s. The area of a regular hexagon is 384√3Cm². Find A. the side length of the hexagon B. the radius of the hexagon C. the apothem of the hexagon​

Answers

Answer 1

The apothem of the hexagon is 8√3 cm.

We are given that;

The area of a regular hexagon= 384√3Cm²

Now,

To find the side length, radius, and apothem of a regular hexagon given its area, we can use the following formulas:

Area = (3√3 s^2) / 2 Area = (1/2) a P Area = (3/2) r a

where s is the side length, a is the apothem, P is the perimeter, and r is the radius of the hexagon. We can solve for any of these variables by rearranging the formulas and plugging in the given area.

A. To find the side length, we can use the first formula and solve for s:

s^2 = (2 Area) / (3√3) s = sqrt((2 Area) / (3√3))

Plugging in Area = 384√3, we get:

s = sqrt((2 * 384√3) / (3√3)) s = sqrt(256) s = 16

Therefore, the side length of the hexagon is 16 cm.

B. To find the radius, we can use any of the formulas and solve for r. For example, using the third formula, we get:

r = (2 Area) / (3 a)

To find a, we can use the second formula and solve for a:

a = (2 Area) / P

To find P, we can use the fact that P = 6s and plug in s = 16:

P = 6 * 16 P = 96

Plugging in P and Area into the formula for a, we get:

a = (2 * 384√3) / 96 a = 8√3

Plugging in a and Area into the formula for r, we get:

r = (2 * 384√3) / (3 * 8√3) r = 32

Therefore, the radius of the hexagon is 32 cm.

C. To find the apothem, we can use any of the formulas and solve for a. For example, using the second formula, we get;

a = (2 Area) / P

Plugging in Area = 384√3 and P = 96, we get:

a = (2 * 384√3) / 96 a = 8√3

Therefore, by polygon the answer will be 8√3 cm.

Learn more about regular polygon here:

https://brainly.com/question/14173422

#SPJ1


Related Questions

Subtract (8n-5)-(-2n-3)

Answers

Answer:

Step-by-step explanation:

( 8n - 5 ) - ( -2n - 3 )

( 8n - 5 ) + ( 2n + 3 )

8n - 5 + 2n + 3

10n - 2

Given f(x)=(1/4)^-x, Evaluate f(-2), f(1), and f(2).

Answers

When we evaluate the function f(x)=(1/4)^-x for x = -2, 1, and 2, we find that f(-2) = 1/16, f(1) = 4, and f(2) = 1/16.

To evaluate f(x)=(1/4)^-x for specific values of x, we can substitute the given values into the function expression and simplify the calculations.

Evaluating f(-2):

Substitute x = -2 into the function f(x):

f(-2) = (1/4)^-(-2) = (1/4)^2 = 1/16

Evaluating f(1):

Substitute x = 1 into the function f(x):

f(1) = (1/4)^-1 = 4^1 = 4

Evaluating f(2):

Substitute x = 2 into the function f(x):

f(2) = (1/4)^-2 = (1/4)^2 = 1/16

Therefore, the evaluations of f(-2), f(1), and f(2) are:

f(-2) = 1/16

f(1) = 4

f(2) = 1/16

In conclusion, when we evaluate the function f(x)=(1/4)^-x for x = -2, 1, and 2, we find that f(-2) = 1/16, f(1) = 4, and f(2) = 1/16. These values represent the corresponding outputs of the function for the given inputs.

For more such questions on evaluation, click on:

https://brainly.com/question/4344214

#SPJ8

The time (t) required to do a job varies inversely as the number of people (p) working on the job.

It takes 9 hours for 4 roofers to complete a certain job. How long would it take 6 roofers to complete the same job?
hours

Answers

Answer:

6 hours

Step-by-step explanation:

Varying inversely simply means using the "inverse proportion" method

So therefore,

4 roofers= 1 hour

1 roofer= 9 * 4

= 36 hours

Why? Because the lesser amount of workers you have, the more time will be needed so as to complete the work.

6 roofers= 36/6=6 hours

The more people you have, the lesser amount of time will be spent on completing the work.

Which inequality is graphed below

Answers

Answer:

wheres it at?

Step-by-step explanation:

#Everything4Zalo

The following data are an example of what type of regression?
13.000
12.000
11,000
10,000-
9.000-
8.000-
7,000
6,000
5.000
4,000
3.000
2.000-
1,000
H
3-2-1
1234567
Model
Linear
Quadratic
Exponential
O A. Exponential
OB. Quadratic
O C. Linear

0.808
0.997
0.813
D. None of the above

Answers

The data given is an example of a B. Quadratic regression.

How to determine the data ?

The r-squared ( r ²) value is a statistical measure that represents the proportion of the variance for a dependent variable that's explained by an independent variable or variables in a regression model.

The r² values are highest for the quadratic model (r ² = 0. 997), meaning this model explains the most variance in your data compared to the linear (r² = 0. 808) and exponential models (r ² = 0. 813). Thus, the data are best modeled with a quadratic regression.

Find out more on Quadratic regression at https://brainly.com/question/14816012

#SPJ1

Tara looks up hotel room prices for a holiday.
A hotel has a 25% off sale on its prices.
A VAT charge of 20% must be added on at the end of the transaction after any discount.
If the regular price of a room is £80 per night, how much will Tara pay for 5 nights?

Answers

Answer:

360

Step-by-step explanation:

80*5=400 and .25*400=100 so it costs 300 for five nights without tax, and adding on the tax raises the cost to 60 (300+(.2*300)=360)

Discounted price = 0.75 * £80 = £60

Total cost for 5 nights = 5 nights * £60 per night = £300

VAT charge = 20% * £300 = £60

£300 + £60 = £360

Therefore, Tara will pay £360 for 5 nights at the hotel after the discount and VAT charge.

A baseball player earns $3 million in 2015. During the next 15 years, the earning increase 4% each year.
Write an exponential growth model giving the earning y (in millions of dollars) t years after 2015. Write the base of the model as a decimal

Answers

The exponential growth model for the baseball player's earnings, in millions of dollars, t years after 2015 is[tex]y = 3 \times (1.04)^t,[/tex]  with a base of 1.04.

To model the exponential growth of the baseball player's earnings, we can use the formula:

[tex]y = a \times (1 + r)^t[/tex]

where:

y represents the earning in millions of dollars

a represents the initial earning in millions of dollars (in this case, $3 million)

r represents the growth rate per year (4%, which can be expressed as 0.04)

t represents the number of years after 2015

In this case, we want to find the earning y (in millions of dollars) t years after 2015.

Since the initial earning in 2015 is $3 million, we can substitute a = 3.

Therefore, the exponential growth model for the player's earnings is:

[tex]y = 3 \times (1 + 0.04)^t[/tex]

Simplifying the expression further, we have:

[tex]y = 3 \times 1.04^t[/tex]

The base of the model is 1.04, which is the decimal representation of the growth rate (4%).

Using this model, we can calculate the player's earnings for any year after 2015 by plugging in the value of t.

For example, if we want to find the earnings 5 years after 2015, we substitute t = 5 into the equation:

[tex]y = 3 \times 1.04^5[/tex]

This will give us the projected earnings in millions of dollars for that particular year.

For similar question on exponential growth.

https://brainly.com/question/30620534

#SPJ11

The felt cover on this pool table needs to be replaced. How much material is needed if the pool table is 86” long by 48” wide?

4,128 sq. in.
4,256 sq. in.
3,284 sq. in.
3,298 sq. in.

Answers

The correct answer is 4,128 square inches.

To determine the amount of material needed to replace the felt cover on the pool table, we need to calculate the surface area of the table.

The pool table has dimensions of 86 inches in length and 48 inches in width.  

Surface area is the measure of the total area of the external or exposed surfaces of a three-dimensional object.

It represents the sum of the areas of all the faces or surfaces of an object, including its top, bottom, and sides.

Surface area is typically measured in square units such as square inches, square centimeters, or square meters.

To find the surface area, we multiply these two dimensions together:

Surface area = Length [tex]\times[/tex] Width

Surface area = 86 inches [tex]\times[/tex] 48 inches

Surface area = 4,128 square inches.

Therefore, the correct answer is 4,128 square inches.

For similar question on surface area.

https://brainly.com/question/30337697  

#SPJ8

100 Points! Algebra question. Photo attached. Please show as much work as possible. Thank you!

Answers

The values of the trigonometry functions are sin(θ) = 3/√13, cos(θ) = 2/√13, tan(θ) = 3/2, csc(θ) = √13/3, sec(θ) = √13/2 and cot(θ) = 2/3

Finding the values of the trigonometry functions

from the question, we have the following parameters that can be used in our computation:

The right triangle

The hypotenuse of the right triangle is calculated as

h² = 2² + 3²

When evaluated, we have

h = √13

The values of the trigonometry functions are then evaluated as

sin(θ) = 3/√13

cos(θ) = 2/√13

tan(θ) = 3/2

csc(θ) = √13/3

sec(θ) = √13/2

cot(θ) = 2/3

Read more about trigonometry functions at

https://brainly.com/question/24349828

#SPJ1

Simplify the expression 5x2+6x+4+x2+x
.

Thank You!

Answers

The simplified solution of the expression 5x²+6x+4+x²+x is 6x²+7x+4.

The given expression is 5x²+6x+4+x²+x

Simplifying the given expression

5x²+6x+4+x²+x

Firstly, put the similar terms together

5x²+x²+6x+x+4

Adding the similar terms

6x²+7x+4

∵ The expression cannot be solved further, 6x²+7x+4 is the final solution.

Therefore, the simplified solution of the expression 5x²+6x+4+x²+x is 6x²+7x+4.

To learn more about simplification of expressions,

https://brainly.com/question/31294154

What is the strength of the association between the two
variables in the scatter plot?
Select from the drop-down menu to correctly complete the
statement.
The strength of association is Choose...
Strong or weak

Answers

The anwser is weak yw.

The shaded square has an area of 55 square units.
Enter the exact value of the side length of the square
and press "Try it."
I
units
Try It

Answers

The exact value of the side length of the square is √55 unit.

Given that the shaded square has an area of 55 square units.

We need to determine the exact value of the side length of the square,

To determine the exact value of the side length of the square, we can use the formula for the area of a square, which is given by the equation:

Area = side length²

In this case, the area is given as 55 square units. Therefore, we can set up the equation as follows:

55 = side length²

To solve for the side length, we need to find the square root of both sides of the equation:

√55 = √(side length)²

Simplifying further:

√55 = side length

Thus, the exact value of the side length of the square is √55 unit.

Learn more about area of a square click;

https://brainly.com/question/27776258

#SPJ1

Suppose you're making a soup that uses 5 cups of chicken broth for 8 servings. You need to make 12 servings of the soup. How much broth do you need?

A) 7.5 cups

B) 2.5 cups

C) 8.7 cups

D) 10 cups

Answers

The answer is A 7.5 cups

Will mark it brilliant

40. What is mzWXY? How do you know?
W
X
69°
Z
Y

Answers

The value of the angle m<WXY is 69 degrees

How to determine angle

We need to know that the shape given is a parallelogram.

The properties of a parallelogram are given as;

Opposite sides of the shape are parallel.Opposite sides of the shape are congruent.Opposite angles of a parallelogram are equal.Same-Side interior angles are supplementary, that is sum up to 180 degrees.Each diagonal of a parallelogram separates it into two equal trianglesThe diagonals of a parallelogram bisect each other.

From the information given, we have that;

Angel WZY and Angle WXY are opposite angles of the parallelogram

Then,

m<WXY = 69 degrees

Learn more about parallelograms at: https://brainly.com/question/10744696

#SPJ1

100 Points! Algebra question. Photo attached. Find the amplitude, if it exists, and period of the function. Then graph the function. Thank you!

Answers

The amplitude and the period of the function f(x) = 2cos[3(θ + 45)] + 2 are 2 and 2π/3

The Phase shift is 45 and the vertical shift is 2

How to determine the amplitude and period of the function

From the question, we have the following parameters that can be used in our computation:

f(x) = 2cos[3(θ + 45)] + 2

A sinusoidal function is represented as

f(x) = Acos(B(x + C)) + D

Where

Amplitude = A

Period = 2π/B

Phase shift = C

vertical shift = D

Using the above as a guide, we have the following:

Amplitude = 2

Period = 2π/2

Next, we have

Phase shift = 45

vertical shift = 2

Hence, the amplitude is 2 and the period is 2π/3

Read more about sinusoidal function at

brainly.com/question/21286958

#SPJ1

a cube with a surface area of 6 square inches is removed from the corner of a cube with a surface area of of 96 square inches.
questions
a. what do you think removing the smaller cube from largers cubes has on its surface area? explain your answer
b. find the surface area of the new solid.

Answers

a. The surface area of the cube is reduced .

b . The new surface area of the new solid is 90 in²

What is surface area?

The area occupied by a three-dimensional object by its outer surface is called the surface area.

a. The surface area of the original cube is 96 in² and a cube of another 6 in² is removed from the old cube.

This means that the surface area of the cube is reduced.

The surface area of a cube is expressed as;

SA = 6l²

where l is the side length of the cube.

b. The surface area of the new solid = surface area of big cube - surface area of old cube = 96-6

= 90 in²

learn more about surface area from

https://brainly.com/question/16519513

#SPJ1

please answer this question correctly.

Answers

The inequality representing the dollar amount, n, that Zack must be paid for each room in order to make a profit of more than $300 is n > $107.50.

Option C is the correct answer.

We have,

Profit = Amount Paid - Cost of Supplies

Given that the cost of supplies for each room is $32.50, we can represent the profit for each room as:

Profit per room = Amount Paid per room - $32.50

Zack wants to make a profit of more than $300 for painting 4 identical rooms.

The total profit for the 4 rooms should be greater than $300.

We can write this inequality as:

4 x (Profit per room) > $300

Substituting the expression for profit per room, we have:

4 x (Amount Paid per room - $32.50) > $300

Now, let's solve the inequality to find the dollar amount that Zack must be paid for each room:

4 x (Amount Paid per room - $32.50) > $300

4 x Amount Paid per room - 4 x $32.50 > $300

4 x Amount Paid per room - $130 > $300

4 x Amount Paid per room > $300 + $130

4 x Amount Paid per room > $430

Amount Paid per room > $430 / 4

Amount Paid per room > $107.50

Therefore,

The inequality representing the dollar amount, n, that Zack must be paid for each room in order to make a profit of more than $300 is n > $107.50.

Learn more about inequalities here:

https://brainly.com/question/20383699

#SPJ1

sin( 3pi/4 ) =
O A. 1/2
OB. -√2/2
O C. √3/2
O D. √2/2

Answers

Answer:

sin( 3pi/4 ) = -√2/2

So, B.

Which statements is true and justify your answer

Answers

Answer:

Step-by-step explanation:

Find an angle in each quadrant with a common reference angle with 311°, from 0°≤θ<360°

Answers

Angles in each quadrant with common reference angle as 311° are :

First quadrant = 49°, second quadrant = 131°, third quadrant = 229° and fourth quadrant = 311°.

Given that,

Reference angle = 311°

We have to find an angle in each quadrant with this reference angle.

311° is in the fourth quadrant.

The equivalent angle on the first quadrant is,

360° - 311° = 49°

Equivalent angle on second quadrant is,

180° - 49° = 131°

Equivalent angle on third quadrant is,

360° - 131° = 229°

Hence the angles are found.

Learn more about Reference Angles here :

https://brainly.com/question/31636488

#SPJ1

There are 40 students trying out for a soccer team. After tryouts, 16 of these
students will make the soccer team and 4 of those who make the team will be
captains. What is the probability that Julie will be captain, given that she makes
the team?

Answers

The probability that Julie will be a captain, given that she makes the team is 1/3.

Given,

Number of students trying out for a soccer team = 40

Case of probability,

P(A) = n(A)/n(S)

n(A) = number of favourable outcomes, n(S) is the total number of events in the sample space.

Given ,

18 of 40 students will make the soccer team.

⇒ n(S) = 18

Let event A: Julie will be a captain, given that she makes the team

⇒ n(A) = 3

So, the probability that Julie will be a captain, given that she makes the team,

= P(A) = n(A)/n(S)

= P(A) = 3/18

= P(A) = 1/6

Therefore, the probability that Julie will be a captain, given that she makes the team is 1/3.

Learn more about probability here:

brainly.com/question/11234923

#SPJ1

A small square has length y cm
A large square has length 40 cm
The area of the small square is of
the area of the large square.
25
Work out the value of y.
Your final line must say, y = ...
y cm
40 cm
Total marks: 3

Answers

Answer:

Step-by-step explanation:

The area of a square is given by the formula A = s^2, where A is the area and s is the length of a side of the square.

Let y be the length of the side of the small square.

Then, the area of the small square is y^2 cm^2.

According to the question, the area of the small square is 1/25 of the area of the large square.

Thus, the area of the large square is (25)(y^2) cm^2.

The length of a side of the large square is given by the formula s = √A.

Therefore, the length of a side of the large square is √(25y^2) = 5y cm.

Since the length of a side of a cube is equal to its height, width, and length, the dimensions of the cube are 5y cm x 5y cm x 5y cm = (5y)^3 cm^3.

Therefore, y = 40/5 = 8.

Thus, the dimensions of the cube are 40 cm x 40 cm x 40 cm.

The rates of on-time flights for commercial jets are continuously tracked by the U.S. Department of Transportation. Recently, Southwest Air had the best rate with 80 % of its flights arriving on time. A test is conducted by randomly selecting 15 Southwest flights and observing whether they arrive on time. (a) Find the probability that exactly 10 flights arrive on time.

Answers

Probability that exactly 10 flights arrive on time is 53.33%.

Given that,

The rates of on-time flights for commercial jets are continuously tracked by the U.S. Department of Transportation.

Recently, Southwest Air had the best rate with 80% of its flights arriving on time.

Total number flights in sample = 15

Probability that exactly 10 flights arrive on time is,

P = 10/15 × 80%

  = 0.5333

  = 53.33%

Hence the required probability is 53.33%.

Learn more about Probability here :

https://brainly.com/question/29083496

#SPJ1

Will mark brilliant

21. If AXYZ ≈ AJKL, which segment corresponds to KJ?

Answers

If triangles ΔXYZ is congruent to ΔJKL, then the segment which corresponds to KJ is YX.

Given that, two triangles ΔXYZ and ΔJKL are congruent to each other.

So the corresponding vertices are,

Vertex X of ΔXYZ corresponds to vertex J of ΔJKL

Vertex Y of ΔXYZ corresponds to vertex K of ΔJKL

Vertex Z of ΔXYZ corresponds to vertex L of ΔJKL

Now, the segment which corresponds to KJ in ΔXYZ will be the segment formed by joining the vertices that corresponds to K and J.

We already have,

K corresponds to Y and J corresponds to X.

So the equivalent segment is YX.

Hence the segment required is YX.

To learn more about Congruence, click on the line given here :

https://brainly.com/question/29084797

#SPJ1

Simplify.

√n/18.

Answer choices:
A 1/6n √2.
B √1/9
C 1/6 √2n

Please explain the answer my radical calculator doesn't work on anything with letters in it.​

Answers

Answer: C 1/6*√2n

Step-by-step explanation:

• Simplify √n/18 as (1/3)^2*n/2

• Multiply them under the radical so the squares 1/3 cancels out to 1/3*√n/2

• Multiply the √n/2 on both sides as √2*n/√2*√2 so it comes out to √2n/2

• Multiply √2n/2 with 1/3 to make √2n/6

√2n/6 is equal to 1/6*√2n

The radical expression √n/18 when simplified is 1/3√n/2

Simplifying the radical expression

From the question, we have the following parameters that can be used in our computation:

√n/18

Express 18 as 9 * 2

So, we have the following representation

√n/18 = √n/(9 * 2)


Rewrite as

√n/18 = √n/(2 * 9)

Take the square root of 9

This gives

√n/18 = 1/3 * √n/2

Evaluate the products

√n/18 = 1/3√n/2

Hence, the expression when simplified is 1/3√n/2

Read more about radical expressions at

https://brainly.com/question/20372424

#SPJ1

Explain each step and answer 50 points

Answers

1 Yes  the set of rational expressions is closed under subtraction

2. Yes  the set of rational expressions is closed under multiplication

3. No  the set of rational expressions is not closed under division

How to determine if the expression is closed

1. The subtraction of two rational expressions results in another rational expression.

=  p(x)/q(x) - r(x)/s(x)= ((p(x)s(x) - r(x)q(x))/(q(x)s(x)))

this is also a rational expression.

2. The multiplication of two rational expressions results in another rational expression.

=(p(x)/q(x)) * (r(x)/s(x)) = ((p(x)r(x))/(q(x)s(x)))

this is a rational expression.

3. Division of two rational expressions may result in an expression that is not a rational expression.

= (p(x)/q(x)) / (r(x)/s(x)))

= ((p(x)s(x)) / (q(x)r(x)))

this may not be a rational expression if q(x)r(x) equals zero at some point, causing division by zero

Learn more about rational expressions at

https://brainly.com/question/29061047

#SPJ1

25. Solve for the missing variables.

Answers

The missing angles in the cyclic quadrilateral are as follows:

a = 101°

b = 67°

c = 84°

d = 80°

How to find the angles in a cyclic quadrilateral?

A cyclic quadrilateral is a quadrilateral which has all its four vertices lying on a circle. The sum of angles in a cyclic quadrilateral is 360 degrees.

Opposite angles of a cyclic quadrilateral is supplementary.

c = 180 - 96

c = 84 degrees

d = 180 - 100

d = 80 degrees

100 = 1 / 2 (a + 99)

100 = 0.5a + 49.5

0.5a = 50.5

divide both sides by 0.5

a = 50.5 / 0.5

a = 101 degrees

84 = 1 / 2 (101 + b)

84 = 50.5 + 0.5b

84  - 50.5 = 0.5b

0.5b = 33.5

b = 33.5 / 0.5

b = 67 degrees

learn more on cyclic quadrilateral here: https://brainly.com/question/14352697

#SPJ1

Susan borrows $1000 for 8 months at 7 1/8% per annum simple interest. What is the amount due?

Answers

Answer:

$1047.50

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

Given:

principal (P) = $1000, time (t) = 8 months, and interest rate (r) = 7 1/8% per annum.

Convert the interest rate to a decimal:

7 1/8% = 7.125% = 0.07125

Convert the time from months to years:

8 months / 12 months per year = 2/3 years.

Now, we can calculate the simple interest using the formula:

I = P * r * tI = $1000 * 0.07125 * (2/3) = $47.50

Finally, add the interest to the principal to find the amount due:

Amount due =  $1000 + $47.50 = $1047.50

Susan's amount due for the loan is $1047.50.

The simple interest amount of Susan for time of 8 months is A = $ 1047.50

Given data ,

To calculate the amount due, we need to consider the principal amount borrowed, the interest rate, and the time period.

Principal (P) = $1000

Time (t) = 8 months

Interest rate (r) = 7 1/8% per annum

First, we need to convert the interest rate from a percentage to a decimal. To do this, we divide the given rate by 100:

r = 7 1/8% = 7.125% = 7.125/100 = 0.07125 (decimal)

Next, we can calculate the simple interest using the formula:

Simple Interest (I) = Prt

I = $1000 x 0.07125 x (8/12)

I = $1000 x 0.07125 x (2/3)

I = $47.50

Finally, to find the amount due, we add the principal amount to the simple interest:

Amount Due = Principal + Simple Interest

Amount Due = $1000 + $47.50

Amount Due = $ 1047.50

Hence , the amount is A = $ 1047.50

To learn more about simple interest click :

https://brainly.com/question/17282817

#SPJ1

Find 3 ways the equation f(x)=3x^{2}+4x+3 can be used in the real world.

Answers

Answer:

Step-by-step explanation:

The equation f(x) = 3x^2 + 4x + 3 is a quadratic function. Here are three ways this equation can be used in the real world:

In physics, this equation can be used to model the height of an object thrown into the air. The equation f(x) = 3x^2 + 4x + 3 can be used to calculate the height of the object at any given time x, where x is the time elapsed since the object was thrown. The coefficient 3 in the equation represents the acceleration due to gravity, and the other terms represent the initial height and velocity of the object.

In economics, this equation can be used to model the profit of a company. If x represents the number of units sold, then f(x) = 3x^2 + 4x + 3 can be used to calculate the profit made by the company at any level of sales. The coefficient 3 in the equation represents the fixed costs of the company, while the other terms represent the variable costs and revenue.

In engineering, this equation can be used to model the trajectory of a projectile. The equation f(x) = 3x^2 + 4x + 3 can be used to calculate the distance traveled by a projectile at any given time x, where x is the time elapsed since the projectile was launched. The coefficient 3 in the equation represents the initial velocity of the projectile, and the other terms represent the effects of air resistance and gravity.

Find the ordered pair solutions for the
system of equations.
f(x)=x²-3x - 10
f(x) = -x-2
([ ? ],
) and (
Enter the smallest x first.

Answers

Answer:

[tex]( - 2, 0 )\; and \; ( 4, - 6)[/tex]

Step-by-step explanation:

To find the ordered pairs set the right side expressions equal to each other and solve for x, then use those values for x to evaluate f(x) values

We get

x² - 3x - 10 = -x - 2

Moving -x - 2 to the left side gives

x² -3x - 10 + x + 2   = 0
(moving an expression from one side to another changes the signs of the terms)

Grouping like terms:
x² - 3x + x -10 +2 = 0

x² -2x -8 = 0

Expression on the left can be factored as (x + 2)(x-4)

This results in
(x + 2)(x - 4) = 0 giving

(x + 2) = 0 ==> x = -2 as one solution for x

(x - 4) =0 ==> x = 4 as the second solution

Plug in x = -2 into the second expression -x - 2 to get

f(-2) = -(-2) -2 = 2 - 2 = 0

So one ordered pair is (-2, 0)

Plug in x = 4 into -x - 2 to get
f(4) = - 4 -2 = -6

So (4, -6) is another ordered pair

Other Questions
describe (words and drawings) the basis by which infrared radiation passes into the sample and back to the detector when using an ATR instrument A symmetric double convex lens with a focal length of 27.5cm is to be made from glass with an index of refraction of 1.52.What should be the radius of curvature for each surface? including a transaction identifier in the fact table is often referred to as: a. Snowflakingb. Degenerate dimension c.. Aggregated fact table d. Galaxy of stars Garath sells hot drinks he sells cups of tea, cuups of coffee and cups of hot chocolateOf all the hot drinks sold last week 2/5 were cups of tea 1/3 were cups of coffeeWhat fraction of all cups of hot drinks sold were cups of hot chocolate? a diverging lens with focal length |f| = 11.0 cm produces an image with a magnification of 0.700. what are the object and image distances? (include the sign of the value in your answers.) which element is being oxidized in the following redox reaction? c5h12o2(aq) kmno4(aq) c5h6o4k2(aq) mno2(aq) All of the following sentences use pronouns clearly and correctly except As soon as a buyer leaves the parking lot with his or her new car, the car begins to lose value. What is the difference between prescription drugs and OTC drugs? What was Joseph Stalin's primary goal after World War II?O to place oversight of all branches of the military under the Secretary of DefenseO to ensure friendly governments on its borders in Eastern EuropeO Truman quickly recognized Israel and pledged to make its defense a cornerstone of U.S. policies in the Middle East.O a massive increase in U.S. defense spending Q5QUESTION 5. 1 POINT Find the first five terms of the following sequence, starting with n = Give your answer as a list, separated by commas. an = (1)"+(6n 10) An infant has autoreactive T cells that have been activated in response to self-antigens present in the gut, skin, and endocrine glands Without treatment the child will likely die by 2 years of age. This condition could be caused bya- the presence of anergic CD4 T cells.b- the lack of functional T-bet transcription factor.c- the lack of functional FoxP3 transcription factor.d- the lack of B7 expression on dendritic cells. what should be the time horizon for your content calendar Decko Co. is a U.S. firm with a Chinese subsidiary that produces cell phones in China and sells them in Japan. This subsidiary pays its wages and its rent in Chinese yuan, which is stable relative to the dollar. The cell phones sold to Japan are denominated in Japanese yen. Assume that Decko Co. expects that the Chinese yuan will continue to stay stable against the dollar. The subsidiary's main goal is to generate profits for itself and reinvest the profits. It does not plan to remit any funds to the U.S. parent. almost any group member can become a charismatic leader with enough training.T/F fixed assets are those that: multiple choice are intangible. include cash. will be used over a long period of time. are similar to loans and advances. does thermal energy ever flow from a lower temp. to a higher temp. donatello's david holds the distinction of being the first Which of the following statements is true?Select one:a. Relativity is the study of how space, energy, and mass are related to time.b. Relativity is the concept that there are no absolutes that can be postulated.c. Relativity is the idea that space bends in relationship to the square of the mass contained within it.d. Relativity is the study of wormholes and time travel. Sam had one cup of sugar. He used 1/4 cup of sugar to make cookiesHow much sugar did he have left? The Rules Committee can end debate in the House ofRepresentative. True or False