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3 years ago

Use Pascal's Triangle to determine the second term of the expansion of (x - 2)^5

Mathematics

1 answer:

goldfiish [28.3K]3 years ago

8 0

Pascal's triangle up to the 5th iteration is

$\begin{array}{cccccc}1\\1&1\\1&2&1\\1&3&3&1\\1&4&6&4&1\\1&5&10&10&5&1\end{array}$

This tells us

$(x-2)^5=\boxed{1}x^5(-2)^0+\boxed{5}x^4(-2)^1+\boxed{10}x^3(-2)^2+\boxed{10}x^2(-2)^3+\boxed{5}x^1(-2)^4+\boxed{1}x^0(-2)^5$

so the second term in the expansion is

$5x^4(-2)^1=\boxed{-10x^4}$

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What is the point-slope form of a line with slope 3/2 that contains the point (-1 2)

Drupady [299]

Answer:

The point-slope form of this equation is y - 2 = 3/2(x + 1)

Step-by-step explanation:

To find the answer to any equation in point slope form, start with the base form of the equation.

y - y1 = m(x - x1)

Now input the slope for m and the point at (x1, y1)

y - 2 = 3/2(x + 1)

3 0

2 years ago

Nicolas has $6,500 to deposit into an account which earns 3.25% interest compounded annually. How interest will he have earned a

agasfer [191]

We have been given that Nicolas has $6,500 to deposit into an account which earns 3.25% interest compounded annually. We are asked to find amount of interest earned at the end on 8 years.

We will use compound interest formula to solve our given problem.

$A=P(1+\frac{r}{n})^{nt}$ , where,

A = Final amount,

P = Principal amount,

r = Annual interest rate in decimal form,

n = Number of times interest is compounded per year,

t = Time in years.

$3.25\%=\frac{3.25}{100}=0.0325$

$A=6500(1+\frac{0.0325}{1})^{1\cdot 8}$

$A=6500(1+0.0325)^{8}$

$A=6500(1.0325)^{8}$

$A=6500(1.2915775352963673)$

$A=8395.253979$

Now we will subtract principal amount from final amount to find amount of interest as:

$\text{interest}=8395.253979-6500$

$\text{interest}=1895.253979\approx 1895.25$

Therefore, Nicolas would have earned $1895.25 in interest at the end of 8 years.

7 0

2 years ago

Which rational number could be graphed between -3 and -4

Snezhnost [94]

Answer:

-3.5

Step-by-step explanation:

An example is -3.5.

3 0

3 years ago

Read 2 more answers

N × $3.05 = $305.00=

sdas [7]

Answer:

n = 100

Step-by-step explanation:

Step 1:

n × $3.05 = $305 Equation

Step 2:

n = $305 ÷ $3.05 Divide

Answer:

n = 100

Hope This Helps :)

4 0

2 years ago

Help Me Plz!!!!!!!!!!!!!

Strike441 [17]

Answer:

$a = 6\sqrt 3,\:\:b =12,\:\:c=6\sqrt 2$

Step-by-step explanation:

$by \: 30 \degree - 60 \degree - 90 \degree \: theorem \\ \\ 6 = \frac{1}{2} b\\ \\ 6 \times 2 = b \\ \\ 12 = b \\ \\ \huge\red {\boxed {b= 12}} \\ \\ a = \frac{ \sqrt{3} }{2} b \\ \\ a = \frac{ \sqrt{3} }{2} \times 12 \\ \\ \huge\purple {\boxed {a = 6 \sqrt{3}}} \\ \\ c = \frac{1}{ \sqrt{2} } b \\ \\ c = \frac{1}{ \sqrt{2} } \times 12 \\ \\ c = \frac{ \sqrt{2} }{2} \times 12 \\ \\ \huge\orange {\boxed {c = 6 \sqrt{2}}} \\ \\$

8 0

3 years ago