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

A website is selling couches for $864. The site got the couches at a cost of $320. What percentage is the mark-up?

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That is a 170% markup

What is the area of the parallelogram?

Answers

Answer:

24cm

Step-by-step explanation:

because 6 x 4 = 24 centimeters

The answer is the third one

Find the unknown side (w) of the rectangular solid. Please help..

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Answer:

Step-by-step explanation:

MAy yoy make it bigger

PLS HELP ME I DON'T GET IT

Answers

Answer:

  (a) $14,912 saved

  (b) $58,000 aid needed

Step-by-step explanation:

(a)

Nola is saving $200 each month. That means she will have saved 60 times that amount after 60 months:

  60 × $200 = $12,000

When she adds that to her current savings she will have saved a total of ...

  $12,000 +2,912 = $14,912 . . . by the time she starts college

__

(b)

The figure is telling you Nola will need $72,912 for 4 years of college. If she funds $14,912 from her own savings, then she will need an additional amount of ...

  $72,912 -14,912 = $58,000 . . . . amount of financial aid needed

How do I find x please I need help asap

Answers

Answer:

x=5

Step-by-step explanation:

Let's say the left side has points A, B, and C, with B in the middle, and the right side has points A, E, and D, with E in the middle

The Triangle Proportionality Theorem Converse states that if a line splits two sides of a triangle proportionally, the line is parallel to the remaining line.

Here, we can see that the sides are split into congruent lengths to each other, making their proportions 1:1. This proves the theorem converse, so 5x is parallel to 8x+10. Because the other two sides are connected to each other, with AB being a part of AC and AE being a part of AD, AB is parallel to AC and AE is parallel to AD. Given this, we can say that triangle ABE is similar to triangle ACD.

In a similar triangle, the lines corresponding to each other have the same ratio as other lines. This means that

AB/AC = AE/ED = BE/CD.

We are trying to find BE and CD to solve for x, and we can do this by finding the ratio between them

AC = AB + BC

BC = AB

AC = 2 * AB

AB / (2*AB) = BE / CD

1/2 = 5x/(8x+10)

multiply both sides by 2 to remove a denominator

1 = 10x / (8x+10)

multiply both sides by 8x+10 to remove the other denominator

8x+10 = 10x

subtract 8x from both sides to put the variable and its coefficients on one side

2x = 10

divide both sides by 2 to solve for x

x = 5

Pls help. I need it asap

Answers

Answer:

18

Step-by-step explanation:

since the equation of AC is y=x-4 then the length of CB and AB must be the same. therefor its (6*6)/2

Dose any one know the answers for geometry A: A semester exam
PLZ I NEED HELP FAST!!

Answers

Answer:

Step-by-step explanation:

82 +9=5000 thank me later

Choose the slope-intercept form of the equation of the line that passes through (-2, 4) and is perpendicular to the graph of 2x + y = -20.

Answers

Y= x/2 + 5 (not sure)

what id the limit of this function? f(x)=2x4+5x3−2x+12

Answers

Your math problem

(==)=24=+53−2+12

f(x)=2x^{4}+5x^{3}-2x+12

Find solutions on the

A turtle swims 15 kilometers in 9 hours. How far does the turtle swim in 24 hours?

Answers

Answer:

about 40 kilometers

Step-by-step explanation:

The weight of an object on moon is 1/6 of its weight on Earth. If weight of an object on Earth is 18/5 kg, what would be its weight on moon? ​Please help me!!!!​

Answers

Answer:

3/5 kg

Step-by-step explanation:

The weight of an object on Moon is 6 times smaller than same on Earth.

If it weights 18/5 kg on Earth then its weight  on Moon is:

18/5 * 1/6 = 3/5 kg

Answer:

Solution given:

weight of moon=1/6 th of Earth

If weight of Earth is 18/5 kg

weight of moon=?

we have

weight of moon: 1/6 of weight of Earth

=1/6*18/5

=3/5kg

Its weight on moon is 3/5 kg

for each fraction below find an equivalent fraction with a denominator 200.

fraction 14/25​

Answers

Answer:

112/200

Step-by-step explanation:

To find an equivalent fraction with a new denominator you can simply multiply by 1. However, you must multiply by different forms of 1. Remember that any number divided by itself is equal to 1. Additionally, because of the identity property of multiplication, any number multiplied by 1 is still equivalent.

In this case, you should multiply by a fraction that will make 25=200. To get 200 from 25 you must multiply by 8. So, multiply the whole fraction by 8/8. This gives you (14/25)*(8/8)=112/200.

Find the value of 3x+ 4 when x = 2

Answers

Answer:

3x+4, x=2

3(2)+4

6+4=10

Hello there! :-)

To find the value of 3x+4 when x=2, all we have to do is substitute the value of 2 into the expression:

3x+4

3(2)+4

6+4

10

Therefore, the answer is 10.

Hope this helps. Use the comment section to clarify your doubts.

Answered by

~A felicitous teen who helps others with a smile on her face

Good luck with your studies. :)

Hazel bought 3/5 of a kilogram of clay for the students in her pottery class. She then divided the clay evenly into pieces that were 1/5 of a kilogram. Into how many pieces did Hazel divide the clay? Write your answer as a fraction or as a whole or mixed number.​

Answers

Answer:

3

Step-by-step explanation:

3/5 kg of clay are divided into 1/5 a kilogram, so how many times is 1/5 in 3/5?

equation is

[tex]=\frac{3}{5} /\frac{1}{5}\\\\=\frac{3}{5}*\frac{5}{1} \\\\=\frac{15}{5} \\=3[/tex]

What is the difference (2 x - 3) - (x - 1)?
x minus 4
x minus 2
x + 2
x + 4

Answers

Answer:

Step-by-step explanation:

It may help you to rewrite this problem in columns:

 2x - 3

-(  x - 1)

------------

   x - 2 (answer) ("x minus 2")

x = 16 - 4y
3x + 4y =8
substitution method

Answers

Answer:

i think x = -4, y = 5

Step-by-step explanation:

x = 16 - 4y

3x + 4y = 8

3(16 - 4y)+4y = 8

48-12y+4y = 8

48-8y = 8

48-8 = 8y

40 = 8y

5 = y

so

x = 16 - 4y

x = 16 - 4(5)

x = 16 - 20

x = -4

need help with this asap………

Answers

Answer:

y= 32

Step-by-step explanation:

HOPE THIS HELPS :)

what is this answer?​

Answers

Answer:

The answer is 16.

Sorry if it's incorrect.

Step-by-step explanation:

The correct answer is 16.
Explanation:
24 = 2 × 2 × 2 × 2 = 16.

PLEASE HELP QUESTION IN PIC.

Answers

Answer:

Perimeter= 40

Area= 120.7

Step-by-step explanation:

What value makes f(x)=11 if f(x)=5(4x-3)-2(x-6)

please answer asap

Answers

Substitute 11 for f(x) and solve
5(4x-3)-2(x-6)=11
Distribute
20x-15-2x+12=11
Combine
18x-3=11
18x=14
x=14/18
x=7/9

Pls help me with this question

Answers

Step-by-step explanation:

A

the answers are already right in picture. we only need to count.

maybe the problem is understanding a cube ? when it says here "the edge of each cube is 1 1/2 in long", then it means that every side length of a cube is the same (length, width, height). it is the principle of a 2-dimensional square in 3 dimensions.

and "prism" is simply another word for "box".

so, we see that there are 5 cubes fitting along the length of the prism.

so, the length of the prism is

5× 1 1/2 in = 5× 3/2 = 15/2 = 7 1/2 in.

3 cubes are the width of the prism.

so, the width of the prism is

3× 1 1/2 in = 3× 3/2 = 9/2 = 4 1/2 in.

B

we know the height of the prism is 3/4 ft.

1 ft = 12 in

3/4 ft = 3/4 × 12 = (3×12)/4 = 36/4 = 9 in

how many layers of cubes fit into 9 in ?

well, that is what we use division for :

9 ÷ 1 1/2

this is the same as

9 / 3/2 = (9/1) / (3/2)

to divide by a fraction is the same as to multiply with the upside-down fraction. therefore :

(9/1) × (2/3) = (9×2) / (1×3) = 18/3 = 6

so, 6 layers of the cubes fit into the prism.

find the distance, midpoint, and slope of line AB. A(-2,-1) and B(6,3)

Answers

Answer:

[tex]Slope (m) = \frac{y}{x}=\frac{1}{2} = 0.5[/tex]

[tex]Distance (d) = \sqrt{x^2+y^2} =\sqrt{80} =8.9442719099992[/tex]

[tex]Mindpoint =\left(2,\:1\right)[/tex]

Step-by-step explanation:

[tex]Slope (m) = \frac{y}{x}=\frac{1}{2} = 0.5[/tex]

[tex]0 = arctan(\frac{y}{x} = 26.565051177078^o[/tex]

[tex]Distance (d) = \sqrt{x^2+y^2} =\sqrt{80} =8.9442719099992[/tex]

X = 6 – -2 = 8

Y = 3 – -1 = 4

Equation of the line:

y = 0.5x

When x=0, y = 0

When y=0, x = -0

Midpoint:

[tex]\mathrm{Midpoint\:of\:}\left(x_1,\:y_1\right),\:\left(x_2,\:y_2\right):\quad \left(\frac{x_2+x_1}{2},\:\:\frac{y_2+y_1}{2}\right)[/tex]

[tex]\left(x_1,\:y_1\right)=\left(-2,\:-1\right),\:\left(x_2,\:y_2\right)=\left(6,\:3\right)[/tex]

[tex]=\left(\frac{6-2}{2},\:\frac{3-1}{2}\right)[/tex]

[tex]=\left(2,\:1\right)[/tex]

How I can answer this question, NO LINKS, if you answer correctly I will give u brainliest!

Answers

Answer:

It is the first one.

Triangle P is rotated 180° about (0, 0) to give triangle Q. Triangle Q is translated by 5 2 to give triangle R. (a) Describe fully the single transformation that maps triangle P onto triangle R.

Answers

Answer:

  (x, y) ⇒ (-x +5, -y +2)

Step-by-step explanation:

Rotation 180° is described by ...

  (x, y) ⇒ (-x, -y)

Translation right 5 and up 2 is described by ...

  (x, y) ⇒ (x +5, y +2)

The two transformations together that map P to R are described by ...

  (x, y) ⇒ (-x +5, -y +2)

What is the equation of the oblique asymptote?
h(x) = x² – 3x - 4/x + 2

Answers

Simplifying h(x) gives

h(x) = (x² - 3x - 4) / (x + 2)

h(x) = ((x² + 4x + 4) - 4x - 4 - 3x - 4) / (x + 2)

h(x) = ((x + 2)² - 7x - 8) / (x + 2)

h(x) = ((x + 2)² - 7 (x + 2) - 14 - 8) / (x + 2)

h(x) = ((x + 2)² - 7 (x + 2) - 22) / (x + 2)

h(x) = (x + 2) - 7 - 22/(x + 2)

h(x) = x - 5 - 22/(x + 2)

An oblique asymptote of h(x) is a linear function p(x) = ax + b such that

[tex]\displaystyle \lim_{x\to\pm\infty} h(x) - p(x) = 0[/tex]

In the simplified form of h(x), taking the limit as x gets arbitrarily large, we obviously have -22/(x + 2) converging to 0, while x - 5 approaches either +∞ or -∞. If we let p(x) = x - 5, however, we do have h(x) - p(x) approaching 0. So the oblique asymptote is the line y = x - 5.

how do you think I'm NOW

Answers

Answer:

u are u and u and u and u and u

Plzzz help me it’s due tonight!!!!!

Answers

Answer:

UV=5, VW=5[tex]\sqrt{3}[/tex], and m∠U=60

Step-by-step explanation:

sin 30=UV/10=>0.5=UV/10=>UV=5

VW=√(10²-5²)=√75=5√3

m∠U=180-90-30=60

Write an equation for a line if m
3 and it passes through the point (1, -5).

Answers

Answer is B:
y - -5 = 3 (x-1)

An account earns 8.4% interest compounded monthly. If 12,000 is invested in the account initially, how much
interest is earned in this account over a 25 year period?

Answers

Answer:

$30,2400

Step-by-step explanation:

First, we need to find how much interest he earns in a month

8.4% of $12,000 = $1,008

Next, we multiply the amount of interest per month by the number of months in 25 years

25 years = 300 months

Now we can multiply the two values to get our final answer

1,008 x 300 = $30,2400

100 points !!!!!1 Drag the answers to match the inequality and the situation it represents. c<10 c>10 c<20 c>20

Answers

Hi!

c < 10

This means that c is less than 10. Any number smaller than 10 works, such as 7, -4, 5.6.

c > 10

This means that c is greater than 10. Any number greater than 10 works, such as 12, 58, 10.9.

c < 20

This means that c is less than 20. Any number smaller than 20 works, such as 6, -2, 19.7.

c > 20

This means that c is greater than 20. Any number greater than 20 works, such as 21, 74, 20.5.

Hope this helps! Have a great day :D

Answer:

here are the answers

Step-by-step explanation:

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