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3 years ago

Which type of function are the following equations?

Mathematics

1 answer:

AleksAgata [21]3 years ago

6 0

Answer:

1 quadric

2 linear

Step-by-step explanation:

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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.

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

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3 years ago

Read 2 more answers

The temperature is -2°C. If the temperature rises by 15°C, what is the new temperature?

Furkat [3]

Answer:

13 C

Step-by-step explanation:

15-2=13

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3 years ago

Find the slope pls thx

Lisa [10]

The gradient formula is (y2-y1)/(x2-x1) aka rise/run, where by (x1,y1) and (x2,y2) are two points on the line.

In this case, the gradient
= -5-(-2))/(2-(-2))
= -3/4

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3 years ago

1.12cm=______mm 2.124mm=_______cm 3.2cm=________mm 4.7mm=_______cm

sashaice [31]

Answer:

1. 11.2 mm

2. 0.2124cm

3. 32mm

4. 4.7cm

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3 years ago

Find the distance between J and K.

Viefleur [7K]

A graph can help you find the appropriate choice to be

... B. 8.49

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