USE FOR MASTERY Number of attempts allowed: 1 Write two rational numbers a/b and c/d, where a, b, c, and d are the digits 2, 3, 4, or 5, such that no digit can be used more than once and that the two rational numbers are the greatest distance apart on the number line. Explain how you got this answer.

Answers

Answer 1

Answer:

We want to craft:

a/b and c/d

where a, b, c and d can be 2, 3, 4 and 5.

Such that the distance in the number line between these two numbers is maximized.

Then we want one number to be really small, and the other to be really large.

Remember two things:

for numbers like a/b.

if a is smaller than b, then a/b is smaller than 1.

Now, if a is larger than b, then a/b is larger than 1.

And two things,

1/10 = 0.1

10/1 = 10

So when the numerator is larger, the distance displaced in the number line is larger.

Then we want to have:

a number where the numerator is the largest option and the denominator is the smallest option:

a/b = 5/2

And the two remaining options in such way that the numerator is smaller than the denominator:

c/d = 3/4.

The distance between these two numbers is:

D = 5/2 - 3/4 = 10/4 - 3/4 = 7/4.


Related Questions

Evaluate 4(3-1)² i need help with this

Answers

The answer to the equation 4 ( 3 - 1 )^2 is 16

Answer:

16

Step-by-step explanation:

You can use PEMDAS to answer this question.

So first you would do whats inside the parenthesis.

4(3-1)².

3-1 is 2 so 2 would be in the parenthesis. Next you have to do exponets.

4(2)².

2² is 4. So now you just have a multiplication problem left.

4(4) which is 16.

Which of the following gives an equation of a line that passes through the point (3.-) and is
parallel to the line that passes through the origin and point (-2, -12)?

Answers

Answer:

A goes through the points

Step-by-step explanation:

Whoever is reading this:
I love u.
U matter.
The world needs u
hang in there ik it may be bad but u deserve the world <3
ur beautiful no matter ur shape, size, color, gender.. anything
don't give up i need u to live.
i wish i could take everyones problems so yall wouldn't have to have em but i cant so just know ily and if anyone needs to talk u can talk to me
Pls pass this on. Everyone deserves to know this. ♥️♥️

Answers

Answer:

Wait aww this is so sweet of you thank you <3

What property is this an example of 56 + 82 = 82 + 56?

Answers

Answer:

Step-by-step explanation:

Commutative property

It will be nice if you give me brainliest.Good luck!

PLS HELP ASAP!!!!! DUE IN 5 MIN!

Answers

Answer:

3^4 y^4

Step-by-step explanation:

Answer:

81y^(4)

Step-by-step explanation:

(-3y)^4

is the same as

-3y * -3y * -3y * -3y

which is

81y^4

C
Paul can spend no more than $26
on his pizza order. Each pizza costs $8 and there
is a $3 delivery fee.

Answers

Answer:

Paul can afford 2 pizzas

Step-by-step explanation:

Equation: 26 = 3 + 8x

Solve for x

26 - 3 = 23

8x = 23

23/8 = 2.875

Round down because he can't buy half a pizza

2 pizzas

Answer:

Paul can buy the pizza with 15 dolars left

step-by-step explanation:

8+3=11

When you solve |2x+6|=4x it has one extraneous solution at x=-1
true or false

Answers

It’s true hope that helped have a good night

the diameter of a certain species of bacteria is 0.00000057 meter. write this number as a single digit times a power of 10​

Answers

Answer: 57 x 10^-8 or 5.7 x 10^-7

Help please before its taken:)

Answers

Answer:

A variable whose variation does not depend on that of another.

a variable (often denoted by x ) whose variation does not depend on that of another.

The total weight of 15 boxes is 45 pounds. How much would 40 boxes weigh? *


Answers

Answer:

120 pounds

Step-by-step explanation:

15 boxes = 45 pounds

45/15= 3

1 box= 3 pounds

40 x 3 = 120

40 boxes would weigh 120 pounds

hope this helps :)

Answer: 120 lbs.

Explanation: One box weighs 3 pounds (divide 45 by 15). 3 times 40 equals 120. So the total weight is 120 pounds.

Plz mark brainliest:)

4. Is the expression (10x + 5 - 6x - 2) equivalent to (5x + 1 - (x - 2))? [True or False]
Prove this using algebra - Show work].

Answers

Here is the answer, with a picture of it!

What is the quotient of 513 divided by 19

Answers

Answer:

The number 513 is called the numerator or dividend, and the number 19 is called the denominator or divisor.

The quotient of 513 and 19, the ratio of 513 and 19, as well as the fraction of 513 and 19 all mean (almost) the same: 513 divided by 19, often written as 513/19.

Step-by-step explanation:

Answer:

27

Step-by-step explanation:

First you set up the equation of your quotient. Then divide it by 19, like so 513÷19 lastly you solve the answer that the math you calculated.

9 hundreds equals how many tens

Answers

Answer:

90 tens

Step-by-step explanation:

900 = 10x

Variable x refers to how many 10's are needed to equal 900

To solve for this, divide both sides of the equation by 10

900 ÷ 10 = 10x ÷ 10

90 = 1x

90 = x

It will take 90 tens to equal 900

9 hundreds are equal to 90 tens

How do I solve −6 + 9(8 − 2b) using distributive property or combining like terms.

Answers

Answer:

66-18b

Step-by-step explanation:

-6+72-18b

66-18b

solving for b

b=3.66 or 3 and 2/3

DON'T tell me it's easy or whatever because I'm having a hard time understanding it and someone on my last question WASTED my points.
PLEASE HELP ASAP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
(02.07 LC)

Two similar triangles are shown below:


Which two sets of angles are corresponding angles?

∠e and ∠h; ∠f and ∠g
∠e and ∠i; ∠f and ∠h
∠e and ∠g; ∠f and ∠h
∠e and ∠i; ∠f and ∠g

Answers

Answer:

im pretty sure the answer is ∠e and ∠i; ∠f and ∠g

but if not im so sorry :(

Answer:

The third answer

Step-by-step explanation:

Each angle on both triangles has a set of lines, either one, two, or three. These lines are used to show congruency over a number of lines or angles. So one angle will correlate with whatever other angles have that same number of lines. For example, e and g both have two lines, this means they are corresponding and congruent.

4
13) While shopping for a gift, you find the perfect wallet on sale
for 89% off its original $5.62 price. How much will you pay for
the wallet?
I
14) A wallet is marked with a sale sticker saying it is 76% off
The original price is $57.41. What is the sale price?
15) Originally priced at $48.69, a wallet was found on a 10% off
rack. What is the sale price of the wallet?

Answers

Answer:

13) 0.61 cent

14) 13.78 $

15) 3.82 $

Step-by-step explanation:

Hope this helps

The required solutions are given as,
13) Discounted price of the walled 0.61 cents,
14) the sale price is given as $ 13.78,
15) sale price of the wallet is  $ 3.82,

What is the percentage?

The percentage is the ratio of the composition of matter to the overall composition of matter multiplied by 100.

Here,
(1)
The perfect wallet is on sale for 89% off its original $5.62 price,
Discounted price, = 5.62 - 89% of 5.62
                               = 5.62 - 0.89 × 5.62
                               = 5.62(1 - 0.89)
                               = 5.62(0.11)
                               = 0.61 cents

Similarly,
14) the sale price is given as $ 13.78,
15) sale price of the wallet is  $ 3.82,

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rewrite 1/6 book 2/3 hour as a unit rate ​

Answers

Answer:

1/4 books per hour

Step-by-step explanation: Pls mark brainliest!

Answer:

it is 1\4 bro you working apix quiz don't be cheating

Step-by-step explanation:

A family built a house in a beach resort area. In 1990, the house was 430 ft from the water. With erosion, the house was 400 ft from the water in 2000. In what year will the house be only 250 ft from the water?

a. 1990

c. 2015

b. 2004

d. 2050

Answers

We develop an equation for the given situation by first writing the general equation for lines,

                                y = mx + b

Substituting to this given the values given above,

(1990)                      430 = b

(2000)                      400 = m(10) + 430

The value of m from the equation in 2000 is -3. Thus, the equation of that relates the variables is,

                              y = -3x + 430

Answer:

 

d.  2050

Step-by-step explanation:

-5.8 + -2.2= a positive number

Answers

Answer:

it would be negative (-8)

Step-by-step explanation:

-5.8 + -2.2 = -5.8 - 2.2

this would result in a negative number (-8)

which set of numbers represents a Pythagorean triple
6,9,12
7,10,12
16,18,25
27,36,45

Answers

Answer:

27,36,45

Step-by-step explanation:

Pythagorean theorem

[tex]a^{2} +b^{2} =c^{2}[/tex]

[tex]6^{2}+ 9^{2}\\ =117\\\neq 12^{2}[/tex]

[tex]7^{2}+ 10^{2}\\ =149\\\neq 12^{2}[/tex]

[tex]16^{2}+ 18^{2}\\ =580\\\neq 25^{2}[/tex]

[tex]27^{2}+ 36^{2}\\ =2025\\= 45^{2}[/tex]

Laura checked her outdoor thermometer and noticed that the temperature rose from 31 degrees in the morning to 45 degrees in the afternoon. What is the approximate percent increase for the day so far?

Answers

Answer: 45%

So for some reason I need to add at least 20 words? So... yeah... the answer is 45%

Answer: 45%

Step-by-step explanation:

- A recipe for ice cream calls for 56 fluid
ounces of milk. How many pints of milk are
there in the recipe?

Answers

Answer:

3.5

Step-by-step explanation:

there are 16 ounces in a pint so you do 56 ÷ 16

There are 16 fluid ounces in one pint which means that there are 3.5 pints in 56 fluid ounce.

How to calculate unit price of something?

Unit means 'single entity', the fundamental constructing block. Usually, it is 1 in mathematics and science.

Thus, unit price of something is price of 1 thing.

Then suppose we're taking about price of mangoes, then unit price will denote the price of 1 mango.

WE have been given a recipe for ice cream calls for 56 fluid ounces of milk.

We need to find How many pints of milk are there in the recipe.

There are 16 fluid ounces in 1 pint then;

56 ÷ 16

= 3.5

The answer is 3.5 pints because there are 16 fluid ounces in one pint which means that there are two pints in 32 fluid ounces and 3.5 pints in 56 fluid ounce.

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I need help with this​

Answers

The answer is 1 and 3.
Because there is no line between the numbers, it’s not a decimal

Hope this helped :)

Answer: obviously 3 and 1

Step-by-step explanation: There are 4 answers in the number line :/  

                                                there are 2 answers in the answer choices

                                                 this is a multi answer question so it is

                                                     3 and 1

Carmen ran one mile in 7 minutes. At this rate, how long will it take her to run 5 miles?

Answers

It would take her 35 minutes to run 5 miles


Hiiii Please help!!!
m/n(x), x≠

Answers

When we evaluate the quotient functions, (mn)(x) for x = -3

(mn)(-3) = 9 and (m/n) (x), x ≠ 0

How did we evaluate the quotient function?

To evaluate the quotient function (mn)(x) for x = -3, we  substituting x = -3 into the function mn(x).

This gives us (mn)(-3) = m(-3) × n(-3) = (-3)² × (-3) = 9.

We then need to evaluate (m/n)(x), x ≠ 0.

This is done by dividing the function m(x) by the function n(x). This gives us (m/n)(x) = m(x) / n(x) = x^2 / x = x. However, this expression is undefined when x = 0, because division by zero is undefine

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Please Answer Quickly!
A car has an initial value of $20,000. The value then "depreciates" or decreases by 10% of its initial value each year. Which equation below gives the value of the car, v, after y years?
v = -2,000 y + 20,000
v = 0.10 y - 2,000
v = 2,000 y - 20,000
v = - 0.10 y + 2,000

Answers

I think it’s the 4th or 2nd option not sure i might be wrong

Answer:

its the second one

i had the question and the last one is wrong soo.....

If you found this helpful I would appreciate it if you thanked or liked.

what angle is this??

Answers

The correct answer is B

Answer:

Acute Triangle

Step-by-step explanation:

Since all of the numbers are below 90 degrees, therefore, it makes it into an acute triangle.

Hope this helps! Stay safe!

bonnie has lived in texas for 768 days how many years have she lived in texas​

Answers

Answer: About 2.1 years

Step-by-step explanation:

768/365 = 2.10

Answer: Roughly 2 year

Exact answer: 2.104109589041096

Step-by-step explanation:

Graph: y – 3=1/2(x+2) ​

Answers

Simplify and get y=1/2x+4
1/2x=slope. 4= y-intercept

Beth's Diner offers its clients a choice of regular and diet soda. Last night, the diner served 88 sodas in all, 66 of which were regular. What percentage of the sodas were regular?

Answers

Answer:

75 Percent

Step-by-step explanation:

66/88 = .75, which equates to 75 percent.

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