Area under the curve

f(x) = x 2 + 2x
g(x) = x + 2

The new store will have a profit of $3400 after its third month in business.

The correct option is D.

For variable x : ax² + bx + c = 0, where a≠0 is a standard quadratic equation, which is a second-order polynomial equation in a single variable. It has at least one solution since it is a second-order polynomial equation, which is guaranteed by the algebraic basic theorem.

Given:

George has opened a new store, and he is monitoring its success closely.

He has found that this store’s revenue each month can be modeled by r(x)=x²+5x+14 where x represents the number of months since the store opens the doors and r(x) is measured in hundreds of dollars.

He has also found that his expenses each month can be modeled by c(x)=x²−3x+4 where x represents the number of months the store has been open and c(x) is measured in hundreds of dollars.

(r−c)(x) = x²+5x+14 -x²+3x-4

(r−c)(x) = 8x+10

(r−c)(3) = 24+10 = 34 in hundreds of dollars.

Therefore, the new store has profit of $3400.

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System components in mathematics involves the study of equations and their solutions, shapes and their properties, rate of change and area under a curve, angles and their relationships, and the properties of numbers.

1. Algebra: This is the study of equations and their solutions, as well as the manipulation of symbols and operations.

2. geometry: This involves the study of shapes and the properties of space, such as angles and distances.

3. Calculus: This involves understanding the rate of change of a function and the area under a curve.

4. Trigonometry: This involves the study of angles and their relationships to one another and to other types of measurements.

5. Number Theory: This involves the study of the properties of numbers, such as divisibility, primes, and multiplicative functions.

System components in mathematics involves the study of equations and their solutions, shapes and their properties, rate of change and area under a curve, angles and their relationships, and the properties of numbers.

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Answers to all the questions form 1 to 10 are illustrated below.

The circumference of a circle is the distance around the circle which is 2πr.

The diameter of a circle is the largest chord that passes through the center of a circle it is 2r.

We know the angle formed at the center of a circle is twice the angle formed at the circumference.

Answering each one in short.

1. x = 136/2 = 68°.

2. x = 146/2 = 73°.

3. x = 2×49 = 98°.

4. x = 2×62° = 124°.

5. As m∠O = 100°, x = 100/2 = 50°.

6. m∠O = 360 - 100 - 150 = 110°, x = 110/2 = 55°.

We know the angle formed by the same chords at the circumference is equal in measure.

7 . x = 18°.

8. x = 27°.

9. x = 180 - 55 - 90 = 35°.

10. x = 180 - 12 - 91 = 77°.

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If sixteen teams compete, the winner will be decided after 15 games.

Since there are 16 teams and each team is playing with some of the other, there are 16/2 =8 pairs

Out of each pair only one team will move on.

So, there are 8 teams left after the first round.

These 8 teams pair up to have 8/2 =4 pairings

Continuing this process, we get the total number of games played to determine the winner is,

8+4+2+1=15

Each game's losing team gets eliminated from the tournament. If sixteen teams participate, the winner will be decided after 15 games.

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The airspeed of each plane if 2 hours after the first plane departs the planes are 3200 kilometers apart.

speed of the first plane=1040km/hour

speed of the second plane=1120km/hour

Two planes start from Los Angeles International Airport and fly in opposite directions. The second plane starts 1 hour after the first plane, but its speed is 80 kilometers per hour faster. Find the airspeed of each plane if 2 hours after the first plane departs the planes are 3200 kilometers apart.

Make a system to solve.

let x=speed of the first plane

x+80=speed of the second plane

distance=speed*travel time

travel time of first plane=2 hour

travel time of second plane=1 hour

2x+1(x+80)=3200

2x+1x+80=3200

3x=3120

x=1040

x+80=1120

The airspeed of each plane if 2 hours after the first plane departs the planes are 3200 kilometers apart.

speed of the first plane=1040km/hour

speed of the second plane=1120km/hour

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Answer: total cost of an international call with a duration of 10 minutes is 5.70 dollars.

Step-by-step explanation:

The expression 2.20 +0.35x represents the total cost of an international call in dollars, as a function of the duration x in minutes.

It is composed of two parts:

The first part, 2.20$, represents the fixed cost of making an international call. This cost does not change regardless of the duration of the call.

The second part, 0.35x$, represents the variable cost of the call, which is based on the duration of the call in minutes. This cost increases with the duration of the call.

When x=10, it means the duration of the call is 10 minutes, so the variable cost of the call would be 0.35*10 = 3.5$

Therefore, the total cost of the international call with a duration of 10 minutes is 2.20 + 3.5 = 5.7$

It's important to notice that this equation represents the total cost of the call not just the variable cost, but also the fixed cost.

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The match from the simplified answer are;

1. 3x³ + 2x + 10

2. 2x² - 4x + 7

3. 3x³ -6x² - 2x + 7

4. 7x³ + 6x² -4x + 7

Algebraic expressions are described as expression that is composed of factors, constants, variables, terms and coefficients.

These algebraic expressions are also composed of mathematical operations, such as;

From the information given, we have that;

(3x³ + 10x² + 2x) - (10x² + 7x - 10)

expand the bracket

3x³ + 2x + 10

(7x² -12x + 4) - (5x² - 8x -3)

expand the bracket

2x² - 4x + 7

(5x³ - 3x + 7) - (2x³ + 6x² -x )

expand the bracket

3x³ -6x² - 2x + 7

(5x³ -3x + 7) +(2x³ +6x² - x)

expand the bracket

7x³ + 6x² -4x + 7

Hence, the expressions are 3x³ + 2x + 10, 2x² - 4x + 7, 3x³ -6x² - 2x + 7 and 7x³ + 6x² -4x + 7

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Answer:

isjsjdjejejrjebdkxn nsksksnenmdnxee nu pot snndnsnenenene

Answer:

it would be the 3rd one I did this in middle school

Step-by-step explanation:

pls give brainly if It's right

Answer:

22

Step-by-step explanation:

All sides of a rhombus are congruent.

[tex]11w=w+20 \\ \\ 10w=20 \\ \\ w=2 \\ \\ \implies VW=2(11)=22[/tex]

The  718.85 < x inequality says that : He must print 719 photos or more.

Inequality:

In mathematics, an inequality is a relationship in which two numbers or other mathematical expressions compare unequal. Most commonly used to compare two numbers on the number line based on size. There are several notations used to represent various types of inequalities.

Given,

In the question:

Rick bought a photo printer and supplies for $186. 90, which will allow him to print photos for $0. 29 each.

and, A photo store charges $0. 55 to print each photo.

To find the how many photos must Rick print before his total cost is less than getting prints made at the photo store?

Now,

According to the question:

Let the photos be x

Rick bought a photo printer be $186.90

A photo store charges $0. 55 to print each photo.

The question is based on inequality:

Photo Printer <  photo store

1.86.90 + 0.29x <  0.55x

            - 0.29x     - 0.29x

______________________

           1.86.90    < 0.26x

Divide by 0.26x on both sides = 718.85 < x

Hence, The  718.85 < x inequality says that : He must print 719 photos or more.

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Answer:

600,000

Step-by-step explanation:

The mathematical concept demonstrated in this question is the process of exponential growth. Exponential growth demonstrates an increase in quantity by a percentage or factor over time. It is represented by the general formula [tex]f(x) = a(1+r)^{x}[/tex] where a is the initial amount, r is the growth rate, and x is the time interval expressed as an integer.

For this problem, we can see that the initial population of the town is 345,000, and it increases by a rate of 20% each year. We can determine that the growth rate is 20% because 1 + r = 1.2, so r must be equal to .20 (or 20%). We are given that t = 3, so we can plug that value in to the function given.

We calculate the population in 3 years to be 596,160. This can be approximated to 600,000.

Each side of the playground is 10[tex]\sqrt{2}[/tex] m.

We know that in a square,

                               d = [tex]\sqrt{2}[/tex] a

            where, d = diagonal of the square

                         a = side of the square

Now, according to the question the walkway forms a diagonal and is 20 meters long.

  So, d = 20 m

        a = ?

          d = [tex]\sqrt{2}[/tex] a

        20 =   [tex]\sqrt{2}[/tex] a

          a  =  20/ [tex]\sqrt{2}[/tex]

              =  [tex]\frac{10\sqrt{2}*\sqrt{2} }{\sqrt{2}}[/tex]

              = [tex]10\sqrt{2}[/tex]

Hence, the side of the playground is [tex]10\sqrt{2}[/tex] meters long.

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Answer:

Step-by-step explanation:

Cross multiply

(2x + 6 + 2x)/(x² + 3x) = 1

(4x + 6) = x² + 3x

x² - x - 6 = 0

x² - 3x + 2x - 6 = 0

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

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

x = -2,3

Jaidee's printing company LLC has 8 of Model A and 5 of Model B press, respectively.

We can find each type of press with the help of the substitution method.

Let Model A = x presses

Model B = y presses

According to the question, the company owns 13 total printing presses, then

x + y = 13

x = 13 - y

Also, according to the question

80x + 30y = 790

Put the value of x = 13 - y in the above equation

80(13 - y) + 30y = 790

1040 - 80y + 30y = 790

1040 - 790  = 80y - 30y

50y = 250

y = 250/50 = 5

Now, put the value of y in x = 13 - y

x = 13 - 5

x = 8

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Answer:  x(2 - xy² - y - y²)

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

                             y²

Step-by-step explanation:

Please give brainliest

x(2 - xy² - y - y²)/y² is the answer

Answer:

(I'm not exactly sure which way you wanted it, so see the answers below!)

Step-by-step explanation:

The area of trapezoid ABCD is 98 square units.

Based on the data given, The area of  ΔDBA  = area of  ΔADE  + area of ΔABE  = 20 + 50  = 70. So  

area of Δ DBA  = 0.5 sin DBA (AB x DB)  = 70

sin DBA = 140 / ( AB x DB)

sin DBA = sin CDB

The area of  ΔCDB  would be 0.5 sin (DBA) (DB x DC)  

The area of  ΔCDB = 0.5 (140 / [(AB x DB] ) (DB x DC)

The area of  ΔCDB = 70 (DC/AB)  = 70 ( DE /BE)

The area of ΔAEB  would be 0.5 sin AEB ( AE * BE)

The area of ΔAEB = 50  (1)

Area Δ ADE  would be 0.5 sin DEA (AE * DE)  

Area Δ ADE  = 20  (2)

Because of  angle AEB  is  supplemental to angle DEA, their sines are equal. So  

sin AEB  = sin DEA

Let rearranging (1), (2). So we will have

sin AEB  =   sin DEA

100 / [ AE * BE] = 40 / [ AE * DE ]

DE / BE  = 40/100  = 2/5

Since area of ΔCDB  equal to  70 (DE / BE) then

ΔCDB = 70 (2/5)  =  28

So...area of trapezoid ABCD  = area of ΔDBA  + area of ΔCDB  

area of trapezoid ABCD =  70 + 28 = 98  

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Answer:-20

Step-by-step explanation:

On solving the provided question, we can say that the value of the function is f(x) =  => f(x) = vf(x,y) = (x² + y²) = (x² + y²),

The subject of mathematics includes quantities and their variations, equations and related structures, shapes and their locations, and places where they can be found. The term "function" refers to the relationship between a set of inputs, each of which has an associated output. A connection between inputs and outputs in which each input leads to a single, distinct result is known as a function. Each function is given a domain and a codomain, or scope. Usually, f is used to denote functions (x). input is an x. There are four main types of functions accessible. based on the following factors: on functions, one-to-one functions, many-to-one functions, inside functions, and on functions.

here, the function is f(x) =

f(x) =

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Answer:

Let's call the number we're trying to find "x".

We know that 35% of x is 77, so we can set up the equation:

0.35x = 77

We also know that 90% of x is 198, so we can set up another equation:

0.9x = 198

We can use the first equation to find the value of x and then substitute that value into the second equation to find 55% of x.

To find x, we divide both sides of the first equation by 0.35:

x = 77 / 0.35 = 220

Now that we know x is 220, we can find 55% of x by multiplying 220 by 0.55:

0.55x = 220 * 0.55 = 121

So 55% of the number is 121.

Answer:

121

Step-by-step explanation:

Because one of the answers is already divisible by 10, allowing us to find 100% of the unknown number, we can first find 10% by dividing the 90% number by 9. 198/9 is 22, meaning 22 is 10% of the number. We can then multiply it by 10 to get 100%, 22(10)=220. Meaning our full number is 220

From here we can simply multiply by our desired percentage, which is 55%. In order to multiply by a percent, you have you divide the percent by 100 to get .55. From there you can do 220*.55= 121. Meaning our answer is 121.

The area of the surface is  S = [tex]\frac{-4}{15}(-1+8\sqrt{2}-9\sqrt{3} )[/tex]

Now, According to the question:

The given equation is:

[tex]z = \frac{2}{3}(x^\frac{3}{2}+y^\frac{3}{2} )[/tex],

0 ≤ x ≤ 1 , 0 ≤ y ≤ 1

Let's know:

Surface Area:

To surface area of a solid E, defined by z = f(x , y) can be found by integrating[tex]\int\limits \int\limits_R \sqrt{(z_x)^2+(z_y)^2+1},dA[/tex] where R is the rectangular region

[0,1] × [0, 1] and [tex]z_x,z_y[/tex] corresponds to the partials of z w.r.t x and y.

Now,

[tex]\sqrt{(z_x)^2+(z_y)^2+1}[/tex] = [tex]\sqrt{1+(\sqrt{x} )^2+(\sqrt{y} )^2}[/tex] = [tex]\sqrt{1+x+y}[/tex]

S = [tex]\int\limits \int\limits_R \sqrt{(z_x)^2+(z_y)^2+1},dA[/tex]

  = [tex]\int\limits^1_0\int\limits^1_0 \sqrt{x+y+1}dy dx[/tex]

  [Integrate with respect to y ]

    =  [tex]\int\limits^1_0 (\frac{2}{3}(x + y + 1)^\frac{3}{2} )|^1_0 dx[/tex]                        

  = [tex]\int\limits^1_0 (\frac{2}{3}(x + (1) + 1)^\frac{3}{2}-\frac{2}{3}(x + (0) + 1)^\frac{3}{2} )dx[/tex]

 = [tex]\int\limits^1_0 ((\frac{2}{3}(x +2)^\frac{3}{2} ) - (\frac{2}{3}(x +1)^\frac{3}{2} ) , dx[/tex]

  =  [tex]\int\limits^1_0 (\frac{2}{3}((x +2)^\frac{3}{2} - (x +1)^\frac{3}{2} )) , dx[/tex]

  [Integrate with respect to x ]

   = [tex]\frac{2}{3} (\frac{2}{5}(x + 2)^\frac{5}{2} - \frac{2}{5}(x +1)^\frac{5}{2} )|^1_0[/tex]

    = [tex]\frac{2}{3}(\frac{2}{5}((1)+2 )^\frac{5}{2}-\frac{2}{5}((1)+1)^\frac{5}{2})-\frac{2}{3}(\frac{2}{5}((0)+2 )^\frac{5}{2} -\frac{2}{5}((0)+1)^\frac{5}{2}[/tex]

    = [tex]\frac{2}{3}(\frac{18\sqrt{3}}{5} -\frac{8\sqrt{2} }{5} )-\frac{2}{3} (\frac{8\sqrt{2} }{5} -\frac{2}{5} )[/tex]

     = [tex]\frac{-4}{15}(-1+8\sqrt{2}-9\sqrt{3} )[/tex]

Hence, The area of the surface is  S = [tex]\frac{-4}{15}(-1+8\sqrt{2}-9\sqrt{3} )[/tex]

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John has 5 red balls and 8 blue balls. What is the ratio of red balls to blue balls? Answer: The ratio of red balls to blue balls is 5:8.

We can solve this problem by using a ratio. Ratios are two values that are compared to each other. In this case, we need to compare the number of red balls to the number of blue balls. We are given that there are 5 red balls and 8 blue balls. To find the ratio, we need to write the numbers as a fraction. The fraction for red balls is 5/8 and the fraction for blue balls is 8/5. We can then simplify the fractions to get the ratio of 5:8. This means that there is a ratio of 5 red balls to 8 blue balls.

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Answer:

410cm^3

Step-by-step explanation:

The Volume of the upper rectangular prism is 10x3x8 which is 240

The volume of the middle prism is 6x5x3 which is 90

And the volume of the bottom prism is 8x2x5 which is 80

If you add them all up, the total volume is 410

Note(The volume of a rectangular prism is base x height x width)

Answer:

See attachment.

Step-by-step explanation:

If CD and MB are parallel, triangle CDE is similar to triangle MBE.

In similar triangles, corresponding sides are always in the same ratio.

[tex]\implies \sf CD:MB=DE:BE=EC:EM[/tex]

From inspection of the given diagram, EM is approximately 0.35 times the length of EC.  Therefore, let EC = 10 and EM = 3.5.

The sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

Therefore, let CD = 7 and let DE = 12.

Substitute these values into the created ratio equation:

[tex]\implies \sf 7:MB=12:BE=10:3.5[/tex]

[tex]\implies \sf \dfrac{7}{MB}=\dfrac{12}{BE}=\dfrac{10}{3.5}[/tex]

Calculate BE:

[tex]\implies \sf \dfrac{12}{BE}=\dfrac{10}{3.5}[/tex]

[tex]\implies \sf \dfrac{12 \cdot 3.5}{10}=BE[/tex]

[tex]\implies \sf BE=4.2[/tex]

Calculate MB:

[tex]\implies \sf \dfrac{7}{MB}=\dfrac{10}{3.5}[/tex]

[tex]\implies \sf \dfrac{7 \cdot 3.5}{10}=MB[/tex]

[tex]\implies \sf MB=2.45[/tex]

Therefore:

[tex]\implies \sf CM=EC-EM[/tex]

[tex]\implies \sf CM=10-3.5[/tex]

[tex]\implies \sf CM=6.5[/tex]

[tex]\implies \sf DB=DE-BE[/tex]

[tex]\implies \sf DB=12-4.2[/tex]

[tex]\implies \sf DB=7.8[/tex]

The absolute value is also called a modulus.

The absolute value (or modulus) | x | of a real number x is the non-negative value of x without regard to its sign, also describes the distance from zero that a number is on the number line, without considering direction.

It is represented as |a|, which defines the magnitude of any integer ‘a’.

Absolute value is a term used in mathematics to indicate the distance of a point or number from the origin (zero point) of a number line or coordinate system.

it defines removing any negative sign in front of a number and thinking of all numbers as positive.

When x itself is negative (x<0), then its absolute value is necessarily positive

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With substitution, you need to solve one of the equations for one of the unknown variables and substitute that value into one of the other equations, then solve for the remaining unknown variable.

To solve a 3 equation problem, you can use elimination or substitution. With elimination, you need to add or subtract the equations to eliminate one of the unknown variables. With substitution, you need to solve one of the equations for one of the unknown variables and then substitute that value into one of the other equations. You can then solve for the remaining unknown variable.

To solve a 3 equation problem, you can use elimination or substitution methods. With elimination, you need to add or subtract the equations to eliminate one of the unknown variables. With substitution, you need to solve one of the equations for one of the unknown variables and substitute that value into one of the other equations, then solve for the remaining unknown variable.

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Graphs, tables and equations that  can be used to find the ratio and the ratio is not constant when the relationship is non-proportional  explanation is given below

let us consider the , The graph of a linear equation is a line.

then , If b = 0 in a linear equation (so y = mx), then the equation is said to be proportional linear relationship between y and x.

If b ≠ 0, then y = mx + b is said to be  non-proportional linear relationship between y and x.

If we are able to draw a straight line through all three points and the line that passes through the origin, (0, 0), in an  ordered pairs which  represents a proportional relationship. in which the Solution to the points on the graph that  represent a proportional relationship. Such that the ordered pairs in the table represent a proportional relationship .Non-Proportional: How to tell the difference: A proportional graph is a straight line that always goes through the origin. A non-proportional graph is a straight line that does not go through the origin. As that of  adjectives the difference between proportional and  which is equal to  that proportional is at a constant ratio (to) two magnitudes (numbers) are said to be proportional if the second graph  varies in a direct relation arithmetically , the first while equal which is (label) the same as  in all respects.

The Difference in the  Proportional and linear functions are almost identical in their representation  form. The only difference is the addition of the “​b​” as constant to the linear function. Indeed, which is  a proportional relationship to a linear relationship where ​b​ = 0, or also said in an another way, in which the  line passes through the origin (0, 0).

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