Let a and b be rational numbers. Is a – b rational or irrational?

Answer: 1 U.S.dollar  = 0.85 euro.

1 euro = 1.18 dollars.

Step-by-step explanation:

The given equation: [tex]E=\dfrac{17}{20}D[/tex]

, where 'E' is the amount of euros that has the same value as 'D' U.S. Dollars.

At D= 1,

[tex]E=\dfrac{17}{20}=0.85\text{ euro}[/tex]

i.e. 1 U.S.dollar  = 0.85 euro.

At E= 1 , we have

[tex]1=\dfrac{17}{20}D\\\\\Rightarrow\ D= 20/17\approx1.18\text{ dollars}[/tex]

Hence, 1 euro = 1.18 dollars.

Answer:

Felipe = 23 messages

Keisha = 31 messages

Manuel = 46 messages

Step-by-step explanation:

Keisha = K

Felipe = F

Manuel = M

=> There are a total of 100 messages.

=> K sent 8 +F => K = 8 + F

=> M sent 2 * F => M = 2F

=> F = F

=> 8 + F + 2F + F = 100

=> 8 + 4F = 100

=> 8 - 8 +4F = 100 -8

=> 4F = 92

=> 4F/4 = 92/4

=> F = 23

So, Felipe = 23 messages.

      Keisha = 8 + F = 8 + 23 = 31 messages.

      Manuel = 2F = 2* 23 = 46 messages.

46 + 31 + 23 = 77 + 23 = 100 messages.

So, the answer is correct.

Answer:

A = ± [tex]\sqrt{\frac{q+3g}{b^2} }[/tex]

Step-by-step explanation:

Given

b²A² - 3g = q ( add 3g to both sides )

b²A² = q + 3g ( divide both sides by b² )

A² = [tex]\frac{q+3g}{b^2}[/tex] ( take the square root of both sides )

A = ± [tex]\sqrt{\frac{q+3g}{b^2} }[/tex]

Answer:

42 = 8x + 13x

42 = 21x

x = 2

8 = 8c -4(c + 8)

8 = 8c - 4c - 32

8 = 4c - 32

40 = 4c

c = 10

Answer:

42 = 21x

42/21 = x

x = 2

check:

42 = 8*2 + 13*2

42 = 16 + 26

8 = 8c -4*c -4*8

8 = 8c - 4c - 32

8 + 32 = 4c

40 = 4c

40/4 = c

c = 10

Check:

8 = 8*10 - 4(10+8)

8 = 80 - 4*18

8 = 80 - 72

Answer:

59.5 feet

Step-by-step explanation:

The second tree is 59.5 feet tall.

Two trees are growing in a clearing.

The first tree is 17 feet tall and casts a 10-foot shadow.

The second tree casts a 35-foot shadow.

Let x be the tall is the second tree.

Then,

The ratio of the height of the tree is;

[tex]\rm \dfrac{17}{10} = \dfrac{x}{35}\\\\17 \times 35 = x \times 10\\\\595 = 10x\\\\x = \dfrac{595}{10}\\\\x = 59.5 \ feet[/tex]

Hence, the second tree is 59.5 feet tall.

To know more about Ratio click the link given below.

https://brainly.com/question/8677748

Answer:

24 kilometers per hour

Step-by-step explanation:

15 kph x 8 h = 120 kilometers

120km/5 hours = 24 kph

Step-by-step explanation:

Hi, there!!!

According to the question,

1st case

At the speed of 15 km/ hr, it takes time 8 hrs to reach a point.

Then, we must find the distance first to calculate your speed in 2nd case,

So, let's find the distance first,

now,

distance (d) = s×t

or, d= 15km/ hr × 8hrs

Therefore, the distance is 120 km.

now,

In 2nd case,

As the question has asked to find speed on same point, it will have same distance covered.

time( t) = 5hrs.

distance (d)= 120km

now,

speed = distance/time taken

or, s= 120 km/5 hrs

or, s = 24km/ hr.

Therefore, your speed in 2nd case will be 24km/hr.

Hope it helps...

Answer: 46.15%

Step-by-step explanation:

From the question, we are informed that a 13 minute video played for 6 minutes. The amount of percent played will be:

= 6/13 × 100

= 0.4615 × 100

= 46.15%

Answer:

a = 2, b = 3

Step-by-step explanation:

The diagonals of a rectangle bisect each other, thus

5a² = 4a² + 4 ( subtract 4a² from both sides )

a² = 4 ( take the square root of both sides )

a = [tex]\sqrt{4}[/tex] = 2

Also

6b - 8 = 4b - 2 ( subtract 4b from both sides )

2b - 8 = - 2 ( add 8 to both sides )

2b = 6 ( divide both sides by 2 )

b = 3

Mentally, rotating the Cartesian Plane 180º, we find that the figure that was in the 4th quadrant goes to the 2nd quadrant.

So, answer B

Answer:

Option a.

Step-by-step explanation:

In the given triangle angle A is a right angle so triangle ABC is a right angled triangle.

Opposite side of right angle is hypotenuse. So, CB is hypotenuse.

From figure it is clear that CA is shorter that segment BA.

All angles are congruent to itself. So angle C is congruent to itself.

We know that, if an altitude is drawn from the right angle vertex in a right angle triangle it divide the triangle in two right angle triangles, then given triangle is similar to both new triangles.

So, triangle ABC is similar to triangle DBA if segment AD is an altitude of triangle ABC.

Therefore, the correct option is a.

Answer:

-5/8

Step-by-step explanation:

(2,4) (-6.9)

m= y2-y1/x2-x1

= 9-4/-6-2

=5/-8

=-5/8

Answer:

The x-axis!

Step-by-step explanation:

Answer:

2.23kg

Step-by-step explanation:

If you can get 1 kg for $4.50. You can perform a ratio to find out how much you get for $10.

1/4.50=x/10

.2222222=x/10

multiply the 10 on both sides

x=2.23 kg for $10

Answer:

[tex]x^2 +4x +3 [/tex]

Step-by-step explanation:

f(x)=x²-1

g(x)= x+2

f(g(x)) =f(x+2)

=(x+2)²-1

=x²+4x+4-1

=x²+4x+3

Answer:

XN = 6

Step-by-step explanation:

Given XY is an angle bisector then the ratio of the sides is equal to the corresponding ratio of the base, that is

[tex]\frac{AX}{XN}[/tex] = [tex]\frac{AY}{YN}[/tex] , substitute values

[tex]\frac{18}{XN}[/tex] = [tex]\frac{12}{4}[/tex] ( cross- multiply )

12XN = 72 ( divide both sides by 12 )

XN = 6

Answer:

A=48.81

Step-by-step explanation:

it is a right angle triangle find the hypotenuse c using Pythagorean theorem:

c²=a²+b²

c²=8²+7²

c=√64+49

c=10.63

sin A =opp/hyp

sin A=8/10.63

A=  48.81

another way :

tan A=opp/adj

tan A=8/7

A=48.81

Answer:

$29252.1669

Approximately $29252.1

Step-by-step explanation:

For Monday,  Tuesday and Sunday:

=> 8.50 x 5 x 3

=> 8.5 x 15

=> 127.5

I multiplied 8.5 and 5 because you work for 5 hours. Then multiplied them with 3 it is for 3 days.

For Friday, Saturday, Thursday:

=> 8.5 x 6 x 3

=> 8.5 x 18

=> 153

I multiplied 8.5 and 6 because you work for 6 hours. Then multiplied them with 3 because it is for 3 days.

In 1 week you get:

=> 153 + 127.5

=> 280.5

In 1 year there are 52.1429 weeks.

So, you get:

=> 52.1429 x 280.5

=> 14626.08345

For 2 years, you get:

=> 14626.08345x 2

=>  29252.1669

=> Approximately $29252.1

Answer:

The area inside the square and outside the circle is changing at a rate of 101.150 square meters per day.

Step-by-step explanation:

According to the statement of the problem, the circle is inside the square and the area inside the square but outside the circle, measured in square meters, is represented by the following formula. It is worth to notice that radius ([tex]r[/tex]) is less than side ([tex]l[/tex]), both measured in meters:

[tex]A_{T} = A_{\square} -A_{\circ}[/tex]

[tex]A_{T} = l^{2}-\pi\cdot r^{2}[/tex]

Now, the rate of change of the total area is calculated after deriving previous expression in time:

[tex]\frac{dA_{T}}{dt} = 2\cdot l\cdot \frac{dl}{dt} -2\pi\cdot r\cdot \frac{dr}{dt}[/tex]

Where [tex]\frac{dl}{dt}[/tex] and [tex]\frac{dr}{dt}[/tex] are the rates of change of side and radius, measured in meters per day.

Given that [tex]l = 20\,m[/tex], [tex]r = 3\,m[/tex], [tex]\frac{dl}{dt} = 3\,\frac{m}{day}[/tex] and [tex]\frac{dr}{dt} = 1\,\frac{m}{day}[/tex], the rate of change of the total area is:

[tex]\frac{dA_{T}}{dt} = 2\cdot (20\,m)\cdot \left(3\,\frac{m}{day} \right)-2\pi\cdot (3\,m)\cdot \left(1\,\frac{m}{day} \right)[/tex]

[tex]\frac{dA_{T}}{dt} \approx 101.150\,\frac{m^{2}}{day}[/tex]

The area inside the square and outside the circle is changing at a rate of 101.150 square meters per day.

Answer:

-11 and -10

Step-by-step explanation:

● -√120 = -1 × √120

● -√120 = -1 × 2√30

● 30 is close to 25 so √30 is close to five but greater than it.

Multiplying 5 by -2 gives -10

Multipluing √30 by -2 gives you a number that is close to -10 but smaller than it.

So -√120 lies between -11 and -10

Answer:

The correct option is;

2. (750 - w)(13) = d (750 + w)(11) = d - 250

Step-by-step explanation:

The items with information given are;

The cruising speed of the planes = 750 km/h

The first plane flies against a constant headwind = w

The second plane flies against a constant tailwind  in magnitude to the headwind

The time duration of flight of the first plane = 13 hours

The time duration of flight of the second plane = 11 hours

The distance flown by the second plane = The distance flown by the first plane - 250 km

When we take the headwind magnitude as, w and the distance flown by the first plane as d, we have;

Speed of flight of the first plane = 750 - w

Speed of flight of the second plane = 750 + w

Therefore, the distance flown by the first plane in 13 hours is given as follows;

(750 - w) × (13) = d

Then we have;

The distance flown by the second plane in 11 hours is (750 + w) × (11) = d.

The correct option is (750 - w)(13) = d, (750 + w)(11) = d - 250

Answer:

Answer choices A, B and C identifies the relevant information in the problem

Step-by-step explanation:

Sarah left the house at 12:15 pm

She spent $42.20 on two books for her children

She spent $5.67 on a toy for her dog

Sarah arrived home at 1:00 pm

How much did Sarah spent on each book?

If she spent $42.20 on two books for her children,

Then, it means she has two children and the book cost $21.10 each

Answer choices A, B and C identifies the relevant information in the problem

Answer:

its A all the other one dont make sence sorry if im wrong but i got it right on my test

Step-by-step explanation:

Answer:

The balance on the loan f(p) = $100 - $20 × p

Step-by-step explanation:

The parameters of the question are;

The loan amount = $100

The amount of monthly payment for the loan = $20

The function rule for the balance of the function f(p) where p is the number of payments is given as follows;

The balance on the loan, f(p) = The loan amount less the total amount paid

The total amount payment Jeania has made = Amount of monthly payment × Number of months paid, p

The total amount payment Jeania has made = $20 × p

∴ The balance on the loan, f(p) = $100 - $20 × p

Which gives;

f(p) = $100 - $20 × p.

Answer:

Answer is A

Step-by-step explanation:

Hope it helps

Answer:

Step-by-step explanation:

1/5 a-5=20   addition properties

1/5 a -5+5=20+5

1/5=25     multiply both sides by 5

5/5 a=25*5

a=125

check the answer:

125/5 -5=20

25-5=20

20=20 correct

Answer:

m = -2

Step-by-step explanation:

First, let's move all variables to one side of the equation. (Don't forget to change the signs when you move the numbers to the other side.)

18m + 7m = -60 + 2 + 8

Now we simplify to get this:

25m = -50

Now we divide -50 by 25 which gets us -2.

Therefore, m = -2

Hope this helps!

Answer:

(x - 5)(x - 5)

Step-by-step explanation:

[tex] {x}^{2} - 10x + 25 \: is \: the \: expansion \\ of \: {(x - 5)}^{2} \\ {(x - 5)}^{2} = (x - 5)(x - 5)[/tex]

The complete factorization of the quadratic expression x² - 10x + 25 is (x - 5)(x - 5). Hence the first option is the right choice.

A quadratic expression of the form ax² + bx + c is factored by using the mid-term factorization method, which suggests that b should be broken in such two components that their product = ac. After this, we can factorize using the grouping method.

In the question, we are asked to factor the quadratic expression x² - 10x + 25 completely.

Comparing x² - 10x + 25 to ax² + bx + c, we get a = 1, b = -10, and c = 25.

To factor the expression we will use the mid-term factorization method, and try to break b in such two numbers whose product = ac.

Now, ac = 1 * 25 = 25. b = -10, which can be broken as -5, and -5.

Therefore, we can write the given expression as:

x² - 10x + 25

= x² - 5x - 5x + 25, mid-term factorization

= x(x - 5) -5(x - 5), grouping

= (x - 5)(x - 5), grouping.

Therefore, the complete factorization of the quadratic expression x² - 10x + 25 is (x - 5)(x - 5). Hence the first option is the right choice.

Learn more about mid-term factorization at

https://brainly.com/question/25829061

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Answer:

The diameter of the bacterium is 4.05 times the diameter of the plant cell

Step-by-step explanation:

Given

The given parameters both represent diameters

Plant Cell; P = 1.26m

Bacterium; B = 5.1m

Required

Compare both diameters;

Write out both expressions

[tex]P = 1.26[/tex]

[tex]B = 5.1[/tex]

Divide B by P

[tex]\frac{B}{P} = \frac{5.1}{1.26}[/tex]

[tex]\frac{B}{P} = 4.04761904762[/tex]

Approximate

[tex]\frac{B}{P} = 4.05[/tex]

Multiply both sides by P

[tex]P * \frac{B}{P} = 4.05 * P[/tex]

[tex]B = 4.05 * P[/tex]

[tex]B = 4.05P[/tex]

This implies that;

The diameter of the bacterium is 4.05 times the diameter of the plant cell

THIS IS THE COMPLETE QUESTION BELOW;

Rosemary walks each week for exercise. Let d represent the distance walked and h represent the number of hours spent walking.

Last week: walked 18 miles in 6 hours

This week: d = 2.5h

Which statement must be true?

A.This week, she walked a greater distance.

B. Last week, she walked a greater distance

C. This week, she walked at a faster pace.

D. Last week, she walked at a faster pace

Answer

OPTION B is correct

B)Last week, she walked a greater distance

Step-by-step explanation:

We were told Rosemary walks each week for exercise.

From the question,

✓d represented the distance walked

✓h represent the number of hours spent walking.

A)Last week: she walked 18 miles in 6 hours

Then, if she walks 18 miles in 6 hours, we can be expressed as (18miles/6hour)

= 3 miles per hour

B)This week: d = 2.5h

This implies that she she walked 2.5 miles per hour this week since the distance is expressed in miles and time in hours.

So we can conclude that last week she walked 3 miles per hour which is more greater than 2.5 miles per hour which she walks this week.

Therefore, OPTION B is correct, (Last week, she walked a greater distance)

Answer:

It's b

Step-by-step explanation:

Answer:

a. La ganancia es de $ 4,060,000.00

b. 31 vehículos

Step-by-step explanation:

(a) Los parámetros dados son;

El número de automóviles tipo sedán fabricados = 24

El número de camiones tipo SUV fabricados = 16

El número de camiones tipo VAN fabricados = 12

El número de camionetas pick-up fabricadas = 8

El número de autos deportivos fabricados = 2

La ganancia por la venta de autos tipo sedán = $ 185,000 - $ 140,000 = $ 40,000

La ganancia por la venta de camionetas tipo SUV = $ 320,000 - $ 250,000 = $ 70,000

La ganancia por la venta de camiones tipo VAN = $ 400,000 - $ 310,000 = $ 90,000

La ganancia por la venta de las camionetas pick-up = $ 285,000 - $ 210,000 = $ 75,000

La ganancia por la venta de los autos deportivos = $ 550,000 - $ 400,000 = $ 150,000

La ganancia = 24 * $ 40 000 + 16 * $ 70 000 + 12 * $ 90 000 + 8 * $ 75 000 + 2 * $ 150 000 = $ 4060 000

(b) Por lo que hay una tasa de producción constante, solo la mitad de los automóviles se producirán dentro del período de 12 horas

Por lo tanto, tu fabricado

12 autos sedán, 8 camionetas tipo SUV, 6 camionetas tipo VAN, 4 camionetas pick-up y 1 auto deportivo para hacer un total de 31 vehículos.

Answer: You are correct, it is the second option.

Step-by-step explanation:

Volume of a cylinder formula is: pi*r^2*h. The diameter is 6 and the radius is half the diameter so we get r=3. The height is 10 inches, so h=10. pi(3)^2(10) is the volume of the vase.

Volume of a sphere (marbles) formula is: 4/3*pi*r^3

The marbles have a diameter of 3 so 3/2=1.5. r=1.5.

The volume of the marbles is 8(4/3*pi*1.5^3).

Then you subtract the volume of the marbles from the volume of the vase to find the volume of the water in the vase.

pi(3)^2(10) - 8(4/3pi(1.5)^3)

Hope this helps. :)

Answer:

You are absolutely correct, second option is the correct answer.

Step-by-step explanation:

Diameter of vase = 6 inches

Therefore, radius r = 3 inches

Diameter of marbles = 3 inches

Radius of marbles = 1. 5 inches

Height of water h = 10 inches

Volume of water in the vase = Volume of vase - 8 times the volume of one marble

[tex] = \pi r^2h - 8\times \frac{4}{3} \pi r^3 \\\\

= \pi (3\: in) ^2(10\: in) - 8( \frac{4}{3} \pi (1.5\: in) ^3) \\\\[/tex]