Find all the solutions to [x^3 - 1] = 0 in the ring Z/13Z. Make sure you explain why you have found all the solutions, and why there are no other solutions.

Step-by-step explanation:

It is multiplication property of equality. The goal is to get d by itself so what we do here is basically a process of

\(5d=75\\\\5d/5=75/5\\\\d=15\)

Answer:

Division property of equality...

Step-by-step explanation:

The person above me was close, and they were right about the process of getting 15, but it is not multiplication property of equality.

Proof:

1. You have to undo what has been done to find out d, the variable that we are solving for. In other words, we're simply solving for x.

2. You can't undo the multiplication by doing more multiplication.

3. Given: 5d=75, and by doing inverse operations, you flip it around to:

75 ÷ 5 = d. this is the division property of equality because we're doing the opposite of multiplication to solve for d, and we're undoing the multiplication.

4. Do the math, or use a calculator to find what 75 divided by 5 is.

5. The answer is 15, so 15 = d.

Therefore,

It is "D," division property of equality.

8,16,24

Given:

the relation between number of sandwiches and time is :

y = 8x

where, y is number of sandwiches

x is time

For 1 hour,

y = 8*1

y = 8.

For 2 hour,

y = 8*2

y = 16.

For 3 hour,

y = 8*3

y = 24.

#123

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sandwiches eaten by Jimmy in consecutive hours are 8, 16, and 24.

Given info;

Jimmy consistently consumes sandwiches. The linear equation y = 8x represents the number of sandwiches(y) that he can consume in an hour(x).

To know how many sandwiches he ate in consecutive hours;

Case(1):

y = 8x

x = 1 hour

y = 8*1

  = 8

Case(2):

y = 8x

x = 2 hours

y = 8*2

  = 16

Case(3):

y = 8x

x = 3 hours

y = 8*3

  = 24

Therefore, sandwiches eaten by Jimmy in consecutive hours are 8, 16, and 24.

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Answer:

11 + m > -23

Step-by-step explanation:

Answer:

m > -34

Step-by-step explanation:

1 - Translate words to math

The sum of 11 and m

11 + m

is greater than -23

> -23

Therefore our inequality is;

11 + m > -23

2 - Solve it algebraicly

Although we dont use this rule here its good to know.

Unless we divide or multiply by negatives our inequality symbol stays the same. If that rule applies we flip the inequality (i.e. > to < and vice versa)

Now with that out of the way we can fully simplify our inequality as long as we know it works like an equality.

11 + m > -23

-11           -11

      m > -34

So with this in mind we know our m value is greater than all numbers greater than -34 which is written as m > -34

Hope this helps :)

Answer:

1.) \(3-6x\)

2.) \(3(x-6)\)

3.) \(x^3-6\)

answers are shown below

Answer:

Step-by-step explanation:

Based on the information provided, it can be concluded that Houa can drive 125 miles for 7 gallons of gas.

To determine the number of gallons this person can drive, just observe the graph presented and determine the value of Y (miles driven) when the value of x (gallons of gas) is 7. Based on this principle it can be concluded that for 7 gallons Houa can drive 125 miles.

This implies that if we compare both cars (Houa's and Lincoln's), the car that requires less gasoline is Lincoln's car.

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The resulting matrix after the given row operations is:

15 26 26

-4 6 8

-55 -77 -72

To fill in the blanks of the resulting matrix after the given row operations, let's go step by step:

Original matrix:

3 8 2

-2 3 4

5 3 8

Row operation 1: 2R2 -> R2

After performing this row operation, the second row is multiplied by 2:

3 8 2

-4 6 8

5 3 8

Row operation 2: R1 + 3R2 -> R1

After performing this row operation, the first row is added to 3 times the second row:

15 26 26

-4 6 8

5 3 8

Row operation 3: R3 - 4R1 -> R3

After performing this row operation, the third row is subtracted by 4 times the first row:

15 26 26

-4 6 8

-55 -77 -72

So, the resulting matrix after the given row operations is:

15 26 26

-4 6 8

-55 -77 -72

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Answer:

0.5

Step-by-step explanation:

Answer: 1/2 or 0.5

Step-by-step explanation:

attached the solution below for better understanding...

Hope that helps...

In the first question, the statement "Using logarithmic differentiation we obtain that the derivative of the function y = x² satisfies the equation y = 4x log x + 2x" is true.

In the first question, using logarithmic differentiation on the function y = x², we differentiate both sides, apply the product rule and logarithmic differentiation, and simplify to obtain the equation y = 4x log x + 2x, which is correct.

In the second question, the statement is false. When using logarithmic differentiation on the function y = (1+x²)²(1 + sin x)²/(1-x²), the derivative is calculated correctly, but the equation given is incorrect. The correct equation after logarithmic differentiation should be y' = (4x/(1 + x²)(1 + sin x))(1-x²) - (2x(1+x²)²(1 + sin x)²)/(1-x²)².

In the third question, the product z²w is calculated correctly as 30-10%.

It is important to accurately apply logarithmic differentiation and perform the necessary calculations to determine the derivatives and products correctly.

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The equation of a line is given by the equation;

From the given graph, the intercept on y-axis is 7.

To find the slope, we would make use of the slope formula given as:

From the graph, we have:

Hence, the equation of the line is:

Considering the expression of a line, the slope of the line that passes through the points (2,4) and (9,12) is 8/7.

A linear equation o line can be expressed in the form y = mx + b

where

Knowing two points (x₁, y₁) and (x₂, y₂) of a line, the slope of the line is calculated as:

m= (y₂ - y₁)÷ (x₂ - x₁)

In this case, being (x₁, y₁)= (2,4) and (x₂, y₂)= (9,12), the slope m can be calculated as:

m= (12 -4)÷ (9 -2)

Solving:

m= 8÷ 7= 8/7

Finally, the slope of the line is 8/7.

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Answer:

0.6 x 25 = x

Step-by-step explanation:

60% of 25

= 60/100 x 25

= 0.6 x 25

= 15

Though the question states as in a "select-all question," Only answer 0.6 x 25 = x will be correct.

The equation which is equivalent to 60% of 25 is x = 0.6 * 25

An equation is used to show the relationship between variables, numbers.

Let x represent the value of 60% of 25. Hence:

x = 60% of 25

x = 0.6 * 25

Hence the equation which is equivalent to 60% of 25 is x = 0.6 * 25

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Answer:

1cm divided by 17 = 32 then subtract the 32 into 17

Complete Question:

The height of a diver jumping from a diving platform is about \(h(t)= 16t^2 +11t+10\), where h is the height of the diver in feet above the water and t is the time measured in seconds, when diving from a platform about 34.3 feet above the water with an upward initial velocity of 11 ft/sec..  After how many seconds is the diver's height above the water 15 feet?

Answer:

0.3125 seconds

Step-by-step explanation:

Given

\(h(t)= 16t^2 +11t+10\)

Required

Time when the diver is above 15ft

This implies that h(t) = 15

So, we have:

\(15= 16t^2 +11t+10\)

Collect Like Terms

\(0= 16t^2 +11t+10 - 15\)

\(0= 16t^2 +11t-5\)

\(16t^2 +11t-5=0\)

Expand:

\(16t^2 + 16t - 5t - 5 = 0\)

Factorize:

\(16t(t + 1) - 5(t + 1) = 0\)

\((16t - 5)(t + 1)=0\)

Split

\(16t - 5 = 0\) or \(t + 1 = 0\)

\(16t = 5\) or \(t + 1 = 0\)

Solve for t

\(t = 5/16\) or \(t = -1\)

\(t = 0.3125\) or \(t = -1\)

But time can't be negative. So:

\(t = 0.3125\)

Hence, it will take the diver 0.3125 seconds to be at a height above 15 feet

It will take t = 0.3125 seconds is the diver's height above the water 15 feet.

Given ,

The height of a diver jumping from a diving platform is h

 h(t) = \(-16t^{2} + vt + 10\)

The diver's height above the water 15 feet

Velocity = v = 11 ft per second

We have to find, t seconds is the diver's height above the water 15 feet.

According to the question,

\(h(t) = -16t^{2} +vt+10\)

Where v = 11, h(t) = 15

15 = -16\(t^{2}\) + 11t + 10  

15 - 10 = \(-16t^{2} + 11t\)

5 = \(-16t^{2} +11t\)

\(16t^{2} -11t +5= 0\)

\(16t^{2} -16t - 5t + 5 = 0\)

16t ( t - 1 ) - 5 ( t + 1 ) = 0

(16t - 5 ) ( t + 1 ) = 0

16t - 5 = 0

16t = 5

t = \(\frac{5}{16}\)

t = 0.3125

And t + 1 = 0

t = -1

Time can not be negative so we can't take t = -1 .

So, The required value of time is t = 0.3125

Hence, it will take t= 0.3125 seconds is the diver's height above the water 15 feet.

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Answer: 15

Step-by-step explanation:

The mode of the data set 12, 19, 22, 17, 15, 18, 15, 14, 16​ will be 15.

A mode is described as the result in a group of items that occurs most frequently.

The data is given below.

12, 19, 22, 17, 15, 18, 15, 14, 16​

Arrange the data in ascending order.

12, 14, 15, 15, 16, 17, 18, 19, 22

Then the mode of the data set will be 15.

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Answer:

15.9 mm²

Step-by-step explanation:

We solve using Area of the circle formula

Area of a circle = πr²

Diameter of his friend's wand = 4.5mm

Radius = 4.5mm/2

= 2.25 mm

How much wire did his friend need to make the circular part of his wand? Use 3.14 for π

= 3.14 × (2.25mm)²

= 15.89625 mm²

Approximately = 15.9 mm²

Answer:

10.8 kilometers

Step-by-step explanation:

Perimeter of a triangle equation is P (perimeter)= a+b+c

put 32.4 of the left side of the equation as it is the answer for the perimeter and replace and and b with your first 2 side legnths like this

32.4= 10.8+ 10.8+c

Now we must solve for the unknown side legnth c. To do this we must simplify the right side of the equation first by adding 10.8+ 10.8

32.4= 21.6+c

Now we can subtract 21.6 from the left side to solve for c

10.8=c

Therefore the third side is 10.8 kilometers

Answer: 10.8 km

Step-by-step explanation:  A triangle has three sides:  a, b, and c

The perimeter is a+b+c and is a total of 32.4 km.   We know a=10.8 km and b = 10.8 km.

10.8 km + 10.8 km + c = 32.4 km

21.6km + c =  32.4 km

c = 10.8 km

The measure of angle Zx cannot be determined without additional information or measurements.

Since the angles are not necessarily drawn to scale, we cannot determine the measure of angle Zx without additional information or measurements. However, we do know that angles PR5 and QSx are given, and we can use the fact that the angles of a triangle sum up to 180 degrees to find the measure of angle Zx.

Assuming that Zx is a part of a triangle with PR and QS as the other two sides, we can use the following equation to find the measure of angle Zx:

Zx + PR5 + QSx = 180

Substituting the given values, we get:

Zx + 57 + QSx = 180

We do not know the value of QSx, so we cannot solve for Zx at this point. Therefore, we need additional information or measurements to determine the measure of angle Zx.

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The probability that at least one of the next four cars that enter the lot is a minivan is 45% The Option A.

To get probability that at least one of the next four cars is a minivan, we need to consider the probability of the complement event and subtract it from 1.

From simulation results:

The total number of non-minivan cars in the simulation results is:

= 6 + 6 + 5

= 17.

The probability of a car being a non-minivan is:

P(non-minivan) = 17 / 20 = 0.85

The probability of none of the next four cars being a minivan is:

P(no minivan in 4 cars) = P(non-minivan) ^ 4 = 0.85 ^ 4 ≈ 0.522

The probability that at least one of the next four cars is a minivan is:

P(at least one minivan in 4 cars) = 1 - P(no minivan in 4 cars)

= 1 - 0.522

= 0.478.

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Answer:

19 days

Step-by-step explanation:

2 weeks = 14 days

14 + 5 = 19

Answer:

19 days

hope this helps

have a good day :)

Step-by-step explanation:

Answer:

y = 70 degree's

Step-by-step explanation:

180 is a straight line therefore the equation would read ...

180 = 110 + y

subtract 110 from both sides ...

70 = y

Answer:

y = 70

Step-by-step explanation:

This is a supplementary angle so:

y + 110 = 180

y = 180 - 110

y = 70

ANSWER is Option C

Use 2πr = 2×3.14×6 = 37.68 inches

Formula for the circumference of a circle: C = pi * Diameter

We are given the diameter, 12 inches, so all we have to do is plug in our values.

C = 3.14 * 12

C = 37.68 inches

Hope this helps!! :)

Answer:

500 mL

Step-by-step explanation:

Divide the total amount by the number of people to see how much each person drank.

Converting from L to mL :

For the given geometric sequence we have:

a) R = 3/4

b) 243/256

c) Aₙ = 3*(3/4)⁽ⁿ⁻¹⁾

The common reason is given by the quotient between two consecutive terms, so using the first two, we will get:

R = (9/4)/3

R = 3/4

That is the common reason.

b) To find the fifth therm, we need to take the fourth one and multiply it by the common reason, so we will get:

81/64*(3/4) = 243/256

c) The n-th term of the sequence is the first term of the sequence multiplied by the common reason (n - 1) times, it gives:

Aₙ = 3*(3/4)⁽ⁿ⁻¹⁾

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Answer:

Correct answer is option D

When it comes to static characteristics, there are many desirable attributes that can make a product or service stand out from the competition.

Quality and reliability are essential and desirable, as these are the main factors customers will consider when making a purchasing decision.

Durability is also important, as it ensures that a product will continue to perform to its highest standards over time.

Additionally, value for money is key, as customers want to be sure that they are getting a product or service that is worth the cost.

Furthermore, flexibility is highly desirable, as customers often need the ability to customize products or services according to their specific needs.

Finally, a good customer service experience is an essential static characteristic, as a positive customer experience can increase customer satisfaction and loyalty.

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Answer:

-1 4/5

Step-by-step explanation:

In mathematics, a fraction is a number that represents a part of a whole. It consists of a numerator and a denominator. The numerator represents the number of equal parts of a whole, while the denominator is the total number of parts that make up said whole. For example, in the fraction 3  5, the numerator is 3, and the denominator is 5. A more illustrative example could involve a pie with 8 slices. 1 of those 8 slices would constitute the numerator of a fraction, while the total of 8 slices that comprises the whole pie would be the denominator. If a person were to eat 3 slices, the remaining fraction of the pie would therefore be 5  8 as shown in the image to the right. Note that the denominator of a fraction cannot be 0, as it would make the fraction undefined. Fractions can undergo many different operations, some of which are mentioned below.

Answer:

(1 , 1)

Step-by-step explanation:

x+3y=4

x-2y=-1

We can solve this system of equations using the elimination method. In this method there must be two identical variables ( which in this case there is, that variable being x ). If there are two identical variables you can subtract the two equations "eliminating" one of the variables. There is then only one variable in which you can solve for.

So first let's subtract the two equations

x + 3y = 4

- ( x - 2y = -1 )

------------------

remove parenthesis and apply negative sign

x + 3y = 4

-x + 2y = +1

-----------------

0 + 5y = 5

We are now left with one variable in which we can solve for.

5y = 5

divide both sides by 5

y = 1

Next we want to find the value of x.

To do so we simply plug in the value of y into one of the equations and solve for x. Note that we could do this to either equation and we would get the same answer.

x + 3y = 4

y = 1

x + 3(1) = 4

multiply 3 and 1

x + 3 = 4

subtract 3 from both sides

x = 1

So x = 1 and y = 1

Therefore the solution to the system of equations is (1,1)