The given function is
f(x) = 4x - 3/2
where
f(x) = number of assignments completed
x = number of weeks required to complete the assignments
We want to find f⁻¹ (30) as an estimate of the number of weeks required to complete 30 assignments.
The procedure is as follows:
1. Set y = f(x)
y = 4x - 3/2
2. Exchange x and y
x = 4y - 3/2
3. Solve for y
4y = x + 3/2
y = (x +3/2)/4
4. Set y equal to f⁻¹ (x)
f⁻¹ (x) = (x + 3/2)/4
5. Find f⁻¹ (30)
f⁻¹ (30) = (30 + 3/2)/4 = 63/8 = 8 (approxmately)
Answer:
Pedro needs about 8 weeks to complete 30 assignments.
Answer:
0.84 square in
Step-by-step explanation:
Since the capacity of the cable is proportional to its cross-sectional area. If a cable that is 0.3 sq in can hold 2500 lb then per square inch it can hold
2500 / 0.3 = 8333.33 lb/in
To old 7000 lb it the cross-sectional area would need to be
7000 / 8333.33 = 0.84 square in
Answer:
C. hyperbola; 
Step-by-step explanation:
The given conic has equation:

Divide through by 225.


This is a hyperbola centered at the origin.
The hyperbola has been translated from the origin to (0,5).
The translated hyperbola will have equation;

Multiply through by 225.

Expand


Rewrite in general form;


The second question:
Consider the division expression
. Select all multiplication equations that correspond to this division expression.


Answer:
1. See Explanation
2.
and 
Step-by-step explanation:
Solving (a):
Given


Required
Interpret
in 2 ways
<u>Interpretation 1:</u> Number of groups if there are 5 students in each
<u>Interpretation 2:</u> Number of students in each group if there are 5 groups
<u>Solving the quotient</u>


<u>For Interpretation 1:</u>
The quotient means: 12 groups
<u>For Interpretation 2:</u>
The quotient means: 12 students
Solving (b):
Given

Required
Select all equivalent multiplication equations
Let ? be the quotient of t 
So, we have:

Multiply through by 2


Rewrite as:
--- This is 1 equivalent expression
Apply commutative law of addition:
--- This is another equivalent expression
X is sugar
y is butter
z is total money
$0.80x + $1.25y = z
the total money spent if the Baker bought 6 pounds of butter and 20 pounds of sugar would be $23.50.