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Anvisha [2.4K]
3 years ago
10

One more than one-fourth the square of anumber x is y​

Mathematics
1 answer:
Tatiana [17]3 years ago
6 0

Answer:

y = 1 + ¼x²

Step-by-step explanation:

Given

One more than one-fourth the square of a number x is y​

Required

Represent algebraically

We start by analysing the expression one after the other.

First, the two numbers to compare are represented by x and y.

Where y is the resulting number.

So, we start with y =;

Then we move backwards

- "the square of a number, x" can be represented with x²

- one-fourth "the square of a number, x".

The expression in quote has already been represented by x².

So, we can replace this expression with x².

This will give us: one-fourth of x²

One-fourth means ¼

Hence, one-fourth of x² = ¼ * x²

- "One more than" means 1 has to be added to the previous expression to give y.

In other words; 1 + ¼ * x²

Finally, we'll bring the expressions together to give

y = 1 + ¼ * x²

y = 1 + ¼x²

Hence, "One more than one-fourth the square of a number x is y​" is represented in algebra by y = 1 + ¼x²

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Step-by-step explanation:

so the length is 23 and the width is 14

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What is 10x-3>3x+11 as a word problem​
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x ----> a number

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> greater than

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7 0
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Expand the following using the Binomial Theorem and Pascal’s triangle. (x + 2)6 (x − 4)4 (2x + 3)5 (2x − 3y)4 In the expansion o
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\begin{array}{llll}
term&coefficient&value\\
-----&-----&-----\\
1&&(2x)^5(+3)^0\\
2&+5&(2x)^4(+3)^1\\
3&+10&(2x)^3(+3)^2\\
4&+10&(2x)^2(+3)^3\\
5&+5&(2x)^1(+3)^4\\
6&+1&(2x)^0(+3)^5
\end{array}

as you can see, the terms exponents, for the first term, starts at highest, 5 in this case, then every element it goes down by 1, till it gets to 0

for the second term, starts at 0, and every element it goes up by 1, till it gets to the highest

now, to get the coefficient, they way I get it, is "the product of the current coefficient and the exponent of the first term, divided by the exponent of the second term plus 1"

notice the first coefficient is always 1

so...how did we get 10 for the 3rd element?  well, 5*4/2
how did we get 10 for the fourth element?  well, 10*2/4


\bf (2x-3y)^4\implies 
\begin{array}{llll}
term&coefficient&value\\
-----&-----&-----\\
1&&(2x)^4(-3y)^0\\
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3&+6&(2x)^2(-3y)^2\\
4&+4&(2x)^1(-3y)^3\\
5&+1&(2x)^0(-3y)^4
\end{array}


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\begin{array}{llll}
term&coefficient&value\\
-----&-----&-----\\
1&&(3a)^8(+4b)^0\\
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6&+56&(3a)^3(+4b)^5\\
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8&+8&(3a)^1(+4b)^7\\
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\end{array}

and from there, you can simplify the elements of the expansion by combining the coefficients

like for example, the 7th element of (3a+4b)⁸ will then be 1032192a²b⁶
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