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1 year ago

If f(x)=x^2 then what is f(x+h)? an explanation would be lovely, but if not that’s okay :)

Mathematics

1 answer:

Nadusha1986 [10]1 year ago

8 0

Answer: $f(\text{x+h}) = \text{x}^2+2\text{x}\text{h}+\text{h}^2$

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Work Shown:

$f(\text{x}) = \text{x}^2\\\\f(\text{x+h}) = (\text{x+h})^2\\\\f(\text{x+h}) = (\text{x+h})(\text{x+h})\\\\f(\text{x+h}) = \text{x}*\text{x}+\text{x}*\text{h}+\text{h}*\text{x}+\text{h}*\text{h}\\\\f(\text{x+h}) = \text{x}^2+\text{x}\text{h}+\text{x}\text{h}+\text{h}^2\\\\f(\text{x+h}) = \text{x}^2+2\text{x}\text{h}+\text{h}^2\\\\$

Explanation:

I replaced each copy of x with x+h. Then I used the FOIL rule to expand things out and combine like terms. The distributive property or the box method are two other pathways you can take.

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The triangles are similar. Find the value of the variable.

stich3 [128]

Answer is s = 13.64
First we need to find the ratio of the like sides of the triangle
For the large triangle side, add both numbers to make 9 compared with small triangle side 4
4/9 = ratio of .44
Now divide the other side by the ratio
6/.44 = 13.64
s= 13.64

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2 years ago

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andrey2020 [161]

First observe that if $a+b>0$ ,

$(a + b)^2 = a^2 + 2ab + b^2 \\\\ \implies a + b = \sqrt{a^2 + 2ab + b^2} = \sqrt{a^2 + ab + b(a + b)} \\\\ \implies a + b = \sqrt{a^2 + ab + b \sqrt{a^2 + ab + b(a+b)}} \\\\ \implies a + b = \sqrt{a^2 + ab + b \sqrt{a^2 + ab + b \sqrt{a^2 + ab + b(a+b)}}} \\\\ \implies a + b = \sqrt{a^2 + ab + b \sqrt{a^2 + ab + b \sqrt{a^2 + ab + b \sqrt{\cdots}}}}$

Let $a=0$ and $b=x$ . It follows that

$a+b = x = \sqrt{x \sqrt{x \sqrt{x \sqrt{\cdots}}}}$

Now let $b=1$ , so $a^2+a=4x$ . Solving for $a$ ,

$a^2 + a - 4x = 0 \implies a = \dfrac{-1 + \sqrt{1+16x}}2$

which means

$a+b = \dfrac{1 + \sqrt{1+16x}}2 = \sqrt{4x + \sqrt{4x + \sqrt{4x + \sqrt{\cdots}}}}$

Now solve for $x$ .

$x = \dfrac{1 + \sqrt{1 + 16x}}2 \\\\ 2x = 1 + \sqrt{1 + 16x} \\\\ 2x - 1 = \sqrt{1 + 16x} \\\\ (2x-1)^2 = \left(\sqrt{1 + 16x}\right)^2$

(note that we assume $2x-1\ge0$ )

$4x^2 - 4x + 1 = 1 + 16x \\\\ 4x^2 - 20x = 0 \\\\ 4x (x - 5) = 0 \\\\ 4x = 0 \text{ or } x - 5 = 0 \\\\ \implies x = 0 \text{ or } \boxed{x = 5}$

(we omit $x=0$ since $2\cdot0-1=-1\ge0$ is not true)

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2 years ago

How to write 6.716 im fraction

Varvara68 [4.7K]

Answer:

To write 6.716 as a fraction you have to write 6.716 as numerator and put 1 as the denominator. Now you multiply numerator and denominator by 10 as long as you get in numerator the whole number.

6.716 = 6.716/1 = 67.16/10 = 671.6/100 = 6716/1000

And finally we have:

6.716 as a fraction equals 6716/1000

7 0

3 years ago

Which parent function is f(x)=x^2

QveST [7]

The function y=x2 or f(x) = x2 is a quadratic function, and is the parent graph for all other quadratic functions. The shortcut to graphing the function f(x) = x2 is to start at the point (0, 0) (the origin) and mark the point, called the vertex.

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3 years ago

A machinist can produce 12 parts in 40 min.how many parts can the machinist produce in 4 hours?

expeople1 [14]

Answer:

72 parts

Steps:

Convert the 4 hours into minutes. There are 60 minutes in an hour. Therefore, 4 hours = 240 minutes.

Divide 240 minutes by 40 minutes. This equals 6. Therefore, the machinist can produce the 12 parts 6 times in 4 hours.

Finally, multiply the 12 parts by the 6 times he can produce. Therefore, the machinist can produce 72 parts in 4 hours.

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3 years ago

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