A tennis racquet bought for €95 was then sold for €132. Find the profit as a percentage of the cost

Polynomial expressions with matching

yuradex [85]

Answer:

The difference of 27x³ and 8y³ → [3x - 2y][9x² + 6xy + 4y²]

The difference of 27x³ and 64y³ → [3x - 4y][9x² + 12xy + 16y²]

The sum of 27x³ and 64y³ → [3x + 4y][9x² - 12xy + 16y²]

The sum of 27x³ and 8y³ → [3x + 2y][9x² - 6xy + 4y²]

Step-by-step explanation:

For the first two, we use the Difference of Cubes [(a³ - b³)(a² + 2ab + b²)] first by taking the cube root of the given expression to get our first factor[s]:

$\displaystyle 3x - 2y = \sqrt[3]{27x^3 - 8y^3} \\ 3x - 4y = \sqrt[3]{27x^3 - 64y^3}$

Then, use the acronym of SOAP {whether the next operations symbols will be negative or positive [SAME (your cube-rooted factor has an IDENTICAL OPERATION SYMBOL as your given expression), OPPOSITE (the first sign in your second factor in the second set of parentheses will be the opposite of what the sign in your given expression, which will be a plus sign), ALWAYS POSITIVE (the last sign in your second factor in the second set of parentheses will ALWAYS stay positive NO MATTER WHAT)]} to get the second factor:

Given: 27x³ - 64y³

[3x - 4y][9x² + 12xy + 16y²]

↑ ↑ ↑

same as opposite ALWAYS POSITIVE

given of given

Given: 27x³ - 8y³

[3x - 2y][9x² + 6xy + 4y²]

↑ ↑ ↘

same as opposite ALWAYS POSITIVE

given of given

Now, for the last two, we use the Sum of Cubes [(a³ + b³)(a² - 2ab + b²)] first by taking the cube root of the given expression to get our first factor[s]:

$\displaystyle 3x + 2y = \sqrt[3]{27x^3 + 8y^3} \\ 3x + 4y = \sqrt[3]{27x^3 + 64y^3}$

Then, use the acronym of SOAP {whether the next operations symbols will be negative or positive [SAME (your cube-rooted factor has an IDENTICAL OPERATION SYMBOL as your given expression), OPPOSITE (the first sign in your second factor in the second set of parentheses will be the opposite of what the sign is in your given expression, which will be a minus sign), ALWAYS POSITIVE (the last sign in your second factor in the second set of parentheses will ALWAYS stay positive NO MATTER WHAT)]} to get the second factor:

Given: 27x³ + 64y³

[3x + 4y][9x² - 12xy + 16y²]

↑ ↑ ↘

same as opposite ALWAYS POSITIVE

given of given

Given: 27x³ + 8y³

[3x + 2y][9x² - 6xy + 4y²]

↑ ↑ ↘

same as opposite ALWAYS POSITIVE

given of given

I am delighted to assist you anytime!

* As you can see, when using the Difference\Sum of Cubes, SOAP can vary depending on how an expression is given to you. They resemble each other though.

6 0

3 years ago

What is the perimeter of a lawn that is 25 feet long and 20 feet wide?

drek231 [11]

Answer:

a. 90 ft

Step-by-step explanation:

20+20+25+25

4 0

3 years ago

Read 2 more answers

If the endpoints of the diameter of a circle are (6, 3) and (2, 1), what is the standard form equation of the circle?

Anastasy [175]

If the endpoints of a diameter are (6,3) and (2,1) the midpoint is the center of the circle so:

(x,y)=((6+2)/2, (3+1)/2)=(4,2)

Now we need to find the radius....the diameter is:

d^2=(6-2)^2+(3-1)^2

d^2=16+4

d^2=20 since d=2r, r=d/2, and r^2=d^2/4 so

r^2=5

The standard form of the circle is (x-h)^2+(y-k)^2=r^2 and we know:

(h,k)=(4,2) from earlier so:

(x-4)^2+(y-2)^2=5

8 0

3 years ago

Convert into slope-intercept form: <img src="https://tex.z-dn.net/?f=y-1%3Dm%28x-3%29" id="TexFormula1" title="y-1=m(x-3)" alt="

aliina [53]

Answer:

y=2x-5

Step-by-step explanation:

First simplify: y-1=2x-6

y-1=2(x-3)

First simplify and distribute everything.

y-1=2x-6

So, x equals 2 because it got distributed into the numbers inside the parenthesis. Same with the 2 and -3. They multiplied to become -6.

Since it's y-1=2x-6, you can simplify it even more so the -1 goes to the other side and turns into positive 1.

y - 1 (+ 1) = 2x -6 (+ 1)

-1(+1)=0 which leaves just the variable y on the left side.

-6(+1)=-5 which leaves 2x-5 on the right side.

This results in y=2x-5. Hope this helped ;)

6 0

3 years ago

Read 2 more answers

The diagram the area of the large square is one square unit 2000 new segments divide a square into 4 equal sized triangles two o

sleet_krkn [62]

The answer is 0 because it cancels itself out

3 0

3 years ago