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2 years ago

Find the variable x in the figure if AB ll CD ll EF where c and d are the midpoints of AE and BF.

Mathematics

1 answer:

dangina [55]2 years ago

5 0

CD is called the middle base and is equal to :(AB + EF)/2

CD = (AB + EF)/2

4x = [(x²+10) + (8-x)]/2

8x = x²+10+8-x

8x= x²-x+18
x²-9x+18 = 0

x' = [-b+√(b²-4.a.c)]/2a & x" = [-b-√(b²-4.a.c)]/2a

x'= 6 and x" = 3, So we have2 values of x

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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

2 years ago

Bart uses 3/12 cup milk to make muffin. Write a fraction that is equivalent to 3/12

vichka [17]

Your fraction that is equal to 3/12 is 1/4

8 0

2 years ago

What is the ratio of 120%

Helga [31]

Answer:

5: 6

Step-by-step explanation:

becuase it was basically 100:120 but divide it by 20 and thats how you get 5;6

7 0

3 years ago

The perimeter of a square is 18 2. Determine the length of the diagonal.

Natalija [7]

The diagonal of the square is 9.1?

5 0

3 years ago

Can you answer these for me ?

vodka [1.7K]

Answer:

B. 4 3/8

Step-by-step explanation:

7/8 X 5 = 4 3/8

6 0

2 years ago