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3 years ago

5

charlene takes the bus to work in the morning,then walks home for lunch,walks back to work, and finally walks home in the evenin

g.the distance one way is 600 meters.how far does she walk each day between home and work?

2 answers:

kolezko [41]3 years ago

7 0

So she walks at least 3 times.The distance is 600 meters So 600·3=1800 meters= 1 kilometers and 800 meters-she going in the single day.

irga5000 [103]3 years ago

4 0

Hey there, Lets solve this problem together.

We know that Charlene takes the bus to work in the morning,then walks home for lunch,walks back to work, and finally walks home in the evening.the distance one way is <span>600 meters.
</span>
Therefore <span>Charlene walks 3 times. To solve the problem we have to multiply. </span>

$600* 3 = 1800 meters
$

= 1 kilometers and 800 meters

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HELP ASAP: Factor By Grouping: 12a^3 - 9a^2 + 4a - 3

MAVERICK [17]

We have been given an expression $12a^3 - 9a^2 + 4a - 3$ . We are asked to factor the given expression by grouping.

First of all, we will make two groups of our expression as:

$(12a^3-9a^2)+( 4a - 3)$

Now we will factor of greatest common factor from each group.

$(3a^2\cdot 4a-3a^2\cdot 3)+( 4a - 3)$

$3a^2(4a-3)+1( 4a-3)$

Now we will factor out common terms $(4a-3)$ as:

$(4a-3)( 3a^2+1)$

Therefore, the factorized form of our given expression would be $(4a-3)( 3a^2+1)$ .

7 0

3 years ago

**Spam answers will not be tolerated**

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

Simplify the expression below

aleksandrvk [35]

3*2 = 6 ;
4^2 = 16;
/-2/ = +2;
16*2 = 32 ;
5 + 6 - 32 = 11 - 32 = -21;
The right answer is D) -21 ;

6 0

3 years ago

A tree that is 4 ft tall is growing at a rate of 1 ft each year a tree that is 12 feet tall is growing at a rate of 1/2 ft each

Andreyy89

Answer:

16 years

Step-by-step explanation:

Given data

For the first tree

let the expression for the height be

y=4+x--------------1

where y= the total height

4= the initial height

x= the number of years

For the second tree, the expression is

y=12+0.5x-------------2

Equate 1 and 2

4+x=12+0.5x

x-0.5x=12-4

0.5x= 8

x= 8/0.5

x=16

Hence it will take 16 years for both trees to have the same height

5 0

3 years ago

What is Bethany's score on the test if she got 23 out of 30 right? (Round to the nearest whole number.)

matrenka [14]

Answer:

77%

Step-by-step explanation:

23 divided by 30 is 0.766666, which percent-wise is rounded to 77% :)

3 0

3 years ago

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