The definition of the absolute value of a number is its magnitude, or distance, from zero. How do these two definitions connect?

Answers

Answer 1

The way that the definitions of the absolute value of a number, connect is that the absolute value of a number is the positive representation of the number's distance from zero.

What is absolute value ?

The absolute value of a number is the numerical value of a real number without regard to its sign. In other words, the absolute value of a number is the number's distance from zero on the number line. The absolute value of a number is always positive or zero, and is written as the number inside of absolute value notation, which is two vertical lines on either side of the number, like so: |number|. For example, the absolute value of -5 is 5, and the absolute value of 5 is also 5.

The distance from zero is the same as the magnitude of a number, and the absolute value of a number is a non-negative representation of its magnitude. So, in other words, the absolute value of a number is its distance from zero on the number line. The two definitions are connected because the absolute value of a number is a positive representation of its distance from zero.

Find out more on absolute value at https://brainly.com/question/12928519

#SPJ1

Related Questions

i dont know the answer to this

Answers

combine like terms. D) 2x+7

XZ.P Point P(-7, 2) is mapped onto P¹ (3, -11) by the reflection y=mx+c. find the values of the constants m and c.

Answers

The values of the constants m and c include the following:

m = -1.3

c = 7.1

What is the slope-intercept form?

In Mathematics and Geometry, the slope-intercept form of the equation of a straight line is given by this mathematical equation;

y = mx + c

Where:

m represent the slope or rate of change.x and y are the points.c represent the y-intercept or initial value.

Since the point P(-7, 2) is mapped onto P' (3, -11) by the reflection y = mx + c, we can write the following system of equations;

2 = -7m + c ...equation 1.

-11 = 3m + c ...equation 2.

By solving the system of equations simultaneously, we have:

2 = -7m - 3m - 11

11 + 2 = -10m

13 = -10m

m = -1.3

c = 7m + 2

c = 7(-1.3) + 2

c = -7.1

Read more on slope-intercept here: brainly.com/question/7889446

#SPJ1

Peter set off from Town A at 10 am, driving at an average speed of 84 km/h. He reached
Town B at 2 pm. If William set off 1 hour 25 minutes earlier than Peter and took the
same route at an average speed of 70 km/h, at what time would William reach Town B?

Answers

Peter left Town A around 10 a.m., traveling at an average speed of 84 km/h. William would reach Town B at 1:23 PM.

Firstly, we need to find the distance between Town A and Town B which can be calculated by calculating the distance travelled by Peter

Time taken by Peter = 2PM - 10AM

= 4 hrs

Speed of Peter = 84 km/h

Distance travelled by Peter = speed × time

= 84 × 4

= 336 km

So, the distance between Town A and Town B = distance travelled by Peter = 336 km.

Now, we will calculate time taken by William.

Speed of William = 70 km / hr

Distance travelled by William = distance between Town A and town B = 336 km

Time taken by William = distance / speed

= 336 / 70 hr

= 4.8 hr

This can b converted into hrs and minutes

4.8 hr = 4 hr + 0.8 × 60

= 4 hr 48 mins

Time William took off = 10 AM - 1hr 25 mins

= 8:35 AM

Now, we will calculate the time William would reach town B.

Time = 8:35 + 4hr 48 mins

= 1:23 PM

To know more about speed:

https://brainly.com/question/31756299

#SPJ1

a) The monthly basic salary of the married Chief of Army Staffs (COAS) General is Rs 79,200 with Rs 2,000 dearness allowance. He gets Dashain allowance which is equivalent to his basic salary of one month. He contributes 10% of his basic salary in Employee's Provident Fund (EPF) and he pays Rs 50,000 as the premium of his life insurance. Given that 1% social security tax is levied upon the income of Rs 6,00,000, 10% and 20% taxes are levied on the next incomes of Rs 2,00,000 and up to Rs 3,00,000 respectively. Answer the following questions. (i) What is his monthly basic salary? (ii) Find his taxable income.

Answers

(i). His monthly basic salary is Rs 79,200.

(ii) His taxable income is Rs 1,02,480.

(i) The monthly basic salary of the married COAS General is given as Rs 79,200, with an additional Rs 2,000 as a dearness allowance.

Total salary = Basic salary + Dearness allowance

Total salary = Rs 79,200 + Rs 2,000

Total salary = Rs 81,200

So his monthly basic salary is Rs 79,200.

(ii)

Total income = Basic salary + Dearness allowance + Dashain allowance

Total income = Rs 79,200 + Rs 2,000 + Rs 79,200

Total income = Rs 1,60,400

From this, we subtract his EPF contribution and life insurance premium:

Taxable income = Total income - EPF contribution - Life insurance premium

Taxable income = Rs 1,60,400 - 10% of Rs 79,200 - Rs 50,000

Taxable income = Rs 1,60,400 - Rs 7,920 - Rs 50,000

Taxable income = Rs 1,02,480

So his taxable income is Rs 1,02,480.

Learn more about the tax here:

https://brainly.com/question/28035447

#SPJ1

if gender would not have mattered, what would have been the number of males that would have survived, given the data for the number of females who survived (296/402) and the total number of passengers on the ship (1207).

Answers

If gender did not matter then the number of males who would have survived would be 593 males

How to find the number who would have survived ?

If gender would not have mattered, the survival rate would be the same for both genders. So, we would use the survival rate of females (which is 296/402) to calculate the expected number of males that would have survived.

First, calculate the survival rate of the females:

Survival rate = Number of females who survived / Total number of females

= 296 / 402

= 0.737

Expected number of male survivors = Number of males * Female survival rate

= 805 x 0.737

= 593 males

Find out more on survival rates at https://brainly.com/question/30894892

#SPJ1

Real World Scenario: Sara and Kim are both three years old. Both have recently talked to their parents about doing chores around the house to earn some money. Both Sara and Kim's parents have agreed to start giving them a constant allowance every week. Sara currently has $1 in her piggy bank. Her parents have agreed to give her $.60 per week for doing her chores. Kim currently has $2.20 in her piggy bank. Her parents have greed to give her $.20 per week for doing her chores.

What equation and graph help support scenario?

Answers

The equation that represents the amount of money in Sara's piggy bank is y = 0.6x + 1 and the equation that represents the amount of money in Kim's piggy bank is y = 0.2x + 2.2.

The equation that represents the amount of money in Sara's piggy bank over time can be written as

Y = 0.6x + 1

Where Y represents the total amount of money in Sara's piggy bank and x represents the number of weeks.

Similarly, the equation that represents the amount of money in Kim's piggy bank over time can be written as

Y = 0.2x + 2.2

Where Y represents the total amount of money in Kim's piggy bank and x represents the number of weeks.

To visualize these equations, we can create a graph where the x-axis represents the number of weeks and the y-axis represents the amount of money in the piggy bank. We can plot the points for each week and draw a line connecting them. The resulting graph will show the trend of the amount of money in each piggy bank over time.

Here is a graph that represents the scenario

In the graph, the red line represents the amount of money in Sara's piggy bank and the blue line represents the amount of money in Kim's piggy bank. As we can see, Sara's piggy bank grows faster than Kim's piggy bank due to the higher allowance she receives for doing her chores.

To Know more about Equations here

https://brainly.com/question/10413253

#SPJ1

1.
A 50 foot rope is stretched tight from the roof of a building to a spot 20 feet from the base of the
building. How tall is the building? Round your answer to TWO decimal places.

Answers

The required height of the building is approximately 45.82 feet.

Given that, a 50-foot rope is stretched from a building's top to a point 20 feet from the building's base.

We can use the Pythagorean theorem to solve the question.

Let h be the height of the building.

Pythagoras's theorem states that in a right-angled triangle, "the square of one side is equal to the sum of the squares of the other two sides".

Then, we have:

h² + 20² = 50²

Simplifying and solving for h, we get:

h² = 50² - 20²

h² = 2500 - 400

h² = 2100

h = √(2100)

h ≈ 45.82

Therefore, the height of the building is approximately 45.82 feet.

Learn more about Pythagoras's theorem here:

brainly.com/question/343682

#SPJ1

In a class of 26 students, 15 play an instrument and 5 play a sport. There are 3 students who play an instrument and also play a sport. What is the probability that a student chosen randomly from the class plays a sport and an instrument?

Answers

Answer:

3:26

Step-by-step explanation:

more equation things

Answers

For the given linear equation y = (1/4)*x + 5/4.

(1, 1.5) is a solution.(12, 4) is not a solution.The x-intercept is (-16/5, 0).

Are these points solutions of the linear equation?

Here we have the linear equation:

y = (1/4)*x + 5/4.

to check if (1, 1.5) is a solution we need to evaluate this in x = 1 and see if we get 1.5.

y = (1/4)*1 + 5/4

y = 6/4 = 3/2 = 1.5

Then (1, 1.5) is a solution.

For the second point we evaluate in x = 12.

y = (1/4)*12 + 5/4

y = 3 + 5/4 = 4.25

So (12, 4) is not a solution.

Finally, to find the x-intercept, we evaluate in y = 0.

0 = (1/4)*x + 5/4

-4/5 = (1/4)*x

4*(-4/5) = x

-16/5 = x

The x-intercept is (-16/5, 0).

Learn more about linear equations:

https://brainly.com/question/1884491

#SPJ1

On the map, the grocery store is 2 inches away from the library. The actual distance is 1.5 miles. The same map shows that the movie theater is 20 inches from the school.

What is the actual distance from the movie theater to the school, rounded to the nearest mile?

A: 15
B:27
C:30
D:60

Answers

The actual distance from the movie theater to the school is given as follows:

A. 15 miles.

How to calculate the actual distance?

The actual distance from the movie theater to the school is obtained applying the proportions in the context of the problem.

On the map, the grocery store is 2 inches away from the library. The actual distance is 1.5 miles, hence the scale factor is of:

2 inches = 1.5 miles

1 inch = 0.75 miles.

The same map shows that the movie theater is 20 inches from the school, hence the actual distance is given as follows:

20 x 0.75 = 15 miles.

More can be learned about proportions at https://brainly.com/question/24372153

#SPJ1

what is the co efficient of x in(2.x+3)²

Answers

What is the Coefficient of x mean?

A coefficient is any constant or numerical term that is in front of one or more variables and is defined as a fixed number that is multiplied by a variable. For example, in the expression 3x+2y+4, 3 is the coefficient of x, 2 is the coefficient of y but 4 is not a coefficient, as it is not being multiplied by a variable.

How do you find the coefficient of x?

To find the coefficient of x, we can encircle it or underline it. Then, take everything else except for x, i.e. 5y. So, the coefficient of x in the term 5xy is 5y. Similarly, the coefficient of y in the term 5xy is 5x.

Solving it with Binomial Theorem

(2.x+3)² = (2x+3)(2x+3)

2x(2x+3)+3(2x+3)=

4x²+6x+3(2x+3)=

4x²+12x+9

so if your using the binomial theorem it would equal 4x²+12x+9

if you just want the coefficient of x that would be 4 ↑

Alondra has $350,000 saved for retirement in an account earning 2.9% interest, compounded monthly. How much will she be able to withdraw each month if she wants to take withdrawals for 22 years? Round your answer to the nearest dollar.

Answers

Alondra will be able to withdraw approximately $1,427 per month to take withdrawals for 22 years from her retirement account.

To calculate the monthly withdrawal amount, we need to use the present value formula, which is:

PMT = (PV * r) / (1 - (1 + r)⁻ⁿ)

where:

PV = present value = $350,000

r = monthly interest rate = 2.9% / 12 = 0.002417

n = number of months = 22 years * 12 months/year = 264 months

Substituting the values into the formula, we get:

PMT = (350000 * 0.002417) / (1 - (1 + 0.002417)⁻²⁶⁴)

PMT ≈ $1,427.07

This calculation assumes that the interest rate remains constant throughout the 22-year period, which may not be the case in reality.

To learn more about interest click on,

https://brainly.com/question/28767734

#SPJ1

879 divided by 8 with remainder as fraction

Answers

in mixed number form 109 7/8
in decimal form 109.875

Question 1b Identify the amount in this statement. 6 is 30% of 20. The amount = The solution is

Answers

The amount in this statement, 6 is 30% of 20 is 6.

The amount in the statement "6 is 30% of 20" is 6.

This statement means that if we take 30% of 20, we get 6.

In other words, the amount 6 is 30% of 20.

We can also verify this by calculating 30% of 20:

30% of 20

= (30/100) × 20

= 0.3 × 20

= 6

Hence, the amount in this statement is 6.

To learn more on Percentage click:

https://brainly.com/question/24159063

#SPJ1

what is the resultant displacement of 6m north 8m east and 10m north west?

Answers

The resultant displacement is approximately 13.071m north and 8m east.

To find the resultant displacement, we need to combine the given displacements in a vector-like manner.

Let's break down the displacements into their components and then add them up.

The first displacement is 6m north.

Since it is purely in the north direction, its components would be 6m in the north direction (along the y-axis) and 0m in the east direction (along the x-axis).

The second displacement is 8m east.

As it is purely in the east direction, its components would be 0m in the north direction and 8m in the east direction.

The third displacement is 10m northwest.

To find its components, we can split it into two perpendicular directions: north and west.

The northwest direction can be thought of as the combination of north and west, each with a magnitude of 10m.

Since they are perpendicular, we can use the Pythagorean theorem to find the components.

The north component would be 10m multiplied by the cosine of 45 degrees (45 degrees because northwest is halfway between north and west).

Similarly, the west component would be 10m multiplied by the sine of 45 degrees.

Calculating the components:

North component = 10m [tex]\times[/tex] cos(45°) = 10m [tex]\times[/tex] 0.7071 ≈ 7.071m

West component = 10m [tex]\times[/tex] sin(45°) = 10m [tex]\times[/tex] 0.7071 ≈ 7.071m

Now, let's add up the components:

North component: 6m (from the first displacement) + 7.071m (from the third displacement) = 13.071m north

East component: 8m (from the second displacement).

For similar question on resultant displacement.

https://brainly.com/question/13309193

#SPJ8

Find the 15th term of the geometric sequence 2,6,18,...

Answers

Answer:

In a geometric sequence, each term is found by multiplying the previous term by a constant value called the common ratio (r).

In this case, the first term (a₁) is 2, and the common ratio (r) can be found by dividing any term by its preceding term. Let's calculate it:

r = 6 / 2 = 3

Now, to find the 15th term (a₅₊₁₋₅), we can use the formula:

aₙ = a₁ * r^(n-1)

Substituting the values, we have:

a₁ = 2

r = 3

n = 15

a₁₅ = 2 * 3^(15-1)

Calculating the exponent first:

3^(15-1) = 3^14 = 4782969

Now, substituting this value back into the formula:

a₁₅ = 2 * 4782969

a₁₅ = 9565938

Therefore, the 15th term of the geometric sequence 2, 6, 18, ... is 9565938.

Step-by-step explanation:

Need help on please

Answers

Answer:

Step-by-step explanation:

The figure is a right triangle with hypotenuse = QS

The base from the graph = 4 units
(or you can just subtract the x-coordinates 2 - (-2) = 4)

The height from the graph is 3 units
(Or you can subtract the y-coordinates: 1 - (-2) = 3)

Since this is a right triangle the square of the hypotenuse = sum of squares of the other two sides

QS² = 3² + 4² = 9 + 16 = 25

QS, the hypotenuse = √25 = 5

The perimeter = sum of the sides = 3 + 4 + 5 = 12 units

If r = 5 units and x = 11units then what is the volume if the cylinder shown above

Answers

The volume of cylinder which is having radius as 5 units and height as 11 units, is 863.5 cubic units.

A "Cylinder" is a 3-dimensional geometric shape that consists of a circular base and a curved surface which extends up from base to fixed height.

The volume(V) of a cylinder is the amount of space enclosed by the cylinder, and it is given by the formula : V = πr²h;, where π is = 3.14, "r" denotes radius of base; "h" denotes the height;

Given that the radius is 5 units and the height is 11 units,

Substituting the values,

We get,

V = π × (5)² × (11);

V = 275π cubic units;

V = 275×3.14 = 863.5 cubic units;

Therefore, the required volume is = 863.5 cubic units.

Learn more about Volume here

https://brainly.com/question/27033747

#SPJ1

The given question is incomplete, the complete question is

If radius is 5 units, and height is 11 units, Find the Volume of the Cylinder.

Select the correct answer. Consider this function. Which graph represents the inverse of function f? f(x)= x+4

Answers

The inverse of the function f(x) = x + 4 is given as f⁻¹(x) = x - 4

What is inverse of a function?

An inverse function or an anti function is defined as a function, which can reverse into another function. In simple words, if any function “f” takes x to y then, the inverse of “f” will take y to x. If the function is denoted by ‘f’ or ‘F’, then the inverse function is denoted by f-1 or F-1.

In this problem, the function given is f(x) = x + 4;

We can find the inverse of the function as;

y = x + 4;

Let's switch the variables by replacing x as y and y as x;

x = y + 4

Solving for y;

y = x - 4

f⁻¹(x) = x - 4

The graph of the function is attached below

Learn more on inverse of a function here;

https://brainly.com/question/14391067

#SPJ1

Use the following sets to answer the question.
A={1,2,3,4,5}
B={5,6,7,8}
Which answer shows the union of sets A
and B?
{5}
{1,2,3,4,6,7,8,9}
{1,2,3,4,5,6,7,8}
{2,4,8}

Answers

The union of sets A and B is {1, 2, 3, 4, 5, 6, 7, 8}.

The union of two sets A and B is the set of all elements that are in A, or B, or both. In this case, the elements in set A are {1, 2, 3, 4, 5} and the elements in set B are {5, 6, 7, 8}.

To find the union of these sets, we simply combine all the elements from both sets but remove any duplicates.

Therefore, the answer that shows the union of sets A and B is {1, 2, 3, 4, 5, 6, 7, 8}, since it contains all the elements from both sets without any duplicates.

Learn more about union of sets on:

brainly.com/question/2166579

#SPJ1

Find the range of the number of points scored.
Range: – =

answer is 56, 41, 15

Answers

It would be 15, 41, 56
This is because I believe it is from smallest to biggest

Roughly how much more does auto insurance cost for a 16 year old compared to a middle aged (40-50 year old) driver

Answers

A 16-year-old on their own policy pays on average $4,000 more per year than a 50-year-old would have to pay

The cost of insurance

Auto insurance costs vary significantly depending on factors such as location, vehicle type, and driving history. However, on average, a 16-year-old driver can expect to pay significantly more for auto insurance compared to a middle-aged driver (40-50 years old).

The exact amount varies, but it's not uncommon for a 16-year-old driver to pay two to three times more for auto insurance than a middle-aged driver. This is mainly because younger drivers are considered riskier due to their inexperience and higher likelihood of being involved in accidents.

Read more on insurance here:https://brainly.com/question/25855858

#SPJ1

The community health clinic you volunteer for aims to develop a strategy allowing the most vulnerable members of the community to have first access to the Flu vaccine. The clinic has collected data finding that the total number of people in their service area is 50,000, 27% of the community is over the age of 65 and immunocompromised, and 11% of the community under 65 is immunocompromised. While the clinic wishes to market to all members of the community, immunocompromised people over 65 are their current priority.2. Explain in a one well-written paragraph, how you will analyze the data in this scenario to arrive at the answer you will provide in number 2.

Answers

In order to understand and prioritize the vaccination strategy for the community health clinic, first accurately assess the demographics of the community based on the data provided.

How to analyze the data ?

Calculating the absolute numbers of people in each group: over 65 and immunocompromised, and under 65 and immunocompromised. For this, we'll apply the given percentage to the total population of 50,000.

Knowing the total number of people in each category will help us understand the size of each target group and prioritize accordingly. The clinic's current priority is immunocompromised people over 65, so having the exact figure will aid in planning for vaccine supply and outreach strategies.

Furthermore, the analysis of this data can also aid in projecting the needs for future vaccine campaigns for the remaining community members. Finally, this detailed analysis will help in crafting an effective communication plan that emphasizes the clinic's priority of serving the most vulnerable first, while still acknowledging the needs of all community members.

Find out more on analyzing data at https://brainly.com/question/28132995

#SPJ1

someone please answer this its confusing me

Answers

24. opposite sides of a parallelogram are always congruent

the line AB will be congruent to line DC so 8t + 7 = 9t - 2 which gives you t = 9

line AD will also be congruent to line BC so 4s + 1 = 2s + 25 which gives you s = 12

By using the trapezoidal rule with 5 ordinates, approximate [sin(x²+1) dx to 4 decimal places.

Answers

Using the trapezoidal rule with 5 ordinates, we approximate the integral [sin(x²+1) dx] over the interval [0,1] to be 0.5047 to 4 decimal places.

To approximate the integral [sin(x²+1) dx] using the trapezoidal rule with 5 ordinates, we can use the following formula:

∫[a,b]f(x)dx ≈ [(b-a)/2n][f(a) + 2f(a+h) + 2f(a+2h) + 2f(a+3h) + 2f(a+4h) + f(b)]

where n is the number of ordinates (in this case, n = 5), h = (b-a)/n is the interval width, and f(x) = sin(x²+1).

First, we need to find the interval [a,b] over which we want to integrate. Since no interval is given in the problem statement, we'll assume that we want to integrate over the interval [0,1].

Therefore, a = 0 and b = 1.

Next, we need to find h:

h = (b-a)/n = (1-0)/5 = 0.2

Now, we can apply the trapezoidal rule formula:

∫[0,1]sin(x²+1)dx ≈ [(1-0)/(2*5)][sin(0²+1) + 2sin(0.2²+1) + 2sin(0.4²+1) + 2sin(0.6²+1) + 2sin(0.8²+1) + sin(1²+1)]

≈ (1/10)[sin(1) + 2sin(0.05²+1) + 2sin(0.15²+1) + 2sin(0.35²+1) + 2sin(0.65²+1) + sin(2)]

≈ (1/10)[0.8415 + 2sin(1.0025) + 2sin(1.0225) + 2sin(1.1225) + 2sin(1.4225) + 1.5794]

≈ 0.5047

Therefore, using the trapezoidal rule with 5 ordinates, we approximate the integral [sin(x²+1) dx] over the interval [0,1] to be 0.5047 to 4 decimal places.

Learn more about Trapezoidal Rule at

brainly.com/question/30401353

#SPJ1

Help My Daughter we not understanding?

Answers

Representation of a number in three different ways:

133: [12 tens and 13 ones], [13 tens and 3 ones], [1 hundred, 3 tens and 3 ones]

678: [67 tens and 8 ones], [60 tens and 78 ones], [6 hundreds, 7 tens and 8 ones]

877: [80 tens and 77 ones], [87 tens and 7 ones], [8 hundred, 7 tens and 7 ones]

543: [54 tens and 3 ones], [50 tens and 43 ones], [5 hundreds, 4 tens and 3 ones]

453: [45 tens and 3 ones], [40 tens and 53 ones], [4 hundreds, 5 tens and 3 ones]

341: [30 tens and 41 ones], [34 tens and one], [3 hundreds,4 tens and one]

555: [50 tens and 55 ones], [55 tens and 5 ones], [5 hundreds, 5 tens and 5 ones]

485: [48 tens and 5 ones], [40 tens and 85 ones], [4 hundreds, 8 tens and 5 ones]

789: [78 tens and 9 ones], [70 tens and 89 ones], [7hundreds, 8 tens and 9 ones]

864: [86 tens and 4 ones], [80 tens and 64 ones], [8 hundreds, 6 tens and 4 ones]

652: [65 tens and 2 ones], [60 tens and 52 ones], [6hundreds, 5 tens and 2 ones]

Here given an example to write a particular number in different representations.

13 tens and 12 ones = 13*10 + 12*1 = 130 + 12 = 142.

14 tens and 2 ones = 14*10 + 2*1 = 140 + 2 = 142.

1 hundred, 4 tens and 2 ones = 1*100 + 4*10 + 2*1 = 100 + 40 + 2 = 142.

So three representations are of number 142.

Rest blanks should be filled in same manner taking different numbers for each rows and three columns of each row should be filled with three different representation of that assumed numbers.

Representations for some numbers: