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3 years ago

A2-b2 ÷5a-5b factorise

Mathematics

1 answer:

katrin2010 [14]3 years ago

3 0

Answer:

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "b2" was replaced by "b^2". 1 more similar replacement(s).

STEP

5a + 5b

Simplify ———————

a2 - b2

STEP

Pulling out like terms

2.1 Pull out like factors :

5a + 5b = 5 • (a + b)

Trying to factor as a Difference of Squares:

2.2 Factoring: a2 - b2

Theory : A difference of two perfect squares, A2 - B2 can be factored into (A+B) • (A-B)

Proof : (A+B) • (A-B) =

A2 - AB + BA - B2 =

A2 - AB + AB - B2 =

A2 - B2

Note : AB = BA is the commutative property of multiplication.

Note : - AB + AB equals zero and is therefore eliminated from the expression.

Check : a2 is the square of a1

Check : b2 is the square of b1

Factorization is : (a + b) • (a - b)

Canceling Out :

2.3 Cancel out (a + b) which appears on both sides of the fraction line.

Final result :

5 / a -b

Step-by-step explanation:

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4 years ago

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Natalija [7]

Answer:

(b) (a) (d) (a) (c)

Step-by-step explanation:

(i) The probability of an even card is 1/2 because the number of even cards and odd cards are the same so there is a 50% of getting an even card. (b)

(ii) Since the card is replaced, there is still a card for all numbers between 1-20. There are 8 prime numbers and 20 cards so the probability of getting a prime number is 8/20 or 4/10 or 2/5. (a)

(iii) The card was not replaced so there are only 19 cards and there are only 5 numbers that are multiples of 3 and greater than 4. The probability must be 5/19. (d)

(iv) A sure event means that it will happen 100%. So P(A) = 1 since the number one represents 100%. (a)

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3 years ago

The sum of five consecutive numbers is 700, what is the first number?

Feliz [49]

Answer:

The first number is 138.

Step-by-step explanation:

Let the first number be x.

Then since they are consecutive numbers, the second number will be (x + 1), the third (x + 2), the fourth (x + 3) and the fifth being (x + 4).

We are given that their sum is 700. Therefore:

$x+(x+1)+(x+2)+(x+3)+(x+4)=700$

Solve for x. Combine like terms:

$5x+10=700$

Subtract 10 from both sides:

$5x=690$

Divide both sides by five. Therefore:

$x=138$

The first number is 138.

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3 years ago

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Answer:

Affects the width of a confidence interval, as the margin of error is a function of the sample standard deviation.

Step-by-step explanation:

When we have the standard deviation for the sample, the t-distribution is used to solve the question.

It does not affect the center of the interval, which is a function only of the sample mean.

Width of a confidence interval:

The width of a confidence interval is a function of the margin of error, which is:

$M = t\frac{s}{\sqrt{n}}$

In which s is related to the sample standard deviation. Thus, since s and M are directly proportional, a higher standard deviation makes the interval wider, lower standard deviation makes the interval narrower, and thus, the sample standard deviation affects the the width of a confidence interval.

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3 years ago

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n200080 [17]

Answer:

D. y=x^2-5

Step-by-step explanation:

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3 years ago

A2-b2 ÷5a-5b factorise​

A2-b2 ÷5a-5b factorise