4 divided by 5/7 in its mixed form and simplest form

Answers

Answer 1

[tex]4\div\cfrac{5}{7}\implies \cfrac{4}{1}\div\cfrac{5}{7}\implies \cfrac{4}{1}\cdot \cfrac{7}{5}\implies \cfrac{28}{5}\implies 5\frac{3}{5}[/tex]


Related Questions

Use the distributive property to write an equivalent expression to:

3 over 4 minus 1 half left parenthesis 4 x minus 1 half right parenthesis

Answers

Answer:

11/4

Step-by-step explanation:

The question in math symbols 3/4 - 1/2(4*-1)

By Pemdas (order of operations) we start with the parenthesis
3/4 - 1/2(4*-1) = 3/4 - 1/2(-4)
Because there are parenthesis next to a number, this is a multiplication

3/4 - 1/2(-4) = 3/4 - (-2)
The double negative can be converted into a positive
3/4 - (-2) = 3/4 + 2

Then we can convert the 2 into a fraction of fourths

3/4 + 2 = 3/4 + 8/4

Now we just add the numerators and keep the denominator

3/4 + 8/4 = 11/4

proving trigonometric identities

2(cosx sinx-sinx cos2x)/sin2x =secx

Answers

This is not an identity.

[tex]\dfrac{2(\cos(x)\sin(x) - \sin(x)\cos(2x))}{\sin(2x)} \neq \sec(x)[/tex]

Check x = π/4, for which we have cos(π/4) = sin(π/4) = 1/√2. Together with sin(2•π/4) = sin(π/2) = 1 and cos(2•π/4) = cos(π/2) = 0, the left side becomes 1, while sec(π/4) = 1/cos(π/4) = √2.

Keeping the left side unchanged, the correct identity would be

[tex]\dfrac{2(\cos(x)\sin(x) - \sin(x)\cos(2x))}{\sin(2x)} = -2\cos(x) + 1 + \sec(x)[/tex]

To show this, recall

• sin(2x) = 2 sin(x) cos(x)

• cos(2x) = cos²(x) - sin²(x)

• cos²(x) + sin²(x) = 1

Then we have

[tex]\dfrac{2(\cos(x)\sin(x) - \sin(x)\cos(2x))}{\sin(2x)} = \dfrac{2\cos(x)\sin(x) - 2\sin(x)\cos(2x)}{\sin(2x)} \\\\ = \dfrac{\sin(2x) - 2\sin(x)\cos(2x)}{\sin(2x)} \\\\ = 1 - \dfrac{2\sin(x)\cos(2x)}{\sin(2x)} \\\\ = 1 - \dfrac{2\sin(x)(\cos^2(x) - \sin^2(x))}{2 \sin(x)\cos(x)} \\\\ = 1 - \dfrac{\cos^2(x) - \sin^2(x)}{\cos(x)} \\\\ = 1 - \cos(x) + \dfrac{\sin^2(x)}{\cos(x)} \\\\ = 1 - \cos(x) + \dfrac{1 - \cos^2(x)}{\cos(x)} \\\\ = 1 - \cos(x) + \sec(x) - \cos(x) \\\\ = -2\cos(x) + 1 + \sec(x)[/tex]

Write down the next term in each of these sequences. a) 19, 15, 11, 7, 3,​

Answers

Answer:

-1

Step-by-step explanation:

Find the difference of each sequence

19 - 15 = 4

15 - 11 = 4

11 - 7 = 4

7- 3 = 4

3 - ? = 4

Subtract 4 from the 3

3 - 4 = -1

Therefore, the next term is -1

2. Find the value of x and y rounded to the nearest tenth.
x
34
45°
30°
a.
x = 24.0, y = 46.4
c.
x = 48.1, y = 139.3
d. x = 48.1, y = 46.4
b. x = 24.0, y = 139.3

Answers

Using relations in a right triangle, it is found that the values of x and y are given by: x = 24, y = 46.4, given by option a.

What are the relations in a right triangle?

The relations in a right triangle are given as follows:

The sine of an angle is given by the length of the opposite side to the angle divided by the length of the hypotenuse.The cosine of an angle is given by the length of the adjacent side to the angle divided by the length of the hypotenuse.The tangent of an angle is given by the length of the opposite side to the angle divided by the length of the adjacent side to the angle.

First, we start with the vertical line h that divides y, that is opposite to an angle of 30º, with hypotenuse 34, hence:

sin(30º) = h/34

0.5 = h/34

h = 17.

Then, h is opposite to an angle of 45º, while the hypotenuse is x, hence:

[tex]\sin{45^\circ} = \frac{17}{x}[/tex]

[tex]x = \frac{17}{\sin{45^\circ}}[/tex]

x = 24.

y is divided into two segments.

The first is the adjacent to the angle of 30º, while the hypotenuse is 34.The second is adjacent to the angle of 45º, while the hypotenuse is 24.

Then:

[tex]\cos{30^\circ} = \frac{y_1}{34}[/tex]

[tex]y_1 = 34\cos{30^\circ} = 29.4[/tex]

[tex]\cos{45^\circ} = \frac{y_2}{24}[/tex]

[tex]y_2 = 24\cos{45^\circ} = 17[/tex]

Then, the value of y is given by:

[tex]y = y_1 + y_2 = 29.4 + 17 = 46.4[/tex].

More can be learned about relations in a right triangle at https://brainly.com/question/26396675

#SPJ1

What a scale drawing a tree is 4 inches tall the scale factor is 1:24. Find the actual height

Answers

Answer:

96 inches

Step-by-step explanation:

1:24

4:x

cross multiply:

x=4*24

x=96

HELP THIS IS URGENT!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! :((((((((((((((((

Answers

Answer:

1)acute triangle

2) right angle

3) obtuse triangle

Step-by-step explanation:

please mark me as brainlest

Answer:

1. Acute 2. Obtuse 3.  Right

Step-by-step explanation:

Obtuse Triangle Definition

An obtuse triangle is one that has an angle greater than 90°. Because all the angles in a triangle add up to 180°, the other two angles have to be acute (less than 90°). It's impossible for a triangle to have more than one obtuse angle.

Acute Triangle Definition

An acute triangle is defined as a triangle in which all of the angles are less than 90°. In other words, all of the angles in an acute triangle are acute.

A Right Triangle has a right angle

Hope this helps.

What is negative 8 times 9 times negative 5 minus negative 14​

Answers

(-8 * 9 * -5 )- -14

360 - - 14 = 360 + 14 = 374

Negative 8 times 9 times negative 5 minus negative 14 is 374

John travelled 450km using 31 litres of petrol. (km/litre)

Answers

Answer:

its SUMMER wth

Step-by-step explanation:

Its time too TURN UPPP!

Answer:

450/31=14.51km/litre

The measure of angle CDE is
degrees.

Answers

CDE = CDB + BDA + ADE

CDE = 42° + 37° + 20°

CDE = 99°

hope it helps...!!!

Answer:99 degrees

Step-by-step explanation:

Angle CDB + Angle BDA + Angle ADE= Angle CDE

42+37+20=99

For his phone service, Chris pays a monthly fee of $25, and he pays an additional $0.06 per minute of use. The least he has been charged in a month is $86.74.
What are the possible numbers of minutes he has used his phone in a month?
Use M for the number of minutes, and solve your inequality for M.

Answers

Answer:

1029 minutes or 17.15 hours

Step-by-step explanation:

25+0.06M=86.74

0.06M=61.74

M=61.74/0.06=1029

A box contains 50 batteries, of which 10 are dead and 5 are weak. Suppose you select batteries at random from the box and set them aside for recycling if they are dead or weak. If the first battery you select is dead and the second one is weak, what is the probability that the next battery you select will be weak?

Answers

Probability of selecting 1 dead, 1 weak, then 1 weak = (1/588).

Given: 50 total batteries, of which 10 are dead and 5 are weak. This is represented by: 10/50 (simplifies to 1/5) and 5/50 (simplifies to 1/10).
If the batteries are being set aside, it likely means no replacement. For every battery taken out of the box, the box holds one less battery.

Probability of selecting 1 dead, 1 weak, 1 weak is written as: (10/50)*(5/49)*(4/48) = 1/588.

5ab^2 - 12a^2b + 3ab + ab^2 + 4a^2b

(a) 6ab^2 + -8a^2b + 3ab
(b) -7ab^2 + 8a^2b + 3ab
(c) 6a^2b^4 - 8a^4b^2 + 3ab
(d) 5a^2b^4 + -8a^4b^2 + 3ab

Answers

Answer:

(a) 6ab² - 8a²b + 3ab

Step-by-step explanation:

Given: 5ab² - 12a²b + 3ab + ab² + 4a²b

In this question, we will be combining like terms.

What are like terms?

Like terms are terms with the same variables and power. For example, 2x and 4x, as well as 2a² and 4a².

Combine like terms:

5ab² - 12a²b + 3ab + ab² + 4a²b

(5ab² + ab²) + (-12a²b + 4a²b) + 3ab

6ab² - 8a²b + 3ab

The account balance on april 1st is $50.51. on april 15th a payment of $15.00 is made. on april 25th a purchase of $19.27 is made. the annual rate is 18%. what is the finance charge using the previous balance method? $ what is the new balance? $

Answers

The finance charge will be $ 0.76. Then the new balance will be $ 55.54.

What is a finance charge?

Finance costs are paid to the provider in exchange for supplying cash or granting the loan.

The account balance on April 1st is $50.51.

On April 15th payment of $15.00 is made.

On April 25th a purchase of $19.27 is made.

The annual rate is 18%.

Then the finance charge will be

⇒ $ 50.51 x 0.18 / 12

⇒ $ 0.76

Then the new balance will be

New balance = $ 50.51 - $ 15 + $ 19.27 + $ 0.76

New balance = $ 55.54

More about the finance charge link is given below.

https://brainly.com/question/2588555

#SPJ1

Identify the lateral area and surface area of a regular triangular pyramid with base edge length 6 cm and slant height 13 cm.

Answers

The lateral area is 117 square centimeters and the surface area is 292.72 square centimeters

How to determine the lateral area?

The given parameters are:

Base length (b) = 6Slant height (l) = 13

The lateral area is calculated using:

Lateral = 0.5 * (Perimeter of base) * Slant height

This gives

Lateral = 0.5 * (3 * 6) * 13

Evaluate

Lateral = 117

Hence, the lateral area is 117 square centimeters

How to determine the surface area?

The surface area is calculated using:

Surface = l²√3

This gives

Surface = 13² * √3

Evaluate

Surface = 292.72

Hence, the surface area is 292.72 square centimeters

Read more about areas at:

https://brainly.com/question/24487155

#SPJ1

Answer:

L = 117 cm2 ; S = 132.6 cm2

Step-by-step explanation:

Substitute the known value of the base edge length s=6 cm into the formula for the perimeter of the regular triangle, P=3s.

P=3(6)=18

Therefore, the perimeter of the regular triangle is 18 cm.

Substitute the known values of the perimeter P=18 cm and the slant height l=13 cm into the formula for the lateral area of a regular pyramid, L=1/2Pl.

L=1/2(18)(13)=117

Therefore, the lateral area of the pyramid is 117 cm2.

The surface area of a regular pyramid with lateral area L and base area B is S=L+B, or S=1/2Pl+B.

The base of the regular triangular pyramid is the equilateral triangle. The area of the triangle with the base b and the height h is B=1/2bh.

To properly use the Addition Property of Equality what number would have to be added in the equation, 14 = x - 6?
A -14
B 14
C -6
D 6

Answers

Addition Property of Equality is basically a complex way of saying add the same number to both sides.  In this problem we are trying to isolate x for it to be by itself so we must deal with -6.  Since we have -6 on one side we must use the "Addition Property of Equality" to add 6 to both sides which would cancel out the -6 and add 6 to 14.

Therefore, the option that best fits the description on what number we would have to use to get added in the equation would be option D, 6.

I think is 6 we’ll letter D hope this help

During ‘Bob a job week’ a Boy Scout decided to earn money by cleaning shoes.It takes him 2 1/2 minutes to clean one pair.At one house he was given 12 pairs to clean.How long did it Take him to complete the task?

Answers

Answer: It took him 30 minutes to clean 12 pairs of shoes.


2 1/2 can be written as a decimal, 2.5, to make the equation simpler. It takes him 2.5 minutes per pair of shoes.

Given 12 pairs, we can find how long it took him using multiplication: 2.5(12) = 30
It took the Boy Scout 30 minutes to complete the task. This is also equivalent to half an hour.

Fwam surveyed 540 of the students in his school about their favorite color. students could choose between red and blue. 55% said their favorite color was blue. how many students' favorite color was red?

Answers

Answer:

243 students' favorite color is red

Step-by-step explanation:

if 55% of the students said their favorite color was blue, then 45% chose that red was their favorite color

we can get 45% of 540 using a cross-multiplication equation

45% is 45/100

45/100 is to ?/540

the (?) represents the value of students who chose red as their favorite color (we do not know this but we can figure it out using cross-multiplication)

45 times 540 is 24300

24300/100 = 243.

Give brainliest, please!

hope this helps :)

enter a number in the box so that the equation will have infinitely many solutions.

Answers

Answer:

5

Step-by-step explanation:

10c+15=5(2c+3)

use distributive property

10c+15=10c+15

Hope this helps!

If not, I am sorry.

Answer:

You would have to insert 5 for there to be infinite solutions.

K, L, and M are points on the circle. KS is a tangent to the circle at K. KM is a diameter and triangle KLM is isosceles. Find the value of z.

Answers

Using the circle theorems, the value of z is 45

Circle Geometry

From the question, we are to determine the value of z

From the given information,

KM is a diameter

∴ ∠KLM = 90° (Angle in a semicircle)

Also, ΔKLM is isosceles

∴ ∠KML = ∠MKL (Base angles of an isosceles triangle)

Then,

∠KML + ∠MKL + ∠KLM = 180° (Sum of angles in a triangle)

2× ∠KML + 90° = 180°

2× ∠KML = 180° - 90°

2× ∠KML = 90°

∠KML = 90°/2

∠KML = 45°

Now, we can observe that

z° = ∠KML (Angles in alternate segment)

But,

∠KML = 45°

∴ z = 45

Hence, the value of z is 45

Learn more on Circle Geometry here: https://brainly.com/question/17074363

#SPJ1

which of the following is true for the relation f(x)-x^2+8

Answers

Answer: A

Step-By-Step Explanation: if n is greater than or equal to 2 is an add integer then the domain of: f(x)-x^2+8 is the solution to the inequality 2+8 greater than or equal to 0. which of the following statements is true?

Which equation represents an inverse variation?
O y = 2x
O y= f
0 y=
4
5
O y = -5x

Answers

Answer:

its y=2x so yaa thats ittt

i need help on this may you help

Answers

Answer:

should be 63

Step-by-step explanation:

i need the answer asap

Answers

Answer:

It b(4) because if you time 3 times 4 it equals 15.

Step-by-step explanation:

Choose the correct alternative.
the earnings of ahmed and bekhit are in the ratio 3:7 and that of bekhit and saeed is 4:9 and that of mohammed and saeed is 7:6. if the sum of the earnings of ahmed, bekhit, saeed, and mohammed is aed 52,950, then what are the earnings of mohammed?

aed 21,050
aed23,050
aed 24,050
aed33,050

Answers

Using a system of equations, it is found that the earnings of Mohammed are given by: 18,212 aed.

What is a system of equations?

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

In this problem, the variables are given as follows:

Variable x: Earnings of Ahmed.Variable y: Earnings of Bekhit.Variable z: Earnings of Saeed.Variable w: Earnings of Mohammed.

The earnings of ahmed and bekhit are in the ratio 3:7, hence:

[tex]\frac{x}{y} = \frac{3}{7}[/tex]

[tex]3y = 7x[/tex]

[tex]y = \frac{7x}{3}[/tex]

That of bekhit and saeed is 4:9, hence:

[tex]\frac{y}{z} = \frac{4}{9}[/tex]

[tex]4z = 9y[/tex]

[tex]z = \frac{9y}{4}[/tex]

[tex]z = \frac{63x}{12}[/tex]

The ratio of mohammed and saeed is 7:6, hence:

[tex]\frac{z}{w} = \frac{7}{6}[/tex]

[tex]7w = 6z[/tex]

[tex]w = \frac{6z}{7}[/tex]

[tex]w = \frac{378x}{84}[/tex]

The sum is of 52950, hence:

[tex]x + y + z + w = 52950[/tex]

[tex]x + \frac{7x}{3} + \frac{63x}{12} + \frac{378x}{84} = 52950[/tex]

[tex]1099x = 52950 \times 84[/tex]

[tex]x = \frac{52950 \times 84}{1099}[/tex]

[tex]x = 4047[/tex]

Hence, Mohammed earnings in aed are given as follows:

[tex]w = \frac{378 \times 4047}{84} = 18212[/tex]

More can be learned about a system of equations at https://brainly.com/question/24342899

#SPJ1

what's the area of a trapezium with a height of 6cm and a length of 9cm and 15cm?

Answers

Answer:

72cm²

Step-by-step explanation:

Hello!

The formula for area of a trapezoid: [tex]A = \frac12(b_1 + b_2)h[/tex]

We find the average of the bases, and multiply it by the height.

Plug in the values and solve[tex]A = \frac12(b_1 + b_2)h[/tex][tex]A = \frac12(9 + 15)6[/tex][tex]A = \frac1224(6)[/tex][tex]A = 12(6)[/tex][tex]A = 72[/tex]

The area of the trapezoid is 72cm²

when the positive integer x is divided by 5, the remainder is 3. what is the remainder when X +19 is divided by five

Answers

Answer:

_4

Step-by-step explanation:

x+19/5=3 cross multiply

x+19=3*5

x+19=15

x=15-19

x=-4

The remainder when (x + 19) is divided by 5 is 2.

If the positive integer x has a remainder of 3 when divided by 5, it can be represented as:

x = 5a + 3, where "a" is a non-negative integer.

Now, let's consider the expression (x + 19) and determine the remainder when it is divided by 5:

x + 19 = (5a + 3) + 19

       = 5a + 22

When we divide 5a + 22 by 5, we find:

(5a + 22) = 5(a + 4) + 2

Therefore, the remainder when (x + 19) is divided by 5 is 2.

Learn more about remainders here:

https://brainly.com/question/29019179?

#SPJ2

Which of the following is the formula for the volume of a cube? a. s3 b. s2 c. π r2 d. π r3​

Answers

Answer:

Step-by-step explanation:

Which of the following is the formula for the volume of a cube?

a. s³

b. s²

c. π r²

d. π r³​

V = s³

Write the equation x + 3y = -4 in slope-intercept form, and then find the slope and y-intercept.

Answers

Answer with step by step explanation

To find the equation of the line from the given equation, you have to make y as the subject in the equation.

Let us find now.

x + 3y = -4

3y = -4 - x

3y = -x - 4

Divide the whole equation by 3.

y = -x/3 - 4/3

Therefore, the equation of the line is:

y = -x/3 - 4/3

And now we have to find the slope and the y - intercept of the line.

That is, we have to find the m & c of y = m x + c.

Here,

m ⇒ slope

c ⇒ y - intercept

So, to find it we have to find the values which were replaced with m & c.

Let us find now.

y = m x + c

y = -x/3 - 4/3

Now it is clear that, -1/3 & -4/3 are replaced with m & c respectively.

Therefore,

slope ⇒ -1/3

y - intercept ⇒ -4/3

HELP ASAP ILL MAKE YOU THE BRAINIEST
fInd the value of x

Answers

Step-by-step explanation:

cos x = 2/6.5 = 0.3

arccos 0.3 = 72.54 degree

Simplify -b/2a where a =-8 and b =-1

Answers

The correct value of this algebraic expression is -1/16

             

Given the expression, [tex]\large \sf \dfrac{-b}{2a}[/tex], let's just: change the letters to the numbers and then perform the given operations.

According to the rules of signals, we will have to:

*Equal signs will be positive ⇒ (-) (-)= + & (+) (+) = +

*Different signs will be negative ⇒ (-) (+) = - & (+) (-) = -

[tex]\\\large \sf \dfrac{-b}{2a} , \ a=-8 \ , \ b=-1[/tex]

[tex]\large \sf \dfrac{-(-1)}{2 \cdot (-8)}[/tex]

[tex]\large \sf \dfrac{1}{2 \cdot (-8)}[/tex]

[tex]\large \sf \dfrac{1}{-16}[/tex]

[tex]\blue{\boxed{\large \sf -\dfrac{1}{16} }}\\[/tex]

Therefore, the final answer to this simplification will be -1/16

Other Questions
How many molecules of o2 are produced from 82g of h2o? 2na2o2 +2h2o= o2 +4naoh Which of the following equations describes the graph?y=-x^2+1 what are the key features of the graph of a trigonometric function? How do you find them from a graph or an equation? Please answer all 3 empty box's 5 points each but beware if you use my points for no reason I'll report you a little later than his Thisbe had,and he could see what surely were the tracksof a wild beast left clearly on deep dust.His face grew ashen. And when he had foundthe bloodstained shawl, he cried: 'Now this same nightwill see two lovers lose their lives.'"Pyramus and Thisbe,"OvidWhich statement best describes how the order of events heightens tension in this passage?If Pyramus had left at the same time as Thisbe, he might have seen that she was not killed by the lion.If the lioness had arrived later, she would have encountered Pyramus rather than Thisbe.If Pyramus had arrived earlier, he would have seen the lion attack Thisbe.If Pyramus and Thisbe had arrived at the same time, they would have encountered the lioness together. Read the passage from "The Seven Voyages of Sindbad the Sailor.In the times of the Caliph Haroun-al-Raschid there lived in Bagdad a poor porter named Sindbad, who on a very hot day was sent to carry a heavy load from one end of the city to the other. Before he had accomplished half the distance he was so tired that, finding himself in a quiet street where the pavement was sprinkled with rose water, and a cool breeze was blowing, he set his burden upon the ground, and sat down to rest in the shade of a grand house. Very soon he decided that he could not have chosen a pleasanter place; a delicious perfume of aloes wood and pastilles came from the open windows and mingled with the scent of the rose water which steamed up from the hot pavement. Within the palace he heard some music, as of many instruments cunningly played, and the melodious warble of nightingales and other birds, and by this, and the appetizing smell of many dainty dishes of which he presently became aware, he judged that feasting and merry making were going on. He wondered who lived in this magnificent house which he had never seen before, the street in which it stood being one which he seldom had occasion to pass.What is Sindbad most motivated by in this passage?fatigue and curiositydiscomfort and peacework and pleasurehunger and greed In triangle $abc,$ angle bisectors $\overline{ad},$ $\overline{be},$ and $\overline{cf}$ meet at $i.$ if $di = 3,$ $bd = 4,$ and $bi = 5,$ then compute the area of triangle $abc.$ In recording an accrual adjusting entry to account for revenues earned but not yet collected, ______. Victor works for a telemarketing company that is on a very tight budget. He has been tasked with finding a method for the company's employees to share, organize, and update their telemarketing records so other employees can follow up. Employee shifts are staggered. Many employees are never in the office at the same time and some work from home. What telecommunications technology can Victor's company use What must writers do when using language taken directly from an outside source? Select three choices. Solve the following inequality using both the graphical and algebraic approach: 8 minus x greater-than-or-equal-to 5 (8 minus x) Graph A On a coordinate plane, a line goes through (0, 8) and (8, 0). Another line goes through (8, 0) and (7, 10). Graph B On a coordinate plane, a horizontal line is at y = 5 and another line goes through (8, 0) and (0, negative 8). a. x greater-than-or-equal-to 8 Graph A b. x less-than-or-equal-to 8 Graph A c. x greater-than-or-equal-to 8 Graph B d. x less-than-or-equal-to 8 Graph B What issue initially created a source of contention and division for Muslims into Sunni and Shi'a?which city should serve as their capitalwho should have the right to leadershipO how to maintain religious tolerancewhy Islam must be a monotheistic religion Which of the following aggregate planning strategies is known to lower employee morale? Group of answer choices back ordering during high demand periods counterseasonal product and service mixing changing inventory levels yield management varying work force size by hiring or layoffs What was the underground rail road and how did it work?. Which of the following are ways drugs work in the brain?Select all that apply.A by imitating the brain's natural chemical messengersB by imitating hungerC by overstimulating the "reward circuit" of the brainD by overstimulating hearing Find the area of the triangle ? Why might some people support the Roe v. Wade decision? For example, in some cases, the environmental impact of border walls has been profound.What does profound mean in this sentence?Choose 1 Answer:severedifficultcleverheartfelt Argelis had he following containers of paint leftover, 1/2 gallon, 3/4 quarts and 1/4 gallon. How many quarts of paint does argelis have left Analyze the painting. using specific examples from the painting, describe the economic changes in medieval europe. what were the lasting effects of these changes? your answer should be a minimum of two to three sentences.