Let x be the mass of the paperbacks and y be the mass of the textbook.
20x + 9y = 44.4 ----------- (1)
25x + 10y = 51 -------------(2)
(1) x 10:
200x + 90y = 444 --------(1a)
(2) x 9:
225x + 90y = 459 --------(2a)
(2a) - (1a):
25x = 15
x = 0.6 -------- sub into (1)
20 (0.6) + 9y = 44.4
12 + 9y = 44.4
9y = 44.4 - 12
9y = 32.4
y = 3.6
So the paperback's mass is 0.6 pounds and textbook is 3.6 pounds
Answer:
40 students
Step-by-step explanation:
In this problem, one is given the ratio ( 8 : 3 ), since a ratio is another way of writing a fraction one can rewrite it as;
(8) represent the number of students who want to learn about magnets, and (3) represents the number of students who want to learn about magic tricks.
In the problem, it is also given that 25 more students wanted to learn about magnets compared to magic tricks. If one uses the parameter (x) to represent the factor by which the fraction
is reduced, then one can get the equation;
8x = 3x + 25
Use inverse operations to solve,
8x = 3x + 25
-3x
5x = 25
/5
x = 5
Substitute back in to find out how many students want to learn about magnets,
8x
= 8(5)
= 40
Answer: 
Step-by-step explanation:
To solve this exercise you need to remember the following:
→ 
Therefore, keeping the above on mind, you can solve for x as following:


Remember that, by definition:
, then you have:

Subtract 6 from both sides of the equation.
Then the value of x is:

Answer:
The speed with which Ryan was rowing was 4 mph
Step-by-step explanation:
With a small boat, Ryan wants to row towards an island and come back at a speed of x mph and the island is 20 miles away from him.
Therefore, total 20 + 20 = 40 miles he rowed for 5 hours.
On the way to the island, there was a wind of 4 mph in the direction of his motion and on the way back also there was a wind of 4 mph in the direction of his motion.
So, in the total journey, he has a speed of (x + 4) mph.
Therefore,
⇒ x + 4 = 8
⇒ x = 4 mph.
Therefore, the speed with which Ryan was rowing was 4 mph. (Answer)
Answer:

Step-by-step explanation:
Given information: |a| = 80, |b| = 50, the angle between a and b is 3π/4.
We need to find the dot product a · b.
The formula of dot product is

where, θ is the angle between a and b.
Substitute the given values in the above formula.


![[\because \cos (\pi-\theta)=-\cos \theta]](https://tex.z-dn.net/?f=%5B%5Cbecause%20%5Ccos%20%28%5Cpi-%5Ctheta%29%3D-%5Ccos%20%5Ctheta%5D)


Rationalize the above equation.



Therefore, the value of a · b is
.