Answer:
52
Step-by-step explanation:
Simplify
-0.75x + 8 + 1.5x + 4.4
Collect like terms
(-0.75x + 1.5x) + (8 + 4.4)
Simplify
<u>0.75x + 12.4 </u>
Answer:
(x+1)^2+(y+1)^2=13
Step-by-step explanation:
Equation of a circle: (x – h)^2 + (y – k)^2 = r^2
center: (-1, -1)
radius: sqrt(6^2+4^2)/2=sqrt(52)/2=2sqrt(13)/2=sqrt(13)
Substitute those values in to get
(x+1)^2+(y+1)^2=13
Answer:
3c=273
c=91
2c= 212
C= 106
c= 91+ 106= 197
so they will need 197 canoes total
Why:
So first you have to determine a set variable to represent the number of canoes, I chose C. Then you make an equation to represent the number of canoes 273 people will use if they group into 3's, from this I got 3c=273. Solve for C and get 91.
The remainder of the group which is 485-273= 212 will use canoes in groups of 2's. To represent this, 2c=212. Solve for C and get 106. Combine 106 and 91 to get the total number of canoes.
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.
