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Juli2301 [7.4K]
3 years ago
7

Mr. Ross is building a square ball room with a square dance floor surround by carpet to the wall. The room has a side length of

3x-4, and the dance floor has a side length of 2x-6. Write an expression that represent how much carpet will Mr. Ross need for his ball room.
Mathematics
1 answer:
katovenus [111]3 years ago
6 0

Answer:

He will need (x+2)(x-2) units squared.

Step-by-step explanation:

Alright, so to solve this it is necessary to find the area of the room and subtract the area of the dance floor from it.

Fortunately, squares are a special case where we only need to... well square the side.

Therefore:

a =  {(3x - 4)}^{2}  -  {(2x - 6)}^{2}

Great. Difference of two squares.

{a}^{2}  -  {b}^{2}  = ( a+ b)(a - b)

Therefore:

a = (3x - 4  +  2x - 6) \\ (3x - 4  -  2x +6 )  \\  \\  a = (5x  - 10)(x + 2) \\ a = 5 {x}^{2}  - 20 \\ a =  {x}^{2}  - 4 \\ a = (x + 2)(x - 2)

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Seiji and Gavin both worked hard over the summer. Together they earned a total of $425. Gavin earned $25 more than Seiji.
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Answer:

Gavin earned $450

Step-by-step explanation:

If Seiji Earned $425 25+25=50

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3 years ago
Gustavo makes sparkling juice by mixing 3 cups of sparkling water with
schepotkina [342]

Answer:

20 cups of apple juice

Step-by-step explanation:

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3 years ago
Alex spends 14 days on vacation. He spends 4 out of the 14 days at the beach and half as many days visiting museums as he spends
zvonat [6]


4 days at the beach.*7 or 5* days of visiting museums.


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3 0
3 years ago
Which equation represents a line which is parallel to the line 6y - 5x = -6?
Pavel [41]

Answer:

5

Step-by-step explanation:

6y - 5x = - 6

6y = 5x - 6

If the num beside the x is not 5, then it's not a parallel line

5 0
2 years ago
The Oxy coordinate plane for two parallel lines a and a' has the equations 2x - 3y-1 = 0 and 2x - 3y + 5 = 0. respectively. Whic
Andru [333]

Answer:

Remember that a vector translation can be written as:

T(a, b)

And if we apply this to a random point, (x, y), the translation gives:

T(a, b)(x, y) = (x + a, y + b)

now, remember that a general line can be written as:

y = m*x + s

Then a point of that line can be written as: (x, m*x + s)

Then if we apply the translation to a point in the line, we get:

T(a, b)(x, m*x + s) = (x + a, m*x + s + b)

Here we have two lines:

2x - 3y - 1 = 0

2x - 3y + 5 = 0

First, let's rewrite both of these in the slope-intercept form:

y = (2/3)*x - 1/3

y = (2/3)*x + 5/3

Now let's assume that we apply a translation to the first line, that has points of the form (x,  (2/3)*x - 1/3), such that we want to get points of the form:

(x, (2/3)*x + 5/3).

Then we must have:

T(a, b)(x,  (2/3)*x - 1/3) = (x + a,  (2/3)*x - 1/3 + b) = (x, (2/3)*x + 5/3).

Then we need to solve:

(x + a,  (2/3)*x - 1/3 + b) = (x, (2/3)*x + 5/3).

This means that:

x + a = x

(2/3)*x - 1/3 + b = (2/3)*x + 5/3

From the first equation, we can see that a = 0

Now we can solve the second one to find the value of b.

(2/3)*x - 1/3 + b = (2/3)*x + 5/3

subtracting (2/3)*x in both sides, we get:

-1/3 + b = 5/3

b = 5/3 + 1/3

b = 6/3 = 2

b = 2

Then the vector translation is:

T(0, 2)

So it moves the whole line 2 units upwards.

7 0
3 years ago
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