Can someone tell me how

Answers

Answer 1

Answer:

the way I get the subsequent term, nevermind the exponents, the exponents part is easy, since one is decreasing and another is increasing, but the coefficient, to get it, what I usually do is.

multiply the current coefficient by the exponent of the first-term, and divide that by the exponent of the second-term + 1.

so if my current expanded term is say 7a³b⁴, to get the next coefficient, what I do is (7*3)/5 <----- notice, current coefficient times 3 divided by 4+1.

anyhow, with that out of the way, lemme proceed in this one.

$\bf ~~~~~~~~\textit{binomial theorem expansion} \n\n \qquad \qquad (1+ax)^n\implies \begin{array}{llll} term&coefficient&value\n \cline{1-3}&\n 1&+1&(1)^n(ax)^0\n\n 2&+((1)(n))/(1)\to n&(1)^(n-1)(ax)^1\n\n 3&+(n\cdot (n-1))/(2)&(1)^(n-2)(ax)^2 \end{array}$

so, following that to get the next coefficient, we get those equivalents as you see there for the 2nd and 3rd terms.

so then, we know that the expanded 2nd term is 24x therefore

$\bf n(1)^(n-1)(ax)1 = 24x\implies n(1)(ax)=24x\implies nax=24x\implies n=\cfrac{24}{a}$

we also know that the expanded 3rd term is 240x², therefore we can say that

$\bf \cfrac{n(n-1)}{2}~~(1)^(n-2)(ax)^2 = 240x^2\implies \cfrac{n(n-1)}{2}(1)(a^2x^2) = 240x^2 \n\n\n \cfrac{(n^2-n)(a^2x^2)}{2}=240x^2\implies \cfrac{(n^2-n)(a^2)}{2}=\cfrac{240x^2}{x^2}\implies \cfrac{a^2n^2-a^2n}{2}=240 \n\n\n a^2n^2-a^2n=480$

but but but, we know what "n" equals to, recall above, so let's do some quick substitution

$\bf a^2n^2-a^2n=480\qquad \boxed{n=\cfrac{24}{a}}\qquad a^2\left( \cfrac{24}{a} \right)^2-a^2\left( \cfrac{24}{a} \right)=480 \n\n\n a^2\cdot \cfrac{24^2}{a^2}-24a=480\implies 24^2-24a=480\implies 576-24a=480 \n\n\n -24a=-96\implies a=\cfrac{-96}{-24}\implies \blacktriangleright a = 4\blacktriangleleft \n\n[-0.35em] ~\dotfill\n\n n=\cfrac{24}{a}\implies n=\cfrac{24}{4}\implies \blacktriangleright n=6 \blacktriangleleft$

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Can anyone help me please 3t-1/4=7/8

Answers

3t − 1/4 = 7/8

Add 1/4 to both sides.

3t + −1/4 + 1/4 = 7/8 + 1/4

3t = 9/8

Divide both sides by 3.

3t/3 = 98/3

t=3/8

Label the number rational or irrational

Answers

The first one rational and the second one is irrational.

2468 is a rational number.
0.830000000000001 is irrational.

A rational number is any whole number.
An irrational number is anything in between, such as decimals and fractions.

A television cost $375 it is on sale for 25% off and there a 6.5% sales tax

Answers

25% of $375 is:
$375* (25/100)= $93.75.

The cost of the television after sale off and before the sales tax is:
$375- $93.75= $281.25

The sales tax is:
$281.25* (6.5/100)= $18.28

The price of the television including everything is:
$281.25+ $18.28= $299.53

Hope this helps~

A television costs 375 dollars.It is on sale for 25% and there’s a sales tax of 6.5%Let’s calculate to get the answer.Original Price = 375 dollarsLet’s add the 6.5% sales tax=> 6.5% = 6.5 / 100 = 0.065=> 375 * 0.065 = 24.375=> 375 + 27.375 = 399.375Let’s subtract the 25% discount=> 25% = 25 / 100 = .25=> 399.375 * .25 = 99.84375=> 399.375 - 99.84375 = 299.53.Thus the new price of the television is 299.53 with the sales tax and discount.

What is the total price of a $21 item including 7.5% sales tax?? plz explain how you get the answer

Answers

In order to get the total price, we need to figure out 7.5% of 21, then add that number to 21.

In order to get 7.5% of 21, we just multiply 21 by 0.075 (since 7.5% ind decimal form is 0.075)

$21(0.075)=1.575$

Then, we add that number to 21.

$21+1.575=22.575$

The answer is 22.575, which we can round to $22.58.

Solve the problem if f(x)=int(-4x), find f(-1.8)

Answers

INT function returns the integer portion of a number .
f(-1.8) = int(7.2) = 7

Final answer:

The function f(x) = int(-4x) requires us to find the integer part of the result when x = -1.8. After substituting and simplifying, we find that f(-1.8) = 7.

Explanation:

The problem given is f(x)=int(-4x), and we are asked to find the value of f(-1.8). The int function refers to integer part of a number, which is the number without its decimal component. It's important to note that for negative numbers, the integer part is the number rounded down.

To solve, we first substitute x = -1.8 into the function:

f(-1.8) = int(-4*-1.8) = int(7.2).

The integer part of 7.2 is 7, so f(-1.8)=7.

Learn more about integer part here:

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What number goes on top

Answers

33 goes on top.

33 goes on top because the number adjacent to a box at the bottom is added up to make the box above it that overlaps it. 3+4=7, 7+9=16, and 16+17=33.

Final answer:

In mathematics, the number that goes on top is typically the numerator in a fraction. It represents the number of parts we have or the value we are considering. For example, in the fraction 3/4, 3 is the numerator and 4 is the denominator.

Explanation:

In mathematics, the number that goes on top is typically the numerator in a fraction. In a fraction, the numerator represents the number of parts we have or the value we are considering. The denominator, which goes on the bottom, represents the total number of equal parts that make up a whole.

For example, in the fraction 3/4, 3 is the numerator and 4 is the denominator. This means we have 3 out of 4 equal parts.

So, depending on the context, the number that goes on top could be the numerator in a fraction or the value we are considering in a mathematical expression.

Learn more about Mathematics here:

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