The function m(x) = |x-441 represents the absolute deviation (in years) of a man's agex (in years) from the average age of men in a
city. The function w(x)=x-47| represents the absolute deviation (in years) of a woman's age x (in years) from the average age of
women in the same city. Compare the absolute deviations for a man and a woman who are both 64 years old.
A
The age of the man is years from the average age of men in the city. The age of the woman isyears from the average age of women in the city.

The simplified form of √84 is 2√21.

To simplify the given value, first, we need to write down the prime factorization of 84.

The prime factorization of 84 = 2² × 3 × 7

Therefore,

√84 = √(2² × 3 × 7)

Applying the radical rule: √ab = √a × √b, we get

√84 = √2² × √(3 × 7)

Applying the radical rule: √a² = a, for a ≥ 0, we get

√84 = 2 × √(3 × 7)

Multiply the numbers 3 and 7 we get 3 × 7 = 21

√84 = 2 × √21

√84 = 2√21

Therefore, the simplified form of √84 is 2√21.

Refer to the attached image for the above steps.

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In the given statement is:

Gravitational Force between two bodies at a distance x is given by:-

F = GmM/ x2 ; If a body of mass ' m' is revolving around the body of mass M and it's orbit is stationary then centrifugal force must be equal to the Gravitational Force i.e. Fg = mv2/x therefore FG = Fg i.e. GmM/ x2 =mv2/x; where v is the orbit motion of the orbiting body of mass.

Now, Let us understand the :

In mechanics, gravity, often known as gravitation, is the constant force of attraction occurring on all matter. It plays no part in shaping the interior features of common stuff because it is easily the weakest force known to exist in nature.

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Answer:

Step-by-step explanation:

The angles lie on a straight line summing to total 180 degrees.

Form an equation:

m∠1 + m∠2 = 180

2x + x + 72 = 180

and solve:

3x + 72 = 180

3x = 180 - 72

3x = 108

x = 36

Answer:

see below

Step-by-step explanation:

We are here given a straight line which is splitted into two parts by a line , such that it makes two angles.

Also we know that the angle measure of a straight line is 180° . Therefore; here the sum of angles 1 and 2 will be 180° .

So that,

==> angle 1 + angle 2 = 180°

==> 2x + x + 72° = 180°

==> 3x = 180° - 72°

==> 3x = 108°

==> x = 108°/3

==> x = 36° .

The equation which we used to solve the problem is ,

==> Equation = 2x + x + 72° = 180°

For finding the individual angels substitute the value of x into their expressions , as ;

==> angle 1 = 2x = 2(36°) = 72°

==> angle 3 = x + 72° = 36° + 72° = 108° .

And we are done!

Answer:

12, 3/5, 25%, -1/12, -0.17

Step-by-step explanation:

The simplest way to do this is to convert all of the numbers into either a fraction, decimal, or a percentage. In my opinion, it is easier to use a percentage here.

25% is already a percentage

-0.17 = -17%

3/5 = 60%

-1/12 (you can use a calculator to divide and find the percentage here) = -8.33

12 = 1200%

Now that the rational numbers are all in the same unit, it is easier to sort them. In the end, we get this list (from greatest to least):

12, 3/5, 25%, -1/12, -0.17

FINAL ANSWER: 12, 3/5, 25%, -1/12, -0.17

Answer:

1. -2/3        3. -5/4         5. 3/2          FOR THE REST OF THE PARTS LOOK THROUGH THE EXPLANATIONS

Step-by-step explanation:

Before I start the workings, I'll give a little explanation on this topic.

So, the equation of a straight line is

y = mx + c

where x and y are any coordinates of any point on the line.

m is the gradient or slope

m can be calculated using 2 formulas,

formula 1: Rise/Run

where rise is the how much a graph goes upwards or downwards, if its upwards use positive integer and if its downwards use negative integer.

Run is how much a graph moves to the right or to the left, if it moves to the right is is positive, if it moves to the left it is negative.

Formula 2: (y2-y1)/(x2-x1)

the values of these are taken through any 2 coordinates on the line.

and c is the y-intercept(the point where the line crosses the y-axis.

MOVING TO ANSWERING NOW

1. Dotted points on the line are (1,0) and (4,-2)

Formula of slope,

U can use any of the 2 formulas given above

I'll show both for this question

m = (y2-y1)/(x2-x1) = (-2-0)/(4-1) = -2/3

OR

m = rise/run = where rise is -2 and run is 3 so -2/3

2. TRY DOING THIS ONE YOURSELF

For the next part I'll do 3 and 5 for your understanding, try doing 2 and 4 on your own to understand.

3. Coordinates given (13,1) and (1,16)

m = (y2-y1)/(x2-x1) = (16-1)/(1-13) = 15/-12  simplify this and it becomes -5/4

5.  (-8,-14) and (-10,-17)

m =  (y2-y1)/(x2-x1) = (-17-(-14))/(-10-(-8)) = -3/-2 = 3/2

FOR THE NEXT PART I'LL DO 7,8 AND 10 FOR YOU, TRY DOING 9 ON YOUR OWN FOR PRACTICE.

I WILL ALSO ATTACH FILES FOR THE NEXT PARTS IN ORDER OF QUESTIONS SO SEE THEM.

7. y = x + 3 this means y = 1x +3 which means:

1 is the gradient

3 is the y-intercept

so 1 as a fraction is 1/1 which means rise is one upwards and run is 1 to the right.

Now go to the graph on the y-axis and plot the point 3, (0,3) is your y-intercept. From their rise by one and run by one this will lead u to point (1,4)

Mark both these points and make a line through them.

8. x = -5

now look at this equation in the form of y = mx + c

0 = 1x + 5 the means y is 0 and it is already told in the question that x = -5

if u rearrange 0 = 1x + 5 it will give you x = -5

now when y is  0 x = -5 put a point on the coordinate (-5,0) and draw a vertical straight line.

10. y = (1/4)x - 1

slope is 1/4 which means rise is 1 and run is 4

y-intercept is -1

now go to y=-1 which is the coordinate (0,-1) and rise by one and run by 4, this will take u to the coordinate (4,0) now put a dot on both coordinates, connect them and put a line through them.

Answer:

41.61

Step-by-step explanation:

Just divide.

[tex]\begin{matrix}4\overline{|\smallspace166.44}\:\:\:\:\:\:\:\end{matrix}[/tex]

Answer: We have the equation:

166.44 ÷ 4 = 41.610

Calculated to 3 decimal places.

 0 4 1. 6 1 0

4 1 6 6. 4 4 0

− 0          

 1 6        

− 1 6        

   0 6      

 −   4      

     2 4    

   − 2 4    

       0 4  

     −   4  

         0 0

       −   0

           0

Step-by-step explanation: hope this helps

The measure of the corresponding central angle for XY in radians is; 229.1°

We know that an arc is a part of the entire perimeter of a circle.

Radian is defined as a unit of plane angular measurement that is equal to the angle subtended by the circle at the center by an arc that is of the length equal to the radius.

We also know that the circle as a whole contains 2π radians. Now, at first we are required to find the perimeter of the circle.

Perimeter of the circle is given by the formula 2πr.

Thus, perimeter of the circle = 2πr = 2π * 10 =20π = 62.851cm

Hence value of arc in radians = 40/62.851 * 2π = 0.636 x 2 π = 1.272π

Radian can be converted to degree by multiplying the radian measure by 180/π

Therefore, angle subtended by arc in degrees =1.272 π * 180 /π =229.1 °

Hence the angle subtended by arc is 229.1°

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Answer:

An angle measures 26° more than the measure of its complementary angle.

Step-by-step explanation:

The amount of Lemon's commission is $4.7

According to the question we have been given that

     Commission earned by Lemon = 3.2%

     Selling price of drone which is sold by Lemon  = $146.97

We need to find the amount of commission she earned by selling the drone.

The formula to be used to find the amount of commission is

                =  percentage of commission * selling price

putting the required value we get

               = 3.2% of $146.97

here 'of' is denoted as multiplication

thus,        =0.032 * 146.97

               = $4.7

Hence the amount of Lemon's commission is $4.7

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Answer:

square of the following

2×2=4

3×3=9

4×4=16

2×2×2=8

now

square root

√4

√2×2

=2 answer likewise other

again

cube root

√8

=√2×2×2

=2 through that you can find these

at first you should know square and cube of different numbers from 1 to 20 is the required you should know then you can easily find out answer

The answer will be  : x = -- 3y -- 9

⇒ -2 (x + 3y) = 18

⇒ -(2x + 2 * 3y) = 18

⇒ -(2x + 6y) = 18

⇒ (-2x -6y) + 6y = 18 + 6y

⇒ -2x -6y + 6y = 6y + 18

⇒ -2x = 6y + 18

⇒ [tex]\frac{2x}{2} = \frac{-6y + 18}{2}[/tex]

⇒ [tex]x = \frac{-(2*3)y + (2*3)^{2} }{2}[/tex]

⇒ [tex]\frac{-2*3\frac{2*3y}{2*3} + \frac{(2*3)^{2} }{2*3} }{2}[/tex]

⇒ [tex]x = \frac {2*3(y + (3)^{2 - 1}) }{2}[/tex]

⇒ [tex]x = \frac{-2*3(y + 3)}{2}[/tex]

⇒ x = -[3(y + 3)]

⇒ x = (3y + 3*3)

⇒ x = -(3y + 9)

⇒ x = - 3y - 9

WORKING NOTES :

-2 (x + 3y) = 18

[We must multiply a term and an expression in order to enlarge this word.

We'll utilize the following product distributive property:

A(B + C) = AB + AC

⇒ -(2x + 2 * 3y) = 18

The final expression, in this case, will have two terms:

The first term is a product of '2' and 'x'

the second term is a product of '2' and '3y'.]

In this term, numerical components have been multiplied.

⇒ -(2x + 6y) = 18

We must group all the variable terms on one side of the equation and all the constant terms on the other in order to solve this linear equation.

⇒ (-2x -6y) + 6y = 18 + 6y

Here, the '-' (minus)  term, -6y will be moved to the right side.

When a term "moves" from one side of the equation to the other, you'll notice that its sign changes.

Parentheses around expressions must be eliminated.

Each term in the expression changes sign if a negative sign is placed in front of it. Otherwise, the expression stays the same.

There is no negative sign in the situation.

⇒ -2x -6y + 6y = 6y + 18

In order to join like terms in this expression, we must first sum all of the numerical coefficients and, if necessary, replicate the literal section.

Nothing in a number suggests a value of 1.

There is just one set of related terms: -6y, 6y.

⇒ -2x = 6y + 18

We must eliminate the coefficient that multiplies the variable in this linear equation in order to isolate it.

If both sides are divided, then the coefficient must be removed (-2)

⇒ [tex]\frac{2x}{2} = \frac{-6y + 18}{2}[/tex]

We must simplify this fraction to its simplest form.

To do this, divide the variables that occur in both the numerator and the denominator.

The common factor, in this case, is 2.

⇒ [tex]x = \frac{-(2*3)y + (2*3)^{2} }{2}[/tex]

We must consider the GCF (Greatest Common Factor).

The GCF and the original expression, split by the GCF, provide the final term.

⇒ [tex]\frac{-2*3\frac{2*3y}{2*3} + \frac{(2*3)^{2} }{2*3} }{2}[/tex]

GCF in this case is 2*3.

The fraction [tex]\frac{2*3y}{2*3}[/tex] must be lowered to its simplest form. To do this, divide the variables that occur in both the numerator and the denominator.

Here, the common factor is 2*3.

⇒ [tex]x = \frac {2*3(y + (3)^{2 - 1}) }{2}[/tex]

The expression must be lowered to its simplest form.

Driving out the components that exist in both the numerator and the denominator will accomplish this.

2*3 is a common factor.

⇒ [tex]x = \frac{-2*3(y + 3)}{2}[/tex]

Numerical terms in the factor {y + (3²⁻¹)} is added which makes it (y + 3)

The fraction will then be broken down into its smallest terms next.

To do this, divide the variables that occur in both the numerator and the denominator.

2 is the common factor.

⇒ x = -[3(y + 3)]

⇒ x = -(3y + 3*3)

We must multiply a term and an expression in order to expand this term.

We'll utilize the following product distributive property:

A=AB+AC = A(B + C)

The final expression, in this case, will have two terms:

"3" and "y" are the product in the first term.

The second term is the result of the numbers 3 and 3.

⇒ x = -(3y + 9)

This term's numerical terms have been multiplied by three (3*3 = 9).

⇒ x = - 3y - 9

The parenthesis around expressions must be eliminated.

Each term in the expression changes sign if a negative sign is placed in front of it.

Otherwise, the expression stays the same.

The signs of the following two terms will now change. -(3y + 9) = - 3y - 9

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Answer:

I think it's C.

Step-by-step explanation:

hope you get it right

Answer:

3t (t²-7t-4t)

Step-by-step explanation:

The highest common factor was 3t

The buffer will probably be destroyed by the addition of HCN.

A weak acid and the conjugate base of the weak acid, or a weak base and the conjugate acid of the weak base, are combined to form the buffer solution, a water-based solvent solution. They withstand being diluted or having modest amounts of acid or alkali added to them without changing their pH.

Given that a 1.0 l buffer solution is 0.15 m in HCN and 0.10 m in NaCN.

We need to find a action which one destroy the buffer solution.

A buffer is a substance made of salt and a weak acid that is beneficial. From the aforementioned chemicals, HCN is a potent acid and NaCN is a salt between HF and NaCN. Therefore, the buffer will probably be destroyed by the addition of HCN.

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Answer:

37/30

Step-by-step explanation:

Answer:

Dot plots are hard to construct when dealing with larger, more precise data sets. This makes it difficult to read multiple data points, and it gets very confusing after a while. Therefore, it would not be a good choice for graphing due to its inaccuracy.

Answer:

Dot plot aren't too good for large sets of datas. If you also got many data that are close together, the more you got the harder it will be might to read the data that your doing

answer is -1 < x < 5

-|x - 2|+ 9 > 6

Rearrange the terms

-|x - 2| > 6 - 9

-|x - 2| > - 3

then divide both sides of the inequality by the co- efficient of variable

|x - 2| < 3

convert the absolute inequality to standard inequality

-3 <x - 2 < 3

separate compound inequalities into system of inequality

{x - 2}> -3

{x - 2 < 3}

Rearrange variable to the left side of the equation

x > -3 + 2                    

calculate the sum or difference

x > -1

x -2 < 3

Rearrange variable to the left side of the equation

x < 3 + 2

calculate the sum or difference

x < 5

x > -1 and x < 5

Find intersection

-1 < x < 5

Equations and inequalities are both mathematical sentences formed by relating two expressions to each other. In an equation, the two expressions are deemed equal which is shown by the symbol =. Where as in an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥.

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Answer:

0 + 47 = 47

Step-by-step explanation:

➟ 0 + __ = 47

Let's Change __ to x

➟ 0 + x = 47

Calculate 0 + x = x

➟ x = 47

∴ 0 + 47 = 47

Property used is Identity property of addition

The domain of the function is -∝ < x < ∝, the range of the function is -∝ < y < ∝, and the x-intercept of the function is (-1, 0)

The equation of the function is given as

g(x) = 4x + 4

The function g(x) is a linear function.

There is no restriction on the input values and output values of a linear function

This means that the domain and the range of a linear function are the set of all real numbers

Set g(x) to 0, to determine the x-intercept

So, we have

4x + 4 = 0

Divide through by 1

So, we have

x + 1 = 0

Evaluate the like terms

x = -1

Hence, the domain of the function is -∝ < x < ∝, the range of the function is -∝ < y < ∝, and the x-intercept of the function is (-1, 0)

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Answer: Your answer is B darling.

Step-by-step explanation:

The branch of statistics that uses sample statistics to estimate a population parameter or test a hypothesis about such a parameter is best referred to as inferential statistics.

Therefore, the branch of statistics that uses sample statistics to estimate a population parameter or test a hypothesis about such a parameter is best referred to as inferential statistics.

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The value of x is 4 and the value of ∠ABC is 68°.

To solve this problem we first have to understand the concept of an angle bisector. Angle bisector is a straight line passes through the vertex of an angle dividing the angle in two equal angles.

According to the condition BD bisects ∠ABC

Therefore the two angles formed by the angle bisector are ∠ABD and ∠CBD.

The angle value of these two angles are equal.

Given:

m∠ABD=11x-10

m∠CBD=8x+2

Therefore from the above condition:

m∠ABD=m∠CBD

Substituting the values we get:

11x-10=8x+2

Solving the linear equation to find the value of x.

[tex]or,11x-10=8x+2\\or,11x-8x=2+10\\or,3x=12\\or,x=4[/tex]

Now let us find the value of ∠ABC

m∠ABC=m∠ABD+m∠CBD

or,∠ABC=11x-10+8x+2

or,∠ABC=19x-8

Substituting the value x=4 in the equation we get:

m∠ABC=19×4-8

or,m∠ABC=68°

Therefore we can conclude that the value of xis 4 and the value of ∠ABC is 68°.

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Answer:

C. integers

Step-by-step explanation:

integers are similar to whole numbers : all numbers without any fractional part, but including negative numbers.

whole numbers only include positive numbers (incl. 0) without any fractional part.

natural numbers (I guess, that is the meaning of "counting numbers") are all positive numbers (but without 0) without any fractional part.

so, C is correct, because A contains also -1.

Answer:

B

Step-by-step explanation:

it cat be a whole number because whole number are set of positive number from 0 and above excluding fraction , negative integer or decimal.

integers include both positive and negative numbers excluding fraction and decimal

The graph of the given piecewise function is plotted at the end of the answer.

A piecewise function is a function that has different definitions, depending on the input.

From the definition in the problem, we have that:

Considering these three definitions, the graph is given at the end of the answer, with the legend of the closed interval given in the text.

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Answer: it is .

Step-by-step explanation:

Rita and Tina each make $11 an hour -> 11r for Rita and 11t for Tina in the week

Rita also worked overtime hours and got paid an extra $32 -> Rita and Tina's total weekly wages can be represented as 11r + 11t + $32 (or 11(r+t) + 32)

Answer: See explanation

Step-by-step explanation:

f=First car seat. s=Second car seat. t=Third car seat

f<=28

15<s<45     ==> Second car seat can hold between 15 and 45 pounds noninclusive.

28<=t<=90   ==> Third car seat can hold between 28 and 90 pounds inclusive.

Answer:

<

Step-by-step explanation:

Negative numbers are always smaller than positive numbers, and "<" is the smaller than symbol, so < is the correct choice. We can eliminate = immediately because a negative number can't equal a positive number (excluding the weird number 0)

Answer: x[tex]\geq[/tex]9

Step-by-step explanation:

5x+3 [tex]\geq[/tex] 48

5x[tex]\geq[/tex]45

x[tex]\geq[/tex]9

Treat inequalities like normal equations. Only when the right side of the equation is introduced to a negative sign via multiplication or division should you flip the inequality sign

Hope this helps!

The distance between the center of the circle to any point in the circle is called the radius of the circle. The student staying in the lounge connected to the said wifi will be in the range of the wifi.

A circle is a curve sketched out by a point moving in a plane so that its distance from a given point is constant; alternatively, it is the shape formed by all points in a plane that are at a set distance from a given point, the center.

The distance between the center of the circle to any point in the circle is called the radius of the circle, while the diameter is twice this distance.

Given that the range of the router, which services the wifi connection of the school has a diameter of 3.5 meters. Therefore, the radius of the wifi will be,

Radius = Diameter/2 = 3.5 meters / 2 = 1.75 meters

Now, it is also given that a router is located in the school library which is 1.5 meters away from the student lounge. Therefore, the distance between the school library and the lounge is less than the radius of the range of the wifi.

Thus, the student staying in the lounge connected to the said wifi will be in the range of the wifi.

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Answer:

63 crayons are broken

Step-by-step explanation:

84 ÷ 4 = 21

21 x 3 = 63

can be checked by 84 - 63 = 21

The results of the equations are listed below:

In this problem we must make use of given formulas and substitute all known variables to determine all the required information:

Case 1

The temperature in Celsius scale in terms of the temperature in Fahrenheit scale is defined by the following formula:

T' = (5 / 9) · (T - 32)

T' = (5 / 9) · (68 - 32)

T' = 20 °C

Case 2

The area of the circle in terms of its radius is presented below:

A = π · r²

A = π · (6 m)²

A ≈ 113.097 m²

Case 3

The area of the triangle as a function of its base and its height is shown in the following formula:

A = 0.5 · b · h

A = 0.5 · (8 ft) · (25 ft)

A = 100 ft²

Case 4

The traveled distance is the product of the velocity and time:

s = v · t

s = (62.5 mi / h) · (5 h)

s = 312.5 mi

Case 5

The simple interest formula is equal to the product of the invested amount, interest rate and time divided by 100:

C' = (C · r · t) / 100

C' = [(300) · (5) · (8)] / 100

C' = $ 120

Case 6

C' = (C · r · t) / 100

C' = [(200) · (2) · (10)] / 100

C' = $ 40

Case 7

s = v · t

s = (45 mi / h) · (0.5 h)

s = 27.5 mi

Case 8

T' = (5 / 9) · (T - 32)

T' = (5 / 9) · (212 - 32)

T' = 100 °C

Case 9

C' = (C · r · t) / 100

C' = [(1200) · (2.5) · (2)] / 100

C' = $ 60

Case 10

The area of the rectangle is equal to the product of its base and its height:

A = b · h

A = (14 ft) · (8 ft)

A = 112 ft²

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