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3 years ago

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In order to avoid heavy traffic, Antonio can drive home after working less than 7 hours (h < 7) or after working more than 9

hours (h >9). How can these inequalities be written as one statement?
a. 7 < h < 9
b. 7 > h > 9
c. h < 7 or h > 9
d. h > 7 or h < 9

2 answers:

emmainna [20.7K]3 years ago

7 0

Answer:

<em>C. </em>h < 7 or h > 9

Step-by-step explanation:

For people on ed2020

lord [1]3 years ago

3 0

A is not correct because h has to be less than 7 hours. it also has to be greater than 9 hours so this condition isnt fulfilled.

B is not correct. h cannot be both larger than 9 and less than 7. I would say that answer isnt correct

C conditions are correct and written exactly as they should be. sepparated. unlike ones in B

D is oposite from C so it is not correct.

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Morgarella [4.7K]

Answer:

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

Step-by-step explanation:

So we have the function:

$f(x)=\frac{4}{\sqrt x}$

And we want to find the derivative using the limit process.

The definition of a derivative as a limit is:

$\lim_{h \to 0} \frac{f(x+h)-f(x)}{h}$

Therefore, our derivative would be:

$\lim_{h \to 0}\frac{\frac{4}{\sqrt{x+h}}-\frac{4}{\sqrt x}}{h}$

First of all, let's factor out a 4 from the numerator and place it in front of our limit:

$=\lim_{h \to 0}\frac{4(\frac{1}{\sqrt{x+h}}-\frac{1}{\sqrt x})}{h}$

Place the 4 in front:

$=4\lim_{h \to 0}\frac{\frac{1}{\sqrt{x+h}}-\frac{1}{\sqrt x}}{h}$

Now, let's multiply everything by (√(x+h)(√(x))) to get rid of the fractions in the denominator. Therefore:

$=4\lim_{h \to 0}\frac{\frac{1}{\sqrt{x+h}}-\frac{1}{\sqrt x}}{h}(\frac{\sqrt{x+h}\sqrt x}{\sqrt{x+h}\sqrt x})$

Distribute:

$=4\lim_{h \to 0}\frac{({\sqrt{x+h}\sqrt x})\frac{1}{\sqrt{x+h}}-(\sqrt{x+h}\sqrt x)\frac{1}{\sqrt x}}{h({\sqrt{x+h}\sqrt x})}$

Simplify: For the first term on the left, the √(x+h) cancels. For the term on the right, the (√(x)) cancel. Thus:

$=4 \lim_{h\to 0}\frac{\sqrt x-(\sqrt{x+h})}{h(\sqrt{x+h}\sqrt{x}) }$

Now, multiply both sides by the conjugate of the numerator. In other words, multiply by (√x + √(x+h)). Thus:

$= 4\lim_{h\to 0}\frac{\sqrt x-(\sqrt{x+h})}{h(\sqrt{x+h}\sqrt{x}) }(\frac{\sqrt x +\sqrt{x+h})}{\sqrt x +\sqrt{x+h})}$

The numerator will use the difference of two squares. Thus:

$=4 \lim_{h \to 0} \frac{x-(x+h)}{h(\sqrt{x+h}\sqrt x)(\sqrt x+\sqrt{x+h})}$

Simplify the numerator:

$=4 \lim_{h \to 0} \frac{x-x-h}{h(\sqrt{x+h}\sqrt x)(\sqrt x+\sqrt{x+h})}\\=4 \lim_{h \to 0} \frac{-h}{h(\sqrt{x+h}\sqrt x)(\sqrt x+\sqrt{x+h})}$

Both the numerator and denominator have a h. Cancel them:

$=4 \lim_{h \to 0} \frac{-1}{(\sqrt{x+h}\sqrt x)(\sqrt x+\sqrt{x+h})}$

Now, substitute 0 for h. So:

$=4 ( \frac{-1}{(\sqrt{x+0}\sqrt x)(\sqrt x+\sqrt{x+0})})$

Simplify:

$=4( \frac{-1}{(\sqrt{x}\sqrt x)(\sqrt x+\sqrt{x})})$

(√x)(√x) is just x. (√x)+(√x) is just 2(√x). Therefore:

$=4( \frac{-1}{(x)(2\sqrt{x})})$

Multiply across:

$= \frac{-4}{(2x\sqrt{x})}$

Reduce. Change √x to x^(1/2). So:

$=-\frac{2}{x(x^{\frac{1}{2}})}$

Add the exponents:

$=-\frac{2}{x^\frac{3}{2}}$

And we're done!

$f(x)=\frac{4}{\sqrt x}\\f'(x)=-\frac{2}{x^\frac{3}{2}}$

5 0

3 years ago

Which pair of fractions and mixed numbers have a common denominator of 20?

mariarad [96]

Answer: The answer is the 4th option

Step-by-step explanation: Hope this helps!

6 0

3 years ago

What is a and b pls answer ASAP I need it !!! Plsss

nlexa [21]

Answer:

The value of a = 5.

the value of b = 6.

Step-by-step explanation:

Given the points on the line

(6, 10)
(a, 8)
(4, b)
(2, 2)

Given that all of the points are on the same line and the line represents a linear function.

Thus, the slope between any two points must be the same.

First, determine the slope between (6, 10) and (2, 2)

(x₁, y₁) = (6, 10)

(x₂, y₂) = (2, 2)

Using the formula

Slope = m = [y₂ - y₁] / [x₂ - x₁]

= [2 - 10] / [2 - 6]

= -8 / -4

= 2

Thus, the slope of the line = m = 2

Determine the value 'a'

(x₁, y₁) = (6, 10)

(x₂, y₂) = (a, 8)

Using the slope formula to determine the value of 'a'

Slope = [y₂ - y₁] / [x₂ - x₁]

As the slope between two points is 2.

now substitute slope = 2, (x₁, y₁) = (6, 10) and (x₂, y₂) = (a, 8) in the slope formula

Slope = [y₂ - y₁] / [x₂ - x₁]

2 = [8 - 10] / [a - 6]

2(a - 6) = 8 - 10

2a - 12 = -2

2a = -2 + 12

2a = 10

divide both sides by 2

a = 5

Therefore, the value of a = 5.

Determine the value 'b'

(x₁, y₁) = (2, 2)

(x₂, y₂) = (4, b)

Using the slope formula to determine the value of 'b'

Slope = [y₂ - y₁] / [x₂ - x₁]

As the slope between two points is 2.

now substitute slope = 2, (x₁, y₁) = (2, 2) and (x₂, y₂) = (4, b) in the slope formula

Slope = [y₂ - y₁] / [x₂ - x₁]

2 = [b - 2] / [4 - 2]

2(4 - 2) = b - 2

8 - 4 =b - 2

4 = b - 2

b = 6

Therefore, the value of b = 6

7 0

3 years ago

Find four consecutive even integers such that if the sum of the first and third is multiplied

Alenkasestr [34]

Answer:

Step-by-step explanation:

-8-10,-12-14

-8 plus -12 is -20

-20 times 5 is -100

-14 times 8 is -112

-100 is 12 more than -112

6 0

3 years ago

Number 6 mainly and any other if you want to help:) looka t the pic

soldier1979 [14.2K]

Let the amount B pays be £x
So,
A pays £125
B pays £x
They pay in the ration 3:2
Therefore,
125/x = 3/2
Cross multiplying we get,
125 x 2 = 3x
3x = 250
x = £63.33

3 0

3 years ago