Find the area to this

What number must be added to the expression below to complete the square?

stiv31 [10]

D. 1/4

Explanation:

a perfect square is written in the form

$(x+a)^2 = x^2 + 2ax +a^2$ (1)

In our problem, we have this perfect square:

$x^2 - x + C$ (2)

with C being unknown. However, by comparing (1) and (2), we know that

$2a=-1$

So, we find

$a=-\frac{1}{2}$

and therefore, the missing term must be

$a^2 = \frac{1}{4}$

so the complete square is

$x^2 -x +\frac{1}{4}$

7 0

2 years ago

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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.

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

8 0

3 years ago

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HELP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

kobusy [5.1K]

Answer:

3 and 7

2 and 6

4 and 8

1 and 8

Step-by-step explanation:

8 0

2 years ago

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What is the estimate of 8244 in the hundreds

yanalaym [24]

Answer:

Step-by-step explanation: Go on answer.com if no one knows it on here. Hope this helps!!

7 0

2 years ago

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Acellus

Step2247 [10]

Answer:

57 cm²

Step-by-step explanation:

Surface area of the yellow prism = front + back + right + left + top

✔️Area of the front = L * W

L = 4 cm

W = 3 cm

Area of the front = 4*3 = 12 cm²

✔️Area of the back = L * W

L = 4 cm

W = 3 cm

Area of the back = 4*3 = 12 cm²

✔️Area of the right face = L * W

L = 4 cm

W = 3 cm

Area of the right face = 4*3 = 12 cm²

✔️Area of the left face = L * W

L = 4 cm

W = 3 cm

Area of the left face = 4*3 = 12 cm²

✔️Area of the top = L * W

L = 3 cm

W = 3 cm

Area of the top = 3*3 = 9 cm²

✅Total = 12 + 12 + 12 + 12 + 9 = 57 cm²

4 0

2 years ago