Answer:
34
Step-by-step explanation:
Add them together
5x+10=180
5x+10-10=180-10
5x=170
5x/5=170/5
x=34
Answer:
2/7
Step-by-step explanation:
For the president position, there are 4 females from a total of 7 people.
For the vice president position, there are 3 males from 6 people left over.
So the probability is 4/7 × 3/6 = 2/7.
Answer:
16 students got an A
Step-by-step explanation:
Set up an equation to compare the ratio to the scores:
Cross multiply:
80 = 5x
Divide each side by 5:
x = 16
Now, check if
16/8 = 2
40/8 = 5
The ratios are the same! Therefore, 16 students got an A!
Hope this helps! Feel free to contact me if you have any questions :)
9514 1404 393
Explanation:
a) The velocity curve is linearly increasing from 0 to 6 m/s over a period of 2 seconds, then linearly decreasing from 6 m/s to 0 over the same period. The acceleration is the rate of change of velocity, so for the first half of the motion the acceleration is a constant (6 m/s)/(2 s) = 3 m/s². Similarly, over the second half of the motion, the acceleration is a constant (-6 m/s)/(2 s) = -3 m/s².
The distance traveled is the integral of the velocity, so the linearly increasing velocity will cause the distance vs. time curve to have a parabolic shape. The shape will likewise be parabolic, but with decreasing slope, as the velocity ramps down to zero. Overall, the distance versus time curve will have an "S" shape.
The motion (position and velocity) will be continuous, but the acceleration will not be. There will be a significant "j.erk" at the 2-second mark where acceleration abruptly changes from increasing the velocity to braking (decreasing the velocity).
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b) The attachment shows the (given) velocity curve in meters per second and its integral, the position curve, in meters.
The integral in the attached works nicely for machine evaluation. For hand evaluation, it is perhaps best written piecewise:
Answer: 18x + 12
Step-by-step explanation:
Step #1: Determine the length of each side.
The polygon is regular, so all the sides are equal. Thus, all sides measure 3x+2.
Step #2: Determine the number of sides in the polygon.
This polygon is identified as a hexagon meaning it consists of 6 sides.
Step #3: Set up an expression and distribute.
(Number of sides) x (Length of each side)
(6)(3x+2)
- 6 times 3x equals positive 18x
- 6 times 2 equals positive 12
So, the answer is 18x + 12.