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2 years ago

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Point GG is located at (-4,2)(−4,2) on the coordinate plane. Point GG is reflected over the xx-axis to create point G'G ′ . What

ordered pair describes the location of G'?G ′ ?

1 answer:

Taya2010 [7]2 years ago

7 0

Answer: (4,2)

Step-by-step explanation:

When a point is reflected over the x axis, only the x value changes to the opposite sign (positive or negative). The y value doesn’t change.

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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

<u>Statement 1: </u>"The pen is 3 feet wider than it is long"

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

------

<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>

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

------

<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>

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

------

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

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

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

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There are 7 cows and 5 chicken in the farmer's filed

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Answer:

7:12

Step-by-step explanation:

Total no of animals in the field = 7 + 5 = 12

Ratio of cows 2 all d animals in the field =

$\frac{no \: of \: cows}{total \: no \: of \: animals \: on \: the \: field}$

Ratio = 7/12 = 7:12

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3 years ago

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464 inches. Hope this helped! :)

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2 years ago

Mrs. Jones has a local bakery. Last week this expression shows how many peanut butter cupcakes she baked. 5 (2x -4) + 3(3 + 4x)

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Answer:

A. $22x-11$

B. $121$ cupcakes

Step-by-step explanation:

Part A:

The simplified form of the expression is

$5(2x-4)+3(3+4x)$

$(10x-20)+(9+12x)$

$(10x+12x)+(9-20)$

$22x-11$

Part B:

Put $x=6$ in the above simplified equation to get the number of cupcakes Mrs. Jones bake last week

$22x-11$

$22(6)-11$

$132-11$

$121$ cupcakes

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3 years ago