Answer:
c
Step-by-step explanation:
Because
is 1 the equation turns into...
which equals...

and
is just c
Answer:
10.5 %
<u>Skills needed: Financial Math Essentials</u>
Step-by-step explanation:
1) First, before getting started, let's assume the price of the product is
. This variable will be used a lot throughout the problem (
).
2) Marking a price above means increasing the price in order to make money off of the purchased product. When raising something by
percent, the new price would be
.
---> In this case, the price increased by
percent.
This means that it would be: 
New price is: 
3) The shopkeeper is then offering a
percent discount off of this marked price. When offering a
percent discount price, the new price (with discount), expressed algebraically is: 
---> the expression above simplifies to 
In this case,
, 
---> 
This means that
, with discount, has been raised
.
10.5 % is the profit percent
(The profit percent being the final marked up price - purchased price)
General Idea:
(i) Assign variable for the unknown that we need to find
(ii) Sketch a diagram to help us visualize the problem
(iii) Write the mathematical equation representing the description given.
(iv) Solve the equation by substitution method. Solving means finding the values of the variables which will make both the equation TRUE
Applying the concept:
Given: x represents the length of the pen and y represents the area of the doghouse
<u>Statement 1: </u>"The pen is 3 feet wider than it is long"

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<u>Statement 2: "He also built a doghouse to put in the pen which has a perimeter that is equal to the area of its base"</u>

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<u>Statement 3: "After putting the doghouse in the pen, he calculates that the dog will have 178 square feet of space to run around inside the pen."</u>

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<u>Statement 4: "The perimeter of the pen is 3 times greater than the perimeter of the doghouse."</u>

Conclusion:
The systems of equations that can be used to determine the length and width of the pen and the area of the doghouse is given in Option B.

Answer:
B and E
Step-by-step explanation:
B = - 6, D = - 2, E = 2
d(B, D) = - 2-(-6)= - 2 + 6 = 4 units
d(D, E) 2 - (-2) = 2 + 2 = 4
Since, d( B, D) = d( D, E)
Therefore, Point D is 1/2 of the distance between B and E.