order from least to greatest:

210%, 2.2 2.2(repeating), 43/20

Answer:

Retailer

Step-by-step explanation:

A retailer buys goods from the manufactures and wholesalers and then sell these products directly to the consumers or users.In the supply chain retailers are the ones who connect with the customers to obtain information on goods and servicers delivered.

To simplify the expression −4(−11+4n)−3(−2n+9), you distribute the multiplication and then combine like terms to get the equivalent expression +17−10n.

The student has asked to simplify the expression −4(−11+4n)−3(−2n+9). To simplify this expression, we need to distribute the numbers outside the parentheses across the terms inside the parentheses. We'll do this step by step.

Now combine like terms:

So, the simplified equivalent expression is +17−10n.

the simplified and equivalent expression is 17 - 10n.

We need to simplify the expression:

[tex]-4(-11+4n)-3(-2n+9)[/tex]

To do this we need to open the brackets which gives us:

[tex]-4(-11+4n)-3(-2n+9) = 44 -16n + 6n -27[/tex]

Now we can solve the expression as follows:

[tex]-4(-11+4n)-3(-2n+9) = (44 - 27) + (-16n + 6n)\\\\ -4(-11+4n)-3(-2n+9) =17 - 10n[/tex]

So, the simplified and equivalent expression is 17 - 10n.

Answer:

Part 1) The system of equations that represent this situation is

[tex]12x+6y=180[/tex] and [tex]x=2y[/tex]

Part 2) The number of hardcover books sold was [tex]12[/tex] and the number of paperback books sold was [tex]6[/tex]

Step-by-step explanation:

Part 1) What is the system of equations that represents this situation?

Let

x---->  number of hardcover books sold

y----> number of paperback books sold

we know that

The system of equations that represent this situation is equal to

[tex]12x+6y=180[/tex] -----> equation A

[tex]x=2y[/tex] -----> equation B

Part 2) What is the solution to the system and what does it represent in the context of this situation?

Substitute equation B in equation A and solve for y

[tex]12(2y)+6y=180[/tex]

[tex]24y+6y=180[/tex]

[tex]30y=180[/tex]

[tex]y=6[/tex]

Find the value of x

[tex]x=2y[/tex]

[tex]x=2(6)=12[/tex]

The solution of the system of equations is the point (12,6)

That means

The number of hardcover books sold was [tex]12[/tex]

The number of paperback books sold was [tex]6[/tex]

Answer:

B

Step-by-step explanation:

Answer:

The correct option is A.

Step-by-step explanation:

The area of a triangle is

[tex]A=\frac{1}{2}\times base\times height[/tex]

From the given figure it is clear that the base of the triangle STR is 6 ft and the height of the triangle 10 ft. So, the area of triangle STR is

[tex]A=\frac{1}{2}\times 6\times 10[/tex]

[tex]A=3\times 10[/tex]

[tex]A=30[/tex]

The area of triangle STR is 30 square ft. Therefore the correct option is A.

Answer:

The Numerator is 6x + 4y - 3z

Step-by-step explanation:

Step  1  :

           z

Simplify   —

           4

Equation at the end of step  1  :

  x    y     z

 (— +  —) -  —

  2    3     4

Step  2  :

           y

Simplify   —

           3

Equation at the end of step  2  :

  x    y     z

 (— +  —) -  —

  2    3     4

Step  3  :

           x

Simplify   —

           2

Equation at the end of step  3  :

  x    y     z

 (— +  —) -  —

  2    3     4

Step  4  :

Calculating the Least Common Multiple :

4.1    Find the Least Common Multiple  

     The left denominator is :       2  

     The right denominator is :       3  

       Number of times each prime factor

       appears in the factorization of:

Prime  

Factor   Left  

Denominator   Right  

Denominator   L.C.M = Max  

{Left,Right}  

2 1 0 1

3 0 1 1

Product of all  

Prime Factors  2 3 6

     Least Common Multiple:  

     6  

Calculating Multipliers :

4.2    Calculate multipliers for the two fractions  

   Denote the Least Common Multiple by  L.C.M  

   Denote the Left Multiplier by  Left_M  

   Denote the Right Multiplier by  Right_M  

   Denote the Left Deniminator by  L_Deno  

   Denote the Right Multiplier by  R_Deno  

  Left_M = L.C.M / L_Deno = 3

  Right_M = L.C.M / R_Deno = 2

Making Equivalent Fractions :

4.3      Rewrite the two fractions into equivalent fractions

Two fractions are called equivalent if they have the same numeric value.

For example :  1/2   and  2/4  are equivalent,  y/(y+1)2   and  (y2+y)/(y+1)3  are equivalent as well.  

To calculate equivalent fraction , multiply the Numerator of each fraction, by its respective Multiplier.

  L. Mult. • L. Num.      x • 3

  ——————————————————  =   —————

        L.C.M               6  

  R. Mult. • R. Num.      y • 2

  ——————————————————  =   —————

        L.C.M               6  

Adding fractions that have a common denominator :

4.4       Adding up the two equivalent fractions  

Add the two equivalent fractions which now have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

x • 3 + y • 2     3x + 2y

—————————————  =  ———————

      6              6    

Equation at the end of step  4  :

 (3x + 2y)    z

 ————————— -  —

     6        4

Step  5  :

Calculating the Least Common Multiple :

5.1    Find the Least Common Multiple  

     The left denominator is :       6  

     The right denominator is :       4  

       Number of times each prime factor

       appears in the factorization of:

Prime  

Factor   Left  

Denominator   Right  

Denominator   L.C.M = Max  

{Left,Right}  

2 1 2 2

3 1 0 1

Product of all  

Prime Factors  6 4 12

     Least Common Multiple:  

     12  

Calculating Multipliers :

5.2    Calculate multipliers for the two fractions  

   Denote the Least Common Multiple by  L.C.M  

   Denote the Left Multiplier by  Left_M  

   Denote the Right Multiplier by  Right_M  

   Denote the Left Deniminator by  L_Deno  

   Denote the Right Multiplier by  R_Deno  

  Left_M = L.C.M / L_Deno = 2

  Right_M = L.C.M / R_Deno = 3

Making Equivalent Fractions :

5.3      Rewrite the two fractions into equivalent fractions

  L. Mult. • L. Num.      (3x+2y) • 2

  ——————————————————  =   ———————————

        L.C.M                 12      

  R. Mult. • R. Num.      z • 3

  ——————————————————  =   —————

        L.C.M              12  

Adding fractions that have a common denominator :

5.4       Adding up the two equivalent fractions  

(3x+2y) • 2 - (z • 3)     6x + 4y - 3z

—————————————————————  =  ————————————

         12                    12      

Final result :

 6x + 4y - 3z

 ————————————

      12    

Answer:

x=2i/3

All you have to do is just to find the square root.

Answer:

x = ±(2/3)i

Step-by-step explanation:

Subtract 4, divide by 9, and take the square root.

9x^2 = -4

x^2 = -4/9

x = ±√(-4/9) = ±(2/3)i . . . . . . the solutions are imaginary numbers

Answer:

The volume of the cylinder is 63π or 197.9 units³

Step-by-step explanation:

* Lets revise how to find the volume of any cylinder

- The volume of the regular solid = area of the base × its height

- The cylinder has two circular bases

- The area of the circle = πr²

∴ The volume of the cylinder = πr² × its height

* Now lets take the dimensions of the cylinder from the problem

- The height of the cylinder is 7 units

- The radius of the cylinder is 3 units

∵ The volume of the cylinder = πr² × its height

∴ The volume = π × 3² × 7 = 63π = 197.9 units³

* The volume of the cylinder is 63π or 197.9 units³

Answer:

The volume of cylinder =197.82 units²

Step-by-step explanation:

Formula:-

Volume of cylinder =  πr²h

Where r - Radius of cylinder and

h - Height of cylinder

To find the volume of cylinder

Here r = 3 units and h = 7 units

Volume = πr²h

 = 3.14  * 3² * 7

 = 3.14 * 9 * 7

 = 197.82 units²

Therefore the volume of cylinder =197.82 units²

Answer:

[tex]Y=(X-7)/2[/tex]

Step-by-step explanation:

we have

[tex]X=2t+3[/tex] -----> equation A

[tex]Y=t-2[/tex] -----> [tex]t=Y+2[/tex] -----> equation B

Substitute equation B in equation A

[tex]X=2(Y+2)+3[/tex]

[tex]X=2Y+4+3[/tex]

[tex]X=2Y+7[/tex]

solve for Y

[tex]2Y=X-7[/tex]

[tex]Y=(X-7)/2[/tex]

Answer:

x=1/2, x=-3

Step-by-step explanation:

2x^2+5x-3 = 0

(2x^2+6x)+(-x-3) = 0

2x(x+3)+-1(x+3) = 0

(2x-1)(x+3)=0

2x-1=0, x+3=0

x=1/2, x=-3

Answer:

The answer is A. F(x)=(X+3)^4

Step-by-step explanation:

1. Whenever the function is in parenthesis, the symbol does the opposite then it usually does. So for (X+3)^4, the + in the parenthesis shifts the graph to the left instead of right.

2. Also, when in parenthesis, function shifts horizontally, not vertically. So answers B and C would shift the graph up and down, instead of left or right.

Please feel free to ask me if you have more questions or concerns with this problem!

Answer:

Step-by-step explanation:

f(x) + n - shift the graph n unit up

f(x) - n - shift the graph n unit down

f(x + n) - shift the graph n unit to the left

f(x - n) - shift the graph n unit to the right

=======================================================

F(x) ← G(x) shifted 3 units to the left

F(x) = G(x + 3) → F(x) = (x+3)⁴

The Value of Pi is actually an infinite number and cannot be calculated. It is not a real number. Usually many just shorten Pi to the decimal 3.14, which it is most commonly used as since there is no exact decimal of Pi.

3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679821480865132823066470938446095505822317253594081284811174502841027019385211055596446229489549303819644288109756659334461284756482337867831652712019091456485669234603486104543266482133936072602491412737245870066063155881748815209209628292540917153643678925903600113305305488204665213841469519415116094330572703657595919530921861173819326117931051185480744623799627495673518857527248912279381830119491298336733624406566430860213949463952247371907021798609437027705392171762931767523846748184676694051320005681271452635608277857713427577896091736371787214684409012249534301465495853710507922796892589235420199561121290219608640344181598136297747713099605187072113499999983729780499510597317328160963185950244594553469083026425223082533446850352619311881710100031378387528865875332083814206171776691473035982534904287554687311595628638823537875937519577818577805321712268066130019278766111959092164201989380952572010654858632788659361533818279682303019520353018529689957736225994138912497217752834791315155748572424541506959508295331168617278558890750983817546374649393192550604009277016711390098488240128583616035637076601047101819429555961989467678374494482553797747268471040475346462080466842590694912933136770289891521047521620569660240580381501935112533824300355876402474964732639141992726042699227967823547816360093417216412199245863150302861829745557067498385054945885869269956909272107975093029553211653449872027559602364806654991198818347977535663698074265425278625518184175746728909777727938000816470600161452491921732172147723501414419735685481613611573525521334757418494684385233239073941433345477624168625189835694855620992192221842725502542568876717904946016534668049886272327917860857843838279679766814541009538837863609506800642251252051173929848960841284886269456042419652850222106611863067442786220391949450471237137869609563643719172874677646575739624138908658326459958133904780275900994657640789512694683983525957098258226205224894077267194782684826014769909026401363944374553050682034962524517493996514314298091906592509372216964615157098583874105978859597729754989301617539284681382686838689427741559918559252459539594310499725246808459872736446958486538367362226260991246080512438843904512441365497627807977156914359977001296160894416948685558484063534220722258284886481584560285060168427394522674676788952521385225499546667278239864565961163548862305774564980355936345681743241125150760694794510965960940252288797108931456691368672287489405601015033086179286809208747609178249385890097149096759852613655497818931297848216829989487226588048575640142704775551323796414515237462343645428584447952658678210511413547357395231134271661021359695362314429524849371871101457654035902799344037420073105785390621983874478084784896833214457138687519435064302184531910484810053706146806749192781911979399520614196634287544406437451237181921799983910159195618146751426912397489409071864942319615679452080951465502252316038819301420937621378559566389377870830390697920773467221825625996615014215030680384477345492026054146659252014974428507325186660021324340881907104863317346496514539057962685610055081066587969981635747363840525714591028970641401109712062804390397595156771577004203378699360072305587631763594218731251471205329281918261861258673215791984148488291644706095752706957220917567116722910981690915280173506712748583222871835209353965725121083579151369882091444210067510334671103141267111369908658516398315019701651511685171437657618351556508849099898599823873455283316355076479185358932261854896321329330898570642046752590709154814165498594616371802709819943099244889575712828905923233260972997120844335732654893823911932597463667305836041428138830320382490375898524374417029132765618093773444030707469211201913020330380197621101100449293215160842444859637669838952286847831235526582131449576857262433441893039686426243410773226978028073189154411010446823252716201052652272111660396

Pi is 3.14, and is an irrational number, meaning that it does not end and has no repetition of numbers in a row.

The area of the circle is calculated by multiplying pi by the radius.

3.14 * 10 = 314.16.

To round it to the nearest tenth, you must know whether the second decimal number is greater or less than 5. If it is 5 or greater, you round the first decimal up 1. If it is 4 or less, then you just remove the second decimal and keep the first one.

In this case, the answer would be approximately 314.2 because 6 is greater than 5, so you round up the 1 to a 2.

Answer:

Domain: [tex]n\ge1[/tex]

Step-by-step explanation:

For a geometric sequence, the n-th term is given by:

[tex]a_n=a_1r^{n-1}[/tex]

From the question, [tex]a_1=1[/tex] and [tex]r=6[/tex].

Hence the explicit formula for the sequence is:

[tex]a_n=6^{n-1}[/tex], where [tex]n\ge1[/tex]

Therefore the domain is natural numbers or positive integers.

Answer:

(4, -3)

Step-by-step explanation:

When you reflect a point across the x-axis, the x-coordinate remains the same, but the y-coordinate is changed to the opposite sign.

The reflection of the point (x, y) across the x-axis is the point (x, -y).

The reflected point across the x-axis of the original point (4,3) would have the coordinates (4, -3), where the x-coordinate remains the same and the y-coordinate changes sign. Hence correct option b.

When a point is reflected across the x-axis, the y-coordinate changes sign, but the x-coordinate remains the same. The reflection of the point across the x-axis means that the x-coordinate (4) does not change, but the y-coordinate (3) becomes its opposite (-3). Thus, the new coordinates of the reflected point are (4, -3).

I think it's B

[tex] - 11 \geqslant n + 0 \\ 1. \: - 11 \geqslant n \\ 2. \: n \leqslant - 11 \\ \\ - 11 \geqslant n \\ 1. \: n \leqslant - 11[/tex]

Answer:

The answer is B. Identity property of Addition

Step-by-step explanation:

Answer:

It extends the time of the collision

Step-by-step explanation:

The correct option is : It extends the time of the collision.

The padding helmets have cushions inside it that moves inwards when a ball hits the helmets.

When the collision occurs, the time will increase and less force will be exerted on helmet that is why the impact of the collision will be less.

Answer:

A. It extends the time of the collision.

Step-by-step explanation:

the picture

Answer:

3,500

Step-by-step explanation:

70% is equal to 0.70.

When you need to find a percent of a population, you multiply the decimal form to the population.

Therefore, with 70% of 5000, you multuiply 5000 by 0.70 which will give you 3500.

3,500 students would select roller coasters as their favorite ride.

The answer to this question would be 3,500 students.

The hypotenuse of the triangle would be the diameter of the semi circle.

Using the Pythagorean theorem you can find that.

8^2 + 6^2 = x^2

64 +36 = x^2

100 = x^2

x = √100

x = 10

The diameter is 10, now find the circumference.

Circumference = diameter x PI = 10 x 3.14 = 31.4

Since it is a semi circle, the circumference would be 1/2 of that.

31.4 / 2 = 15.7

The perimeter would be 8 + 6 + 15.7 = 29.7

ANSWER

See explanation

EXPLANATION

The point (3,-6) is the fourth quadrant.

In this quadrant only the cosine ratio and the secant ratio are positive.

The remaining four trigonometric ratios are negative.

The diagram is shown in the attachment.

We use the Pythagoras Theorem to find the hypotenuse, h.

[tex] {h}^{2} = {6}^{2} + {3}^{2} [/tex]

[tex] {h}^{2} = 36 + 9[/tex]

[tex] {h}^{2} = 45[/tex]

[tex]h = \sqrt{45} [/tex]

[tex]h = 3 \sqrt{5} [/tex]

[tex] \sin( \theta) = - \frac{opp}{hyp} [/tex]

[tex]\sin( \theta) = - \frac{6}{3 \sqrt{5} } [/tex]

[tex]\sin( \theta) = - \frac{2 \sqrt{5} }{ 5 } [/tex]

[tex]\sin( \theta) = - \frac{2}{ \sqrt{5} } [/tex]

[tex]\ cos(\theta) = \frac{adj}{hyp} [/tex]

[tex]\ cos(\theta) = \frac{3}{3 \sqrt{5} } [/tex]

[tex]\ cos(\theta) = \frac{1}{ \sqrt{5} } [/tex]

[tex]\ cos(\theta) = \frac{ \sqrt{5} }{5} [/tex]

[tex]\tan(\theta)= - \frac{opp}{hyp} [/tex]

[tex]\tan(\theta)= - \frac{6}{3} = - 2[/tex]

[tex]\csc(\theta)= - \frac{hyp}{opp} [/tex]

[tex]\csc(\theta)= - \frac{3 \sqrt{5} }{6} = - \frac{\sqrt{5} }{2} [/tex]

[tex] \sec( \theta) = \frac{hyp}{adj} [/tex]

[tex]\sec( \theta) = \frac{3 \sqrt{5} }{3} = \sqrt{5} [/tex]

[tex]\cot( \theta) = - \frac{adj}{opp} [/tex]

[tex]\cot( \theta) = - \frac{3}{6} = - \frac{1}{2}[/tex]

Step-by-step explanation:

[tex]\text{If}\ 10+\dfrac{6}{2}+3=10+3+3=16\\\\\text{If}\ \dfrac{10+6}{2+3}=\dfrac{16}{5}[/tex]

To simplify 10+6/2+3, we first perform the division operation (6 ÷ 2 = 3), and then carry out the addition operations in order (10 + 3 + 3), giving us a final result of 16.

To simplify 10+6/2+3, we have to follow the order of operations as guided by the mnemonic PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction). In the given expression, there are no parenthesis, exponents, so we proceed by carrying out division and then addition.

Step 1: Perform the division operation 6 ÷ 2 = 3.

Step 2: Simplify the expression by performing the addition operations in the order from left to right. So, 10 + 3 (from division) + 3= 16.

Therefore, the simplified form of the original expression is 16.

https://brainly.com/question/15840745

#SPJ3

Answer:

4 inches.

Step-by-step explanation:

Convert 10ft in to inches

10 ft = 120 inches

So, 10ft/30inches =120inches/30 inches

120÷30=4

The requried, 10 ft / 30 inches simplified is 4

To simplify the expression 10 ft / 30 inches, we need to convert the units to a common format. We can convert both feet and inches to inches to make the division easier.

1 foot is equal to 12 inches. So, 10 feet can be written as 10 * 12 = 120 inches.

Now we have 120 inches / 30 inches, which simplifies to:

120 inches / 30 inches = 4.

Therefore, 10 ft / 30 inches simplified is 4.

Learn more about simplification here:

https://brainly.com/question/15242961

#SPJ6

ANSWER

[tex]3{a}^{4 } [/tex]

EXPLANATION

The cube root of

[tex]27 {a}^{12} [/tex]

is

[tex] \sqrt[3]{27 {a}^{12} } [/tex]

This is the same as:

[tex](27 {a}^{12} )^{ \frac{1}{3} } [/tex]

[tex]( {3}^{3} ({a}^{4})^{3} )^{ \frac{1}{3} } [/tex]

[tex] = (3{a}^{4} )^{3 \times \frac{1}{3} } [/tex]

[tex] = 3{a}^{4 } [/tex]

Answer:

20 Meters

Step-by-step explanation:

5 Sides a Pentagon has - with a length at 4 meters per side you have a perimeter of 20 meters.

the answer is 2yx^3/(2y^2)^3

Answer:

x = 8.5

L = 17

W = 6.5

Step-by-step explanation:

P = 2*(L + W)

W = x - 2

L = 2x

P = 47

47 = 2 * (2x + x - 2)

47 = 2 * (3x - 2)          Remove the brackets.

47 = 6x - 4                 Add 4 to both sides.

47 + 4 = 6x - 4+4       Combine

51 = 6x                       Divide by 6

6x/6=51/6                  Combine

x = 8 3/6 or 8.5

x = 8.5

========

L = 2*x

L = 2*8.5

L = 17

=====

W = x - 2

W = 8.5 - 2

W = 6.5

Answer:

x=8.5, length is 17, and width is 6.5

Step-by-step explanation:

To solve for x, you would add the two sides together, getting x-2+2x+3x-2. Now, you would multiply this figure by two, because you only have half of the perimeter as of now. (3x-2)*2+6x-4. Now, because the perimeter is 47, you have this equation

6x-4=47

Add four to both sides

6x=51

Divide by 6

x=51/6=8.5

Now, you would plug this into both of the other sides of the rectangle.

The length, or the longest side, measures 2x

2*8.5=17

The width, or the shorter side, measures x-2

8.5-2=6.5

Hope this helped

Answer:

Interest earned at 3.9 percent rate is $31.2

Interest earned at 2 percent rate is $5.8

Step-by-step explanation:

A = P(1 + rt)

Where 'A' is the amount, 'r' is the rate and 't' is the time in years

When;

P = $1200

r = 3.9%

t = [tex]\frac{8}{12}[/tex] years

Then,

A = $1200(1 + 0.039([tex]\frac{8}{12}[/tex]))

A = $1200 + $31.2 = $1231.2

Interest = Amount - Principal

Interest earned at 3.9 percent rate is $1231.2 - $1200 = $31.2

When;

P = $580

r = 2%

t = [tex]\frac{6}{12}[/tex] years

Then,

A = $580(1 + 0.02([tex]\frac{6}{12}[/tex]))

A = $580 + $5.8 = $585.8

Interest earned = Amount - Principal

Interest earned at 2 percent rate = $585.8 - $580 = $5.8

Thesimple interest, you use the formula I = PRT, with P representing principal, R the annual interest rate in decimal form, and T the time in years. For $1200 at 3.9% over 8 months, the interest is $37.20. For $580 at 2% over 6 months, the interest is $5.80.

The simple interest earned on two separate principals with different interest rates and time periods. To calculate simple interest, we use the formula I = PRT, where I is the interest earned, P is the principal amount, R is the annual interest rate (in decimal form), and T is the time in years. If the time is given in months, we must convert it into years by dividing by 12.

Example 1:
Principal (P) = $1200
Annual Interest Rate (R) = 3.9% = 0.039
Time (T) = 8 months = ({8}{12}) years

Simple Interest (I) = $1200 (times) 0.039 (times) \(frac{8}{12}) = $37.20 to the nearest cent

Example 2:
Principal (P) = $580
Annual Interest Rate (R) = 2% = 0.02
Time (T) = 6 months = ({6}{12}) years

Simple Interest (I) = $580 (times) 0.02 (times) \({6}{12}) = $5.80 to the nearest cent

In conclusion, we have two amounts of simple interest for the different principals, rates, and times provided. To find the total future amount with simple interest, we would add the interest earned to the principal amount.

Answer:

b 93

Step-by-step explanation:

Answer:

Step-by-step explanation:

Alright, lets gets started.

The dimensions of the given triangle is 24 , 52 and 17.

The another triangle is given congruent to this triangle.

It means the dimensions of another triangle will also be 24, 52 and 17.

So the perimeter will be addition of these sides.

Hence the perimeter will be = [tex]24+52+17[/tex]

Hence the perimeter will be = 93 feet   :    Answer

Hope it will help :)

Answer:

Alex walks more miles

Step-by-step explanation:

Answer:

Jenna walks more miles per day

Step-by-step explanation:

i got this answer by doing 12 divided by 5 = 2.4 and 7 divided by 3 = 2.33333333333  and 2.4 is more that 2.33333333333  so Jenna walked futher,

i hope that this answer helped you, pls give me good votes if it did, because im new here and trying to get points.

Answer: $33

Step-by-step explanation: Divide 27/9 which is $3

-so you pay $3 for each pack

-then to find how much you need to pay for 11 packs you just multiply 11*3=33

Answer:

QC=16 this is correct on usa testprep

Step-by-step explanation:

The centroid of a triangle is the point of concurrency of the median lines of

the triangle.

The length of segment [tex]\overline{QC}[/tex] is C) 16

Reasons:

The given parameters are;

Point C = The centroid of ΔPQR

[tex]\overline{CZ}[/tex] = 8

Required:

The length of  segment QC

Solution;

Given that point C is the centroid of the triangle ΔPQR, we have;

[tex]\overline{QC} = \dfrac{2}{3} \times \overline{QZ}[/tex]

[tex]\overline{CZ}= \dfrac{1}{3} \times \overline{QZ}[/tex]

Therefore;

[tex]\overline{CZ}= \dfrac{1}{2} \times \overline{QC}[/tex]

[tex]\overline{QC} = 2 \times \overline{CZ}[/tex]

[tex]\overline{QC} = 2 \times 8 = 16[/tex]

Learn more here:

https://brainly.com/question/1747484

Answer:

[tex]d(P,D)= \sqrt{41}\\d(P,D)=6.40312[/tex]

Step-by-step explanation:

We need to find the distance between the points P=(-2,3) and D(2,-2)

The formula used to find distance between points is:

[tex]d(P,D)= \sqrt{(x2-x1)^2 + (y2-y1)^2)}[/tex]

Here, x2 =2 and x1 = -2,  y2=-2 and y1= 3

Putting values in formula

[tex]d(P,D)= \sqrt{(2-(-2))^2 + (-2-3)^2}\\d(P,D)= \sqrt{(2+2)^2 + (-2-3)^2}\\d(P,D)= \sqrt{(4)^2 + (-5)^2}\\d(P,D)= \sqrt{16 + 25}\\d(P,D)= \sqrt{41}\\d(P,D)=6.40312[/tex]