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o-na [289]
3 years ago
6

Factorise x^2/4-y^2/4​

Mathematics
1 answer:
Nuetrik [128]3 years ago
3 0

Answer:

\large\boxed{\left(\dfrac{x}{2}-\dfrac{y}{2}\right)\left(\dfrac{x}{2}+\dfrac{y}{2}\right)=\dfrac{x-y}{2}\cdot\dfrac{x+y}{2}}

Step-by-step explanation:

\dfrac{x^2}{4}-\dfrac{y^2}{4}=\dfrac{x^2}{2^2}-\dfrac{y^2}{2^2}\qquad\text{use}\ \left(\dfrac{a}{b}\right)^n=\dfrac{a^n}{b^n}\\\\=\left(\dfrac{x}{2}\right)^2-\left(\dfrac{y}{2}\right)^2\qquad\text{use}\ (a-b)(a+b)=a^2-b^2\\\\=\left(\dfrac{x}{2}-\dfrac{y}{2}\right)\left(\dfrac{x}{2}+\dfrac{y}{2}\right)=\dfrac{x-y}{2}\cdot\dfrac{x+y}{2}

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1. Find the slope of the line.<br><br> 2. Find the rate of change.
d1i1m1o1n [39]

Answer:

the slope of the line is 2 over 1 which means the answer is 2

the rate of change is c

To find the slope of the line you have to go rise over run.

to find the rate of change you have to see how much does the numbers in y go by.

8 0
3 years ago
PLEASE HELP
dsp73

Answer:

All events are independent

Step-by-step explanation:

You are given the table

\begin{array}{cccc}&\text{Chocolate}&\text{Vanilla}&\text{Total}\\\text{Adults}&0.21&0.39&0.60\\\text{Children}&0.14&0.26&0.40\\\text{Total}&0.35&0.65&1.00\end{array}

Two events A and B are independent when

Pr(A\cap B)=Pr(A)\cdot Pr(B)

a) A="Chocolate"

B="Adults"

A and B="Chocolate and Adults"

Pr(A)=0.35\\ \\Pr(B)=0.60\\ \\Pr(A\cap B)=0.21

Since 0.35\cdot 0.60=0.21 events are independent

b) A="Children"

B="Chocolate"

A and B="Children and Chocolate"

Pr(A)=0.40\\ \\Pr(B)=0.35\\ \\Pr(A\cap B)=0.14

Since 0.40\cdot 0.35=0.14 events are independent

c) A="Vanilla"

B="Children"

A and B="Vanilla and Children"

Pr(A)=0.65\\ \\Pr(B)=0.40\\ \\Pr(A\cap B)=0.26

Since 0.65\cdot 0.40=0.26 events are independent

4 0
3 years ago
Which of the following estimates at a 95% confidence level most likely comes from a small sample
Nikitich [7]

Answer:

Answer is c

Step-by-step explanation:

In hypothesis testing whether to accept or reject null hypothesis, normally we find one method as using confidence interval.  If the test statistic lies within confidence interval, we accept otherwise we reject.

For arriving confidence intervals we add and subtract margin of error from the mean we use in null hypothesis.

Margin of error = std error * critical value of test (Z or t etc)

For the same std deviation, std error = std dev/sq rt of sample size

Thus std error is inversely proportional to the square root of sample size.

If n becomes larger, std error becomes smaller and vice versa.

So margin of error increases for smaller sample size.

Since we have to select confidence level from a small sample, we have to select one which has the greatest margin of error=18

Hence answer is

c)  71%(+/-18%)

5 0
3 years ago
V289<br> Rational<br> Irrational
Diano4ka-milaya [45]
Answer: Irrational

Explanation: bc it is
8 0
3 years ago
Mrs. Kelly creates a garden. She buys 15 flowers and 3 bushes for a total cost of $160.32. Each bush costs $11.50 more than each
m_a_m_a [10]

Each bush costs $18.49

Step-by-step explanation:

Mrs. Kelly creates a garden

  • She buys 15 flowers and 3 bushes for a total cost of $160.32
  • Each bush costs $11.50 more than each flower

We need to find how much each bush costs

Assume that the cost of each flower is $x and the cost of each

bush is $y

∵ She by 15 flowers and 3 bushes for a total cost $160.32

∵ The cost of each flower is $x

∵ The cost of each bush is $y

∴ 15x + 3y = 160.32 ⇒ (1)

∵ Each bush costs $11.50 more than each flower

- That mean equate y by x plus 11.50

∴ y = x + 11.50 ⇒ (2)

Now we have system of equations to solve it

Substitute y in equation (1) by equation (2)

∵ 15x + 3(x + 11.50) = 160.32

- Simplify the left hand side

∴ 15x + 3x + 34.5 = 160.32

- Add like terms in the left hand side

∴ 18x + 34.5 = 160.32

- Subtract 34.5 from both sides

∴ 18x = 125.82

- Divide both sides by 18

∴ x = 6.99

Substitute the value of x in equation (2) to find y

∵ y = 6.99 + 11.5

∴ y = 18.49

Each bush costs $18.49

Learn more:

You can learn more about the system of equations in brainly.com/question/2115716

#LearnwithBrainly

3 0
3 years ago
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