Given function, r(x) = x/3, determine value of x for when r(x) = - 2

Hi, I'm happy to help!

To find the slope, you need to use the slope formula, where m is the slope:

m=[tex]\frac{y_{2}-y_{1 } }{x_{2} -x_{1} }[/tex]

Slope means rise over run, or how much the line rises per the amount the line moves forward. This equation shows the movement from the y points to show rise, over the difference in the x points to show run.

Now, to find the slope we insert our values, starting with our second y point:

m=[tex]\frac{2-y_{1 } }{x_{2} -x_{1} }[/tex]

Now insert our first y point:

m=[tex]\frac{2-4 }{x_{2} -x_{1} }[/tex]

Now we insert our second x point:

m=[tex]\frac{2-4 }{-3 -x_{1} }[/tex]

And finally our first x point:

m=[tex]\frac{2-4 }{-3 -3 }[/tex]

Now, we solve:

m=[tex]\frac{-2 }{-6}[/tex]

So, our slope is -2/-6, to simplify it, we remove both negatives because they cancel each other out.

m=[tex]\frac{2 }{6}[/tex]

Now, we simplify our fraction by dividing the top and bottom by 2:

m=[tex]\frac{1}{3}[/tex]

So, our slope is 1/3. This means that for every 1 unit the line rises, it goes to the right 3 units. The y-intercept is where the line hits the y axis.

If the question is asking for slope intercept form for the equation, you use y=mx+b

y represents any y coordinate on your line, m represents your slope (1/3), x represents any x coordinate on your line, and b represents your y-intercept (3).

If you were to insert these values, you would get:

y=[tex]\frac{1}{3}[/tex]x+3

You use this to find what a y coordinate would be so you can draw your line.

For the next equation we do the same thing:

m=[tex]\frac{y_{2}-y_{1 } }{x_{2} -x_{1} }[/tex]

Insert our values:

m=[tex]\frac{4-1}{2-(-4)}[/tex]

Get rid of the double negative:

m=[tex]\frac{4-1}{2+4}[/tex]

Solve:

m=[tex]\frac{3}{6}[/tex]

Simplify:

m=[tex]\frac{1}{2}[/tex]

Now that we know our slope, let's plug it in to our slope intercept form equation.

y=[tex]\frac{1}{2}[/tex]x+3

I hope this was helpful! Keep learning! :D

Answer:

1

Step-by-step explanation:

A rational number between 3.623623 and 0.484848 is 1.

Answer:

Remember: rational numbers are numbers that can be written as fractions and decimals that either terminate or repeat. Here are some rational numbers:

0.5, 3/4, 1, 1.5...3, 3.5

Step-by-step explanation:

BRAINLIEST, PLEASE!

Answer:

125/343

Step-by-step explanation:

This question asks for us to evaluate: (5/7)³

(5/7)³

- 5/7 x 5/7 x 5/7

= 25/49 x 5/7

= 125/343

Answer: t = 9

Step-by-step explanation:

Given

-t = 9 (t - 10)

Expand parentheses and apply the distributive property

-t = 9 · t - 9 · 10

-t = 9t - 90

Subtract 9t on both sides

-t - 9t = 9t - 90 - 9t

-10t = -90

Divide -10 on both sides

-10t / -10 = -90 / -10

[tex]\boxed{t=9}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

Answer:

Read explanation Please (I spent alot of time on it and its important to understand where the answer came from not just the answer!)

Step-by-step explanation:

This problem is in the form of y=mx+b where m is the ratio y grows accordinly to x and b is the value of y when x is 0 (mx0 is 0, 0+b is b).

In you problem we can identify that 1 is the y intercept or when x is 0. All we have to do is find another point since 2 points make alike. Let's say x was 1. 43 * 1 +1 = 44 so when x is 1 y is 44.

Our two points are, (0,1)(1,44)

I left a picture of the graphed btw!,

Hoped this helped, Eddie

Step-by-step explanation:

A whole number that is not able to be divided by two into two equal whole numbers. Example: 1, 3, 5, and 7 are odd numbers

Answer:

Step-by-step explanation:

200=2w²h

The equations are -

200 = 2[tex]w^{2}[/tex]h

2w x w x h = 200

We have a prism and the formula to calculate its volume is given.

We have to select all of the equations that rewrite the volume formula by making substitutions for V = 200 cubic centimeter and L = 2w.

A Prism is a three-dimensional shape, which consists of two identical polygons, which do not lie in the same axis.

According to the question, we have -

Volume of Prism = 200 cubic centimeter

L = 2w

The formula to calculate the volume of prism equals to -

V = Lwh

Substituting values, we get -

200 = 2[tex]w^{2}[/tex]h

or

2w x w x h = 200

Hence, the equations are -

200 = 2[tex]w^{2}[/tex]h

2w x w x h = 200

To solve more questions on prism, visit the link below-

https://brainly.com/question/17619973

#SPJ2

Answer:

1 . 4 hrs , 2 . total 400 miles because the first train had travelled 160 miles and 2nd one had travelled 240 miles

Step-by-step explanation:

in 1. use relative motion concept I. e. you sir on 1st train and put velo. of same mag. and in oppo. direction on the train on which you have sit and do the same with the velocity only with 2nd train means you stop the train on which you are sitting and put the velocity of the train on which you are sitting on 2nd train but in oppo. direction , so now the relative velocity comes out to be 20 mph and then apply formula time = Srel / Vrel and here we can find S rel by multiplying the velo. of 1st train by given time I. e. 2 hrs and in 2. multiply the time calculated by us by the velocity of both trains and by which you get the dist. travelled by both trains and then add them to get final answer.

Step-by-step explanation:

2 option is the answer.

hope it helps

Answer:

ii. is the answer .

Step-by-step explanation:

option ii. is the answer .

The simple interest rate need by Teri will be 4%.

Step-by-step explanation:

Given:

Teri has $125,000 to deposit in his accounts so that he gets $200,000 in 16 years along with the simple interest.

To find:

The simple interest rate needed to grow $125,000 into $200,000 in 16 years.

Solution:

The principle amount Teri has = P = $125,000

The total amount Teri wants to have in 16 years = A = $200,000

The simple interest that will Teri earn = S.I

[tex]S.I= A - P =\$200,000-$125,000=\$ 75,000[/tex]

The rate of interest per year = R

The time for which money is deposited = T = 16 years

The simple interest is calculated by the formula:

[tex]S.I=\frac{P\times R\times T}{100}\\\$75,000=\frac{\$125,000\times R\times 16}{100}\\R=\frac{$75,000\times 100}{$125,000\times 16}=3.75\% \approx 4\%[/tex]

The simple interest rate need by Teri will be 4%.

Learn more about Simple interest here:

https://brainly.com/question/19222840

#learnwithbrainly

Simple interest rate (R) is 3.75%

Given:

Amount deposit as saving (P) = $125,000

Number of year (n) = 16 year

Amount needed (A) = $200,000

Find:

Simple interest rate (R)

Computation:

Amount of interest (I) = A - P

Amount of interest (I) = 200,000 - 125,000

Amount of interest (I) = 75,000

So,

I = (P)(R)(T)

75,000 = (125,000)(R)(16)

75,000 = 2,000,000(R)

R = 75,000 / 2,000,000

R = 0.0375

Simple interest rate (R) = 3.75%

Learn more:

https://brainly.com/question/22004878?referrer=searchResults

There are two ways to list the angles:

1) Simply name them based on the points:

∠W , ∠X , ∠Y , ∠Z

2) The way that I believe that you are supposed to list them in this case. List them as such:

∠WYZ , ∠YZX , ∠ZXW , ∠XWY

~

Answer:

B

Step-by-step explanation:

Answer:

the first, third and fourth options are correct

Answer:

They're congruent by Side-Angle-Side (SAS)

Step-by-step explanation:

Midpoint Q makes sides LQ and QN equal, as well as MP and QP, so there's a side, depending on which one you choose.

We're told that angle L = angle N, so there's the equal angle.

Finally, we're told that LM = NP, so there's the other side.

Answer:

GCF = 4

Step-by-step explanation:

The factors of 8 are: 1, 2, 4, 8

The factors of 12 are: 1, 2, 3, 4, 6, 12

The greatest common factor is 4.

I hope this helps :).

Answer:

4

Step-by-step explanation:

8 = 2 * 2 * 2

12 = 2 * 2 * 3

Since 2 times 2 is common in both the numbers,

Greatest Common Factor = 2 * 2 = 4

[tex]\rule[225]{225}{2}[/tex]

Hope this helped!

Answer:

-8, -9, -10, -100, -999, -999.99 etc

Step-by-step explanation:

Anynumber below or same as -8

Answer:

6x+1<9-2x

6x+2x<9-1

8x<8

x<1

2x-1 ≤ 5x+20

2x-5x≤20+1

-3x≤21

x≥-7

3-(2x-7) ≤ 34-6x

3-2x+7 ≤ 34-6x

-2x+6x ≤ 34-3-7

4x ≤ 24

x ≤ 6

Answer:

diameter of the track=49.02m

Answer:

49.04m

Step-by-step explanation:

stpes are in picture below

Answer:

12

Step-by-step explanation:

[tex]4 \sqrt{9} [/tex]

[tex] \sqrt{9} = \sqrt{ {3}^{2} } = 3[/tex]

[tex]4 \times 3[/tex]

[tex] = 12[/tex]

Hi ;-)

[tex]u+51^o=79^o\\\\u=79^o-51^o\\\\\huge\boxed{u=28^o}[/tex]

The required equation is,

→ 51° + U = 79°

Now we should,

find the required value of U.

→ 51° + U = 79°

→ U = 79° - 51°

→ [U = 28°]

Let's check whether the required value of U is correct or incorrect,

→ 51° + U = 79°

→ 51° + 28° = 79°

→ 79° = 79°

→ LHS = RHS

Hence, 28° is the required value of U.

Answer: 3m + 28

 ———————

    4  

Answer:

B

Step-by-step explanation:

Substitute x = 5 into the expression

[tex]\frac{4(5+5)(5+1)}{(5+3)(5-3)}[/tex]

= [tex]\frac{4(10)(6)}{8(2)}[/tex]

= [tex]\frac{240}{16}[/tex]

= 15 → B

Answer:

15

Step-by-step explanation:

Numerator ; 4(X+5)(X+1)

substitute : X=5

The first expression becomes : 4(5+5)(5+1)

= 4(10)(6)

=4×10×6

=240

Denominator : (X+3)(x-3)

substitute: X=5

=(5+3)(5-3)

=(8)(2)

=16

Now, Dividing the numerator by the denominator we have 240÷16=15

Answer:

C

Step-by-step explanation:

y=kx or xy=k are true such that k=0.3

in C, 1.2=4*0.3, 2.4=8*0.3, and 3.9=13*0.3, so C follows this rule

Answer:

30 and 35

Step-by-step explanation:

Distance covered of 85km=1hour=60minutes

Distance covered of 1km=60minutes/85km

Distance covered of 43km=60mins/85km × 43mins

= 30.35mins

Note:If you need to ask question about it I'll reply gladly

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Explanation:

Let's say that all of the 11 songs are 2 minutes each, which is just a bit under the "2 minute 1 second" mark of the shortest song. I'm going for the lowest time value possible and rounding to the nearest minute.

This would mean the entire album is 2*11 = 22 minutes long. This is the lower bound or the shortest the album can be.

If we go to the other end of the spectrum, and say each song is 6 minutes (I rounded "5 minutes 37 seconds" up to the nearest minute), then the album is now 6*11 = 66 minutes long. This is the upper bound or the longest the album can be.

While we don't know how long the album is exactly, due to the fact we don't know the individual song lengths (other than the shortest and longest songs), we do know 100% that the album length is somewhere between 22 minutes and 66 minutes.

In other words, 22 < x < 66 where x is the album length in minutes.

Of the four answer choices, 44 is the only one that fits, i.e. 22 < 44 < 66.

So I would say 44 minutes is a reasonable estimate. Or better yet, we can rule out 4 minutes, 88 minutes and 10 minutes as they don't fit in the interval 22 < x < 66.

Answer:

c) 6/35

Step-by-step explanation:

− 4/5 − (− 2/5 ) + 4/7

= − 4/5 + 2/5 + 4/7

= 6/35

Answer:

The choose C. 6/35

Step-by-step explanation:

[tex] - \frac{4}{5} + \frac{2}{5} + \frac{4}{7} \\ \frac{ - 28 + 14 + 20}{35} = \frac{6}{35} [/tex]