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3 years ago

Factor 9x^2+66xy+121y^2

1 answer:

7 0

Answer: (3x + 11y)^2

Demonstration:

The polynomial is a perfect square trinomial, because:

1) √ [9x^2] = 3x

2) √121y^2] = 11y

3) 66xy = 2 *(3x)(11y)

Then it is factored as a square binomial, being the factored expression:

[ 3x + 11y]^2

Now you can verify working backwar, i.e expanding the parenthesis.

Remember that the expansion of a square binomial is:

- square of the first term => (3x)^2 = 9x^2
- double product of first term times second term =>2 (3x)(11y) = 66xy
- square of the second term => (11y)^2 = 121y^2

=> [3x + 11y]^2 = 9x^2 + 66xy + 121y^2, which is the original polynomial.

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Convert 5.00 inches to centimeters

tensa zangetsu [6.8K]

Answer:

5 inches x 2.54 = 12.7 cm

Step-by-step explanation:

1 inche = 2.54cm

therefore, 5 inches x 2.54cm = 12.7cm

6 0

3 years ago

In an arithmetic sequence, the nth term an is given by the formula an=a1+(n−1)d, where a1 is the first term and d is the commo

Dmitry_Shevchenko [17]

Answer:

$a_{10} = \frac{10}{65536}$

Step-by-step explanation:

The first step to solving this problem is verifying if this sequence is an arithmetic sequence or a geometric sequence.

This sequence is arithmetic if:

$a_{3} - a_{2} = a_{2} - a_{1}$

We have that:

$a_{3} = 40, a_{2} = 10, a_{3} = \frac{5}{2}$

$a_{3} - a_{2} = a_{2} - a_{1}$

$\frac{5}{2} - 10 = 10 - 40$

$\frac{-15}{2} \neq -30$

This is not an arithmetic sequence.

This sequence is geometric if:

$\frac{a_{3}}{a_{2}} = \frac{a_{2}}{a_{1}}$

$\frac{\frac{5}[2}}{10} = \frac{10}{40}$

$\frac{5}{20} = \frac{1}{4}$

$\frac{1}{4} = \frac{1}{4}$

This is a geometric sequence, in which:

The first term is 40, so $a_{1} = 40$

The common ratio is $\frac{1}{4}$ , so $r = \frac{1}{4}$ .

We have that:

$a_{n} = a_{1}*r^{n-1}$

The 10th term is $a_{10}$ . So:

$a_{10} = a_{1}*r^{9}$

$a_{10} = 40*(\frac{1}{4})^{9}$

$a_{10} = \frac{40}{262144}$

Simplifying by 4, we have:

$a_{10} = \frac{10}{65536}$

3 0

3 years ago

What is the y-intercept of the graph of the equation y=4(3^x)?

eimsori [14]

Answer:

The y-intercept is (0, 4).

Step-by-step explanation:

At the y-intercept x = 0 so

y = 4(3^0)

y = 4*1 = 4.

So the y-intercept is (0, 4).

8 0

2 years ago

Read 2 more answers

The variable Z is inversely proportional to X. When X is 6, Z has the value 2.

Vera_Pavlovna [14]

Inverse proportion is of the form:

y=k/x, in this case the variables are

z=k/x, and we are given the point (6,2) so we can solve for k

2=k/6

12=k, so our equation is:

z=12/x, so when x=13

z=12/13

6 0

3 years ago

24 is 3 more than a number p

rewona [7]

Answer: 24 = 3 + P

Step-by-step explanation: 24 is 3 more than a number P can be represented in the equation form of 24 = 3 + P

To solve it:

3 + P = 24

3 - 3 + p = 24 -3

p = 21

7 0

3 years ago