Which best describes the linear association shown in the scatter plot?

Patrick has just finished building a pen for his new dog. The pen is 3 feet wider than it is long. He also built a doghouse to p

zalisa [80]

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

Statement 1: "The pen is 3 feet wider than it is long"

$Length \; of\; the \; pen = x\\ Width \; of\; the\; pen=x+3$

------

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"

$Area \; of\; the\; Dog \; house=y\\ Perimeter \; of\; Dog\; house=y$

------

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."

$Area \; of \; the\; Pen - Area \;of \;the\;Dog \;House=\;Space\;inside\;Pen\\ \\ x \cdot (x+3)-y=178\\ Distributing \;x\;in\;the\;left\;side\;of\;the\;equation\\ \\ x^2+3x-y=178\Rightarrow\; 1^{st}\; Equation\\$

------

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

$Perimeter\; of\; the\; Pen=3\; \cdot \; Perimeter\; of\; the\; Dog\; House\\ \\ 2(x \; + \; x+3)=3 \cdot y\\ Combine\; like\; terms\; inside\; the\; parenthesis\\ \\ 2(2x+3)=3y\\ Distribute\; 2\; in\; the\; left\; side\; of\; the\; equation\\ \\ 4x+6=3y\\ Subtract \; 6\; and \; 3y\; on\; both\; sides\; of\; the\; equation\\ \\ 4x+6-3y-6=3y-3y-6\\ Combine\; like\; terms\\ \\ 4x-3y=-6 \Rightarrow \; \; 2^{nd}\; Equation\\$

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.

$178=x^2+3x-y\\ \\ -6=4x-3y$

8 0

3 years ago

Read 2 more answers

The half life of a radioactive kind of cadmium is 14 years. How much will be left after 28 years, if you start with 72 grams of

nlexa [21]

Answer:

18 grams

Step-by-step explanation:

8 0

2 years ago

Twice the complement of an angle is 24 degrees less than its supplement. What is the measure of the angle?

Artyom0805 [142]

Answer:

2(90-x)=180-x-24

solve this

180-2x=156-x

solve the rest on your own

Hope it helps!

7 0

2 years ago

If you drive 9hours and 465 kilometers how long would it take you to drive 768 kilometers

romanna [79]

I think it would be 13 hours possibly

8 0

3 years ago

Find the 12th and 37th term for each arithmetic sequence.

shutvik [7]

Answer:

3. f(12) = -10; f(37) = -60

4. f(12) = -102; f(37) = -352

Step-by-step explanation:

3. Put the numbers in the formula and do the arithmetic:

f(12) = 12 -2(12-1) = 12 -22 = -10

f(37) = 12 -2(37-1) = 12 -72 = -60

__

4. The explicit formula for an arithmetic sequence with first term a1 and common difference d is ...

an = a1 +d(n -1)

Your sequence has a first term a1=8 and a common difference d=-10.

As above, fill in the numbers and do the arithmetic.

f(12) = 8 -10(12 -1) = -102

f(37) = 8 -10(37-1) = -352

5 0

3 years ago