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1 year ago

4x^2 - y^2 - 2x- y Factorise each of the following expressions completely

Mathematics

1 answer:

Sergeu [11.5K]1 year ago

3 0

Answer:

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

Step-by-step explanation:

4x² - y² - 2x - y

4x² - y² is a difference of squares and factors in general as

a² - b² = (a - b)(a + b) , then

4x² - y²

= (2x)² - y²

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

expression is now

(2x - y)(2x + y) - (2x + y) ← factor out (2x + y) from each term

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

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Parking spaces at a business school are arranged by a random monthly lottery. there are 3 spaces for every 10 students who want

Alexus [3.1K]

27.034%
Let's define the function P(x) for the probability of getting a parking space exactly x times over a 9 month period. it would be:
P(x) = (0.3^x)(0.7^(9-x))*9!/(x!(9-x)!)
Let me explain the above. The raising of (0.3^x)(0.7^(9-x)) is the probability of getting exactly x successes and 9-x failures. Then we shuffle them in the 9! possible arrangements. But since we can't tell the differences between successes, we divide by the x! different ways of arranging the successes. And since we can't distinguish between the different failures, we divide by the (9-x)! different ways of arranging those failures as well. So P(4) = 0.171532242 meaning that there's a 17.153% chance of getting a parking space exactly 4 times.
Now all we need to do is calculate the sum of P(x) for x ranging from 4 to 9.

So
P(4) = 0.171532242
P(5) = 0.073513818
P(6) = 0.021003948
P(7) = 0.003857868
P(8) = 0.000413343
P(9) = 0.000019683
  And
0.171532242 + 0.073513818 + 0.021003948 + 0.003857868 + 0.000413343
+ 0.000019683 = 0.270340902
So the probability of getting a parking space at least four out of the nine months is 27.034%

5 0

3 years ago

What is more accurate, mean or average? Explain why.

Airida [17]

It can be viewed different to what is more accurate depending on the relation of this question to another.

3 0

2 years ago

What are the potential solutions of In(x^2-25)=0?

Maslowich

Answer:

$x =\pm \sqrt{26}$

Step-by-step explanation:

Given :-

ln ( x² - 25 ) = 0

And we need to find the potential solutions of it. The given equation is the logarithm of x² - 25 to the base e . e is Euler's Number here. So it can be written as ,

Equation :-

$\implies log_e {(x^2-25)}= 0$

In general :-

If we have a logarithmic equation as ,

$\implies log_a b = c$

Then this can be written as ,

$\implies a^c = b$

In a similar way we can write the given equation as ,

$\implies e^0 = x^2 - 25$

Now also we know that $a^0 = 1$ Therefore , the equation becomes ,

$\implies 1 = x^2 - 25 \\\\\implies x^2 = 25 + 1 \\\\\implies x^2 = 26 \\\\\implies x =\sqrt{26} \\\\\implies x = \pm \sqrt{ 26}$

Hence the Solution of the given equation is ±√26.

6 0

2 years ago

naomi needs 2 cups of chopped apples for a fruit salad she is making .she only has a 1/4 cup. how many times will naomi need to

Lilit [14]

1/4 × 8 times = 2 cups
ANSWER : 8 times

5 0

3 years ago

Read 2 more answers

You plan to construct a brick wall measuring 14.5 ft. in length, 5.5 ft. high, and 0.5 ft. in width. If a brick measures 6 in. x

Licemer1 [7]

Answer: There are 1436 bricks that he will need to make a brick wall.

Step-by-step explanation:

Since we have given that

Dimensions of a brick wall is given by

Length = 14.5 feet

Width = 0.5 feet

Height = 5.5 feet

Dimensions of a brick is given by

Length = 6 inch

Width = 4 inch

Height = 2 inch

We need to find the number of bricks :

So, Number of bricks is given by

$\text{ Number of bricks }=\frac{\text{ Volume of brick wall }}{\text{ Volume of brick}}\\\\=\frac{14.5\times 5.5\times 0.5\times 12\times 12\times 12}{6\times 4\times 2}\\\\=1435.5\\\\=1436$

Hence, there are 1436 bricks that he will need to make a brick wall.

5 0

3 years ago