Step-by-step explanation:
x = number of true/false questions
y = number of multiple choice questions
x + y = 40
2x + 3y = 144
from the first equation we get
x = -y + 40
this identity we can then use in the second equation
2(-y + 40) + 3y = 144
-2y + 80 + 3y = 144
y + 80 = 144
y = 64
and
x + 64 = 40
x = -24
that does not make any sense.
something is wrong with the problem description.
just think about it :
40 questions - if all of them would be multiple choice tests (creating the max. possible points for 40 questions), we could have only 40×3 = 120 points.
but the description says 144 points.
for 144 points we need at least 48 (144/3) questions.
that does not fit.
the described system does not have any natural number solution. therefore we are getting such crazy numbers as result, when we try.
The only way to write 42 as the product of primes (except to change the order of the factors) is 2 × 3 × 7. We call 2 × 3 × 7 the prime factorization of 42.
Answer: 160 miles
Step-by-step explanation:
Given that :
Miles ran = r ; at the speed of 5 miles per hour
Miles biked = b ; at the speed of 10 miles per hour
Total miles biked and ran = 200 miles
If she biked for twice as many hours as she ran
Let hours
Total number of miles Morgan biked
r + b = 200 - - - (1)
From speed = distance / time
Hours biked = distance / speed = b / 10
Hours ran = distance /speed = r / 5
b/ 10 = 2 (r/5)
b / 10 = 2r / 5
Cross multiply
5b = 20r
b = 4r
Substitute into (1)
r + b = 200
r + 4r = 200
5r = 200
r = 200/5
r = 40 miles
Total number of Miles biked ;
r + b = 200
40 + b = 200
b = 200 - 40
b = 160 miles
To solve this problem you must apply the proccedure shown below:
1. You have:
<span>
In(2x+3)=7
2. Then, you must apply log(e), as below:
</span><span>
In(2x+3)=ln(e^7)
3. Now, you obtain:
2x+3=e^7
4. Youy must clear the variable "x", as below:
2x=e^7-3
</span> x=(e^7-3)/2
<span>
5. Therefore, the value of "x" is:
x=546.817
</span><span>
The answer is: </span>x=546.817<span> </span>