Determine if 0.868668666866668666668...0.868668666866668666668... is rational or irrational and give a reason for your answer.

Answer:

Step-by-step explanation:

The given inequality can be written as 2m - 5/4 ≤ -7/8.

An inequality -7/8 is at most the difference of twice a number m and 5/4 which is 2m - 5/4 ≤ -7/8.

Difference of twice a number 'm' and 5/4 is 2m - 5/4 and this is at most -7/8 means less than or equal to.

∴ The given statement can be written as 2m - 5/4 ≤ -7/8

Answer:

2m - 5/4 ≤ -7/8

Step-by-step explanation:

hope this helps

Answer:

y=2x-5

Step-by-step explanation:

y - 2x = -5
add 2x to both sides.
y=-5+2x

Answer:

y = 2x - 5 is a line. determine the two points that this line intersects with the axes then connect these points to graph it.

Step-by-step explanation:

Given y = 2x -5 set y = 0 then solve for the abscissa

y = 2x - 5

0 =2x - 5

2x=5

x = 5/2

we now have the point (5/2,0)

set now x = 0 then solve for ordinate

y = 2x - 5

y = 2(0) - 5

y = -5

we now have the point (0, - 5)

we now simply draw a line passing thru the two points ( 5/2, 0) and (0, - 5)

kindly see the graph of y = 2x - 5 with points (5/2, 0) and (0, - 5)

Hope this helps

According to the table, the value of the function f(2) is 3

Functions are equations, ordered pairs, tables and graphs that are used to represent a relation

From the question, the function is represented by the table of values given as

X: 0 1 2 3 4

f(x): 4 2 3 9 1

From the question, the function to calculate is given as

f(2)

This means that we calculate the value of the function, when x = 2

i.e.

We calculate f(x), when x = 2

So, we look at the table of values for this function value

From the table of values, we have

When x = 2, f(x) = 3

This means that

f(2) = 3

So, we can conclude that the value of the function f(2) based on the given table when x =2 is 3

Hence, the function f(2) has a value of 3

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Answer:

Answer down below!

Step-by-step explanation:

We can tell from ABC and A'B'C' that they are similar, but not alike

Segment AC = 6 and segment A'C' =4

They just subtracted two from the 6

Let's do the same thing for segment BC!

If BC = 3, then we know that B'C' = 1

Answer:

The average cost for a gallon of gasoline in 2006 was $2.45. In 2007, the average cost of a gallon of gasoline was $3.29.

Slope-intercept form is y = 21.

The equation y = mx + c is the general equation of any straight line where m is the gradient of the line (how steep the line is) and c is the y -intercept (the point in which the line crosses the y -axis).

Given that,

The line is horizontal. It means slope of this line is zero. We can use the point-slope form for a linear equation since we know the slope and the point (15, 21).

Point-slope form: [tex](y-y_{1}) = m(x-x_{1})[/tex]

Where,

m = slope and [tex](x_{1}, y_{1})[/tex] is the points.

Then,

[tex](y-y_{1}) = m(x-x_{1})[/tex]

[tex](y-21) = 0(x-15)[/tex]

[tex]y-21 = 0\\y=21[/tex]

Hence, the Slope-intercept form is y = 21.

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In the polygon, The triangles are not similar

The term similar triangles refers to triangles that the ratio of the sides are equal.

In the problem, the sides of the triangles are given as

The ratio of the sides

In DQRS: QR / RS = 4/15 = 0.27

In DUVT: VT / TU = 8/32 = 0.25

0.27 ≠ 0.25

since the ratio of the sides are not equal the two triangles are not similar

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The constant of proportionality (K ) we will write

Perimeter = 3 ( side)  where K = 3

Perimeter of any polygon is defined as the sum of all sides of  polygon.

Given polygon is a triangle. A triangle is any polygon which has three sides.

And as the sides of a polygon increases the perimeter also increases.

One can say that perimeter and side of a polygon has a direct relationship.

That is when we write it mathematically we write it like:

Perimeter ( P ) ∝ Sides of polygon

However given is an equilateral triangle

this means that all sides of the triangle are equal

so let us consider the side of the triangle as "s"

Thus we get that perimeter will be 3 times s

which when mathematically written will be:

Perimeter ∝ ( side)

to remove the constant of proportionality (K ) we will write

Perimeter = 3 ( side)  where K = 3

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y=2/3x-3 that is the slope intercept form

The least number of main courses that the restaurant should offer is 8.

The mathematical expression with unequal sides is known as an inequality in mathematics. Inequality is referred to in mathematics when a relationship results in a non-equal comparison between two expressions or two numbers. In this instance, any of the inequality symbols, such as greater than symbol (>), less than symbol (), greater than or equal to symbol (), less than or equal to symbol (), or not equal to symbol (), is used in place of the equal sign "=" in the expression. Polynomial inequality, rational inequality, and absolute value inequality are the various types of inequalities that can exist in mathematics.

let m be  the number of main courses restaurant serves

so, 2m is the number of appetizers  

then the number of dinner combination is =  2m x m x 3 = 6m^2

since the customer wants to eat a different dinner in all 365 days of 2003,

we must have ,

[tex]6m^{2}[/tex] ≥  365

[tex]m^{2}[/tex]  ≥ 60.83.....

also the 2003 is not a leap year

because 2003 / 4 is not equal to an integer

the smallest integer value satisfies this is 8 .

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Answer:

Step-by-step explanation:

Answer:

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Step-by-step explanation:

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As shown in the reference graph attached hereby with the question statement, if the linear model represents the height, f(x), of a water balloon thrown off the roof of a building over time "x" measured in seconds, then,

(A) During (2 ≤ x ≤ 5) seconds in the time domain, the water balloon's height remains the same.

(B) During (0 ≤ x ≤ 2) seconds, the height of the water balloon is increasing.

(C) During (5 ≤ x ≤ 6) seconds, the height of the water balloon decreases the fastest.

(D) From Part (C), it can be justified that 5 ≤ x ≤ 9.5 is the interval where the balloon's height is decreasing, and, (5 ≤ x ≤ 6) is the interval where the slope is the steepest.

As per the question statement and the reference graph attached alongside, the linear model represents the height, f(x), of a water balloon thrown off the roof of a building over time "x" measured in seconds.

We  are required to determine the correct time domains for four different situations, by observing the plotted graph.

Part (A) is to determine the correct time domain where the water balloon's height remains the same.

From the graph, it is clear that, the height remains constant at (y = 70), parallel to the x-axis from the 2nd second to the 5th second. Hence, During (2 ≤ x ≤ 5) seconds in the time domain, the water balloon's height remains the same.

Part (B) is to determine the correct time domain where the height of the water balloon is increasing.

From the graph, it is clear that, the slope of the concerned graph rises only from [(y = 40) to (y = 70)], starring from the 0th second until the 2nd second. Hence, During (0 ≤ x ≤ 2) seconds in the time domain, , the height of the water balloon is increasing.

Part (C) is to determine the correct time domain where the height of the water balloon decreases the fastest.

From the graph, it is clear that, the graph decreases thrice, first from [(y = 70) to (y = 40)], starting at the 5th second uptil the 6th second, then from [(y = 40) to (y = 10)], starting at the 6th second uptil the 9th second and lastly, from [(y = 10) to (y = 0)], starting at the 9th second till the 9.5th second. Here, we can easily calculate that, the balloon dropped 30ft in 1 sec at the first instance, 30ft in 3 seconds at the second instance and, 10ft in 0.5 seconds.

Since, [(30/1) > (10/0.5) > (30/3)],

Or, [30 > 20 > 10],

Thus, During (5 ≤ x ≤ 6) seconds, the height of the water balloon decreases the fastest.

Part (D) is to determine the correct statement mentioned under it's options, with judgement based on Part (C).

Option (i) states that [(5 ≤ x ≤ 9.5) is the interval where the balloon's height is decreasing] which is true, as we can observe from the graph that the slope is decreasing during the time interval of 5 to 9.5th seconds, although at different rates at different intervals.

Option (ii) states that [(8 ≤ x ≤ 9.5) is the interval where the slope is the steepest] which means that, during this above said interval, the height of the balloon drops the fastest which is false, as we have already proved in part (C) that during (5 ≤ x ≤ 6) seconds, the height of the water balloon decreases the fastest.

Option (iii) states that, [(6 ≤ x ≤ 8) is the interval where the balloon's height decreases the most] which is false, as balloons height falls the farthest by 30fts in two separate intervals, between (5 ≤ x ≤ 6) seconds and (6 ≤ x ≤ 9) seconds.

Finally, Option (iv) states that [(5 ≤ x ≤ 6) is the interval where the slope is the steepest] which means that, during this above said interval, the height of the balloon drops the fastest which is true, as we have already proved in part (C) that during (5 ≤ x ≤ 6) seconds, the height of the water balloon decreases the maximum in the shortest time period.

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For x = 28, the value of [y] such that [x] is directly proportional to [y] will be 112.

Direct proportion or direct variation is the relation between two quantities where the ratio of the two is equal to a constant value. Mathematically, direct proportionality is represented by a straight line and it equation is of the form -

y = kx

k = y/x

where [k] is the constant

Given is the value of [y], which is directly proportional to the value of [x], and when [x] = 3.5, the value of [y] is 14.

We have the following data -

[y] = 14 at [x] = 3.5

Now, since [y] is directly proportional to [x], we cam write -

y = kx

k = y/x

k = 14/3.5.            [1]

Now, for x = 28, we can write the relation as -

y/x = k

k = y/28            [2]

Now, equating equation [1] and [2], we get -

14/3.5 = y/28

y = (14 x 28)/3.5

y = (140 x 28)/35

y = (140 x 4)/5

y = 28 x 4

y = 112

Therefore, for x = 28, the value of [y] such that [x] is directly proportional to [y] will be 112.

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The greatest common divisor (24,6) is 6 and the least common multiple (24,6) is 24.

As per the question statement, the greatest common divisor of two integers is (x+2) and the least common multiple x(x+2). It is given that one of the integers is 24.

Let us assume that "b" is the value of other one.

greatest common divisor(24,b) = (x+2)

least common multiple(24,b) = x(x+2)

Formula:

greatest common divisor(24,b)*least common multiple(24,b) = 24*b

24*b = (x+2)*x(x+2)

[tex]b = \frac{x(x+2)^{2} }{24} \\[/tex]

Hence, the smallest possible value of the other one is "6" and x = 4.

Hence, the greatest common divisor (24,6) is 6 and the least common multiple (24,6) is 24.

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The solutions for each statement are given below.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

We have,

The initial amount of the company = -$200,000

Earnings for selling one batch = $40,000

Now,

1.

The two quantities that are changing in this situation are:

The number of batches.

The amount of profit.

2.

The independent variable is the number of batches.

The dependent variable is the profit.

3

The number of batches = x

The amount of profit = y

The equation for the profit.

P = -200,000 + B x 40,000

Where B is the number of batches.

4.

Batches of tires   Profits

   B                        P

0                         -200,000

1                          -160,000

2                          -120,000

3                           -80,000

4                           -40,000

5                            0

5.

The unit rate of change.

= (-120,000 + 160,000) / (2 - 1)

= 40,000

Thus,

The statements are given above.

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Answer:

a. -5x³ + 29x² - 56x + 15

b. 8x² + 9x + 5

c. 18t³ - 42t² - 14t - 30

d. x³ - 2x² - 5x + 6

e. -2b⁴ + a² + 6b² - 24a

Step-by-step explanation:

a. 3(x³ − x² + 5) − 8(x³ − 4x² + 7x)

3x³ - 3x² + 15 - 8x³ + 32x² - 56x

-5x³ + 29x² - 56x + 15

b. 7x² + 2x + 5 + x(x + 7)

7x² + 2x + 5 + x² + 7x

8x² + 9x + 5

c. 10(t³ − 4t² + 1) − t(2t + 6) + 8(t³ − t − 5)

10t³ - 40t² + 10 - 2t² - 6t + 8t³ - 8t - 40

18t³ - 42t² - 14t - 30

d. (x − 1)(x + 2)(x − 3)

(x - 1)(x + 2)

x(x + 2) - 1(x + 2)

x² + 2x - x - 2

x² + x - 2(x - 3)

x(x² + x - 2) - 3(x² + x - 2)

x³ + x² - 2x - 3x² - 3x + 6

x³ - 2x² - 5x + 6

e. (3a − 2b²)(3a + 2b²) − 3(4a − b²)2 + 2(−2a − b²)(2a − b²)

3a(3a - 2b²) + 2b²(3a - 2b²)

9a² - 6ab² + 6ab² - 4b⁴ - 3(4a − b²)2 + 2(−2a − b²)(2a − b²)

9a² - 4b⁴ - 24a + 6b² + 2(−2a − b²)(2a − b²)

                                                               (−2a − b²)(2a − b²)

                                                              -2a(2a - b²) - b²(2a - b²)

                                                               -4a² + 2ab² - 2ab² + b⁴

                                                                -4a² + b⁴

                                                                 2(-4a² + b⁴)

                                                                  -8a² + 2b⁴

9a² - 4b⁴ - 24a + 6b² - 8a² + 2b⁴

-2b⁴ + a² + 6b² - 24a

The angle x has a measure of 37

Angles are formed when two or more lines intersect. This in other words means that angles is the measure of space between the intersection of rays or lines

The given parameter is the figure

On the figure, we have the following angle measures

2x, 79, 32 and 5x

The sum of angles in a quadrilateral is 360 degrees

So, we have the following equation

2x + 79 + 32 + 360 - 5x =  360

Evaluate the like terms in the above equation

So, we have the following equation

-3x + 79 + 32  =  0

Evaluate the like terms in the above equation

So, we have the following equation

-3x =  -111

Divide both sides of the equation by 3

x = 37

Hence, the value of x is 37

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Answer:

Step-by-step explanation:

Answer: p= 6-0.5

solve 1.5m + 3p=18

p= 6-0.5m

From the given parameter, the total amount that Lou spent on the gas is; $30.8

We are told that Lou​'s car had 6.2 gallons in the 15 gallons in the ​-gallon tank on the coldest day of the year.

Now, Lou filled the tank with gas that cost ​$ 3.50 per gallon.

Thus;

Amount of gas that Lou bought = 15 - 6.2

Amount of gas that Lou bought = 8.8 gallons

Since he bought these gallons at the cost of ​$3.50 per gallon, then it means that;

Total amount he spent = 8.8 * 3.5

Total amount he spent = $30.8

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Complete question is;

Some people advise that in very cold​ weather, you should keep the gas tank in your car more than half full. Some people advise that in very cold​ weather, you should keep the gas tank in your car more than half full. Lou​'s car had 6.2 gallons in the 15 gallons in the ​-gallon tank on the coldest day of the year.

Lou filled the tank with gas that cost ​$ 3.50 per gallon. How much did Lou spend on​ gas?

Answer:

m<2=m<5=50

m<4=85

m<6=45

Step-by-step explanation:

Answer:

1:85 2:50 3:45 4:85 5:50 6:45

Step-by-step explanation:

pls give brainliest

1 should be like 4 and 3 should be like 6.

Like 6+1 is 130 so 2 is 50

⇒To get the difference we subtract.

[tex]2.5-7.5=-5\\[/tex]

⇒To get the sum we add.

[tex]2.75+9.55=12.3[/tex]

Goodluck!!

Answer:

31cm

Step-by-step explanation:

Add AC and BC together to get AB.

AC = 2x - 13 and

BC = 3x + 4 and

AB = 36 (this is all the given information)

The two smaller pieces can be combined to equal the whole segment.

AC + BC = AB

2x - 13 + 3x + 4 = 36

combine like terms.

5x - 9 = 36

Add 9

5x = 45

Divide by 5.

x = 9

But you're not done because they asked for BC.

BC = 3x + 4

substitute 9 for x.

BC = 3(9) + 4

BC = 27 + 4

BC = 31

BC is 31 cm.

The number of tornadoes is 77

total time for occurrence is 70 years

using these

= ( 77/70)

= (  1.1 )

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there are two aircraft​ carriers, a and​ b, and carrier a is longer in length than the carrier b. then Carrier A is 2,104 feet and Carrier B is 2,094 feet.

Since there are two aircraft carriers, A and B, and carrier A is longer in length than the carrier B, and the total length of these two carriers is 4198 feet, while the difference of their lengths is only 10 feet, to determine the length of each aircraft carrier, the following calculation must be performed:

(4,198 - 10) / 2 = X

4.188 / 2 = X

2,094 = X

2,094 + 10 = 2,104

2,094 + 2,104 = 4,198

Therefore, Carrier A is 2,104 feet and Carrier B is 2,094 feet.

the complete question is

There are two aircraft carriers, A and B, and carrier A is longer in length than the carrier B. The total length of these two carriers is 4198 feet, while the difference of their lengths is only 10 feet.

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// ignore, made mistake//

Answer:

(4.7) and (5.-7)

Step-by-step explanation:

find the gradient using the formula:

y2-y1 (divide this by the bottom)

x2-x1

-7-7

5-4

=-14/1

-14 is the answer

then you will say y-y1= m(x-x1)

you can choose to sub any point

I will use (4;7)

therefore...

y-7=-14(x-4)

y= -14x+56+7

y= -14x+63

Answer:

D. 22.50

Step-by-step explanation:

22.5 - 8 = 14.5

14.5 + 22.5 = 37

Answer:

use a calculator or try math app

The solution of  the value is mathematically given as

√6 =2.449

This is further explained below.

Generally, In mathematics, the term "square root" refers to a component of a number that, when multiplied by itself, results in the same value as the original number.

As an example, both 3 and –3 are square roots of the number 9.

A number y is said to have a square that is equal to a given number x if and only if it satisfies the following condition: y2 = x.

Another way to express this is to say that the number y has the same value as its own square. For example, the square roots of 16 are 4 and -4, since 42 divided by 2 is 16.

In conclusion,

√6 is not -4

because

√6 =2.449

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