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4 years ago

3. What is the slope of a line perpendicular to the line y =-2/3 x+12

Mathematics

1 answer:

goldenfox [79]4 years ago

6 0

Answer:

Slope of line (i) = 1.5

Step-by-step explanation:

Line (i) is perpendicular to;

Line (ii) whose equation is y = $-\frac{2}{3} x + 12$

The slope of line (ii) = $-\frac{2}{3}$

* <u>Mathematics rule</u>: <em>The product of slopes of two perpendicular lines = -1</em>

∴ The slope of line (i) = -1 ÷ $-\frac{2}{3}$ = 3/2 = 1.5

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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?

777dan777 [17]

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

8 0

3 years ago

What is the value of y in the equation y-7=21

Usimov [2.4K]

Its 28!!! y=28
.....................

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3 years ago

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A bookshop has an offer.

VMariaS [17]

All you have to do is 5.99x4 which equals 23.96

7 0

3 years ago

The amount of coffee that people drink per day is normally distributed with a mean of 17 ounces and a standard deviation of 4 ou

Setler [38]

Answer:

Step-by-step explanation:

(a)

The distribution of X is Normal Distribution with mean $= \mu =17$ and Variance $= \sigma^{2} = 16 \ i.e., X \sim N (17, 16),$

(b)

The distribution of $\bar{x}$ is Normal Distribution with mean $= \mu =17$ and Variance = $\sigma^{2}/n = 16/15= 1.0667$ .i.e., $\bar{x}\sim N(17,1.0667)$

To find P(15.5 < X < 18):

Case 1: For X from 15.5 to mid value:

Z = (15.5 - 17)/4 = - 0.375

Table of Area Under Standard Normal Curve gives area = 0.1480

Case 2: For X from mid value to 18:

Z = (18 - 17)/4 = 0.25

Table of Area Under Standard Normal Curve gives area = 0.0987

So,

P(15.5 < X< 18) = 0.1480 +0.0987 = 0.2467

So,

Answer is:

0.2467

(d)

$SE = \sigma/\sqrt{n}\\\\= 4/\sqrt{15}$

= 1.0328

To find $P(15.5 < \bar{x}< 18):$

Case 1: For $\bar{x}$ from 15.5 to mid value:

Z = (15.5 - 17)/1.0328 = - 1.4524

Table of Area Under Standard Normal Curve gives area = 0.4265

Case 2: For X from mid value to 18:

Z = (18 - 17)/1.0328 = 0.9682

Table of Area Under Standard Normal Curve gives area = 0.3340

So,

$P(15.5 < \bar{x}< 18) = 0.4265 + 0.3340 = 0.7605$

So,

Answer is:

0.7605

(e)

Correct option:

because Population SD is provided.

(f)

(i)

Q1 is given by:

$- 0.6745 = (\bar{x} - 17)/1.0328$

So,

X = 17 - (0.6745 * 1.0328) = 17 - 0.6966 = 16.3034

So,

Q1 = 16.3034

(ii)

Q3 is given by:

$0.6745 = (\bar{x} - 17)/1.0328$

So,

X = 17 + (0.6745 * 1.0328) = 17 + 0.6966 = 17.6966

So,

Q3= 17.6966

(iii)

IQR = Q3 - Q1 = 17.6966 - 16.3034 = 1.3932

Answers are:

Q1 = 16.3034 ounces

Q3 = 17.6966 Ounces

IQR = 1.3932 Ounces

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3 years ago

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Nadusha1986 [10]

Answer:

The circumference is a little more than 3 times the diameter.

Step-by-step explanation:

The value of dividing the circumference of a circle by its diameter will always yield the value of π. π is about 3.14 and therefore shows that the circumference of any circle is a little more than 3 times the diameter.

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3 years ago

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