Answer:
C. 4x = 12
Step-by-step explanation:
You and three friends= you + 3 friends=4 people
Pizza= 12 pieces
Each person eats equal pieces of pizza
x= number of pieces each person ate
Equation
4x=12
Divide both sides by 4
x=12/4
=3
x=3
Therefore, each person ate 3 pieces of pizza each
Check:
4x=12
4(3)=12
12=12
9514 1404 393
Answer:
a) w(4w-15)
b) w²
c) w(4w -15) = w²
d) w = 5
e) 5 by 5
Step-by-step explanation:
a) If w is the width, and the length is 15 less than 4 times the width, then the length is 4w-15. The area is the product of length and width.
A = w(4w -15)
__
b) If w is the side length, the area of the square is (also) the product of length and width:
A = w²
__
c) Equating the expressions for area, we have ...
w(4w -15) = w²
__
d) we can subtract the right side to get ...
4w² -15w -w² = 0
3w(w -5) = 0
This has solutions w=0 and w=5. Only the positive solution is sensible in this problem.
The side length of the square is 5 units.
__
e) The rectangle is 5 units wide, and 4(5)-15 = 5 units long.
The rectangle and square have the same width and the same area, so the rectangle must be a square.
Answer:
True
Step-by-step explanation:
A number and its reciprocal have the same sign.
The cosecant is the reciprocal of the sine.
Therefore, the cosecant has the same sign as the sine.
Part (a)
<h3>Answer: 0.2</h3>
----------------------------------
Work Shown
It costs $15 to rent a bike for 3 hours. We can write the following ratio below
15 dollars : 3 hours
To represent the connection of the two concepts (dollars connecting with hours)
We want the "15 dollars" to turn into "1 dollar". This is because the phrasing "per dollar" really means "per 1 dollar".
Divide both sides of the ratio by 15 to achieve this goal.
15 dollars : 3 hours
15/15 dollars : 3/15 hours
1 dollar : 1/5 hours
1 dollar : 0.2 hours
0.2 hours : 1 dollar
So we get 0.2 hours per dollar.
As a side note, 0.2 hours = 0.2*60 = 12 minutes.
========================================================
Part (b)
<h3>Answer: 3.38</h3>
----------------------------------
Work Shown
27 pages : 8 minutes
27/8 pages : 8/8 minutes
3.375 pages : 1 minute
3.38 pages : 1 minute
I'm dividing both parts of the original ratio by 8 to turn "8 minutes" into "1 minute" (due to the phrasing "per minute"). Don't forget to round to 2 decimal places.
Answer:
= A(t) = 120000(1.06)^t t = 1 year
We just add ^12 to equal 1/12 months.
Then use the notation below.
Step-by-step explanation:
We simply want to write an equivalent form of the same equation that will allow for the time period to be calculated in years.
For one year, t = 1, we want it to grow 6% = 1.06
Yearly Rate of Growth annual equation: = 7200
P(i) 7200/ 120000 x 100% = 6% per year growth rate
the yearly growth factor is 1 + appreciation rate = 1+i =1+0.06= 1.06
So time in years can be added to t
= A(t) = 120000(1.06)^t t = 1 year
The yearly growth factor = 1.06
To equate monthly we add the exponent t*12*1/12 before 120000(1.06)^t
then add 1/12 to replace ^t = monthly, or just keep the t= time
A(t) = 120000(1.06)^12t
