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2 years ago

Factor completely 9x^2-25

Mathematics

1 answer:

attashe74 [19]2 years ago

4 0

Answer:

$9x^{2} - 25$ = (3x -5)(3x+5)

Step-by-step explanation:

Here, the given expression is $9x^{2} - 25$

Now, we know that $9 = 3^{2} , 25 = 5^{2}$

So, the given expression is transformed in to

$9x^{2} - 25$ = $(3x)^{2} - 5^{2}$

Also, by ALGEBRAIC IDENTITY

$a^{2} - b^{2} = (a-b)(a+b)$

Similarly here taking : a = 3x and b =5

$(3x)^{2} - 5^{2}$ = (3x -5)(3x+5)

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Step-by-step explanation:

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Find the volume of a right square pyramid with base square edges measuring 5 feet each and a height of the pyramid be 4 feet.

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2 years ago

A car dealership sells 0, 1, or 2 luxury cars on any day. When selling a car, the dealer also tries to persuade the customer to

melisa1 [442]

Answer:

Mean = 1.42

Variance = 0.58

Step-by-step explanation:

Given: X denote the number of luxury cars sold in a given day, and Y denote the number of extended warranties sold.

Also, joint probability function of X and Y are given.

To find:

mean and variance of X

Solution:

From the given joint probability function of X and Y,

$P(X=0)=\frac{1}{6}\\P(X=1)=\frac{1}{12}+\frac{1}{6}=\frac{1+2}{12}=\frac{3}{12}\\P(X=2)=\frac{1}{12}+\frac{1}{3}+\frac{1}{6}=\frac{1+4+2}{12}=\frac{7}{12}$

Mean of X:

$E(X)=\sum XP(X)\\=0\left ( \frac{1}{6} \right )+1\left ( \frac{3}{12} \right )+2\left ( \frac{7}{12} \right )\\=0+\frac{3}{12}+\frac{14}{12}\\=\frac{17}{12}=1.42$

Variance of X:

$E(X^2)=\sum X^2P(X)\\=0^2\left ( \frac{1}{6} \right )+1^2\left ( \frac{3}{12} \right )+2^2\left ( \frac{7}{12} \right )\\=0+\frac{3}{12}+\frac{28}{12}\\=\frac{31}{12}$

$var(X)=E\left [ X^2 \right ]-\left ( E\left [ X \right ] \right )^2\\=\frac{31}{12}-\left ( \frac{17}{12} \right )^2\\=\frac{31}{12}-\frac{289}{144}\\=\frac{372-289}{144}\\=\frac{83}{144}\\=0.58$

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3 years ago

Two times the greater of two consecutive integers is 9 less than three times the lesser integer. What are the integers?

blondinia [14]

Let the two integers be x and x + 1, then
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x = 11

Therefore, the integers are 11 and 12.

6 0

3 years ago