Why is the product of two rational numbers always rational?

Select from the drop-down menus to correctly complete the proof.



Let ab and cd represent two rational numbers. This means a, b, c, and d are
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, and
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. The product of the numbers is acbd, where bd is not 0. Because integers are closed under
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, ​acbd​ is the ratio of two integers, making it a rational number. Integers or rational numbers.

The inequality that represents the number of songs and albums that Jorge could download is:

$2*s + $12*a ≤ $50

Here we have the variables:

s = number of songs.

a = number of albums.

Then the total cost can be written as:

$2*s + $12*a

And we know that Jorge has a maximum of $50 to spend, so the total cost can be equal to or smaller than $50, so the inequality is:

$2*s + $12*a ≤ $50

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Answer:

Step-by-step explanation:

Area of circle equation:

Circumference of circle equation:

Use circumference equation to find the radius:

Find the area:

If  the price of a used car is discounted $200 each week then the grapg will be linearly decreasing in nature

A linear graph can be either increasing, decreasing or constant.

Here the price of the car is being discounted $200 every week, so as the number of weeks increase, the price of the car decreases

So, the graph for this situation will be linearly decreasing.

The slope of this kind of graph is negative/

Therefore, If  the price of a used car is discounted $200 each week then the grapg will be linearly decreasing in nature

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Answer: I don't know  

Step-by-step explanation:

Answer:

Step-by-step explanation:

Correct Answer: C.

First we can see that the slope is negative, meaning the graph is decreasing.

Then we go to the point (-1,0) and go down 2 and 3 right. if that point is on the line, then we know it's correct.

The sequence is geometric and the common ratio is 1/7

An arithmetic sequence is a sequence of numbers in which each differs from the preceding one by a constant value e.g 2, 4, 6, etc. That is: 6-4 = 4-2 = 2

A geometric sequence is a sequence of numbers with a constant ratio between each number and the one before e.g.  9, 27, 81, etc. That is: 81/27 = 27/9 = 3

Given: 147, 21, 3

This sequence does not have a common difference. Thus, it is not arithmetic

This sequence has a common ratio. Thus, it is geometric

common ratio = 21/147 = 1/7 or 3/21 = 1/7

Therefore, the sequence is geometric and has a common  ratio of 1/7

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The division of 5.375 divided by 0.25 results to 21.5

One of the fundamental mathematical operations is division, which involves breaking a bigger number into smaller groups with the same number of components. How many groups will be created,

for instance, if 30 students need to be separated into groups of five for a sporting event?

In this case, we must divide 30 by 5. 30 x 5 = 6 will be the outcome.

Given:

5.375 divided by 0.25

Now, dividing the above decimal

= 5.375/ 0.25

= 5375 x 100 / 25 x 1000

= 215 / 10

= 21.5

Hence, the division results to 21.5

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[tex]y = \cfrac{2}{5}x + 0\implies y=\cfrac{2}{5}x\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}[/tex]

Answer:

- 3/4

PLEASE GIVE BRAINLIEST THANK YOU!!!

The rule for given translation is (x,y)→(x + 3, y - 4).

In mathematics, the phrases translation, rotation, and reflection are all used to describe the change of forms. This refers to a form moving beyond a mirror line or a fixed point. While being translated, rotated, or reflected, the shape doesn't change. The constant rotation of a shape around a fixed point or across the mirror line is known as translation. Rotation defines the way a form moves about a central axis. Shapes can be rotated by a specific number of degrees either clockwise or counterclockwise.

The rule for translation of given figure will be,

We need to move x for 3 units to left and y for 4 units downwards to get the translation, so the rule is:

(x,y)→(x + 3, y - 4).

Therefore, the rule for given translation is (x,y)→(x + 3, y - 4).

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Answer:

The two numbers are 17 and 44.

Step-by-step explanation:

x --> smaller number

y --> larger number

x + y = 61

y = 3x - 7

x + 3x - 7 = 61

4x - 7 = 61

4x = 68

x = 17

y = 3(17) - 7

y = 51 - 7

y = 44

Answer:

$193.60

Step-by-step explanation:

160x1.21=$193.60

160+21%=$193.60

If the dealer gives Bernie the listed trade- in price for his car,  he will pay $391.97  monthly.

Given that,

Bernie has decided to purchase a new car of $ 18,575.

The sales tax is 7.40%

Now,

18,575 x 7.40% = 1,374.55

Now, summing up the result of sales tax and purchase price, we get,

18,575 + 1,374.55 = 19,949.55

Bernie will give registration fees of $795

and, a documentation fees: $110

Now , we will sum up all the above information, i.e.,  

= 19,949.55 + 795 + 110

= 20,854.55

Now, divide the result of documentation fees and registration fees by 5

                         20,854.55 ÷ 5 = 4,170.91

Dividing the above result by 12,                      

                          4,170.91 ÷ 12 = 347.58

Now, the finance the rest of the cost for five years at an interest rate 12.77%.

                       347.58  x 12.77% = 44.39

And,

                       347.58 + 44.39 = 391.97

Therefore, If the dealer gives Bernie the listed trade - in price for his car,  he will pay $391.97  monthly.

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Answer:

Solution

=5(X+10)+X

=5×x+5×10+x

=5x+50+X

=6x+50

Step-by-step explanation:

Your answer is 6x+50.

The values of m<4 and m<6 are 160° and 20° respectively

To solve this problem, we need some angle geometry knowledge:

Given that: m<6 = 1/8 m<4

Since m<6 = 1/8 m<4. Thus, m<4 = 8.m<6

m<6+ m<4 =  m<6 + 8.m<6 = 9.m<6    (Algebra)

m<6+ 8.m<__ = 180° will be:

m<6+ 8.m<6 = 180°      

Note: m<6 + m<5 = 180° (angles on a straight line) and m<5 = m<6 (alternate angles)

m<6+ 8.m<6 = 180°

9.m<6 = 180°

m<6 = 180/9 = 20°

m<4 = 8 x m<6

m<4 = 8 x 20° = 160°

Therefore, the values of m<4 = 160° and m<6 = 20°

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Answer:

slope = - [tex]\frac{7}{13}[/tex]

Step-by-step explanation:

calculate the slope m using the slope formula

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

with (x₁, y₁ ) = (9, - 10 ) and (x₂, y₂ ) = (- 4, - 3 )

m = [tex]\frac{-3-(- 10)}{-4-9}[/tex] = [tex]\frac{-3+10}{-13}[/tex] = [tex]\frac{7}{-13}[/tex] = - [tex]\frac{7}{13}[/tex]

Answer:

$2940

Step-by-step explanation:

30 percent *4200 =

(30:100)*4200 =

(30*4200):100 =

126000:100 = $1260

4200-1260=$2940

Answer: y= (7a+9b)/8

Step-by-step explanation:

I can only provide the answer now, If you want more explanations reply this

Step-by-step explanation:

(2y - a)/3 = (a + 3b)/4

first we get rid of the fractions by multiplying everything first by 3 and then also by 4 ;

(2y - a) = 3(a + 3b)/4

4(2y - a) = 3(a + 3b)/4

8y - 4a = 3a + 9b

8y = 7a + 9b

y = (7a + 9b)/8

Using the Work time problem solving technic, Betty and Bullwinkle to mow the entire lawn in 30 minutes if they are working together.

As we know that if A is complete the work of z in x days and B is complete the same work (z) in y days then both of can do complete work together then Equation of both A and B are completing work (z) together in

( 1/x + 1/y = 1/z ) days

Since Betty can mow a lawn is 120 minutes, then

Betty's mowing rate is 1/120th of a lanw per minute.

Since Bullwinkle can mow a lawn is 40 minutes, then Bullwinkle mowing rate is 1/40th of a lawn per minute.

Suppose working together they can a lawn in x minutes.

both together they can mow a lawn is x minutes, then their combined mowing rate is 1/x th of a lawn per minute.

To get the equation,

the sum of their mowing rates must equal their combined mowing rate,

1/40 + 1/120 = 1/x

Solve that by multiplying through by LCD of 40 and 120 is 120 then 4x = 120 => x = 30

Hence, when both are working together they complete the work together in 30 minutes .

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Answer: 13g

Step-by-step explanation: because each gram is 1000 milligrams

Using the theories of quantitative​ variables, we got that Graphical display is the first thing that should be​ done when we are analyzing two quantitative​ variables.

Comparing the Two Quantitative Variables As we did when considering only one variable, we begin with the graphical display. A scatterplot is the most useful display technique for comparing the two quantitative variables. We plot on the y-axis the variable we consider for the response variable and on the x-axis we place the explanatory or the predictor variable.

Hence, When analyzing two quantitative​ variables,  the first thing that should be​ done is Graphical display.

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95km/h is the average speed for the whole journey

Speed is the time rate at which an object is moving along a path, while velocity is the rate and direction of an object's movement

Given,

Simon drives 75 km at an average speed of 120 km/h

9 km at 70 km/h without stopping.

We need to find the average speed.

Average speed = Total distance/Total time

The total distance is 75km+9km

84 km

The average speed is sum of speeds by two

120+70=190/2=95km/h

Hence, 95km/h is the average speed for the whole journey

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The set of ordered pairs that represent 90 degrees counter clockwise rotation about he origin is

3) A' (-6, 1) B' (-6, 6) C' (-2, 1)

Rotation is a from of transformation that involves circular movement about an axis.

There two types of rotation

The transformation rule for 90 degrees clockwise rotation is as follows

(x, y) for a scale factor of r → (-y, x)

From the graph the coordinates are read and following the given transformation rule we have

preimage   image

A (1, 6)   →   A' (-6, 1)

B (6, 6)  →  B' (-6, 6)  

C (1, 2)  →   C' (-2, 1)

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Answer:

27 miles, 40.5 miles, and 47.25 miles

Step-by-step explanation:

9 miles in 2/3 hours. To get to a whole number, we can multiply by the reciprocal of 2/3, which is 3/2. 2/3*3/2=1. Now lets multiply 9 by 3/2. 9*3/2=13.5

We now have a unit rate which is 13.5 miles each hour.

Now lets solve for 2 hours.

13.5*2= 27 miles

Now lets solve for 3 hours.

13.5*3=40.5 miles

Now lets solve for 3.5

13.5*3.5= 47.25 miles

The given statement is FALSE.

If one or more data items are much greater than the other items, the median, rather than the mean, is more representative of the data.

When one or more data items are much greater than the other items, these extreme values can greatly influence the mean.

When you have a skewed distribution, the median is a better measure of central tendency than the mean

The median and mean can only have one value for a given data set. The mode can have more than one value

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Answer:

1/2 teaspoon of salt per 1 teaspoon of baking soda.

Step-by-step explanation:

If you're starting with 1/2 tsp of baking soda and 1/4 tsp of salt, you can multiply that by two and still have the same ratio of salt to baking soda.

:)

Answer:

$712.50

Step-by-step explanation:

.95(750) = 712.5  If they give 5% to the seller, they get to keep 95%

The shopper bought a watermelon costing $4.45.

Let x represent the cost of watermelon

y = cost of napkin + cost of paper plates

The tax rate on non-food items is 5%, hence:

5% of y = 0.19

0.05y = 0.19

y = $3.8

The total for the three items he bought was $8.25 before tax,

x + y = 8.25

x + 3.80 = 8.25

x = 4.45

The shopper bought a watermelon costing $4.45.

A tax is a compulsory monetary charge or a few other sorts of levy imposed on a taxpayer (a man or woman or criminal entity) by using a governmental agency if you want to fund authorities' spending and numerous public expenses (regional, neighborhood, or countrywide), and tax compliance refers to coverage movements and character behavior geared toward making sure that taxpayers are paying the right amount of tax on the proper time and securing the right tax allowances and tax reliefs. the first known taxation passed off in historical Egypt around 3000–2800 BC. A failure to pay in a well-timed way (non-compliance), together with evasion of or resistance to taxation, is punishable by means of regulation. Taxes consist of direct or oblique taxes and may be paid in cash or as its labor equivalent.

Maximum nations have a tax system in the region, so as to pay for public, common societal, or agreed-on country-wide needs and for the capabilities of the presidency. a few levies a flat percentage rate of taxation on private annual profits, however, maximum scale taxes are modern and based on brackets of annual earnings amounts. most nations charge a tax on a character's profits as well as on corporate earnings. nations or subunits regularly additionally impose wealth taxes, inheritance taxes, estate taxes, gift taxes, property taxes, sales taxes, use taxes, payroll taxes, duties, and/or tariffs.

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The average speed for the whole journey is 95.3km/hour

The average speed is the total distance traveled by the object in a particular time interval. The average speed is a scalar quantity. It is represented by the magnitude and does not have direction.

Average speed = Total distance/total time taken

The distance covered in the first journey is 75km and the time spent is calculated as Distance/speed

= 75/110 = 0.68hour

The time used for the second journey is

= distance/speed

= 7/40 = 0.18 hour

The total time spent = 0.68+0.18 = 0.86 hour

The total distance traveled = 75+7 = 82km

Therefore the average speed = 82/0.86 = 95.3 km/hour.

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