let and let have critical numbers -2, 0, and 2. use the second derivative test to determine which critical numbers, if any, give a relative maximum

Answer:

= -10g - 5 + 7h

Step-by-step explanation:

= -7g +3 - 8 - 3g + 7h

Grouping of like terms

= -7g -3g + 3 - 8 +7h

= -10g - 5 + 7h.

y = -2/3x + 4 is an equation in slope-intercept form that could be the second equation in the system.

simultaneous equations, a system of equations Two or more equations in algebra must be solved jointly (i.e., the solution must satisfy all the equations in the system). The number of equations must match the number of unknowns for a system to have a singular solution.

There are four methods for solving systems of equations: graphing, substitution, elimination, and matrices.

Given, The solution of a system of equations is (3,2). One of the solutions in the system is 2x + 3y = 12.

From the general formula of Slope intercept form:

y = mx + c

where,

m = slope

c = y-intercept of the equation

Thus in our case,

2x + 3y = 12

=> 3y = -2x + 12

=> y = -2/3x + 4

thus, the Slope of the line = -2/3

and another coordinate (0, 4)

Therefore,  an equation in slope-intercept form that could be the second equation in the system is y = -2/3x + 4.

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The maximum area of a triangle with a base and height of 10 cm is 50 cm^2. The dimensions for this would be a base of 5 cm and a height of 5 cm.

1. The area of a triangle is calculated by taking the base multiplied by the height, then dividing by 2.

2. Since the sum of the base and the height of the triangle is 10 cm, the base and the height must be equal.

3. Therefore, the base and the height are both 5 cm, and the area of the triangle is (5 cm * 5 cm) / 2, which equals to 50 cm^2.

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The interval over which the function is continuous equation is (-∞, 3) U (3, +∞).

The function f(x) = (x2 - 5x - 6)/(x - 3) is continuous over all real numbers except x = 3, since the denominator is equal to 0 at x = 3.

We can use the properties of combinations of continuous functions to determine the interval(s) over which the function f(x) is continuous equation.

First, we need to consider the function f(x) in two parts. The first part is f(x) when x ≠ 3, and the second part is when x = 3.

For the first part, when x ≠ 3, the function f(x) is continuous over all real numbers, since both the numerator and denominator are continuous over all real numbers.

For the second part, when x = 3, the function f(x) is discontinuous, since the denominator is equal to 0.

Therefore, the interval over which the function f(x) is continuous is (-∞, 3) U (3, +∞).

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Using the formula for the average value between two numbers, we will see that bag B weighs 11.9 kg

If we have two values x and y, the average value between these two is given by the formula below.

average = (x + y)/2

Here we know that the average between the wheights of bags A and B is 6.4 kg, and A = 0.9kg

Then we can write the equation:

6.4kg = (B + 0.9kg)/2

We can solve that equation for B to get:

2*6.4kg = B + 0.9kg

12.8kg - 0.9kg = B

11.9kg = B

Bag B weighs 11.9 kilograms.

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The dimensions of the rectangular prism would be (1,8,9), (2,5,7), and (3,4,6).

What is a rectangular prism?

A rectangular prism is a solid geometric shape that has three mutually perpendicular rectangular faces, and is also known as a rectangular parallelepiped or a box. It has six faces, eight vertices, and twelve edges.

The shape is defined by three dimensions: length, width and height, and is specified by the three sets of parallel and mutually perpendicular edges that form its six faces. The opposite faces of a rectangular prism are equal in area and parallel to each other. The opposite edges are also parallel and equal in length.

You can’t get a perfect match, but you can get pretty close, with dimensions of (1,8,9), (2,5,7), (3,4,6)

Hence, the dimensions of the rectangular prism would be (1,8,9), (2,5,7), and (3,4,6).

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The third side is represented by the inequality 7 < x < 43, where x is the third side.

When you know two sides of a triangle, you can calculate the range for the third side.

Let x would be the third side.

First, since 25 - 18 = 7, the third leg must be greater than 13. Otherwise, the two smaller legs would not be able to connect to form the third leg.

Second, if we combine 18 with 25 and get 63, the third leg must be smaller than 69. Otherwise, the third leg would be able to reach further than the previous two legs.

This means 7 < x < 43.

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The required total income generated by planting corn in 2008 is the amount of $1917.85.

The function is defined as a mathematical expression that defines a relationship between one variable and another variable.

The yield of corn on Mr. Geller's farm since 2001 can be modeled by the function N(t) = 10t + 88.5

Let's find the amount of corn produced in 2008:

N(7) = 10 x 7 + 88.5 = 158.5 (kilograms)

Next, let's find the price of corn in 2008:

P(7) = 81 - 10 x 7 + 1.1 = 12.1 ($/kilogram)

Finally, we can multiply the amount of corn by the price per kilogram to find the total income:

158.5 x 12.1 = 1917.85

Rounding to the nearest cent, the total income generated by planting corn in 2008 is $1917.85.

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Answer:

Step-by-step explanation:

we have a right triangle, therefore with an angle of 90° (red sign) and an angle of 40°, knowing that the sum of the interior angles of all triangles is 180° we remove the known angles from 180° and find the value of angle "?"

180 - 90 - 40 =

50°

A specific example of a non-representative sample can be seen in the 2016 US presidential election.

The national polls indicated that Hilary Clinton had a lead in the polls, but Donald Trump went on to win the election. This is because the sample used in the polls was not representative of the population. The sample was disproportionately composed of college-educated individuals, when the actual electorate was more evenly balanced between college-educated and non-college-educated individuals. This caused the samples to be biased and not representative of the population.

For example, if we assume that the population is composed of 50% college-educated individuals and 50% non-college-educated individuals, then the sample should also be composed of 50% college-educated individuals and 50% non-college-educated individuals to be representative. If the sample is not composed of 50% college-educated individuals and 50% non-college-educated individuals, then the sample is not representative of the population.

This can be calculated by using the formula: (Number of College Educated Individuals in Sample/Total Sample Size) X 100.

For example, if the sample size is 100 and there are 75 college-educated individuals in the sample, then the sample is not representative of the population because (75/100) X 100 = 75%, which is not equal to the 50% of the population that is college-educated.

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the set of all z ∈ (-3,1) such that neither 2+z nor 2-3z is in the interval (-1,2].

Interval Notation is a way of expressing a subset of real numbers by the numbers that bound them. We can use this notation to represent inequalities.

the set of all z such that neither 2+z nor 2-3z is in the interval (-1,2].

here, we shall assume two cases,

case first.

z > -1,

2+z > -1

z > -1 -2

z > -3

and,

2-3z > -1

-3z > -3

z > 1

z belongs to ( -3 , 1)

case 2nd,

z<=2

2+z < = 2

z <= 2-2

z ≤ 0

and 2-3z ≤ 2

-3z ≤ 0

z ≤ 0

z is less than equal to 0

So, by above conditions

z belongs to (-3,1).

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the value of theta in the given complex expression is equal to 16°.

Given, a number. [tex]rcis\theta, is[/tex] expressed by.

cis75° + cis83° + cis91°+.... + cis147°.

we have to find the value of angle in degrees.

The function cisA is a shorthand way of writing the equivalent expression cisA=cosA+i sinA

By definition: CisA=CosA+iSinA

This form simplifies complex arithmetic and allows for the study of complex analysis, as well as reduces the workload in writing the expressions.

now, we have to find the sum of the given expressions.

[tex]cis75+cis83+cis91+...+cis147 as, cis\theta=e^{i\theta}[/tex]

[tex]e^{75i}+e^{83i}+e^{91}+....+e^{147i}\\\\e^{\frac{75\pi}{180} }+e^{\frac{83\pi}{180} }+.....+e^{\frac{147\pi}{180} }[/tex]

on using geometric sum of the series we get,

[tex]Sum=\frac{e^{\frac{75i\pi}{180}}(1-e^{\frac{72i\pi}{180} ) }}{(1-e^{\frac{8i\pi}{180} })}\\ \\\theta=16[/tex]

the value of theta of the angle be 16 degree.

the complete question is.

The number cis 75 + cis 83 + cis91 +...+ cis 147 is expressed in the form r cis(theta), where 0 <= theta < 360.

Find theta in degrees.

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The equation of cost of each ticket is 11k = 231 and the exact cost of each ticket is $21.

What is algebraic expression ?

Algebraic expression can be defined as the combination of variables and constants .

Given,

Kathleen spent $231 on concert tickets for herself and 11 friends. Each ticket cost the same.

So we have to find the cost of each ticket. Write an equation to show your work and the exact cost of each ticket. Compare your answer to your estimate to check for reasonableness.

From the given information ,

The equation to show the work could be ,

231 = k * 11

SO, this is the equation 11k = 231 .

we can say that,

= $231 / 11

= $21

Hence, the equation of  cost of each ticket is 11k = 231 and the exact cost of each ticket is $21

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Answer:0.3

Step-by-step explanation:

answer my question next please its about zara sells apples one

Answer:3/10

Step-by-step explanation: 4x3 is 12 and 4x10 is 40, so 12/40, the GCF of these numbers are 4 so 12/4=3 and 40/4= 10

So 3/10

The Institute of Medicine compared the United States to comparable high-income countries in terms of  various health outcomes.

The findings revealed that the United States had lower rates of birth outcomes than other countries (including infant and maternal mortality). The US also  life expectancy than most other countries, as well as more years lost to alcohol and drug use. Lastly, the US had lower rates of adolescent pregnancy than most other countries.

The Institute of Medicine also calculated the health gap between the US and other countries, which was defined as the difference between the health outcomes of the US and the health outcomes of the other countries. This gap was calculated by subtracting the US health outcome rate from the average of the other countries' health outcome rates. For example, to calculate the infant mortality gap, the infant mortality rate in the US (5.8 deaths per 1,000 live births in 2018) was subtracted from the average infant mortality rate of the other countries (3.5 deaths per 1,000 live births). This resulted in a health gap of 2.3 deaths per 1,000 live births.

Overall, the Institute of Medicine's comparison revealed that the US was lagging behind other countries in terms of various health outcomes.

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An inequality which represents the value of t for which the water temperature is still safe is t ≤ 2 and it has been plotted in the graph attached below.

In order to write, solve, and graph an inequality that represents the value of t for which the water temperature is still safe, we would take note of the following important information;

Now, we can write an inequality that represents the value of t for which the water temperature is still safe as follows;

102 + t ≤ 104

By subtracting 102 from both sides of the inequality, we have the following:

102 - 102 + t ≤ 104 - 102

t ≤ 2

Next, we would use an online graphing calculator to graph the above inequality as shown in the image attached below.

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The general statement for the previous question is that if a homogeneous system of equations has at least one non-zero solution, then it has infinitely many solutions, which can be found by taking multiples of the non-zero solution.

(a) (i)

Let p = (1,3,4) and q = (5,8,12) be two points in R3. The line joining p and q can be written as lq + (1-\p) where l is a real number. By substituting in the coordinates of p and q, we get l(5,8,12) + (1-\1,3,4) = (l + 1-\, l+3-\, l+4-\). This is the equation for the line joining p and q, where l can be any real number.

(ii)

To check that all points on the line joining p and q are also solutions to the system of linear equations, we substitute the equation of the line into the system of equations.

01111 + 212.22 + 213.43 = 21

(l + 1-\) + 2(l+3-\) + 3(l+4-\) = 21

Simplifying, this gives: l + 6 - \ = 21. Therefore, all points on the line joining p and q are solutions to the system.

(b)

To check that any multiple of p, i.e., a vector of the form (1,3,4) where is any real number, is also a solution of the system, we substitute the equation of the multiple of p into the system.

01111 + 212.22 + 213.23 = 0

(l + 1-\) + 2(l+3-\) + 3(l+4-\) = 0

Simplifying, this gives: l + 6 - \ = 0. Therefore, all multiples of p are solutions to the system.

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The most appropriate time-series plot will depend on the data being visualized. The title, axes labels, and scale should all be chosen to accurately describe the data and provide the clearest understanding of the data.

The most appropriate time-series plot for a particular dataset will depend on the data being visualized. The title, axes labels, and scale should all be chosen carefully to accurately describe the data and provide the clearest understanding of the data. For example, for a time series of stock prices, the title could be "Stock Price Over Time", the axes could be labeled "Time" and "Price", and the scale could range from the lowest to the highest stock price. Additionally, the time intervals should be appropriately labeled, such as monthly, quarterly, or annually. It is important to choose the right type of plot to ensure that the data is accurately and clearly represented.

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The complete question is

which of the following time-series plots is the most appropriate? hint: pay close attention to the title, axes labels, and scale should all be chosen to accurately.

Step-by-step explanation:

that's so easy just learn it times

Due to weaker aggregate demand, the negative demand shock will cause the aggregate demand curve to move to the left.

Result: A lower output and price level.

Part B:

Explanation of part B

Result of negative supply shock , aggregate demand falls cause the lower demand for the money . This will lead towards the left shift in money demand.(MD 1 TO MD 2(R1 TO R2)

Part c:

Interest rate and bond price are related inversely . Due to negative demand shock the interest rate falls down. vice-versa bond price will rise.

Part D:

Due to fall in the interest rate central banks will follow contractionary fiscal policy which will increase interest rate and reduce the money supply.

Part E :

If the central banks need to increase the money supply by $80 billion. Central banks need to buy securities in exchange of cash .This will Raise the money supply.

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The total distance traveled by the particle over 5 units of time is 140 units.

What is the total distance?

To find the total distance a particle travels over a certain time interval, we need to find the definite integral of its velocity function over that interval. The velocity function is the derivative of the position function.

In this case, the position function of the particle is x(t) = t³ - 6t + 9t - 2 and we need to find the total distance traveled by the particle over 5 units of time.

The velocity function is x'(t) = 3t² - 6 + 9 = 3t² + 3

The total distance traveled over 5 units of time is the definite integral of the velocity function evaluated between 0 and 5.

∫(3t²+3) dt from 0 to 5

= [t³ + 3t] from 0 to 5

= (5³ + 3*5) - (0 + 0) = 125 + 15 = 140

The total distance traveled by the particle over 5 units of time is 140 units.

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In the given oblique triangle , the required value of c using cosine rule is given by c = 34.4.

As given in the question,

In the given oblique triangle ABC,

a = 12 feet

b = 30 feet

∠A = 20°

Let us consider in triangle side opposite to angle A, B, and C are a, b, and c respectively.

Using cosine rule we have,

a² = c² + b² - 2cbcos A

Substitute the values we get,

⇒ 12² = c² + 30² - 2(c )(30) cos 20°

⇒ 144 = c² + 900 - 60c ( 0.9396)

⇒ c² -56.376c + 900 - 144 = 0

⇒ c² -56.376c +756 = 0

using quadratic formula :

c = [ ( 56.376) ± √56.376² -4(1)(756) ]/ 2

  =  [ 56.376 ± 12.42 ] / 2

  =  (56.38 + 12.42) / 2 or (56.38 - 12.42) / 2

  = 34.4 or 21.98

Correct value is c = 34.4

Therefore, using the cosine rule the required values c of the triangle is equal to 34.4 .

The above question is incomplete, the complete question is :

One of the cases for the known measures of an oblique triangle is given. In triangle ABC, where a = 12 feet, b = 30 feet, and A = 20°. State whether the Law of Cosines can be used to solve the third side of the triangle .

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The area of the figure/geometric shape U will be 15 yard^2.

What are geometric shapes in mathematics?

In Mathematics, Geometric shapes are the figures which demonstrate the shape of the objects we see in our everyday life. In geometry, shapes are the forms of objects which have boundary lines, angles and surfaces. There are different types of 2d shapes and 3d shapes.

Shapes are also classified with respect to their regularity or uniformity. A regular shape is usually symmetrical such as a square, circle, etc. Irregular shapes are asymmetrical. They are also called freeform shapes or organic shapes. For example, the shape of a tree is irregular or organic.

In plane geometry, the two-dimensional shapes are flat shapes and closed figures such as circles, squares, rectangles, rhombus, etc.  In solid geometry, the three-dimensional shapes are cube, cuboid, cone, sphere and cylinder. We can observe all these shapes in our daily existence also. For example books (cuboid shape), glasses (cylindrical shape), traffic cones (conical shape) and so on.

Now

As the scale factor for similar shapes V and U is 5:1.

Then their area should also be in same ratio.

Given Area of V=75 square yard

Therefore,

                Area of U=75/5

                 Area of U =15 square yard

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The TRUE statements about the inequality y ≤ 150x - 3100 are:

Inequality refers to a mathematical statement claiming the inequality of two or more mathematical expressions.

The following types and inequality symbols represent inequalities:

Check:

Ordered pairs (40, 2900)

y ≤ 150x - 3100

y ≤ 150(40) - 3100

y ≤ 6,000 - 3100

y ≤ 2900

Thus, the true statements about this inequality are Options A and E.

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The rate at which shadow is decreasing On a morning of a day when the sun will pass directly overhead, the shadow of an 80-ft building on level ground is 60 ft long and is 10.4 inches per minute.

Given,

Height of the building, [tex]h[/tex] = 80 ft = 960 inches

Length of shadow, [tex]x[/tex] = 60 ft = 720 inches

The angle that the sun makes with the ground is increasing,

[tex]\frac{d\theta}{dt} = 0.27[/tex] degree [tex]= \frac{3\pi }{2000} rad/min[/tex]

[tex]tan\theta = \frac{960}{x} \\\frac{d }{dy} tan\theta = \frac{d}{dy} \frac{960}{x} \\sec^{2}\theta \frac{d\theta }{dt} = -\frac{960}{x^{2} } \\\\\frac{dx}{dt} = \frac{(60^{2})(\frac{5}{3})^{2} }{960} \\\\\\\frac{dx}{dt} = 10.4 inches /min[/tex]

Hence, the shadow is decreasing at a rate of 10.4 inches per minute.

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Answer:

D

Step-by-step explanation:

because

( 5 + 2 + 1 ) is (x + y + z)

The correct option is C for the frequency table.

A table that depicts the frequency of occurrence of a given characteristic according to a specified set of class intervals.

The correct two-way frequency table for the date will look like this:

                                               RAP      ROCK     COUNTRY     TOTAL

Grades 9-10             40           30            55                  125

Grades 11-12            60           25            35                  120

TOTAL                    100          55            90                  245

The sum of the row total is equal to the sum of the column total

125 + 120 = 100 + 55 + 90

245 = 245

The correct option for the frequency table is C.

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The smallest amount of rotation about a vertex from one ray to the other can be calculated by subtracting the sum of the two ray measures from 180°.

The smallest amount of rotation about a vertex from one ray to the other can be calculated using the formula θ = 180° - (α + β), where θ is the measure of the angle of rotation, α and β are the measures of the two rays that are connected by the vertex. The amount of rotation between two rays is measured in degrees, which is equal to the angle between the two rays. The formula used to calculate the amount of rotation is the arctangent of the ratio of the difference in the y-coordinates to the difference in the x-coordinates. For example, if the two rays have measures of 90° and 30°, the smallest amount of rotation from one ray to the other would be 60°. This can be calculated by taking 180° - (90° + 30°) = 180° - 120° = 60°. In conclusion, the smallest amount of rotation about a vertex from one ray to the other can be calculated by subtracting the sum of the two ray measures from 180°.

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Answer:

-2

Step-by-step explanation:

y = −2− x 2 y = - 2 - x 2

Answer:

[tex]24x^{2}y^2[/tex]

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{5cm} \underline{Binomial Theorem}\\\\$\displaystyle (a+b)^n=\sum^{n}_{k=0}\binom{n}{k} a^{n-k}b^{k}$\\\\\\where \displaystyle \binom{n}{k} = \frac{n!}{k!(n-k)!}\\\end{minipage}}[/tex]

We can use the Binomial Theorem to find any term of a binomial expansion.  

The first term is when k = 0, so the third term is when k = 2.

Compare the given expression (x + 2y)⁴ with the formula to find the values of a, b and n.  

Therefore:

Substitute the values into the formula to find the third term:

[tex]\implies \displaystyle\binom{4}{2}x^{4-2}(2y)^2[/tex]

[tex]\implies \dfrac{4!}{2!(4-2)!}x^{2}2^2y^2[/tex]

[tex]\implies \dfrac{4 \times 3\times \diagup\!\!\!\!2\times \diagup\!\!\!\!1}{2\times 1\times \diagup\!\!\!\!2\times \diagup\!\!\!\!1}\;x^{2}4y^2[/tex]

[tex]\implies \dfrac{12}{2}\:x^24y^2[/tex]

[tex]\implies 6x^{2}4y^2[/tex]

[tex]\implies 24x^{2}y^2[/tex]