so that's fine. Normally, if that term had a non-square coefficient, you would need to multiply all terms a value that would change that constant to a perfect square.
Because it's already square (1), we can simply move to the next step, separating the -6 into a value that can be doubled to give us the 2, the coefficient of the second term. That value will of course be 1, giving us:
x² + 2x + 1 - 1 - 6 = 0
Now can group our perfect square on the left and our constants on the right:
x² + 2x + 1 - 7= 0
x² + 2x + 1 = 7
(x + 1)² = 7
To check our answer, we can solve for x:
x + 1 = ± √7
x = -1 ± √7
x ≈ 1.65, -3.65
Let's try one of those in the original equation:
-2x = x² - 6
-2(1.65) = 1.65² - 6
- 3.3 = 2.72 - 6
-3.3 = -3.28
Good. Given our rounding that difference of 2/100 is acceptable, so the answer is correct.
Arc length from A to C (red line) is the given inside angle times 2, so AC = 50*2 = 100 degrees.
A full circle is 360 degrees, so arc ABC (blue line) would be 360 - 100 = 260 degrees.
The answer is D.
