9 / 16 + 1/2 =?
Step 1. To add fractions, they must share the same denominator. Here the denominators are 16 and 2. Since 16 is 8 times 2, multiply 1/2 by 8 to match denominators.
(1 * 8) / (2 * 8) = 8 / 16
Step 2. Add the numerators over the common denominator.
9/16 + 8/16 = (9+8) / 16 = 17 / 16
Step 3. Reduce the fraction if possible.
17/16 is already in simplest form. Therefore, 9/16 + 1/2 = 17/16
The equation given is –2x – 4 + 5x = 8, and the task is to find the value of x. To start, combine like terms and reorganize the equation:
-2x + 5x = 8 + 4
Next, simplify both sides:
3x = 12
Divide both sides by 3 to isolate x:
x = 4.
Therefore, the solution for x is 4.
A function and its inverse, when graphed, exhibit symmetry about the line y = x. Without viewing your graphs, I can't specify if g or h is the inverse. Identify the function that reflects f over the diagonal line y = x, which passes through the origin.
The distance from point Y to the flag post measures 38.13 m. Step-by-step explanation: Assuming point Y is located at the intersection of both lines shown. Point X is positioned 34 meters east of point Y. The flagpole at point X is observed at a bearing of N18°W, meaning it creates an angle of 18° to the west from the north at point X. Conversely, at point Y, the flagpole has a bearing of N40°E, which makes a 40° angle towards the east from the north.
Considering ∆ AXY as a right triangle, the angle FXY is established. Then, concerning ∆ BYX as another right triangle, the angle FYX is also determined. To find the third angle ∠YFX in triangle FYX, the angle sum property of triangles can be applied:
∠YFX + ∠FYX + ∠FXY = 180°
Thus, we have: ∠YFX + 50° + 72° = 180° leading to ∠YFX = 58°.
Now we can calculate the distance FY using the sine rule.
