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3 years ago

could you pls tell me the answer to part a and b thx, and could you also give me a step by step explanation of how you did it?

Mathematics

1 answer:

777dan777 [17]3 years ago

8 0

Answer:

sure Gigi, as below

Step-by-step explanation:

we want to know the rates. so this like like in MPH (Miles per hour) or feet per second but something that we can compare each walker with the other .... so we want some type of scale that makes sense. what are the given units.... they are distance in miles and time in hours.. so maybe MPH would work for this.

there is a very good, basic formula that you should just remember for this type of problem... I can it the dirt formula... partly b/c it's dirt easy.. and partly b/c it really is about how much dirt you cover.. i mean.. how far you do... in a distance .. and you can use any unit you want... like we'll use miles here.. for our units.. we will you d = rt where d= distance , r= rate and t = time.

d = rt.... notice the formula looks a lot like the word "dirt" handy huh...

use it to make all the walks have a number... their rate... the r in the formula... to compare with, so use your algebra skills to rearrange the formula... to

d/t = r now we can plug in each of the walkers and get a rate to comparr them

Aisha 5/2 = r so 5/2 MPH

Bob 7.5 / 5 = r so 7.5 = 15/2 then (15/2) / 5 = (15/2) * (1/5) ( cross cancel the 15 and 5 so you get (3/2) * (1/1) = 3/2

Bob = 3/2 MPH

Cora = 9 / 3.6 or 9 / 3 $\frac{6}{10}$ or (9/1) / ( $\frac{36}{10}$ ) or (9/1) * (10 / 36) cross cancle the 9 and 36 so you get (1/1) * ( 10 / 4) = 10/4 = 5 /2

Cora = 5/2 MPH

Dylan = 3.75 /2.5 or 3 $\frac{3}{4}$ / 2 $\frac{1}{2}$ or (15/4) / (5/2) or (15/4 ) * (2/5) cross cancel the 2 and 4 and also cross cancel the 15 and 5 then, (3/2) * ( 1/1)= 3/2

Dylan = 3/2 MPH

MPH

Aisha = 5/2

Bob = 3/2

Cora = 5/2

Dylan = 3/2

you can now make fair comparisons among the 4 people

d = rt

d/t = r

Emilio = 19.2 / 6 or 19 $\frac{2}{10}$ / 6 or (192/10 ) / (6/1) invert and multiply to bring the denominator up (192/10) * (1/6) cross cancle 6 into 192 = 32

so(32/10) * ( 1/1) = 32/10 or 16/5 = 3 $\frac{1}{5}$ or 3 $\frac{2}{10}$ which is 3.2 MPH

Fala = 10.5 / 3 or 10 $\frac{1}{2}$ /3 or $\frac{21}{2}$ / 3 or (21/2) / (3/1) invert and multiply the denominator (21/2) * ( 1/3) , cross cancel 3 and 21 (7/2) * ( 1/1) = 7/2

so now you have all the rates.. how fast they are walking. in Miles per hour and that's what the scale of the number line is.. so, good.. just mark each of their speeds

Bob and Dylan = 3/2 or 1.5 MPH... pretty slow.. huh :P

Cora and Aisha = 5/2 or 2.5 MPH faster but not fast

Emilo 3.2 MPH pretty quick

Fala 3.5 MPH she's fast. :D speed walking

3.2 on the number line is not marked.. 3.25 is.. so just a bit below the 3.25 mark.. that's 3 $\frac{1}{4}$ , see it?

all the others are marks on the number line.. just count marks for 1//2s

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On using the method of splitting the middle term we have:

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Hence from both the cases we did not get the required region.

Hence, option 1 is incorrect.

We are given the second inequality as:

$x^2+2x-8$

On using the method of splitting the middle term we have:

$x^2+4x-2x-8$

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And we know that the product of two quantities are negative if either one of them is negative so we have two cases:

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Hence, we do not get a common region.

Case 2:

$x-2$ and $x+4>0$

i.e. x<2 and x>-4

Hence the common region is (-4,2) which is same as the given option.

Hence, option B is correct.

$x^2-2x-8>0$

On using the method of splitting the middle term we have:

$x^2-4x+2x-8>0$

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And we know that the product of two quantities are positive if either both of them are negative or both of them are positive so we have two cases:

Case 1:

$x+2>0$ and $x-4>0$

i.e. x>-2 and x>4

Hence, the common region is (4,∞)

Case 2:

$x+2$ and $x-4$

i.e. x<-2 and x<4

Hence, the common region is: (-∞,-2)

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Hence, option C is incorrect.

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$x^2+4x-2x-8>0$

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3 years ago

could you pls tell me the answer to part a and b thx, and could you also give me a step by step explanation of how you did it? ​

could you pls tell me the answer to part a and b thx, and could you also give me a step by step explanation of how you did it?