What is the simplest form of 145 over 261

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"

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

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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"

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

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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."

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

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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

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Which statement about g(x)=x^2-576 is true

goldenfox [79]

We can answer without the picture or answer options

5 0

3 years ago

Berry Delicious is a popular shop that sells chocolate-covered strawberries. Last year, the shop used 5,900 kilograms of strawbe

Ugo [173]

The answer is 25%, the others are wrong

8 0

3 years ago

Don’t solve just write the equation!!!

erastovalidia [21]

Answer:

2(x - 4) = 16

8 0

2 years ago

2 5/8 ×3 1/7 What's the answer for this ?

nikdorinn [45]

Answer:

$8 \frac{1}{4}$

Step-by-step explanation:

Let us solve

$2 \frac{5}{8} \times 3 \frac{1}{7} \\ \frac{21}{8} \times \frac{22}{7} \\ \frac{462}{56} \\ \frac{462 \div 2}{56 \div 2} \\ \frac{231}{28} \\ \frac{231 \div 7}{28 \div 7} \\ \frac{33}{4} \\ 8 \frac{1}{4}$

hope this helps you.

Please let me know if you have another questions :-)

5 0

2 years ago

Read 2 more answers