Answer:
x < 7
Step-by-step explanation:
First apply the -2 onto each term that it is being multiplied onto.
-2x + 6 > - 8
Now subtract six from both sides.
-2x > -14
Now divide by -2.
x < 7
<u>REMEMBER</u>
When doing greater than and less than equations like this, if you divide by a negative you must flip the greater than/less than.
Answer:
11 of 20p, 22 of 10p and 33 of 5p
Step-by-step explanation:
Eva has 20p, 10p and 5p coins, total of £6.05 = 605p
Let 20p=x, 10p=y, 5p=z
<u>Then</u>:
- 20x + 10y + 5z = 605
- y : x = 2 : 1 ⇒ x= y/2
- y : z = 2 : 3 ⇒ z= 3y/2
<u>Rewriting the first equation considering next two:</u>
- 10y + 10y + 7.5y = 605
- 27.5y = 605
- y= 605/27.5
- y= 22
- x= y/2 = 22/2 = 11
- z = 3y/2 = 3*11 = 33
<u>Answer:</u> 11 of 20p coins, 22 of 10p coins and 33 of 5p coins
a. Use the mean value theorem. 16 falls between 12 and 20, so
(Don't forget your units - 5 m/min^2)
b. 
gives the Johanna's velocity at time 
. The magnitude of her velocity, or speed, is 
. Integrating this would tell us the total distance she has traveled whilst jogging.
The Riemann sum approximates the integral as
If you're not sure how this is derived: we're given 5 sample points, so we can cut the interval [0, 40] into 4 subintervals. The lengths of each subinterval are 12, 8, 4, and 16 (the distances between each sample point), and the height of the rectangle approximating the area under the plot of is determined by the value of at each sample point, 200, 240, |-220| = 220, and 150.
c. Bob's velocity is given by 
, so his acceleration is given by 
. We have
and at 
his acceleration is 
m/min^2.
d. Bob's average velocity over [0, 10] is given by the difference quotient,
m/min
