EASY POINTS, PLEASE HELP ASAP, WILL MARK FIRST ANSWER BRAINLESIT,

restaurant at the food court in a mall is offering a lunch special. The table shows the relationship between the number of side dishes and the total cost of the special.


Restaurant
Number of Side Dishes Total Cost
2 $8.50
4 $11.50
5 $13.00
8 $17.50


Which of the following graphs shows the relationship given in the table?

EASY POINTS, PLEASE HELP ASAP, WILL MARK FIRST ANSWER BRAINLESIT,restaurant At The Food Court In A Mall
EASY POINTS, PLEASE HELP ASAP, WILL MARK FIRST ANSWER BRAINLESIT,restaurant At The Food Court In A Mall
EASY POINTS, PLEASE HELP ASAP, WILL MARK FIRST ANSWER BRAINLESIT,restaurant At The Food Court In A Mall
EASY POINTS, PLEASE HELP ASAP, WILL MARK FIRST ANSWER BRAINLESIT,restaurant At The Food Court In A Mall

Answers

Answer 1

Answer: The last graph

Step-by-step explanation:

i did the test on flvs .

Answer 2

The last graph shows the relationship given in the table

What is Slope of Line?

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

Slope = 11.50-8.5/4-2

=1.5

Let us take a point (5, 13), let us check this point which correctly matches the graph

Hence, the last graph shows the relationship given in the table

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Related Questions

¿cuánto ganaría un accionista que tiene 100 acciones, si cada acción que él compró aumenta de $20. 00 a $30. 00?

Answers

Assuming 100 transactions, the investor will receive $1,000.

Explicación paso a paso:

The difference between the values of each action represents the gain or loss of each action; if this difference decreases, a loss would be apparent.

Gain = Increase in each action times the number of actions

Capital of the Acionista in Acciones = Cantidad of Acciones * Acción Value

If each share the investor purchased rises from $20 to $30

$30 - $20 = $10 profit per action

Assuming 100 transactions, the investor will receive $1,000.

100* $10 = $100

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The question is:

How much money would a shareholder with 100 shares make if each one grew in value from $20 to $30?

if the maximum value of the function y=cos x/sin x is at x = pi/4 , what is the value of m?

Answers

The maximum value of the function y=cos x/sin x at x = pi/4 is 1, so the value of m is 1.

The maximum value of the function y=cos x/sin x is when the cos x and sin x terms have the same magnitude. This happens when x=pi/4. In this case, the function reduces to y=cos(pi/4)/sin(pi/4) = 1.

Therefore, the value of m = 1.

The maximum value of the function y=cos x/sin x at x = pi/4 is 1, so the value of m is 1.

The function y=cos x/sin x has a maximum value of 1 when x = pi/4. This is because when x = pi/4, the cos x and sin x terms have the same magnitude, and the function reduces to y=cos(pi/4)/sin(pi/4) = 1. Therefore, the maximum value of the function y=cos x/sin x is 1, and the value of m is 1. This result holds true for any value of x, and is a useful tool when working with trigonometric functions.

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differentiate the function. f(z) = ez/(z − 7)

Answers

The derivative of f(z) = ez/(z − 7) is therefore f'(z) = (ez(z - 6))/(z - 7)^2.

The derivative of f(z) = ez/(z − 7) can be calculated using the quotient rule. The quotient rule states that the derivative of the quotient of two functions is equal to the denominator times the derivative of the numerator minus the numerator times the derivative of the denominator, all divided by the denominator squared. Therefore, the derivative of f(z) = ez/(z − 7) is equal to (ez(z - 7) - (ez)(1))/(z - 7)^2. This simplifies to ez/(z - 7)^2. Therefore, the derivative of f(z) = ez/(z − 7) is equal to ez/(z - 7)^2.

For our purposes, we can substitute in g(z) = ez and h(z) = (z − 7). Then, we can calculate the derivatives of each part. The derivative of g(z) is g'(z) = ez, and the derivative of h(z) is h'(z) = 1. Now, we can plug these values into the Quotient Rule and calculate the derivative of the function f(z) = ez/(z − 7).

f'(z) = (ez(z − 7) - ez(1))/(z − 7)^2

f'(z) = (ez(z - 6))/(z - 7)^2

The derivative of f(z) = ez/(z − 7) is therefore f'(z) = (ez(z - 6))/(z - 7)^2.

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Redraw the triangle with sides that are 1/3 as long as the sides of the original 15 m 9 m Original 12 m a Calculate the perimeters of BOTH triangles. Perimeter (P = s + s + s) of original Perimeter of new A b. Calculate the areas of BOTH triangles. Area (A= 1 2 b^ * h) of original Area of new A . What is the relationship between the perimeters of the triangles?

Answers

The new triangle has sides of 3m, 4m, and 5m as the attached picture below.

The perimeter of the original triangle is 36 and the new triangle is 12. The area of the original triangle is 54 and the new one is 6The new triangle's perimeter is a third of the original's perimeter, which represents the ratio of both triangles

The new triangle has sides of 1/3 of the original. Then:

1/3 x 15 m = 5m

1/3 x 9 m = 3 m

1/3 x 12 m = 4 m

The new triangle is as the attached picture below

The perimeter of the original triangle is:

P original = 15 + 9 + 12

P original = 36 m

The perimeter of the new triangle is:

P new = 5 + 3 + 4

P new =  12 m

The area of the original triangle is:

Area original = 1/2 x 12 x 9

Area original = 54 m

The area of the new triangle is:

Area new = 1/2 x 4 x 3

Area new = 6

The relationship between both triangles' perimeter is:

P original : P new = 36 : 12

                             = 3 : 1 --> ratio of both triangles

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Use guess and check to find an anti-derivative
F(x)
for
f(x)=sin(x)cos(x)
. Explain why you chose particular guesses, and how you checked them.

Answers

When finding an antiderivative using the method of guess and check, it is important to use a guess that is based on the original function and the rules of differentiation.

One approach to finding an antiderivative of a function is the method of guess and check. This involves making an educated guess for the antiderivative and then verifying it by taking the derivative of the guess and comparing it to the original function.

To find the antiderivative of f(x) = sin(x)cos(x), we can start with a guess based on the product rule for differentiation: d/dx (uv) = u * dv/dx + v * du/dx

Since f(x) = sin(x)cos(x), we can write: d/dx (sin(x)cos(x)) = cos^2(x) + sin^2(x) = 1

This suggests that the antiderivative of f(x) = sin(x)cos(x) might be: F(x) = sin(x)sin(x) + C, where C is an arbitrary constant of integration.

To check our guess, we need to take the derivative of F(x) and compare it to the original function f(x): d/dx (sin(x)sin(x) + C) = cos(x)sin(x)

If our guess is correct, the derivative of F(x) should equal f(x). However, in this case, our guess does not match the original function f(x), so we need to make another guess. A second guess could be:

F(x) = -cos(x)cos(x) + C

Taking the derivative: d/dx (-cos(x)cos(x) + C) = -sin(x)cos(x)

This time, the derivative of F(x) does match the original function f(x), so our guess is correct and the antiderivative of f(x) = sin(x)cos(x) is:

F(x) = -cos(x)cos(x) + C.

Thus, In conclusion, when finding an antiderivative using the method of guess and check, it is important to use a guess that is based on the original function and the rules of differentiation. By checking the derivative of the guess and comparing it to the original function, we can determine whether or not our guess is correct.

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Pls Help will give brainlyest (15 pts)

Answers

Answer:

r ≥2,  r<0

Step-by-step explanation:

1st blank:

1. Multiply both sides by 2

2. Simplify. 7r-20≥ -6

2nd blank:

1. multiply both sides by 2 to get (2(r+14))/2 < 7*2.

2. Simplify. You should get r+14 <14

3. Subtract 14 from both sides to isolate r.

4. Answer is r<0

How many ways can 3 baseball players and 5 basketball players be selected from 12 baseball players and 12 basketball players ?

Answers

Many ways can 3 baseball players and 5 basketball players be selected from 12 baseball players and 12 basketball players are 173040 ways.

This is a combination problem, and we want to find the number of ways to choose 3 baseball players and 5 basketball players from a pool of 12 baseball players and 12 basketball players.

The formula for combinations is: C(n, k) = n! / (k! (n - k)!).

For the baseball players, n = 12 and k = 3, so C(12, 3) = 12! / (3! (12 - 3)!) = 12! / (3! 9!) = 220.For the basketball players, n = 12 and k = 5, so C(12, 5) = 12! / (5! (12 - 5)!) = 12! / (5! 7!) = 792.

The total number of combinations is the product of the number of combinations for each group, so 220 * 792 = 173040.

Therefore, there are 173040 ways to choose 3 baseball players and 5 basketball players from a pool of 12 baseball players and 12 basketball players.

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How many inches is 5 3 height?

Answers

Height is 63 inches, or 5 3 inches.

Explain about the inches?

A measurement of distance or length in US units. A foot is 12 inches long and a yard is 36 inches long. 2.54 cm are exactly one inch.

A measurement of 1 inch is about equivalent to 2.54 cm. Add 2.54 cm to the provided inch number to convert it to centimetre values. 0.393701 inches are equal to 1 centimetre.

The smallest length you can measure with a ruler is 1/16 inch since each inch is divided into 16 lines, each of which is 1/16 inch long.

If you don't have a measuring device around, use the top of your thumb or another item that is roughly the same length to estimate measurements in inches. A foot is made up of 12 inches.

   = (5 x 12) + 3.

   = 60 +3

     = 63

   You now have 63 inches altogether.

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What kind of transformation is the function h(n) = 2(0. 8)n from the original function, h(n) = 10(0. 8)n?


A a vertical compression

B a vertical stretch and reflection

C a vertical stretch

D a vertical compression and reflection

Answers

The transformation of h(n) = 2(0.8)n from the original function, h(n) = 10(0.8)n, is a vertical compression.

Hence, option (a) is correct choice.

In a vertical compression, the graph of the transformed function is obtained by multiplying the y-coordinates of the points on the graph of the original function by a constant factor less than 1.

In this case, the factor is 2/10 = 1/5, which is less than 1, so the transformation is a vertical compression.

It is not a vertical stretch and reflection because the factor is less than 1, so it is not stretching the graph.

It is not a vertical stretch because the factor is less than 1, so it is not stretching the graph.

It is not a vertical compression and reflection because the factor is positive, so it is not reflecting the graph.

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Suki typed 245 words in 3 1/2 minutes. Find the following unit rates. Write the answer as a simplified

fraction and do not forget UNITS. (Decimal answers will not be accepted. )

a. How many words per minute?

b. How many minutes per word?

Answers

A. Suki typed 175/7 words per minute. B. It takes Suki 7/490 minutes per word.

A. To find the number of words per minute, we can divide the total number of words by the total time:

words per minute = 245 words / (3 1/2 minutes)

words per minute = 245 words / (7/2 minutes)

words per minute = 245 * 2 / 7 words/minute

words per minute = 175/7 words/minute

So, Suki typed 175/7 words per minute.

B. To find the number of minutes per word, we can divide the total time by the total number of words:

minutes per word = (3 1/2 minutes) / 245 words

minutes per word = (7/2 minutes) / 245 words

minutes per word = 7/2 * 1/245 minutes/word

minutes per word = 7/490 minutes/word

So, it takes Suki 7/490 minutes to type one word.

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3 1/2 minutes at 245 words per minute.

245 syllables per minute / 7 and a half minutes.

syllables per minute are calculated as 245 * 2/7.

175/7 words per minute is the word speed.

Suki's typing speed was 175/7 lines per minute.

hours per word equals (3 1/2 hours) / 245 words

syllables per minute = (7/2 minutes) / 245

minutes per word equals 7/2 * 0.245 minutes per word.

words/minute ≈ 7/490 minutes/word

When angle of elevation of the Sum is 45°, the shadow of a coconut tree is 15 m in length. What is the height of the coconut tree?

Answers

When the angle of elevation of the Sun is 45° and the shadow of a coconut tree is 15 m in length, the height of the coconut tree is 15 meters.

We have,

Denote the height of the coconut tree as AB.

A right triangle is formed by the coconut tree, its shadow, and the line connecting the top of the tree to the tip of the shadow.

From the figure,

tan(45°) = AB / 15

tan 45 = 1

So,

1 = AB / 15

Therefore,

The height of the coconut tree is 15 meters.

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Goran buys candy that costs $8 per pound. He will spend at least $56 on candy. What are the possible numbers of pounds he will buy?
Use P for the number of pounds Goran will buy.
Write your answer as an inequality solved for p.

Answers

The inequality is written as 8p ≤ 56. Then the number of pounds of candy will be 7 pounds.

What is inequality?

Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.

Goran buys candy that costs $8 per pound. He will spend at least $56 on candy.

Let 'p' be the number of pounds of the candy. Then the inequality is given as,

8p ≤ 56

p ≤ 56 / 8

p ≤ 7

The inequality is written as 8p ≤ 56. Then the number of pounds of candy will be 7 pounds.

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what is 9 minus 9 divided by 9 plus 9 minus 9 divided by 9

Answers

the answer is 16 i used pemdas
The answer is sixteen(:

Samantha is making bows. Each bow is made from a piece of ribbon that is 1\2 yards long. How much ribbon would she need to make 19 bows?

Answers

Answer:

9.5

Step-by-step explanation:

She would need 9.5 yards of ribbon to make 19 bows, since 1/2 * 19 = 9.5

A sequence can be generated by using an=4an−1, where a1=7 and n is a whole number greater than 1.

What are the first 3 terms in the sequence?

4, 28, 196
7, 28, 112
4, 11, 18
7, 11, 15

Answers

Answer: 7, 28, 112

Step-by-step explanation: The first three terms in the sequence can be found by using the formula an = 4an-1, starting with the initial value a1 = 7:

a2 = 4a1 = 4 * 7 = 28

a3 = 4a2 = 4 * 28 = 112

So, the first three terms in the sequence are 7, 28, 112.

Able, Baker, and Charlie are the only three stocks in an index. The stocks sell for $37, $312, and $94, respectively. If Able undergoes a 3-for-4 reverse stock split, what is the new divisor?

Answers

In order to calculate the new divisor for a 3-for-4 reverse stock split, we must first calculate the new share price for Able. Since 3/4 of the shares are being replaced with just 1/4 of the old shares, the new price for Able will be $111 (3 x $37 = $111).

The divisor is used to calculate the new index value by dividing the sum of the new share prices by the divisor. Therefore, the new divisor will be 1.33 ($111 + $312 + $94 = $517 / 1.33 = $389.28). This is because the new share prices will total $517 and when you divide that by the divisor, the index value will be $389.28.

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How do you guess the limit of (7n^3 +8n) / (2n^3 - 31) and prove that your guess is correct using the ε-N approach?

Answers

By using the ε-N approach, the value of the function is 2.71828.

The ε-N approach is a mathematical tool used to determine the limit of a function as the independent variable approaches infinity or zero.

In this problem, we are asked to guess the limit of

=> (7n³ +8n) / (2n³ - 31)

as n approaches infinity.

To do this, we need to use the ε-N approach. The first step is to make an educated guess about the limit.

Next, we use the ε-N approach to prove our guess is correct.

This involves finding an ε (epsilon) value, which is a small positive number, and an N value, which is the input value for n, such that for all n greater than N, the absolute value of the difference between the function and the limit is less than ε.

To use various symbols to denote the Epsilon values too because Epsilon has no interest in the meaning of its own like other mathematical symbols like π(pi) and it has the value 3.14.

Here the symbol e and has value 2.71828.

This means that the function is arbitrarily close to the limit.

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if x represents quantity and y represents the quantity which of the tables below represnt a direct proportion

Answers

If I put a quantity and y represents

Cameron baked two pans of brownies for the school bake sale. She couldn't wait and ended up eating 1/6 of a pan. How many brownies does she have left

Answers

Cameron is left with 11/6 of a pan by using mathematical operation known as subtraction.

Given,

Total number of brownies = 2 pans

Cameron ate = 1/6 of a pan

In this question we will be using mathematical operation known as subtraction.

Subtraction is an arithmetic operation that involves finding the difference between two numbers. In other words, it is the process of removing a quantity from another. It is a fundamental mathematical concept that is widely used in everyday life, from calculating the change from a purchase to determining the difference between two quantities. Subtraction can be performed with whole numbers, decimals, fractions, and even with negative numbers. In all cases, the process of subtraction involves aligning the numbers to be subtracted, either vertically or horizontally, and then subtracting the smaller quantity from the larger one.

Brownies left = 2 pans - 1/6 of pan

                      = 12/6 -1/6

                      = 11/6 pan

Hence, she is left with 11/6 of a pan to eat.

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approximate the sum of the series correct to four decimal places. [infinity] (−1)n 2nn! n = 1 s ≈

Answers

The sum of the series correct to four decimal places is 7.0000

To approximate the sum of the series, we can use the ratio test. The ratio test states that if the limit of the ratio of consecutive terms approaches a number L, then the series converges if |L| < 1 and diverges if |L| > 1.

The nth term of the series is given by

[tex]T_n = (-1)^n (3n)(n!)[/tex]

The consecutive terms is

[tex]R_n = T_{n+1}/T_n = (-1)^{n+1} (3n+3)(n+1) / (-1)^n (3n)(n!) \\= (-1)^{n+1} * 3 * (n+1) / (n!)[/tex]

Taking the limit as n approaches infinity:

[tex]L = lim_{n - > \infty} \ R_n = lim_{n - > \infty} (-1)^{n+1} * 3 * (n+1) / (n!)[/tex]

Since [tex](-1)^{n+1}[/tex] alternates between -1 and 1, the limit approaches 0 and |L| < 1, which means the series converges.

To approximate the sum of the series, we can use a numerical method such as the Euler-Maclaurin formula. The formula approximates the sum of an infinite series by the sum of its first few terms and the remainder term:

[tex]\Sigma_n^\infty=1T_n \approx \Sigma_{i=1}^m T_i + R_m[/tex]

where [tex]R_m[/tex] is the remainder term that decreases as m increases

For example, let's choose m = 5:

[tex]\Sigma_{i=1}^5 T_i = T_1 + T_2 + T_3 + T_4 + T_5[/tex]

= -3! + (-1) * 3 * 2! + (-1) * 2 * 3 * 1! + (-1) * 3 * 4! + (-1) * 4 * 3 * 2! = -6 + 6 - 2 + 24 - 24 = -2

The remainder term [tex]R_m[/tex] can be estimated using the Euler-Maclaurin formula:

[tex]R_m = -B_{2m} / (2m)! * T_{m+1}[/tex]

where B_k are the Bernoulli numbers.

For [tex]m = 5, B_2m = B_{10} = -1/252[/tex], so

[tex]R_m = -B_{10} / (10)! * T_{m+1} = -1/252 * (-1)^6 * 3 * 6! = 1/252 * 3 * 720 = 9[/tex]

Therefore, the sum of the series is approximately

[tex]\Sigma_{i=1}^\Infty T_i \approx \Sigma_{i=1}^5 \ T_i + R_m \\= -2 + 9 = 7[/tex]

To four decimal places, this is 7.0000

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predict the sign of δsol for the solution

Answers

The sign of δsol for the solution will depend on the concentration of the solute and the temperature.

The sign of δsol for the solution will depend on two main factors: the concentration of the solute and the temperature. If the concentration of the solute is increased, the solute's tendency to dissolve in a solvent will also increase, resulting in a higher solubility. This increase in solubility will cause the sign of δsol to be positive. On the other hand, if the temperature is increased, the solubility of the solute will decrease, resulting in a decrease in the solubility. This decrease in solubility will cause the sign of δsol to be negative. Therefore, the sign of δsol for the solution will depend on the concentrations of the solute and the temperature. If the concentration of the solute is increasing, the sign of δsol will be positive; if the temperature is increasing, the sign of δsol will be negative.

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which type of chart makes this most apparent

Answers

A bar chart is the best type of chart to visualize the comparison of values over a period of time. It is easy to read and makes it easier to compare and contrast each value. The bars make it easy to see the changes in values over time.

A bar chart would make this most apparent.

A bar chart is the best type of chart to visually represent the comparison of values over a period of time. It is simple to read, and makes it easier to compare and contrast each value.

A bar chart is the best type of chart to visualize the comparison of values over a period of time. It is easy to read and makes it easier to compare and contrast each value. The bars make it easy to see the changes in values over time.

A bar chart is the best type of chart to visually represent the comparison of values over a period of time. It is simple to read, and makes it easier to compare and contrast each value.

A bar chart is the best type of chart to visualize the comparison of values over a period of time. It is easy to read and makes it easier to compare and contrast each value. The bars make it easy to see the changes in values over time.

the complete question is :

Which type of chart makes it most apparent that one group has a significantly higher value than the other?

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Combine like term (combine the poitive term and combine the negative term). 18-6-155-91

Answers

The combined like terms are -234.

Combining like terms means adding or subtracting any expressions that have the same variable. For example, in the expression:

2x + 3x

The terms 2x and 3x have the same variable (x), so they can be combined to form 5x.

Similarly, in the expression:

4y - 7y

The terms 4y and -7y have the same variable (y), so they can be combined to form -3y. The goal of combining like terms is to simplify expressions and make them easier to understand and manipulate.

In this case, the first two terms, 18 and -6, have no variable, so they can be combined to form 12. The next two terms, -155 and -91, also have no variable, so they can be combined to form -246. Finally, the combined terms, 12 and -246, can be combined to form -234. So, the final result is:

18 - 6 - 155 - 91 = -234.

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A truck that is 10 ft. by 12 ft. by 14 ft. carries cube shaped boxes that
have a length of 2.5 ft. How many of these boxes can this truck hold?
Round your answer to the nearest whole number.
*10

Answers

Answer:

108

Step-by-step explanation:

The volume of the truck is 10*12*14=1680

So, answer = the volume of the truck / the volume of a cube

answer= 1680/15.625=107.52 = 108.

The set of 6 dining chairs together cost $1845.00. The 6 chairs were sold to make a profit of 100%. How much was the selling price of the 6 chairs?​

Answers

The selling price of the 6 dining chairs is $3690

What is an equation?

An equation is an expression showing the relationship between two or more numbers and variables. An equation can either be linear, quadratic, cubic and so on depending on the degree.

6 dining chairs together cost $1845.00. The chairs were sold to get a profit of 100%. Let x represent the selling price

The formula needed is:

Profit = [(selling price - cost price)/cost price] * 100%

Hence, substituting:

100% = [(x - 1845]/1845] * 100%

(x - 1845]/1845 = 1

x - 1845 = 1845

x = 3690

The selling price is $3690

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use the chain rule of differentiation to find the derivative with respect to t of g(t)=cos(ωt) .

Answers

the integral by substituting the limits of integration for x and y and integrating with respect to x first. We get: ∫∫ df(x,y)dxdy = ∫-2 to 2 x2(1x2- 2x2)dx = ∫-2 to 2 x2(-x2)dx = ∫-2 to 2 -x4dx = [-x5/5]from -2 to 2 = -2^5/5 + 2^5/5 = 0

a. The region D in the x-y plane is illustrated in the figure below.

b. ∫∫ df(x,y)dxdy = ∫-2 to 2 ∫2x2 to 1x2 x2(y)dxdy = ∫-2 to 2 x2(1x2-2x2)dx = ∫-2 to 2 x2(-x2)dx = ∫-2 to 2 -x4dx = [-x5/5]from -2 to 2 = -2^5/5 + 2^5/5 = 0

a. The region D in the x-y plane is the area bounded by the two parabolas y= 2x2 and y= 1 x2. This can be seen in the sketch below.

b. To evaluate the integral ∫∫ df(x,y)dxdy, we need to evaluate the integral of the function f(x,y) = x2y over the region D. We can do this by setting up the integral as follows:

∫∫ df(x,y)dxdy = ∫-2 to 2 ∫2x2 to 1x2 x2(y)dxdy

Next, we can evaluate the integral by substituting the limits of integration for x and y and integrating with respect to x first. We get:

∫∫ df(x,y)dxdy = ∫-2 to 2 x2(1x2-2x2)dx = ∫-2 to 2 x2(-x2)dx = ∫-2 to 2 -x4dx = [-x5/5]from -2 to 2 = -2^5/5 + 2^5/5 = 0

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6.

Parallelogram ABCD has coordinates A(1,5), B(6,3), C(3,-1), and D(-2,1).

What are the coordinates of E, the intersections of diagonals AC and BD?

a (4. 5,1)

b (2,2)

c (3. 5, 2)

d (-1,3)


help with this please

Answers

The coordinates of E, the intersections of diagonals AC and BD is; B: (2, 2)

How to find the coordinates of the diagonals?

A parallelogram is simply defined as a quadrilateral with two pairs of parallel sides.

Now, the diagonals of a parallelogram usually intersect at their midpoints. Formula to find the midpoint of a line with coordinates is;

Midpoint = (x2 + x1)/2, (y2 + y1)/2

Thus;

Midpoint of AC = ((1 + 3)/2, (5 - 1)/2

= (2, 2)

Similarly,

Midpoint of BD = (6 - 2)/2, (3 + 1)/2

= (2, 2)

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Find an equation for the surface consisting of all points p for which the distance from p to the x-axis is 4 times the distance from p to the yz-plane.

Answers

The equation that represents the distance is -25x² + y² + z² = 0

What is an Equation in Math?An expression, often known as a mathematical expression, is a finite collection of symbols that are well-formed in accordance with context-dependent principles. A mathematical statement called an equation demonstrates the equality of two mathematical expressions.Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.In mathematics, an equation is a relationship between two expressions that is expressed as an equality on each side of the equal to sign. An equation would be 3y = 16, for instance.Equations can be divided into the three categories of linear equations, quadratic equations, and cubic equations depending on their degree.

Given data :

The distance between two points, is the number of units between them.

The equation that represents the distance is -25x² + y² + z² = 0

The distance between a point and the x-axis is represented as:

D = ( y² + x² ) [tex]\frac{1}{2}[/tex]

From the question, we have:

D = 5x

Equate both expressions for D

5x =- ( y²  + z² ) [tex]\frac{1}{2}[/tex]

Square both sides

25x² =  y² + z²

Equate to 0

y² + z² - 25x² = 0

Rewrite as:

-25x² + y² + z² = 0

Hence, the equation that represents the distance is -25x² + y² + z² = 0

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What is the volume of the following rectangular prism? Volume ==equals units^3 3 cubed

Answers

Answer:

To find volume of rectangular prism you must find the length, width, and height!

Step-by-step explanation:

Volume = (Width) (height) (length)

Volume= Width x height x Length

you must multiple the length, width, and height together to get VOLUME:)

HOPE THIS HELPS :)

Determine the sum of the solutions to:

Answers

For the quadratic equation 5x² - 16x + 3 = 0, the sum of solutions is 3.02.

What is a quadratic function?

A polynomial function with one or more variables, where the largest exponent of the variable is two, is referred to as a quadratic function. It is also known as the polynomial of degree 2 since the greatest degree term in a quadratic function is of second degree.

The quadratic expression is given as -

5x² - 16x + 3 = 0

The expression is written in the form  ax² + bx + c

Where a = 5, b = -16 and c = 3

Use the quadratic formula -

x = [-b ± √(b² - 4ac)] / 2a

Substitute the values into the formula -

x = [-(-16) ± √{(-16)² - 4(5)(3)}] / 2(5)

x = [16 ± √{256 - 60}] / 10

x = [16 ± √196] / 10

x = [16 + √196] / 10 and x = [16 - √196] / 10

x = [16 + 14] / 10 and x = [16 - 14] / 10

x = 30/10 and x = 2/10

x = 3 and x = 0.2

The solutions are x = 3 and x = 0.2.

The sum of solutions are = 3 + 0.2 = 3.02

Also, the formula for sum of solutions for a quadratic equation is -b/a.

Sum of solutions = -(-16) / 5

Sum of solutions = 16 / 5

Sum of solutions = 3.02

Therefore, the sum of solutions is 3.02.

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Complete question:

Determine the sum of the solutions to:

5x² - 16x + 3 = 0

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