Answer:
x = 5m/s
Step-by-step explanation:
Distance flying out = 12 km (headwind)
Distance flying back = 12 km (tailwind)
total distance = 12 + 12 =24 km
wind speed = 1km/h
speed going out (with headwind) = (x - 1) km/h
speed coming back (with tailwind) = (x + 1) km/h
Time taken to go out = distance going out / speed going out
= 12 / (x-1)
Time taken to come back = distance coming back / speed coming back
= 12 / (x+1)
total time = time taken to go out + time taken to come back
5 =[ 12/(x-1) ] + [ 12/(x-1)]
expanding this, we will get
5x² - 24x - 5 = 0
solving quadratic equation, we will get
x = -1/5 (impossible because speed cannot be negative)
or
x = 5 (answer)
Answer:
The equation in slope-intercept form for the path of the trumpet players is
.
Step-by-step explanation:
Consider the provided information.
The drummers will march along the line y=-5x-8.
The trumpets players will march along a perpendicular line that passes through (-2,2).
The slope of line y=-5x-8 is: m₁ = -5.
The slope of perpendicular lines are: 


Hence, the slope of the line should be 1/5.
The line passes through (-2,2).
Now use point slope form to find the equation of line.

Substitute m=1/5, x₁=-2 and y₁ = 2 in above formula.




Hence, the equation in slope-intercept form for the path of the trumpet players is
.
Answer: Fraction= 3 3/4kg
Decimal= 3.75kg
Step-by-step explanation:
15 kilograms of rice are separated equally into 4 containers. To get the number of kilograms of rice are in each container, we divide the total kilograms of rice by the number of containers. This will be:
Kilograms of rice in each container=
15/4 =3 3/4kg as a fraction.
To convert the fraction to decimal, we divide 3 by 4 and add to 3. 3/4 equals 0.75. We then add 3 to 0.75. This will be:
Decimal of 3 3/4 = 3+0.75 = 3.75kg
<u>Answer:</u>
x = 4 (extraneous solution)
<u>Step-by-step explanation:</u>

This solution is extraneous. Reason being that even if it can be solved algebraically, it is still not a valid solution because if we substitute back
, we will get two fractions with zero denominator which would be undefined.
So for this, this can be written into the equation

(x = number of months, y = total cost).
To solve this problem, we need to plug in 1325 into the y-variable and solve from there.

Subtract 35 on each side to get

Then just divide by 50 on each side, and your answer should be

And because we cannot go past budget, we will have to round down to 25.
In context, the maximum amount of months Abbey can do is 25 months.