If x^3 - 5x - 4x + 20 is going to factor, then one of these combinations is going to “work”, that is, the polynomial will divide evenly and give f(k) = 0 according to the Factor Theorem. So the best thing to do is employ a little trail and error. Let’s start with the smaller numbers, they will be easier to evaluate.

1. Substitute for x: 1, -1, 2, -2, 4, -4 ...20, -20.

Answer:

3 players each

Step-by-step explanation:

12 divided by 4 is 3

Answer:

each team has 3 players because

Step-by-step explanation:

As you said the tournament has 4 team, each team has same number of players and there is 12 people in all. So,

12/4=3

3+3+3+3=12

Answer:

sin(x)=1/[tex]\sqrt10[/tex]

Step-by-step explanation:

The trigonometric identities involve trigonometric functions. Here we will be using Trigonometric identity

sin²x  = 1 /( 1+cot²x )

now cot(x)= -3

⇒ cot²x= (-3)²

⇒ cot²x= 9

sin²x= 1/( 1+9)

⇒ sin²x = 1/10

taking under root on both the sides we get

√sin²x=[tex]\sqrt1[/tex]/[tex]\sqrt10[/tex]

⇒ sin(x)=± 1/[tex]\sqrt10[/tex]

Answer:

10.78moles

Step-by-step explanation:

Avogadro's hypothesis gives us a background understanding that 1mole of any substance contains 6.02x10^23 atoms.

Now, If 1 mole of K3PO4 contains 6.02x10^23 atoms,

Then Xmol of K3PO4 will contain = 6.49x10^24 atoms i.e

Xmol of K3PO4 = 6.49x10^24/6.02x10^23 = 10.78moles

To find the number of moles of K3PO4 in 6.49 x 10^24 formula units, divide the number of formula units by Avogadro's number, resulting in 10.78 moles of K3PO4.

To calculate the number of moles of K3PO4 in 6.49 x 1024 formula units, we use Avogadro's number, which is 6.022 x 1023 formula units per mole. This is the key conversion factor for converting between the number of formula units and the number of moles.

First, we have the given number of formula units of K3PO4:

To convert this to moles, we divide by Avogadro's number:

Number of moles = (6.49 x 1024 formula units) / (6.022 x 1023 formula units/mole)

= 10.78 moles of K3PO4

This calculation shows that there are 10.78 moles of K3PO4 in 6.49 x 1024 formula units of K3PO4.

Answer:

23 groups :)

Step-by-step explanation:

Answer:

23

Step-by-step explanation:

Ok so heres the deal: You want to somehow take all 414 of those delicious pretzels and put them into x groups of 18. To do that you would divide 414 by the number of groups (x).

414/x=18

To solve this you just have to get x by itself.

So, multiply both sides by x.

414=18x.

Now divide by 18

414/18=x

23=x

SPANISH

Como el peso específico del objeto es Y = 9016 N / m ^ 3, puede ver que será Y = 300 N / V m ^ 3

V (m ^ 3) = 300 N / (9016 N / m ^ 3)

V (m ^ 3) = 0, =. 033 m ^ 3

1 Litro es 0,001 m ^ 3

(.033 m ^ 3) * (1 L / 0,001 m ^ 3) = 35,937 L

ENGLISH

Since the specific weight of the object is  Y = 9016 N/ m^3 you can see that it will be Y = 300 N / V m^3

V(m^3) = 300 N / (9016 N/m^3)

V(m^3) = 0,=.033 m^3

1 Litro es  0,001 m^3

(.033 m^3) * (1 L / 0,001 m^3) = 35,937 L

Espero que esto ayude, ahora sabes la respuesta y cómo hacerlo. ¡QUE TENGAS UN DÍA BENDITO Y MARAVILLOSO! :-)

- Cutiepatutie ☺❀❤

The specific weight is the weight of the per unit volume of a material.  The volume of the olive oil is 34 L.

The specific weight is the weight of the per unit volume of a material. It is given by the formula,

[tex]\rm Specific\ Weight, \gamma= Density \times g = \dfrac{Weight}{Volume}[/tex]

As the weight of the oil is given and the specific density is also given, therefore, we can find volume as,

[tex]\rm \gamma = \dfrac{Weight}{Volume}\\\\\rm 9016= \dfrac{300}{Volume}\\\\Volume = \dfrac{300}{9016}\\\\Volume = 0.0333\ m^3[/tex]

Now, we know that 1 m³ = 1000 litres, therefore,

[tex]\rm Volume = 0.034\ m^3\\\\Volume = (0.034 \times 1000)\ liters\\\\Volume = 34\ liters[/tex]

Hence, the volume of the olive oil is 34 L.

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Answer:

50 Oranges

Step-by-step explanation:

4 kg = 4000 grams because 1 kg = 1000 grams.

4000 grams divided by 80 grams gives us the number of oranges in the box since each orange weighs 80 grams.

4000/80 = 50.

Answer:

50 oranges

Step-by-step explanation:

First we need to know the conversion measure.

1kg=1000grams

And if a box is 4kg heavy, it means only oranges weighing 4 times 1000grams can fill it up.

If an orange now weigh 80grams. It means how many oranges will measure up to 1000grams.

1000/80 = 50

50 oranges, each weighing 80grams will fill up a box to weigh 4kg

Answer:

7/20

Step-by-step explanation:

The probability is 7/20.

Probability is a branch of mathematics that deals with the occurrence of a random event.

The hazard that a given event will arise. The ratio of the variety of results in an exhaustive set of similarly probable results that produce a given occasion to the overall number of feasible results.

possibility = the number of methods of reaching achievement. the total number of possible outcomes.

explanation:

Tails up represents white ducks

and heads up represents black ducks

probability of two white ducks number tails from the table = 7

total sample = 20

Hence probability = 7/20

The possibility is the branch of mathematics regarding the incidence of a random event, and four major styles of opportunity exist: classical, empirical, subjective, and axiomatic. the possibility is synonymous with possibility, so you should say it is the possibility that a particular event will show up.

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Answer:

1.  y = -3/2 x +11

2.  y = -2 x -7

Step-by-step explanation:

Slope intercept form is y = mx+b

1. A (8, –1) and B (–4, 17)

First we need to find the slope

m = (y2-y1)/(x2-x1)

m = (17--1)/(-4-8)

   =(17+1)/(-4-8)

   =18/-12

Dividing top and bottom by 6

  =-3/2

Given the slope

y = -3/2 x+b

Using the point (8,1) we can find b

-1 = -3/2(8) +b

-1 =-12 +b

Add 12 to each side

-1+12 = -12+12 +b

11 =b

The equation is y = -3/2 x +11

2. C (–19, 31) and D (1, –9)

First we need to find the slope

m = (y2-y1)/(x2-x1)

m = (-9-31)/(1--19)

   =(-40)/(1+19)

   = -40/20

   =-2

Given the slope

y = -2 x+b

Using the point (1,-9) we can find b

-9 = -2(1) +b

-9 =-2 +b

Add 2 to each side

-9+2 = -2+2 +b

-7 =b

The equation is y = -2 x -7

Answer: 14gallons

Step-by-step explanation:

12gallons/144miles = 1gallon/12miles

Therefore 6gallons = 12*6 = 72miles.

In order to cover 240miles, she will need 240/12 = 20gallons.

20-6 = 14gallons

She will need 14gallons of gas more.

Answer:

1,782 CM

Step-by-step explanation:

Answer:

It is the transitive property of equality

Answer: Transitive Property of Equality

Step-by-step explanation: The transitive property of equality states that if a = b and b = c, then a = c.

For example, if we're given the segment shown in the image provided and we know that the length of segment WX = XY and the length of segment XY = YZ, then based on the transitive property, he length of segment WX = YZ.

Answer:

x=5, 8, 9

Step-by-step explanation:

in a function, one x value must be paired with one and only one y value, this means there cannot be two points where x values are the same, however the y values can repeat.

if x = 5, 8, or 9, the relation is not a function because there are 2 same x values.

At the denominator you have

(x-5)×4=4x-20.

But:

2(x+4)/(4(x-5))=(x+4)/2/(x-5)

Answer:

see explanation

Step-by-step explanation:

Given

[tex]\frac{2(x+3)(x+4)}{(x+1)(x-5)}[/tex] × [tex]\frac{(x+1)}{4(x+3)}[/tex]

Cancel the common factors (x + 1), (x+3) on the numerator/ denominator

and cancel 2 and 4 on the numerator/ denominator by 2

= [tex]\frac{x+4}{2(x-5)}[/tex]

37000 letters were written in all. The reason for this is because to solve this you would do 940x40 which gets you to 37000.

Answer:

37,600

Step-by-step explanation:

You have to multiply 940 and 40 because your trying to figure out the total amount of letters that were written.

940 x 40 = 37,600

you can also check your work by dividing 37,600 by any of those numbers or multiplying just to make sure.

Answer: 3.2

Step-by-step explanation:

There are three whole, and 2 last.

Answer:3.667

Well, you divide 11 and 3 and round it.

Answer:

1 and 6

2 and 5

3 and 8

4 and 7

Step-by-step explanation:

vertical angles: each of the pairs of opposite angles made by two intersecting lines.

The given sum is based on the concept of percentage.0.54 is 2.25[tex]\%[/tex] out of 24.

Percentage is a way of expressing a fraction or proportion out of 100. It is represented by the symbol "%". The word "percent" comes from the Latin phrase "per centum", which means "per hundred."

Percentages are commonly used to describe ratios, rates, or proportions in various fields such as mathematics, finance, statistics, and everyday life. They allow us to compare quantities or express relative changes easily.

To find 2.25[tex]\%[/tex] of 24, multiply 24 by 2.25[tex]\%[/tex] (or 0.0225):

2.25[tex]\%[/tex] [tex]\times[/tex] 24 = 0.0225 [tex]\times[/tex] 24

                   = 0.54.

Therefore, 2.25[tex]\%[/tex] of 24 is 0.54.

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Answer:

Draw a model ⇒ See the attached figure

Tennis balls to tennis rackets ⇒ 5 : 3

Tennis balls to total pieces of tennis equipment​ ⇒ 5 : 8

Step-by-step explanation:

Let the number of tennis balls ⇒ x

Let the number of tennis rackets ⇒ y

The general form represents the situation is ⇒ y = mx

Where m is the slope

Given: For every 5 tennis balls in the bin, there are 3 tennis rackets.

So, when x = 5 ⇒ y = 3

So, 3 = m * 5⇒ m = 3/5 = 0.6

∴ y = 0.6 x

See the attached figure which represents a model to show the ratio of tennis balls to tennis rackets.

Tennis balls to tennis rackets = 5 to 3 or  5 : 3

Total pieces of tennis equipment​ = 5 + 3 = 8

Tennis balls to total pieces of tennis equipment​ = 5 to 8 or 5 : 8

Answer:

Step-by-step explanation:

√14 cannot be rewritten as the ratio of two integers and thus is irrational.

Similarly, √99 is irrational; √99 = √9√11 is irrational even though √9 is not.

Answer:

the value of x and y is 4 and -5 respectively.

Step-by-step explanation:

from the equation we say let;

2x + y = 3 .............. equation  1

4x + 3y = 1.............. equation 2

from equation 1

2x + y = 3 .............. equation  1

y = 3 - 2x................ equation 3

Substitute for y in equation 2

4x + 3y = 1.............. equation 2

we have,

4x + 3(3- 2x) = 1

4x + 9 -6x = 1

we have to collect the like terms

9-1 = 6x -4x

8 = 2x

divide both sides by 2

8/2 = 2x/2

4 = x

therefore x = 4

put x = 4 in equation 3

y = 3 - 2x................ equation 3

y = 3 - 2(4)

y = 3 -8

y = -5

therefore the value of x and y is 4 and -5 respectively.

to check if your answer is correct, put the value of x and y in any of the equations.

2x + y = 3 .............. equation  1

2(4) + (-5) = 3

8 -5 = 3

3 = 3......................... proved

Answer:

16 cm

Step-by-step explanation:

EFP is a right angle triangle

EP² = ED² + DP²

EP² = 24² + 10²

EP² = 676

EP = 26

EF = EP - FP

EF = 26 - 10 = 16

Answer:

The answer would be x=7.3 cm

Step-by-step explanation:

Since you are using the angle of 20 degrees and you have the measure of 10 cm for its adjacent side, solving for x would mean you would use tan.

20=x/10

10*20tan=x

200tan=x

7.279404......=x

But when you do 200 tan on the calculator, you have to make sure you press the equal sign after.

Answer:

$33 for each grandchild.

Step-by-step explanation:

If Cher has $330 to give to 10 grandkids equally you have to devide.

So you would do $330 divided by 10 (number of grandchildren), which equals $33. So each child gets $33.

Answer:

Step-by-step explanation:

sum of for angles of a quadrilateral=360

111+134+69+x=360

314+x=360

x=360-314=46

fourth angle=46°

Answer:

if a 5 liter jug is 7.5 kg, The 2 liter jug weighs 3 kg

Step-by-step explanation:

7.5 / 5  = 1.5

1.5 x 2 = 3

Answer:

3kg

Step-by-step explanation:

w/2 = 7.5/5

w = 7.5/5 * 2

w = 15/5

w = 3

The greatest common factor (GCF) of the expression 12² + 6²³ − 9 is 3. So, factored form is c) 3xy (4x² + 2xy – 3y²).

To factor out the greatest common factor (GCF) from the expression

12² + 6²³ − 9, we need to identify the highest common factor among the terms.

First, let's list the factors of each term:

12² can be factored into 3 × 2 × 2 × × ×

6²³ can be factored into 3 × 2 × × × × ×

9 can be factored into 3 × 3 × ×

The highest common factor among these terms is 3.

Now, we divide each term by 3:

12² ÷ 3 = 4

6²³ ÷ 3 = 22

9 ÷ 3 = 3

So, the factored expression becomes 3 (4² + 2² −3). This is the result of factoring out the GCF 3 from the given expression.

Complete Question:

Factor the GCF: 12x2y + 6x2y3 – 9xy?

a) 3x²y (4x² + 2xy - 3)

b) 3xy (4x + 2xy - 3y²)

c) 3xy(4x² + 2xy – 3y²)

d) 3x²y(4x³y – 2x²y² - 3xy³)

Answer:

19 hours

Step-by-step explanation: he needs to work 19 hours because if you divide the sum of money(162$) he got from working 9 hrs you get that he makes 18$ per hour then divide that by the sum of money that he needs(342$)

Matt earns $18 per hour and needs to work a total of 19 hours to afford a $342 video game system.

Matt earned $162 this week by working 9 hours. This means that Matt earns $18 per hour (since 162 ÷ 9 = 18). To find out how many total hours Matt needs to work to buy a new video game system that costs $342, we divide the total cost of the video game system by his hourly wage. So, $342 ÷ $18 = 19 hours. Therefore, Matt needs to work a total of 19 hours to afford the video game system.

Answer:

I think that the answer is option A

Answer:

a

Step-by-step explanation:

Answer:

Carpenters can install about 123 hinges.

Step-by-step explanation:

Since each hinge requires 3 screws. Divide 371 by 3.

= 123.666667

Answer:

123

Step-by-step explanation:

   [tex]\lim_{n \to \infty} a_n \pi \beta[/tex][tex]\left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right] \alpha \leq x^{2} \sqrt{x} x^{2}[/tex]that's how I got it

[tex]\lim_{n \to \neq \geq \leq x^{2} x^{2}[/tex]

Answer:

-37

Step-by-step explanation:

Slope = y2 - y1/x2 - x1

Given

x1 = -99

y1 = -25

x2 = -98

y2 = -62

Therefore

Slope = -62 -(-25) /-98 -(-99)

Negative negative becomes positive

= -62 + 25 /-98 + 99

= -37/1

= -37