Who wants to help with a math discussion?

The distance between two points, a and b, on a number line is expressed as
|a – b|, where a and b are rational numbers. Think about locating a point halfway between a and b on a number line. How can you find the coordinate for such a point? Develop a formula in terms of a and b that you can use to find the coordinate. Your formula must work for positive and negative values of a and b. Does absolute value play a role in your formula? Why or why not? Under what circumstances might your formula be used in the real world? Explain.

Discuss how you can find the coordinate of a point located other fractional distances from a to b (or from b to a). For example, locate a point three-fourths of the distance from a to b. What kind of calculation is involved?

Answers

Answer 1

The distance between two points is the number of units between them.

Halfway points (a) and (b)

To locate a point halfway points (a) and (b), we use the following steps

Calculate the absolute difference between both pointsDivide the absolute difference by 2Add the quotient to the smaller point.

Assume the smaller value is (a), the point (P) halfway points (a) and (b) would be

[tex]P = a + \frac{|a - b|}{2}[/tex]

Take for instance, a = 5, and b = 10.

The halfway point would be:

[tex]P = 5 + \frac{|5 - 10|}{2}[/tex]

[tex]P = 5 + \frac{5}{2}[/tex]

[tex]P = 5 + 2.5[/tex]

[tex]P = 7.5[/tex]

The halfway point between 5 and 10 is 7.5

The formula works for negative values, and absolute values are used to return the actual difference between both points

Real world circumstance

The formula can be used to calculate the halfway distance between a school gate and the school library (as an instance)

Fractional distance

To determine the fractional distance, we simply replace the 1/2 in the original formula with the appropriate fraction.

Take for instance, three-fourths from (a) to (b) would be:

[tex]P = a + \frac{3|a - b|}{4}[/tex]

Read more about distance at:

https://brainly.com/question/9935574


Related Questions

The 250 gallons of maple sap will be
boiled until only 3% of its original
volume is left. How many gallons are
left?

Answers

Answer:

7.5 gallons

Step-by-step explanation:

3 x 250/100

= 7.5

A video game that normally sells for $80 is on sale for 60 what is the percent of discount for the sale price

Answers

Answer:

20% discount

Step-by-step explanation:

Which function represents the following graph? On a coordinate plane, a cubic function has an inflection point at (negative 3, 3) and crosses the x-axis at (0, 4. 5). Y = StartRoot x minus 3 EndRoot 3 y = StartRoot x 3 EndRoot 3 y = RootIndex 3 StartRoot x minus 3 EndRoot 3 y = RootIndex 3 StartRoot x 3 EndRoot 3.

Answers

The function represents the graph is (d) [tex]y = \sqrt[3]{x+3} + 3[/tex]

The points on the graph are given as:

[tex](x,y) = (-3,3)[/tex] --- the inflection point

[tex](x,y) = (0,4.5)[/tex] --- the y-intercept

The function that satisfy the above points is:

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

The proof is as follows:

At the inflection point, we have the x value to be -3.

So, the function becomes

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

[tex]y = \sqrt[3]{-3+3} + 3[/tex]

[tex]y = \sqrt[3]{0} + 3[/tex]

[tex]y = 0+ 3[/tex]

[tex]y = 3[/tex] ---- the y-value at the inflection point is true for x = -3

Also, at the y-intercept, we have the x-value to be 0

So, the function becomes

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

[tex]y = \sqrt[3]{0+3} + 3[/tex]

[tex]y = \sqrt[3]{3} + 3[/tex]

[tex]y = 1.45+ 3[/tex]

[tex]y = 4.45[/tex] ---- the y-value at the y-intercept is true for x = 0

Hence, the function represents the graph is (d) [tex]y = \sqrt[3]{x+3} + 3[/tex]

Read more about graphs and functions at:

https://brainly.com/question/25918641

Answer:

D

Step-by-step explanation:

i keep this all day what is 6 + 6 × 6 + 6 ÷ 6=

Answers

Answer:

43

Step-by-step explanation:

6 + 6 × 6 + 6 ÷ 6

using BIDMAS, we do the division first

6÷6=1

then multiplication

6×6=36

leaving us with:

6+36+1=43

Hopefully this helped- have a good day)

Let's do

6+6×6+6÷66+36+17+3643

Done!

Plz help with this question.

Answers

a] x/5=3

x=15

b] x/2=8.5

x=17

Express the following as:
ax+by+c=0

-2x+3y=6​

Answers

[tex] \color{magenta} \huge{answer}{} [/tex]

it can be expressed as -2x + 3y = 6

on comparing with ax+by+c=0

We can find out that

[tex] \green{ \huge{a= -2}{} }[/tex]

[tex] \pink{ \huge{b = 3}{} }[/tex]

[tex] \color{magenta} \huge{c = 6}{} [/tex]

hope it helps

The expression -22x + 3y = 6 in the form ax + by + c = 0 is -2x + 3y - 6 = 0

Linear Equations

The given equation is:

-2x + 3y = 6

Comparing the equation above with ax + by + c = 0

Rewrite -2x + 3y = 6 in the form ax + by + c = 0

-2x + 3y - 6 = 0

If -2x + 3y - 6 = 0 is compared with ax + by + c = 0

a = -2, b = 3, c = -6

Therefore, the expression-22x + 3y = 6 in the form ax + by + c = 0 is -2x + 3y - 6 = 0

Learn more on linear equations here: https://brainly.com/question/14323743

Gas grills are on sale 20% off. The sale price of the grill that I like is $399.20. What was the original price of the grill?

Answers

Answer:

499

Ste-by-step explanation

80 percent of the original price is left.

If you divide by 4 you get 99.8 which is 20% of the original price. Then if you multiply 99.8 by 5 you will get 100% of the original price which is 499

You can also do 399.2 * 1.25 = 499

Subtract. Show complete procedure.

4m - 3
3m + 1
-----------

Answers

Answer:

m - 2

Step-by step explanation:

4m - 3  - 3m + 1=> 4m - 3m - 3 + 1=> m - 2

Conclusion:

Therefore, 4m - 3  - 3m + 1 equals m - 2.

Hoped this helped.

[tex]BrainiacUser1357[/tex]


Please help answer this question also with explanation

Answers

You would have to calculate the percent first.
Add the total number of students
3420+4680= 8100 students TOTAL

Then you would divide the amount of students by the total

3420 part time/8100 students total = .42 or 42%

4680 full time/8100 total = .58 or 58%

Then you multiply the percentages by 90

(90)(.58)= 52.2

(90)(.42)= 37.8

Rounded

52 full time and 38 part time students

Find the value of x.

Answers

Answer:

x = 19

Step-by-step explanation:

(5x+4)+(x-2)+(3x+7) = 180

5x+4+x-2+3x+7 = 180

9x+9 = 180

9x = 171

x = 171/9

x = 19

X=19 hope this helps

What is the area of 2.4

Answers

4.8 because that’s the area of 2.4

Felipe swam 29 kilometers to an island. Then he swam 19 kilometers to a boat. How far did he swim in all?

Answers

48 kilometers

29 + 19 = 48

hope this is helpful!

29+19=48 in all! (Add how much he swam each way)

-salary of £1410
-26% of the total profit the company makes from her sales

Answers

Answer:

I'm not sure what the question is actually asking but 26% of the profit is 366.60

Step-by-step explanation:

if u subtract the profit, u have 1043.40 remaining

(1)Pradnya had 5 dozen copies. She gave half of the copies to Anushka and 1/5 times of the copies to Prajwal. How many copies are remaining with her ?
(2) Shrikant bought a watch at Rs. 900. He gave equal number of notes of denomination Rs. 10, Rs. 20, Rs. 50 and Rs. 100. Find the number of notes of Rs. 20 that he gave to the shopkeeper.
(3) Mangalakaku purchased 6016 saplings of lemon. She planted 47 saplings in each row. How many rows will be formed of those saplings?​

Answers

Explanation:

(i)Total number of copies are at Pradnya = 5 dozen

We know that 1 dozen = 12

⇛5×12 = 60

Given copies to Anushka = half of 60

⇛60/2 = 30 copies

Given copies to Prajwala = 1/5 the copies

⇛ (1/5)×60

⇛60/5

⇛12 copies

Total number of given copies = 30+12 = 42

Remaining copies = 60-42 = 18

Answer: Remaining copies = 18

(ii)Let the number of Rs. 10 notes be X

So given that

all are equal in number

So, Number of Rs 20 notes = Number of Rs. 50 notes = Number of Rs. 100 = X

Total number of notes

= X+X+X+X = 4X

Value of Rs. 10 = 10X

Value of Rs. 20 = 20X

Value of Rs. 50 = 50X

Value of Rs. 100 = 100X

Total amount = Rs. 900

⇛10X +20X +50X+100X = 900

⇛180X = 900

⇛X = 900/180

⇛X = 5

Number of Rs. 10 notes = Number of Rs. 20 notes = Answer: number of Rs. 50 notes = Number of Rs. 100 = 5

(iii) Let the number of rows be X

Number of saplings per each row = 47

Total number of saplings of X rows = 47X

According to the given problem,

Total number of saplings purchased by Mangalakaku = 6016

⇛47X = 6016

⇛X = 6016/47

⇛X = 128

Answer: Total number of rows = 128

Choose the angle which is represented by the name.

RUN and NUG

Answers

Answer:

Option C

Step-by-step explanation:

Both RUN and NUG have U in the middle of them, so the bottom one would be correct as U is in the center.

Find the value of x so that the function has the given value. g(x)=8x-11;(x)=5

Answers

Answer:

29

Step-by-step explanation:

Solve: 3x²+9x+6 = 0
Thank you.​

Answers

Given quadrant equation:

3x² + 9x + 6 = 0

Here we see that,

→ Product of coefficient of x² and constant term = 3 × 6 = 18

→ Sum of coefficient of x² ans constant term = 3 + 6 = 9

So the given equation can be written as,

⇛3x² + 6x + 3x + 6 = 0

On taking the common terms, we get

⇛3x(x + 2) + 3(x + 2) = 0

On grouping the common terms, we get

⇛(3x + 3)(x + 2) = 0

Here either (3x + 3) = 0 or (x + 2) = 0. So,

⇛3x + 3 = 0 or x + 2 = 0

⇛3x = -3 or x = -2

⇛x = -3/3 or x = -2

⇛x = -1 or x = -2

also read similar questions:- These are the two roots of the equation.

Julian used these steps to solve the equation 9x=?6+3(3x+2) 9 x = - 6 + 3 ( 3 x + 2 ) . Which choice describes the meaning of his result, 0=0 ?

https://brainly.com/question/11808722?referrer

what are the zeros of the function of y=x^2-3x+2​

Answers

Answer:

(x-1)(x-2)

x=1, x=2

Step-by-step explanation:

Factor the function into (x-2)(x-1) and set each part equal to zero and solve for x.
x-2=0 x=2
x-1=0 x=1

solve similar triangles (advanced)

Answers

Answer:

12 =x

Step-by-step explanation:

We  can use proportions to solve

6           x

---- = -------

10        10+10

Using cross products

6 ( 10+10) = x*10

6*20 = 10x

120 = 10x

Divide by 10

120/10 = x

12 =x

Answer:

x = 12

Step-by-step explanation:

ABC ~ ADE

AB/AD = BC/DE

 10/20 = 6/x

x = 20 x 6 ÷ 10

x = 12

Help me solve these

Answers

Answer:

hello  you need to tell me the equation not the worksheet

Step-by-step explanation:

put b for everything‍️

Write the inequality represented by the graph below.

Answers

I believe this is an inequality because this doesn’t pass the origin point 0

Does not pass 0,0

If I’m wrong so sorry

Which graph represents the solution of the inequality |3x+12| ≥ 3?

Answers

Answer:  A

Step-by-step explanation:

The solution to the inequality is x <= -5 and x>=-3 so A is correct

Make y the subject of the formula
12m + 24y = 20

Answers

Answer: m=5/3-2y  or if your solving for y  y=-m/2+5/6

Step-by-step explanation:

Answer:

y = 5/6 - m/2

Step-by-step explanation:

4(3m + 6y) = 20

3m + 6y = 5

6y = 5 - 3m

y = 5/6 - 3m/6

y = 5/6 - m/2

What is the equation of a line that is perpendicular to the line y = - 1/2 x + 1 and passes through the point (8, - 1)? A y = −1/2 x + 8 B y = 2x - 17 C y = −1/2 x − 2 D y = 2x - 1

Answers

Answer is B y = 2x - 17

First find the negative reciprocal of the gradient for y = -1/2 x + 1 to find the perpendicular line gradient.

-1/2 = 2

Gradient of perpendicular line = 2

Perpendicular line is y=2x + c

Substitute (8,-1) into the line to find the y-intercept (c).

-1 = 2(8) + c
-1 = 16 + c
c = -17

Therefore, the perpendicular line is y = 2x - 17.

PLS ANSWER QUICK I HSVE EXAMS COMING UP VERY SOON у
42) Which equation best represents the line of best fit for this
scatter plot?
A. y = 4x - 4
B.y= 4x-2
C. y = x-4
D. y=x-2
-5-4-3-

Answers

C
If we drew a line of best fit, the gradient would be roughly equal to 1, and the y intercept would be at around -4

Q). A man ₹ x. He gave half of it to his wife, 1/4th to his son and ₹1200 of his daughter. Form an equation and also find x.​

Answers

Given that

Money of a man = Rs. X

Money given to his wife = half of the money

= Rs. X/2

Money given to his son = 1/4th of the money

⇛Rs. X/4

Money given to his daughter = Rs. 1200

Total money

⇛ (X/2)+(X/4)+1200 = X

⇛ (2X+X+4800/4 = X

⇛ (3X+4800)/4 = X

⇛ (3X+4800) = 4X

⇛4X=3X+4800

⇛4X-3X = 4800

⇛X = 4800

⇛X-4800 = 0 is the required equation

⇛X = 4800

The money of the man = Rs. 4800 Ans.

also read similar questions: what if a man has 19 cows and he wants to give Half of them to his brother 1/4th to Son and 1/5th to daughter?

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DOM
The weight of a car is modeled with the polynomial 3x2 – 25x + 204. The weight of a truck is modeled with the polynomial x² + 17x + 40
What polynomial represents the total weight of the car and truck?

Answers

Answer:

4x^2-8x+244

Step-by-step explanation:

Pls help pls help it’s my last question

Answers

Answer:

5

Step-by-step explanation:

Answer:

3 3/4

Step-by-step explanation:

whats 1 + 1

ahsdugiywayhdyhawdwahdwahidwadad

Answers

2 or 11 or window or whatever

Answer:

11

Step-by-step explanation:

It's clearly 11

1 + 1 = 11

just put the 2 numbers together

Plz help ToT I'm horrible at math

Answers

Answer:

192

Step-by-step explanation:

multiply by each side to find the answer. 4x2 is 8 and 8 x 24 is 192. Which ever order you multiply the numbers in you will always get 192. Hope this helps ^^

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