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If f(x)= x2/x+3, find f(x+h)?

kompoz [17]

f(x+h) = $\frac{x^{2}+2xh+h^{2} }{x+h+3}$

Step-by-step explanation:

Given,

f(x) = $\frac{x^{2} }{x+3}$

To find the value of f(x+h) we need to replace x by x+h

Hence,

f(x+h) = $\frac{(x+h)^{2} }{x+h+3}$

= $\frac{x^{2}+2xh+h^{2} }{x+h+3}$

[Here, we apply the formula of $(a+b)^{2}= a^{2} +2ab+ b^{2}$ ]

6 0

3 years ago

Expand the expression (3-2y)^6 using binomial theorem

Nitella [24]

She should have added 2 to both sides of the equation instead of subtracting 2.

2x -2 = 14

Add 2 to both sides:

2x = 16

Divide both sides by 2:

x = 8

5 0

3 years ago

(3-4i)(6i+7)-(2-3i)

Sergeu [11.5K]

Answer:

43-7i

Step-by-step explanation:

We are given the expression:

$\displaystyle \large{(3 - 4i)(6i + 7) - (2 - 3i)}$

First, expand 3-4i in 6i+7. To expand binomial with binomial, first we expand 3 in 6i+7 then expand -4i in 6i+7.

$\displaystyle \large{[(3 \cdot 6i) + (3 \cdot 7) + ( - 4i \cdot 6i) + ( - 4i \cdot 7)]- (2 - 3i)} \\ \displaystyle \large{[18i + 21 - 24 {i}^{2} - 28i]- (2 - 3i)}$

Now combine like terms.

$\displaystyle \large{[ - 10i+ 21 - 24 {i}^{2} ]- (2 - 3i)}$

Imaginary Unit

$\displaystyle \large{i = \sqrt{ - 1} } \\ \displaystyle \large{ {i}^{2} = - 1 }$

Therefore:-

$\displaystyle \large{[ - 10i+ 21 - 24 ( - 1) ]- (2 - 3i)} \\ \displaystyle \large{[ - 10i+ 21 + 24]- (2 - 3i)} \\ \displaystyle \large{[ - 10i+ 45]- (2 - 3i)}$

Then expand negative sign in 2-3i; remember that negative times negative is positive and negative times positive is negative.

$\displaystyle \large{- 10i+ 45 - (2 - 3i)} \\ \displaystyle \large{- 10i+ 45 - 2 + 3i}$

Combine like terms.

$\displaystyle \large{43 - 7i}$

5 0

2 years ago

What is the result of subtracting 4x^2 + 3xy +2y^2 from 5x^2 + 3xy + 6y^2?

erica [24]

x^2 + 6xy + 8y2

4x^2 + 3xy + 2y^2 - 5x^2 + 2xy + 6y^2

= 4x^2 + 3xy + 2y^2 + -5x^2 + 3xy + 6y^2

Combine like terms:

= 4x^2 + 3xy + 2y^2 + -5x^2 + 3xy + 6y^2

= (4x^2 + -5x^2) + (3xy + 3xy) + (2y^2 + 6y^2)

= -x^2 + 6xy + 8y^2

5 0

2 years ago

A researcher records the hospital admission rates for coronary heart disease at 10 local hospitals. She finds that 2 different h

In-s [12.5K]

The central tendency researcher use to describe these data is "mode".

The value that appears most frequently in a data set is called the mode. One mode, several modes, or none at all may be present in a set of data. The mean, or average of a set, and the median, or middle value in a set, are two more common measurements of central tendency.

Calculation of mode is done by-

The number that appears the most frequently in a piece of data is its mode.
Put the numbers in ascending order by least to greatest, then count the occurrences of each number to quickly determine the mode.
The most frequent number is the mode.
Simply counting how many times each number appears in the data set can help you identify the mode, which is the number that appears the most frequently in the data set.
The figure with the largest total is the mode.
Example: Since it happens most frequently, the mode for the data set [5, 7, 8, 2, 1, 5, 6, 7, 5] is 5.

To know more about the mode of the data, here

brainly.com/question/27951780

#SPJ4

6 0

1 year ago