Please answer this recent question CORRECTLY for 30 points and brainliest!!

Answer:

[tex]x=\frac{-(-2)\pm \sqrt{(-2)^2-4(-3)(6)}}{2(-3)}[/tex]

Step-by-step explanation:

The given quadratic equation is

[tex]-3x^2-2x+6=0[/tex]            .... (1)

If a quadratic equation is defined as

[tex]ax^2+bx+c=0[/tex]            .... (2)

then the quadratic formula is

[tex]x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]

On comparing (1) and (2), we get

[tex]a=-3,b=-2,c=6[/tex]

Substitute [tex]a=-3,b=-2,c=6[/tex] in the above formula.

[tex]x=\frac{-(-2)\pm \sqrt{(-2)^2-4(-3)(6)}}{2(-3)}[/tex]

Therefore, the correct substitution of the values a, b, and c in the quadratic formula is [tex]x=\frac{-(-2)\pm \sqrt{(-2)^2-4(-3)(6)}}{2(-3)}[/tex].

Answer:

I believe it's the statement is always true.

Step-by-step explanation:

test it by substituting x = an odd number:

x=1

so

x = 1 odd number

x + 2 = 1+2 = 3 odd

x + 6 = 1 + 6 = 7 odd

x + 10 = 1+10=11 odd

Answer:

the statement is always true.

Answer:

  about 8 cm

Step-by-step explanation:

The formula for the area of a regular polygon is ...

  A = 1/2Pa . . . . where P is the perimeter and "a" is the apothem, the distance from the center to a side

Filling in your numbers, we have ...

  20 cm^2 = (1/2)P(5 cm)

Dividing by the coefficient of P, we find ...

  2×(20 cm^2)/(5 cm) = P = 8 cm

The perimeter of the pentagon is about 8 cm.

_____

Comment on the problem

This calculation makes use of the area formula, as apparently intended. A regular pentagon with an apothem of about 5 cm will have an area of about 90.8 cm^2. The given geometry is impossible, as the pentagon is nearly 10 cm across. It cannot have a perimeter of only 8 cm.

Answer:

[tex]x\geq 29,000[/tex]  and  [tex]x\leq 41,000[/tex]

Step-by-step explanation:

Let

x -----> the altitude of a commercial aircraft

we know that

The expression " A minimum altitude of 29,000 feet" is equal to

[tex]x\geq 29,000[/tex]

All real numbers greater than or equal to 29,000 ft

The expression " A maximum altitude of 41,000 feet" is equal to

[tex]x\leq 41,000[/tex]

All real numbers less than or equal to 41,000 ft

therefore

The compound inequality is equal to

[tex]x\geq 29,000[/tex]  and  [tex]x\leq 41,000[/tex]

All real numbers greater than or equal to 29,000 ft and less than or equal to 41,000 ft

The solution is the interval ------> [29,000,41,000]

Answer:

A

Step-by-step explanation:

Final answer:

To find the total number of votes polled in the election with three candidates and invalid votes, the sum of votes received by each candidate and the invalid votes is calculated. The total number of votes polled is 1,027,601.

Explanation:

The question pertains to vote totals and calculating the overall number of votes polled in an election with three candidates. To solve this, we will perform simple addition of the votes received by each candidate and also include votes that were declared invalid.

Candidate A received 345,983 votes. Candidate B won the election by a margin of 15,967 votes more than Candidate A, which means Candidate B received 345,983 + 15,967 = 361,950 votes. Candidate C received 279,845 votes, and there were 39,823 invalid votes.

To find the total number of votes polled, add together all the votes:

Votes for Candidate A: 345,983

Votes for Candidate B: 361,950 (since Candidate B won by 15,967 votes more than Candidate A)

Votes for Candidate C: 279,845

Invalid votes: 39,823

Adding these together:

345,983 + 361,950 + 279,845 + 39,823 = 1,027,601

Therefore, the total number of votes polled in the election is 1,027,601.

Answer:

  see below for a graph

Step-by-step explanation:

Each of the functions:

will only be graphed in the specified domain. You know that ...

  y = -x

is a line with slope -1 through the origin. It won't go through the origin on your graph, because it stops at x = -2. f(x) is not defined as -(-2) at x=-2, so there will be an open circle at the end of this portion of the graph.

__

You know that

  y = x+2

is a line with slope +1 through the y-intercept (0, 2). It will only be part of your graph for x-values between -2 and 2, inclusive. Because f(x) is defined as x+2 at the end points of this segment, those points will be shown as solid dots.

__

You know that

  y = 5

is a horizontal line. It will be part of your graph for x > 2, and will have an open circle on the end at x=2. f(2) is not defined as 5, but is defined as 4 (see above), which is why the circle is open.

Answer:

see below

Step-by-step explanation:

1.  y = mx+b where m is the slope

The first slope is -1/3

The second slope is 3

m1 = m2 means they are parallel  False

m1*m2 = -1  means they are perpendicular

-1/3 *3 = -1  True

2.  Squares and rhombi have all 4 sides with the same length.  Squares however, have 4 angles that must equal 90 degrees.  Squares are a special form of rhombi

3.  To find the slope

m = (y2-y1)/(x2-x1)

   = (2-11)/(-5-0)

   =-9/-5

   = 9/5

The distance is found by

d = sqrt( (x2-x1)^2 + (y2-y1)^2)

  = sqrt( (-5-0)^2 + (2-11)^2)

  = sqrt( 5^2 + (-9)^2)

  = sqrt( 25+81)

  = sqrt( 106)

Answer:

See below

Step-by-step explanation:

y = -1/3x + 2

y = 3x - 5

Slopes are -1/3 and 3, they are opposite-reciprocal, it means the lines are perpendicular

2. Difference between squares and rhombus:

3. points A(0,11)  and B(-5,2)

Slope:

m= (y2-y1)/(x2-x1)= (2-11)/(-5-0)= -11/-5= 11/5

Distance between points:

√(x2-x1)²+(y2-y1)²= √ 25+121= √146 ≈ 12

Simplifying it, convert it to a radical form, and evaluate it.. Either way it all equals to a simple whole number, which is '4',

well, except when you convert the expression to radical form using the formula 'a^x/n=n√a^x' then it'll be '^3√8^2'.

____

I hope this helps, as always. I wish you the best of luck and have a nice day, friend..

Answer:

4

Step-by-step explanation:

8 ^ (2/3)

The 2 means squared and the 3 means root

8^2  ^ (1/3)

Rewriting 8 as 2^3

2^3 ^ (2/3)

We know a^ b^c = a^ (b*c)

2 ^ (3*2/3)

2^ 2

4

OR

8 ^ (2/3)

The 2 means squared and the 3 means root

8^2  ^ (1/3)

64 ^ 1/3

We know 4*4*4 = 64

(4*4*4)^ 1/3

4

To find the height of the football after 1.2 seconds, we substitute t with 1.2 in the polynomial −16t2 + 32t + 3, simplifying to 18.36 feet, which corresponds to answer option C.

The student asked to find the height of a kicked football after 1.2 seconds, with the height given by the polynomial −16t2 + 32t + 3, where t is the time in seconds. To solve for the height after 1.2 seconds, we substitute t with 1.2 in the polynomial, which gives us:

−16(1.2)2 + 32(1.2) + 3

Calculating this gives:

−16(1.44) + 38.4 + 3

−23.04 + 38.4 + 3

15.36 + 3

18.36 feet.

Therefore, after 1.2 seconds, the height of the football is 18.36 feet, making the correct answer option C.

Ques 4)

The system is:

                      [tex]y=x-4[/tex]

                     [tex]y=\dfrac{x-4}{x+2}[/tex]

Ques 5)

The system is:

                         [tex]6x+y=-27[/tex]

             and     [tex]y=x^2+5x+3[/tex]  

Ques 4)

After looking at the graph we observe that :

The first graph is a line which passes through (4,0) and (0,-4)

Hence, the equation of such a line is:

                y=x-4

and the second graph is a curve such that the vertical asymptote is at x= -2

and also x= 4 is a root of the rational function.

Since, the graph passes through (4,0)

Hence, the system equation which best represents the graph is:

                           [tex]y=x-4[/tex]

                     [tex]y=\dfrac{x-4}{x+2}[/tex]

Ques 5)

One of the curve is :

a line that passes through (-5,3) and (-6,9)

Hence, the equation of line is given by:

[tex]y-3=\dfrac{9-3}{-6-(-5)}\times (x-(-5))\\\\i.e.\\\\y-3=\dfrac{6}{-6+5}\times (x+5)\\\\i.e.\\\\y-3=\dfrac{6}{-1}\times (x+5)\\\\i.e.\\\\y-3=-6(x+5)\\\\i.e.\\\\y-3=-6x-30\\\\i.e.\\\\y=-6x-30+3\\\\i.e.\\\\y=-6x-27[/tex]

i.e. Equation of line is:

[tex]6x+y=-27[/tex]

While the other graph is a upward facing parabola such that the vertex is in third quadrant this means that the coefficient of x^2 must be positive and that of x must also be positive.

Hence, the system in which the equation of line satisfies is:

                          [tex]6x+y=-27[/tex]

             and     [tex]y=x^2+5x+3[/tex]  

Answer:

h = 32.25.

Step-by-step explanation:

h^2 = 28^2 + 16^2 (Pythagoras theorem).

h = √1040

h = 32.25.

Using the Pythagorean theorem, the length of the hypotenuse in a right triangle with legs of lengths 28 and 16, rounded to the nearest hundredth, is 32.25.

The question asks for the length of the hypotenuse in a right triangle with legs of lengths 28 and 16. To find this, we use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the two legs (a and b). Thus, according to the equation a² + b² = c², we substitute the given values to find the hypotenuse length.

Using the given lengths:

a = 28

b = 16

We calculate:

c = √(28² + 16²)

c = √(784 + 256)

c = √(1040)

c = 32.249

Rounded to the nearest hundredth, the length of the hypotenuse is therefore 32.25.

Answer:

27%

Step-by-step explanation:

take the number of times it is at 2 cars (16) and divide by the number of surveyed times in total (60). multiply by 100 to show answer as a percent

Answer:

27%

Step-by-step explanation:

We are given the results of survey of one thousand families to determine the distribution of families by their size.

We are to find the probability (to the near percent) that a line has exactly 2 cars in it.

Frequency of 2 cars in a line = 16

Total frequency = 2 + 9 + 16 + 12 + 8 + 6 + 4 + 2 + 1 = 60

P (2 cars in line) = (16 / 60) × 100 = 26.6% ≈ 27%

Answer:

  (-12, 5), (12, -5)

Step-by-step explanation:

Reflection across the origin is the transformation ...

   (x, y) ⇒ (-x, -y)

Look for coordinates that are the opposites of their counterparts. You will find the appropriate answer choice is ...

  (-12, 5), (12, -5)

Answer:

(-12, 5), (12, -5)

Step-by-step explanation:

Since, the rule of point symmetry with respect to the origin is,

[tex](x,y)\rightarrow (-x, -y)[/tex]

That is, the mirror image of the point (x, y) with respect to the origin is (-x,-y),

Thus, in the point symmetry with respect to the origin,

[tex](-12, 5)\rightarrow (-(-12), -5))[/tex]

So, the mirror image of point (-12,5) with respect to the origin is (12, -5),

Hence, the set of ordered pairs has point symmetry with respect to the origin is,

(-12, 5), (12, -5)

Second option is correct.

Answer:

(C)

10

Step-by-step explanation:

Let y = cost of items

Let x = number of items

Total cost  = fixed charge + (cost per item x number of items)

Given:

company A fixed charge = $50 , cost per item = $7

company B fixed charge = $30 , cost per item = $9

For company A,

Total Cost = $50 + ($7 x number of items),

          or

     y = 50 + 7x

Similarly for company B,

Total Cost = $30 + ($9 x number of items),

          or

     y = 30 + 9x

Hence (C) is the correct answer.

For the cost to be the same, Total cost for A = total cost for B

i.e 50 + 7x = 30 + 9x

x = 10 items  (Answer)

The correct system to solve the problem is y=50+7x and y=30+9x. The cost will be the same at both companies when there are 10 items.

The correct system that could be used to solve the problem is (C) y=50+7x and y=30+9x.

To find the number of items where the cost will be the same at both companies, we need to set the two equations equal to each other and solve for x.

50+7x = 30+9x

20 = 2x

x = 10

Therefore, the cost will be the same at both companies when there are 10 items.

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Answer:

Since we have BC ║ DE, we know that:

AB/AD = BC/DE

12/(12 + 4) = BC/12

12/16 = BC/12

BC = (12 · 12)/16 = 9 (in)

Applying the pythagorean, we have:

AB² + BC² = AC²

12² + 9²     = AC²

225           = AC²

AC             = √225 = 15 (in)

Using the information about the parallel lines again, we have:

AC/CE = AB/BD

15/CE = 12/4

CE = (15 · 4)/12 = 5 (in)

So the answer is B

Answer:

D. not congruent

Step-by-step explanation:

Only two pairs of congruent sides are given to us, when we need either 3 pairs of congruent sides (SSS) or two pairs of congruent sides & 1 pair of congruent angles (SAS), or two pairs of congruent angles & one pair of congruent sides (ASA).

~

Answer:

a = 13 and b = 12-5i

Step-by-step explanation:

We need a common denominator

3+2i         5-i

---------- + ---------

3-2i          2+3i

(3+2i) (2+3i)         (5-i)(3-2i)

------------------ + --------------------

(3-2i) (2+3i)          (2+3i) (3-2i)

Foil the numerators

6 +4i+9i+6i^2 +15-3i-10i+2i^2        

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

         (2+3i) (3-2i)

Combine like terms

21 +8i^2          

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

(2+3i) (3-2i)

We know that i^2 = -1

21 +8(-1)        

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

(2+3i) (3-2i)

21 -8        

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

(2+3i) (3-2i)

13        

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

(2+3i) (3-2i)

Foil the denominator

13

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

6 +9i -4i -6i^2

Combine like terms

13

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

6+ 5i -6(-1)

13

----------

12 +5i

We know have

13

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

12 + 5i

Multiply by the conjugate

13               ( 12-5i)

------------- * -------------

12 + 5i         12 -5i

13 (12-5i)

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

144 +25

13(12-5i)

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

169

12-5i

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

13

The parentheses are (12-5i)/13

We need the reciprocal to make the equation become 1

which is 13/ 12-5i

a = 13 and b = 12-5i

Answer:

a = 13

b= 12-5i

Step-by-step explanation:

Simplify the values and i squared will be -1

Answer:

n = -174

Step-by-step explanation:

What I did was 696 divided by -4 and got B) n = -174.

Please mark brainliest and have a great day!

[tex]_7P_5=\dfrac{7!}{(7-5)!}=\dfrac{7!}{2!}=3\cdot4\cdot5\cdot6\cdot7=2520\\_7C_5=\dfrac{7!}{5!2!}=\dfrac{6\cdot7}{2}=21\\\\\\_7P_5> {_7C_5}[/tex]

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

[tex]_nP_k[/tex] is always greater than [tex]_nC_k[/tex]. And it's greater [tex]k![/tex] times.

[tex]\dfrac{_nP_k}{_nC_k}=\dfrac{\dfrac{n!}{(n-k)!}}{\dfrac{n!}{k!(n-k)!}}=\dfrac{n!}{(n-k)!}\cdot \dfrac{k!(n-k)!}{n!}=k![/tex]

Answer:

the functions f(x) and g(x) are equivalent

Step-by-step explanation:

Your full question is attached below

The equations of your problem are

f(x) = √(16^x)

f(x) = √(4^(2x))

f(x) = √(4^(2x)) = √(4^x.4^x)

f(x) = 4^(x)

and

g(x) = ∛64^x

g(x) = ∛4^(3x)

g(x) = ∛4^(3x)  =  ∛4^(x) .4^(x) .4^(x)

g(x) = 4^(x)

Thus, the functions f(x) and g(x) are equivalent

Answer:

0.75 inches

Step-by-step explanation:

The value that has z=2 is 2 standard deviations from the mean. The value that has z=1 is 1 standard deviation from the mean. The difference between these two values is 1 standard deviation:

1 standard deviation = 3.75 in - 3 in = 0.75 in

Answer:

0.75

Step-by-step explanation:

Answer: 900,000 for the city/2,304,000

Step-by-step explanation:

I used the exponential growth formula with initial population rate of growth and time passed.

In 2002, the population of the city was 416,000 and the population of the suburbs was 884,000.

In 2000, the city's population was 400,000 and the suburban population was 900,000. Each year, 5% of the city's population moves to the suburbs (and 95% stays in the city), and 4% of the suburban population moves to the city (and 96% remains in the suburbs). To calculate the population of the city in 2002, we need to subtract 5% of the city's population in 2000 from the 2000 city population and add 4% of the suburban population. To calculate the population of the suburbs in 2002, we need to subtract 4% of the suburban population in 2000 from the 2000 suburban population and add 5% of the city population.

Population of city in 2002 = (City population in 2000) - 5% of (City population in 2000) + 4% of (Suburban population in 2000)

Population of suburbs in 2002 = (Suburban population in 2000) - 4% of (Suburban population in 2000) + 5% of (City population in 2000)

By substituting the given values, we can calculate the population of the city and suburbs in 2002.

Population of city in 2002 = 400,000 - 0.05 * 400,000 + 0.04 * 900,000

Population of city in 2002 = 400,000 - 20,000 + 36,000

Population of city in 2002 = 416,000

Population of suburbs in 2002 = 900,000 - 0.04 * 900,000 + 0.05 * 400,000

Population of suburbs in 2002 = 900,000 - 36,000 + 20,000

Population of suburbs in 2002 = 884,000

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We're given pairs (A,B) and asked if we have

enough calcium,

5A + 4B >= 24

enough iron

4A + 6B >= 15

and enough vitamins

7A + 4B >= 15

We check each constraint on each pair; if we find any false we can stop for that pair.

(A,B)=(1,4)

5(1)+4(4)=21   under 24, NO CHECK

(A,B)=(1,5)

5(1) + 4(5) = 25, bigger than 24, good

4(1) + 6(5) = 34, bigger than 15, good

7(1) + 4(5) = 27, bigger than 15, good   CHECK

(A,B)=(2,3)

5(2)+4(3)=22, NO CHECK

(A,B)=(3,2)

5(3)+4(2)=23, NO CHECK

(A,B)=(4,1)

5(4) + 4(1) = 24, ok

4(4) + 6(1) = 22, ok

7(4) + 4(1) = 32, ok, CHECK

Answer:

(1,5),  (4,1)

Step-by-step explanation:

Let's check the possible answers and see if they will Steve to meet his requirements:

We'll start by looking if each answer (dose) will provide enough calcium first.  If it does, we'll get iron and vitamins if needed.

a) (1,4)

Calcium, at least 24 mg

24 ≤ 5x + 4y

24 ≤ 5 (1) + 4 (4)

24 ≤ 5 + 16

24 ≤ 21

NO!

b) (1,5)

Calcium, at least 24 mg

24 ≤ 5x + 4y

24 ≤ 5 (1) + 4 (5)

24 ≤ 25   YES!

Iron, at least 15 mg

15 ≤ 4x + 6y

15 ≤ 4(1) + 6(5)

15 ≤ 34 YES!

Vitamins, at least 16 mg

16 ≤ 7x + 4y

16 ≤ 7 (1) + 4 (5)

16 ≤ 27  YES

YES, YES, YES...

c) (2,3)

Calcium, at least 24 mg

24 ≤ 5x + 4y

24 ≤ 5 (2) + 4 (3)

24 ≤ 22 NO!

d) (3,2)

Calcium, at least 24 mg

24 ≤ 5x + 4y

24 ≤ 5 (3) + 4 (2)

24 ≤ 23 NO!

e) (4,1)

Calcium, at least 24 mg

24 ≤ 5x + 4y

24 ≤ 5 (4) + 4 (1)

24 ≤ 24   YES!

Iron, at least 15 mg

15 ≤ 4x + 6y

15 ≤ 4(4) + 6(1)

15 ≤ 22 YES!

Vitamins, at least 16 mg

16 ≤ 7x + 4y

16 ≤ 7 (4) + 4 (1)

16 ≤ 32 YES

YES, YES, YES...

Answer:

[tex]330\ kg[/tex]

Step-by-step explanation:

Remember that

1 kg=1,000 g

1 m= 100 cm

The volume of the granite countertop in cubic centimeters is equal to

[tex]V=(100)(300)(4)\ cm^{3}[/tex]

The density in kg per cubic centimeter is equal to

[tex]D=2.75(\frac{1}{1,000}) \frac{kg}{cm^{3}}[/tex]

Multiply the density by the volume

[tex]2.75(\frac{1}{1,000})(100)(300)(4)[/tex]

[tex]2.75(120)=330\ kg[/tex]

The cost for talking 3.1 minutes, according to the graph, would be  Option C) 4 cents due to rounding up to nearest minute.

1. Understanding the ceiling function: The ceiling function takes a number as input and rounds it up to the nearest whole number. For example, the ceiling of 2.3 is 3, because 3 is the next whole number greater than 2.3.

2. Analyzing the graph: The graph provided represents the cost of a long-distance phone call in cents based on the duration of the call in minutes. The x-axis represents the minutes of the call, and the y-axis represents the cost in cents.

3. Identifying the jumps: From the graph, we can observe that the cost increases in steps or jumps at specific points along the x-axis. These jumps indicate where the cost increases by 1 cent.

4. Determining the cost for 3.1 minutes: Since 3.1 minutes fall between 3 and 4 minutes on the x-axis, we need to find out which whole number the ceiling function would round 3.1 up to. Since it rounds up to the nearest whole number, 3.1 would be rounded up to 4.

5. Conclusion: Therefore, the cost of talking for 3.1 minutes would be the same as talking for 4 minutes according to the graph. Looking at the y-axis corresponding to the point where x = 4, we see that the cost is 4 cents.

So, to answer the question, the cost to talk for 3.1 minutes would be 4 cents. Option C)

Complete Question:

Distance = rate * time

Replace D with f. Instead of writing D(t), write f(t).

f(t) = 65t

Let t = 3.5

f(3.5) = 65(3.5)

f(3.5) = 227.5

Did you follow?

Final answer:

The distance a car travels at 65 mph is a function of time, expressed as f(t) = 65t. Evaluating it for 3.5 hours, the car would travel 227.5 miles.

Explanation:

The distance a car travels at a rate of 65 mph is a function of the time, t, the car travels. This can be expressed mathematically as f(t) = 65t, where f(t) is the distance in miles and t is the time in hours. To evaluate this function for f(3.5), we multiply 65 miles/hour by 3.5 hours.

f(3.5) = 65 miles/hour × 3.5 hours = 227.5 miles

Therefore, a car traveling at a constant speed of 65 mph for 3.5 hours will have traveled 227.5 miles.

b)

A - wins at both games

[tex]P(A)=0.3\cdot0.4=0.12[/tex]

c)

A - wins at just one of the games

[tex]P(A)=0.3\cdot0.6+0.7\cdot0.4=0.18+0.28=0.46[/tex]

Answer:

The area of the polygon = 216.4 mm²

Step-by-step explanation:

* Lets talk about the regular polygon

- In the regular polygon all sides are equal in length

- In the regular polygon all interior angles are equal in measures

- When the center of the polygon joining with its vertices, all the

 triangle formed are congruent

- The measure of each vertex angle in each triangle is 360°/n ,

  where n is the number of its sides

* Lets solve the problem

- The polygon has 9 sides

- We can divide it into 9 isosceles triangles all of them congruent,

 if we join its center by all vertices

- The two equal sides in each triangle is 8.65 mm

∵ The measure of the vertex angle of the triangle = 360°/n

∵ n = 9

∴ The measure of the vertex angle = 360/9 = 40°

- We can use the area of the triangle by using the sine rule

∵ Area of the triangle = 1/2 (side) × (side) × sin (the including angle)

∵ Side = 8.65 mm

∵ The including angle is 40°

∴ The area of each triangle = 1/2 (8.65) × (8.65) × sin (40)°

∴ The area of each triangle = 24.04748 mm²

- To find the area of the polygon multiply the area of one triangle

 by the number of the triangles

∵ The polygon consists of 9 congruent triangles

- Congruent triangles have equal areas

∵ Area of the 9 triangles are equal

∴ The area of the polygon = 9 × area of one triangle

∵ Area of one triangle = 24.04748 mm²

∴ The area of the polygon = 9 × 24.04748 = 216.42739 mm²

* The area of the polygon = 216.4 mm²

Answer

[tex]216.4 {mm}^{2} [/tex]

Explanation

The regular polygon has 9 sides.

Each central angle is

[tex] \frac{360}{n} = \frac{360}{9} = 40 \degree[/tex]

The area of each isosceles triangle is

[tex] \frac{1}{2} {r}^{2} \sin( \theta) [/tex]

We substitute the radius and the central angle to get:

[tex] \frac{1}{2} \times {8.65}^{2} \times \sin(40) = 24.05 {mm}^{2} [/tex]

We multiply by 9 to get the area of the regular polygon

[tex]9 \times 24.05 = 216.4 {mm}^{2} [/tex]

Answer:

B. 2 m

Step-by-step explanation:

20 da is equal to 2 m.

Answer:

Paula must sell at least 2,500 windows in a year to earn a profit of at least $48,000.

Step-by-step explanation:

Let [tex]x[/tex] be the number of windows that Paula sells in a year.

Paula's revenue is the number of windows that she sell times the price that she charge for each window. That is:

[tex]\text{Revenue} = \text{Price}\times \text{Quantity} = \$\;28x[/tex].

Paula's cost comes in two parts:

[tex]\begin{aligned}\text{Cost} = \text{Total Cost}&= \text{Fixed Cost} + \text{Marginal Cost}\\ & = \$\;12,000 +\$\; 4x \\ & = \$\;(12,000 + 4x)\end{aligned}[/tex].

Consider the inequality in the picture:

[tex]\text{Revenue} - \text{Cost} \ge \text{Profit}\\ \$\; 28x - \$\; (12,000 + 4x)\ge 48,000\\\$\; 24x \ge 60,000[/tex].

Multiply both sides with 1/24. It is important that this number is positive. Otherwise, the direction of the inequality operator will flip.

[tex]\displaystyle x \ge \frac{\$\;60,000}{\$\; 24}[/tex].

[tex]x\ge 2,500[/tex].

In other words, Paula must sell at least 2,500 windows in a year to earn a profit of at least $48,000.