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tigry1 [53]
2 years ago
7

If f(x) = x² – 5, evaluate: f(x+h)-f(x)/ h

Mathematics
1 answer:
Likurg_2 [28]2 years ago
6 0

The first derivative of the function f(x) = x² - 5 is equal to f'(x) = 2 · x.

<h3>How to find the derivative of a quadratic equation by definition of derivative</h3>

In this question we have a quadratic function, in which we must make use of the definition of derivative to find the expression of its first derivative. Then, the procedure is shown below:

f(x) = x² - 5                                         Given

f' = [(x + h)² - 5 - x² + 5] / h                Definition of derivative

(x² + 2 · x · h + h² - 5 - x² + 5) / h       Perfect square trinomial

(2 · x · h + h²) / h                                Associative, commutative and modulative properties / Existence of additive inverse

2 · x + h                                              Distributive, commutative and associative properties / Definition of division / Existence of multiplicative inverse

2 · x                                                     h = 0 / Result

The first derivative of the function f(x) = x² - 5 is equal to f'(x) = 2 · x.

To learn more on derivatives: brainly.com/question/25324584

#SPJ1

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Find the total cost of a spa treatment of $42 including 6% sales tax and 20% tip
Naily [24]
Cost of the spa treatment = $42
Percentage of sales tax = 6%
Percentage of tips = 20%
Normally the tips amount is calculated before adding sales tax.
Then
Amount of tips given = (20/100) * 42
                                  = (1/5) * 42
                                  = 8.40 dollars
Amount of sales tax taken = (6/100) * 42
                                           = 252/100
                                           = 2.52 dollars
Then 
The total amount spent for spa treatment = (42 + 8.40 + 2.52) dollars
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So we can see that $52.92 has been spent in total for spa treatment and this amount includes a sales tax of $2.52 and a tip of $8.40.
7 0
3 years ago
Find the length of the missing side
OLga [1]

a^2+b^2=c^2

a^2+24^2=25^2

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The answer is 7.

4 0
3 years ago
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Stanley has a collection of seashells. He found 35% of his collection on Florida beaches. If Stanley has 49 seashells from Flori
m_a_m_a [10]

Answer:

The number of seashells he have in his collection all together is <u>140</u>.

Step-by-step explanation:

Given:

Stanley has a collection of seashells. He found 35% of his collection on Florida beaches.

Stanley has 49 seashells from Florida.

Now, to find the number of seashells of his collection altogether.

Let the number of seashells all together be x.

Percentage of seashells found on Florida beaches = 35%.

Number of seashells found on Florida beaches = 49.

Now, to get the number of seashells altogether we put an equation:

35\%\ of\ x=49.

⇒ \frac{35}{100} \times x=49

⇒ 0.35\times x=49

⇒ 0.35x=49

Dividing both sides by 0.35 we get:

⇒ x=140.

Therefore, the number of seashells he have in his collection all together is 140.

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Mrac [35]
The answer would be angles UVX and RSQ.
Hope this helps
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