All categories

4 years ago

Simplify (4x+5y)(2x-3)+3xy

Mathematics

2 answers:

tatiyna4 years ago

6 0

Answer:

Mathematics is never a challenge on my side.

Step-by-step explanation:

hope that will help you

LUCKY_DIMON [66]4 years ago

6 0

Answer:

Step-by-step explanation:

=(4x+5y)(2x-3)+3xy

=4x(2x-3)+5y(2x-3)+3xy

=8x²-12x+10xy-5y+3xy

=8x²-12x-5y+13xy(Answer)

You might be interested in

Write the standard form of the equation of each line. y=1/4 x+2

sweet-ann [11.9K]

y=mx+c where m = 1/4

c=2

3 0

3 years ago

Read 2 more answers

What is the value of log 43? Use the calculator. Round your answer to the nearest tenth

Orlov [11]

Answer:

1.6

Step-by-step explanation:

The value of log 43 to the nearest tenth is 1.6

3 0

3 years ago

Read 2 more answers

Lim (n/3n-1)^(n-1) n → ∞

n200080 [17]

Looks like the given limit is

$\displaystyle \lim_{n\to\infty} \left(\frac n{3n-1}\right)^{n-1}$

With some simple algebra, we can rewrite

$\dfrac n{3n-1} = \dfrac13 \cdot \dfrac n{n-9} = \dfrac13 \cdot \dfrac{(n-9)+9}{n-9} = \dfrac13 \cdot \left(1 + \dfrac9{n-9}\right)$

then distribute the limit over the product,

$\displaystyle \lim_{n\to\infty} \left(\frac n{3n-1}\right)^{n-1} = \lim_{n\to\infty}\left(\dfrac13\right)^{n-1} \cdot \lim_{n\to\infty}\left(1+\dfrac9{n-9}\right)^{n-1}$

The first limit is 0, since 1/3ⁿ is a positive, decreasing sequence. But before claiming the overall limit is also 0, we need to show that the second limit is also finite.

For the second limit, recall the definition of the constant, e :

$\displaystyle e = \lim_{n\to\infty} \left(1+\frac1n\right)^n$

To make our limit resemble this one more closely, make a substitution; replace 9/(n - 9) with 1/m, so that

$\dfrac{9}{n-9} = \dfrac1m \implies 9m = n-9 \implies 9m+8 = n-1$

From the relation 9m = n - 9, we see that m also approaches infinity as n approaches infinity. So, the second limit is rewritten as

$\displaystyle\lim_{n\to\infty}\left(1+\dfrac9{n-9}\right)^{n-1} = \lim_{m\to\infty}\left(1+\dfrac1m\right)^{9m+8}$

Now we apply some more properties of multiplication and limits:

$\displaystyle \lim_{m\to\infty}\left(1+\dfrac1m\right)^{9m+8} = \lim_{m\to\infty}\left(1+\dfrac1m\right)^{9m} \cdot \lim_{m\to\infty}\left(1+\dfrac1m\right)^8 \\\\ = \lim_{m\to\infty}\left(\left(1+\dfrac1m\right)^m\right)^9 \cdot \left(\lim_{m\to\infty}\left(1+\dfrac1m\right)\right)^8 \\\\ = \left(\lim_{m\to\infty}\left(1+\dfrac1m\right)^m\right)^9 \cdot \left(\lim_{m\to\infty}\left(1+\dfrac1m\right)\right)^8 \\\\ = e^9 \cdot 1^8 = e^9$

So, the overall limit is indeed 0:

$\displaystyle \lim_{n\to\infty} \left(\frac n{3n-1}\right)^{n-1} = \underbrace{\lim_{n\to\infty}\left(\dfrac13\right)^{n-1}}_0 \cdot \underbrace{\lim_{n\to\infty}\left(1+\dfrac9{n-9}\right)^{n-1}}_{e^9} = \boxed{0}$

7 0

3 years ago

Help me answer this question please

Lynna [10]

Answer:

The hours times 4 equals the miles. The answer is B.

Step-by-step explanation:

7 0

4 years ago

What is the value of x? Then determine the measure of each angle. will brainlist first correct answer

kherson [118]

Answer:

Step-by-step explanation:

I have to go with 9r-18= -27 is my answer for your math

4 0

3 years ago