A rectangle is bounded by the x- and y-axes and the graph of y= (6 - x)/2 (see figure). What length (x) and width (y) should the rectangle have so that its area is a maximum?​

Start at -2 on the number line and move 7 to the left.

A number line is a visual representation of the real numbers as a straight line. It is a useful tool for understanding and comparing numbers, as well as for performing operations on them.

The number line is typically drawn horizontally, with zero in the center and positive numbers to the right of zero and negative numbers to the left of zero. The distance between any two points on the number line represents the difference between the corresponding numbers.

The number line is also commonly used for representing fractions, decimals, and irrational numbers. For example, fractions can be represented as points on the number line by dividing the line into equal segments, with each segment representing one unit fraction. Decimals can be represented as points on the number line by marking off the appropriate place value.

In addition to basic arithmetic operations such as addition, subtraction, multiplication, and division, the number line can be used to perform more advanced operations such as finding absolute value, calculating distance between two points, and solving linear equations.

Overall, the number line is a powerful visual tool that helps to deepen our understanding of the real numbers and their relationships.

Start at -2 on the number line and move 7 to the left.

To know more about fraction visit:

https://brainly.com/question/17658856

#SPJ1

The complete question is:

Answer:

Yes

Step-by-step explanation:

we all know there is 60 minutes in an hour. So in order to answer this question we need to know the percentage of 15 to 60 which is really really just 15/60=0.25 so Henry's answer is correct:
6.25 Hours are 6 hours and 15 minutes

and 0.25 really is just a quarter because 4 x 0.25 = 1 so in fraction it is 1/4 so Jenny is also correct on :

6 1/4 hours are 6 hours and 15 minutes

Answer:

To translate triangle ABC 3 units up, we need to add 3 to the y-coordinate of each vertex:

A = (-3, 3 + 3) = (-3, 6)

B = (0, 7 + 3) = (0, 10)

C = (-3, 0 + 3) = (-3, 3)

Therefore, the coordinates of the vertices for the image triangle A'B'C' are A(-3, 6), B'(0, 10), and C(-3, 3).

So the correct answer is: A(−3, 6), B(0, 10), C(−3, 3).

The most precise description of quadrilateral ABCD is a square.

We have,

Quadrilateral ABCD.

We see that,

AB is parallel to CD

AB = CD _____(1)

AD is parallel to BC.

AD = BC _____(2)

Now,

AB = AD ______(30

From (1), (2), and (3).

AB = BC = CD = AD

This means,

The Quadrilateral ABCD is a square.

Thus,

The most precise description of quadrilateral ABCD is a square.

Learn more about squares here:

https://brainly.com/question/22964077

#SPJ1

A sampling distribution is a frequency distribution using the means computed from all possible random samples of a specific size taken from a population.

To get the possible samples, use the formula "N choose n", where N is the population size, and n is the sample size to be taken. The total probability of the sample mean must be equal to 1.

Since the mean of all possible samples must be equal to the population mean. The sampling distribution is an important concept in statistics as it allows us to make inferences about the population based on the characteristics of the sample, and helps us estimate parameters and test hypotheses.

To learn more about frequency distribution here:

https://brainly.com/question/14926605

#SPJ1

the third term of the expansion of (11x+3y)⁶ is 798,720x³y³.we can use the binomial theorem to solve this .

what is  binomial theorem ?

The binomial theorem is a theorem in algebra that describes the algebraic expansion of powers of a binomial. A binomial is a polynomial with two terms, such as (a + b) or (x - y).

In the given question,

To find the third term of the expansion of (11x+3y)⁶, we can use the binomial theorem, which states that:

(a + b)ⁿ = C(n,0)aⁿb⁰ + C(n,1)*aⁿ⁻¹*b¹+ C(n,2)*aⁿ⁻¹*b² + ... + C(n,n)a⁰bⁿ

where C(n,k) denotes the binomial coefficient, which is the number of ways to choose k items from a set of n items.

In this case, we have a = 11x and b = 3y, and n = 6. We want to find the third term, which corresponds to k = 3 in the expansion. Therefore, we need to compute the binomial coefficient C(6,3), as well as the powers of 11x and 3y that appear in the third term.

The binomial coefficient C(6,3) can be computed as follows:

C(6,3) = 6! / (3! * (6-3)!) = 20

To find the powers of 11x and 3y that appear in the third term, we need to look at the general pattern in the expansion. Each term in the expansion consists of a product of powers of a and b, with the powers of a decreasing by 1 from n to 0, and the powers of b increasing by 1 from 0 to n. Therefore, the kth term in the expansion will have powers of a and b given by aⁿ⁻ᵇand bᵃ, respectively.

In the third term, we have k = 3, so we need to find the coefficient of a³ = a³ = (11x)³ and b³ = (3y)³. The third term is given by:

C(6,3)(11x)³(3y)³

Plugging in the values for C(6,3), (11x)³, and (3y)³, we get:

20*(11x)³*(3y)³ = 2011³x³3³y³ = 798,720x³y³

Therefore, the third term of the expansion of (11x+3y)⁶ is 798,720x³y³.

To know more about binomial theorem, visit:

https://brainly.com/question/26406618

#SPJ1

The given input-output relation is a nonlinear function of the input signal x(t), since it involves squaring the signal at every point in time. A linear system must satisfy the property of superposition, which states that the output to a linear combination of inputs must be the same as the linear combination of the outputs to each individual input.

To determine whether the system is time-invariant, we need to check if a time shift in the input signal produces the same time shift in the output signal. That is, if: [tex]y(t) = T{x(t)}[/tex] for all values of t. Then we want to check [tex]y(t - τ) = T{x(t - τ)}[/tex] for all values of [tex]τ[/tex] and [tex]t[/tex].

We shall the consider the case where [tex]τ > 0[/tex], then we have:

[tex]y(t - τ) = (x(t - τ))^2[/tex]

[tex]T{x(t - τ)} = (x(t - τ))^2[/tex]

Since [tex]y(t - τ) = T{x(t - τ)}[/tex], we can conclude that the given system is time-invariant.

Therefore, the given system is nonlinear but time-invariant.

Answer:

60 seconds

Step-by-step explanation:

Let's start by finding how much more water needs to be added to the solution to reach a total of 10 ml of water:

10 ml - 5.8 ml = 4.2 ml

Now we can use the formula:

time = amount of water added / rate of addition

to calculate the time it will take to add 4.2 ml of water at a rate of 0.07 ml/s:

time = 4.2 ml / 0.07 ml/s

time = 60 seconds (rounded to the nearest second)

Therefore, it will take 60 seconds to add enough water to the solution to make a total of 10 ml of water.

Can you mark me asbrainliest if you appreciate my effort just for favor. Thank you^^

The result of adding -3 (row 1) to row 2 is determined as (0  10) |-14.

The result of the row multiplication in the matrix is calculated by applying the following method;

row 1 in the given matrix = [1  -4] | 8

To multiply row1 by -3, we will multiply each entity by -3 as shown below;

= -3(1  -4) | 8

= (-3  12) | -24

To add the result to 3;

(-3  12) | -24  +  (3   -2)|10

= (0  10) |-14

Thus, the result of the row multiplication is determined by multiplying each entry in row 1, by - 3.

Learn more about row multiplication here: brainly.com/question/31531585

#SPJ1

 The third player hit 4 more home runs than the first player. The algebraic expression that shows the relationship between a and b is:  a = 3b. So option A is correct

A linear equation in one variable is an equation that has only one variable. It is of the form Ax B = 0, where A and B are  two real numbers and x is an unknown variable with only one solution. For example, 9x + 78 = 18 is a linear equation in one variable.

 2) Each player's home runs are labeled A, B, C, and D, where A is the first baseman, B is the second baseman, C is the third baseman, and D is the shortstop. We know this:

C = 2B (the third player hit twice as many home runs as the second player)

C/B = D/B = A/C (numbers for first baseman and shortstop are proportional to numbers for third baseman and second baseman)

B = D 4 (second baseman hit 4 more home runs than  shortstop)

To solve for the values ​​of A, B, C, and D, we can use the second equation to write:

C/B = D/B

C = D (multiply both sides by B)

C = B - 4 (using the fourth equation to substitute  D)

2B = B - 4 (using the first equation to substitute  C)

B = 4 (interface to both sides 4)

C = 8 (using the first equation to find C)

D = 4 (using the fourth equation to find D)

A = C/2 = 4 (use another equation to find A)

Therefore the third player (C) hit 8 home runs and the first player (A) hit 4 home runs, so the third player hit 4 more home runs than the first player.

3) The relative relationship between a and b can be expressed as follows:

a/b = 6/2 = 3/1

To write this relationship as an algebraic equation, we can cross multiply to get:

a = 3b

Therefore, the algebraic expression that shows the relationship between a and b is:

a = 3b. So option A is correct

Learn more about  linear equation here

https://brainly.com/question/11897796

#SPJ1

Answer:

40

Step-by-step explanation:

Hope this helps! =D

Brainliest! =D

a) Jill receives £45

b) Jack receives £20 the following Christmas

c) Jack will be 5/4 years old, which is equivalent to 1 year and 3 months when he receives £25 from Uncle Fred.

Explain the term years

Years are a unit of time measurement used to quantify the duration of one complete orbit of the Earth around the sun. A year consists of 365 days, except in a leap year when an extra day is added. The concept of a year is used in various fields, including astronomy, geology, and history.

According to the given information

(a) Let's first find the total ratio of their ages:

1 + 3 = 4

So Jack's share will be:

1/4 x £60 = £15

And Jill's share will be:

3/4 x £60 = £45

Therefore, Jill receives £45.

(b) The next Christmas, Jack will be 2 and Jill will be 4. We can use the same ratio to find Jack's share:

2/6 x £60 = £20

So Jack receives £20.

(c) Let x be the age of Jack when he receives £25 from Uncle Fred. We know that:

1/4 x £60 = £25

Multiplying both sides by 4/60, we get:x = 5/4

So Jack will be 5/4 years old, which is equivalent to 1 year and 3 months, when he receives £25 from Uncle Fred.

To know more about years visit

brainly.com/question/14510285

#SPJ1

Answer:

Part a 6 and 9

Step-by-step explanation:

Part B is 7.3 because u just find the sq root of 54 which can't go down the easiest is finding the decimal form

The answer is Option 2: The measure of angle 5 is corresponding to angle 1. Angle 1 is supplementary to 86. So, measure angle 1 = 94. Since corresponding angles are equal angle 5 = 94.

An angle that, when combined with another angle, creates a straight angle (measuring 180 degrees), is known as a supplementary angle. In other words, if the sum of the measurements of two angles is 180 degrees, they are supplementary. Contrarily, a complimentary angle is one that, when combined with another angle, creates a right angle (which has a 90-degree angle). In other words, if the sum of the measurements of two angles is 90 degrees, they are complimentary. A straight angle and a right angle are not the same thing, hence it is crucial to understand that one angle cannot be both supplementary and complimentary at the same time.

From the given figure we see that the measure of angle 5 is corresponding to angle 1. Angle 1 is supplementary to 86. So, measure angle 1 = 94. Since corresponding angles are equal angle 5 = 94.

Hence, option 2 is correct.

Learn more about supplementary angle here:

https://brainly.com/question/13045673

#SPJ1

The complete question is:

From the circle graph of the survey, 52 more people prefer pigs than chickens.

A sort of data visualisation tool used to depict data as a circular chart is a circle graph, commonly referred to as a pie chart. Each slice of the circle graph, also known as a sector, represents a certain category or chunk of the entire. Each slice's size is proportional to how much data or what percentage it represents, and the sum of all slices is 100%.

Circle graphs are frequently used to depict percentages or categorical data, and they are especially helpful for comparing and illustrating relative proportions among several categories within a data collection.

From the circle graph we see that the percentage of people who prefer chickens are 29%.

Thus, 29/100 (400) = 116 people

Also, 16% people prefer pig:

Thus, 16/100 (400) = 64 people

Thus, the difference is:

116 - 64 = 52

Hence, from the circle graph of the survey, 52 more people prefer pigs than chickens.

Learn more about circle graph here:

https://brainly.com/question/13298277

#SPJ1

The complete question is:

Answer:

a. 110°

Positive coterminal angles: 110° + 360° = 470°, 110° + 2(360°) = 830°

Negative coterminal angles: 110° - 360° = -250°, 110° - 2(360°) = -610°

b. 165°

Positive coterminal angles: 165° + 360° = 525°, 165° + 2(360°) = 885°

Negative coterminal angles: 165° - 360° = -195°, 165° - 2(360°) = -555°

c. -10°

Positive coterminal angles: -10° + 360° = 350°, -10° + 2(360°) = 710°

Negative coterminal angles: -10° - 360° = -370°, -10° - 2(360°) = -730°

Step-by-step explanation:

When an angle is in the standard position, it means that the initial side of the angle is the positive x-axis, and the terminal side of the angle is located in one of the four quadrants of the coordinate plane.

To find coterminal angles, we need to add or subtract multiples of 360 degrees to the given angle while keeping the terminal side in the same position. This is because a full rotation around the origin in the coordinate plane is 360 degrees.

For positive coterminal angles, we add multiples of 360 degrees to the given angle. In the case of 110 degrees, we can add 360 degrees once or twice to get 470 degrees or 830 degrees, respectively.

For negative coterminal angles, we subtract multiples of 360 degrees from the given angle. In the case of -10 degrees, we can subtract 360 degrees once or twice to get -370 degrees or -730 degrees, respectively.

It's important to note that there are infinitely many coterminal angles for any given angle, but we usually restrict our answers to the smallest positive and negative angles that differ from the given angle by a multiple of 360 degrees.

To determine if (2, 6) is a solution to the system of equations:

y = 3/2x + 3 ... (equation 1)

y = -9x + 1 ... (equation 2)

We need to substitute x = 2 and y = 6 into both equations and check if they are true.

Substituting x = 2 and y = 6 into equation 1, we get:

6 = 3/2(2) + 3

6 = 3 + 3

6 = 6

This equation is true.

Substituting x = 2 and y = 6 into equation 2, we get:

6 = -9(2) + 1

6 = -18 + 1

6 = -17

This equation is false.

Since (2, 6) does not satisfy equation 2, it is not a solution to the system of equations. Therefore, the answer is: no.

Programme 2 in Los Angeles will be well received by 22 out of 25 people.

Given that the chances of a positive response from Los Angeles residents to two government programmes are 78.4% for Programme 1 and 88.1% for Programme 2, the likelihood of a positive response for Programme 2 given that the person is from Los Angeles must be calculated as follows:

88.1 / 100 = X 44.05 / 50 = X 22,025 / 25 = X

Therefore, Programme 2 will be well-received by 22 out of 25 people in Los Angeles.

To learn more about probability visit:

brainly.com/question/23374236

#SPJ1

Answer:

Step-by-step explanation:

Okay but seriously though, you would have to write the whole question down.

a) The break-even point for the division is: 4000 units

b) The level of sales for 10% profit is: 4681 units

The break-even point is defined as the point at which total cost and total revenue are equal, meaning there is no loss or gain for your small business. In other words, you've reached the level of production at which the costs of production equals the revenues for a product.

a) We are told that:

Selling price for income tax app = $8

Monthly fixed cost = $20000

Variable cost producing each app = $3

Thus:

8x = 3x + 20000

5x = 20000

x = 4000 units

b) 8x = 1.1(3x + 20000)

8x = 3.3x + 22000

4.7x = 22000

47x =220000

x = 4681 units

Read more about Break even point at: https://brainly.com/question/15281855

#SPJ1

Missing questions are:

(a) Find the break-even point for the division.

(x,y)=

(b) What should be the level of sales in order for the division to realize a 10% profit over the cost of making the income tax apps? (Round your answer up to the nearest whole number.)

The given exponents 9⁻³/9¹² in the form 9ⁿ is 9⁻¹⁵ respectively.

A number's power or exponent, in other words, tells how many times it must be multiplied by itself.

Any integer, fraction, or decimal can serve as the basis in this situation.

Additionally, the exponent might have either a positive or negative value.

Subtract the exponents to divide exponents (or powers) with the same base.

Given that division is the inverse operation of multiplication, it stands to reason that, just as exponents are added when multiplying numbers with the same base, exponents are subtracted when dividing numbers with the same base.

So, we have the exponents as;
9⁻³/9¹²

Then, solve as follows:

9⁻³/9¹²

9⁻³⁻¹²

9⁻¹⁵

Therefore, the given exponents 9⁻³/9¹² in the form 9ⁿ is 9⁻¹⁵ respectively.

Know more about Exponentiation here:

https://brainly.com/question/11975096

#SPJ1

Answer:

∠ A = 76°

Step-by-step explanation:

the sum of the 3 angles in a triangle = 180°

sum the 3 angles and equate to 180

9x - 5 - 5 + 6x + 55 = 180

15x + 45 = 180 ( subtract 45 from both sides )

15x = 135 ( divide both sides by 15 )

x = 9

Then

∠ A = 9x - 5 = 9(9) - 5 = 81 - 5 = 76°

Since p and q are real numbers, the value of q is 21.

In Mathematics and Geometry, a quadratic equation can be defined as a mathematical expression that can be used to define and represent the relationship that exists between two or more variable on a graph.

In Mathematics, the standard form of a quadratic equation is represented by the following equation;

ax² + bx + c = 0

Next, we would solve the given quadratic equation by using the completing the square method;

x² - 8x - 5 = 0

x² - 8x = 5

In order to complete the square, we would have to add (half the coefficient of the x-term)² to both sides of the quadratic equation as follows:

x² - 8x + (-8/2)² = 5 + (-8/2)²

x² - 8x + 16 = 5 + 16

x² - 8x + 16 = 21

By simplifying, we have;

(x - 4)² = 21

p = 4 and q = 21

Read more on quadratic functions here: brainly.com/question/14201243

#SPJ1

the total number of boxes with at least 20 but fewer than 60 broken crayons is  33.To answer this question, we need to use the stem-and-leaf plot to count the number of boxes with at least 20

what is at least ?

"At least" is a phrase that is used to indicate a minimum quantity or degree of something. It means that the stated quantity or degree is the smallest amount that is acceptable or possible. For example, if someone says "I need at least 10 dollars,"

In the given question,

To answer this question, we need to use the stem-and-leaf plot to count the number of boxes with at least 20 but fewer than 60 broken crayons.

From the stem-and-leaf plot, we can see that the stems 2, 3, 4, and 5 have leaves that add up to at least 20 but fewer than 60:

Stem 2 has leaves 3 and 8, which add up to 11.

Stem 3 has leaf 3, which adds up to 3.

Stem 4 has leaves 0 and 9, which add up to 9.

Stem 5 has leaves 1 and 9, which add up to 10.

Therefore, the total number of boxes with at least 20 but fewer than 60 broken crayons is 11 + 3 + 9 + 10 = 33.

To know more about at least, visit:

https://brainly.com/question/14979872

#SPJ1

The expressions that are equivalent to 6x²y + 2xy⁵; are 2(3x²y + xy⁵), 2xy(3x + y⁴), xy(6x + 2y⁴) and 4xy(3/2x + 1/2y⁴). So, the correct options are a, b, e and g.

Algebra is known to be a branch of mathematics in which problems are represented as mathematical expressions using letters or variables (x, y, z, etc.) to represent unknown values ​​that may change. The purpose of algebra is to understand what the unknown values ​​are in order to find solutions to problems. The degree of an algebraic equation is the largest power that exists for the variables in the equation. Algebraic equations can be classified by degree as follows:

Equation A: 2(3x²y + xy⁵) = 6x²y + 2xy⁵

Equation B: 2xy(3x + y⁴) = 6x²y + 2xy⁵

Equation C: 2x²y(6 + 5y) = 12x²y + 10x²y²

Equation D: 6x²y.2xy⁵

Equation E: xy(6x + 2y⁴) = 6x²y + 2xy⁵

Equation F: 2y(3x + xy⁴)⁰ = 2y

Equation G: 4xy(3/2x + 1/2y⁴) = 6xy + 2xy⁵

Hence, Equation A, B, E and G are the equations found equivalent to the given equation, 6x²y + 2xy⁵.

To know more about algebraic equation, visit:

https://brainly.com/question/953809

#SPJ1

Answer: 6 units

Step-by-step explanation: To find the mass of the lamina, we need to integrate the density function fi(x,y,z) over the volume of the lamina. The lamina is a portion of the cone z=sqrt(x^2+y^2) between the planes z=1 and z=3. We can express this volume using cylindrical coordinates, where rho is the distance from the origin to the point (x,y,z), phi is the angle between the positive x-axis and the line connecting the origin to the point (x,y,z), and z is the height of the point (x,y,z) above the xy-plane.

We have:

1 <= z <= 3

0 <= rho <= 3sin(phi)

0 <= phi <= 2pi

The density function is given by fi(x,y,z) = x^2z. In cylindrical coordinates, we have x = rhocos(phi), y = rhosin(phi), and z = z. Therefore, we can express the density function as:

fi(rho, phi, z) = (rhocos(phi))^2 * z = rho^2cos^2(phi) * z

The mass of the lamina is given by the triple integral of the density function over the volume of the lamina:

M = ∭ fi(rho, phi, z) dV

= ∫∫∫ rho^2cos^2(phi) * z dz dA

= ∫∫[1,3] ∫[0,2pi] ∫[0,3sin(phi)] rho^2cos^2(phi) * z dz d(phi) drho

= ∫[0,2pi] ∫[0,3] ∫[0,rhosin(phi)] rho^2cos^2(phi) * z dz drho d(phi)

= ∫[0,2pi] ∫[0,3] (1/3)rho^3sin(phi)cos^2(phi) d(phi) drho

= ∫[0,2pi] (1/3)[9sin(phi)cos^2(phi)] d(phi)

= (1/3)[9(2/3)]

= 6

Therefore, the mass of the lamina is 6 units.

Johannes will need to pay $8.61 for 5 pounds of ground beef

Since Johannes needs 5 pounds of ground beef, and the available pounds are 1.5, 2, 3, and 3.75 pounds.

To reduce the cost, he need to select the package with the lowest cost per pound.

The cost per pound for each package is:

Package 1: $5.58 / 1.5

              = $3.72 per pound

Package 2: $7.44 / 2

              = $3.72 per pound

Package 3: $1.16 / 3

              = $0.39 per pound

Package 4: $13.95 / 3.75

                = $3.72 per pound

Therefore, the package with the lowest cost per pound is Package 3 and package 2  which will give us 5 pounds

So he can do it as:

$1.16 + $7.44

= $8.6

Or

(1 package of 3 pounds x $0.39 per pound) + (1 package of 2 pounds x $3.72 per pound)

= $1.17 + $7.44

= $8.61

Therefore, Johannes will need to pay $8.61 for 5 pounds of ground beef.

Learn more about pounds from

https://brainly.com/question/30400750

#SPJ1

The graph of the piecewise function can be seen in the image attached below where (x+2)² terminates at x = -1,  |x - 1| between the interval of x = -1 to x = 1, and  [tex]-\sqrt[3]{x}[/tex] from +x-axis to infinity [tex]\infty[/tex]

A piecewise function is a type of function that has different expressions or formulas for different parts or intervals of its domain. This means that the formula that defines the function changes depending on which part of the domain we are looking at.

Now, to graph the piecewise function, we need to start by identifying the different intervals on which the function is defined and the corresponding expressions that define the function on each interval.

If we have a piecewise function f(x) defined as:

The graph of the piecewise function can be seen in the image attached below.

Learn more about graphing piecewise function here:

https://brainly.com/question/30348444

#SPJ1