Which table represents a linear function example?

The surface area of the triangular prism in this problem is given as follows:

46 cm².

The surface area of a prism is calculated as the sum of the areas of all the figures that compose the prism.

The figure in this problem is composed as follows:

The area of the square is given as follows:

As = 2² = 4 cm².

The area of the two right triangles is given as follows:

At = 2 x 1/2 x 2 x 7 = 14 cm².

The area of the two rectangles is given as follows:

Ar = 2 x 2 x 7 = 28 cm².

Hence the surface area of the prism is given as follows:

S = As + At + Ar

S = 4 + 14 + 28

S = 46 cm².

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Answer:

2x^2 + x + 9 + (18/(x+2))

Step-by-step explanation:

To find the result when 2x^3 - 5x^2 - 9x + 18 is divided by x + 2 using the long division method, you can follow these steps:

Divide the first term of the dividend (2x^3) by the first term of the divisor (x). The result is 2x^2.

Multiply the divisor (x + 2) by 2x^2. The result is 2x^3 + 4x^2.

Subtract this result from the dividend (2x^3 - 5x^2 - 9x + 18). The result is -x^2 - 9x + 18

Bring down the next term of the dividend (-5x^2) and add it to the result from step 3. The result is -6x^2 - 9x + 18

Divide -6x^2 by -6x and the result is x.

Multiply the divisor by x. The result is x^2 + 2x

Subtract this result from the result of step 4. The result is -9x + 18

Bring down the next term of the dividend (-9x) and add it to the result from step 7. The result is -18x + 18

Divide -18x by -18 and the result is x

Multiply the divisor by x. The result is x^2 + 2x

Subtract this result from the result of step 8. The result is 18

Therefore, the quotient is 2x^2 + x + 9 and the remainder is 18

So the result when 2x^3 - 5x^2 - 9x + 18 is divided by x + 2 is 2x^2 + x + 9 + (18/(x+2))

The number of hot cocoas that Mei Mei would be predicted to sell if the day’s high temperature was of 42 ºF is given as follows:

58.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

For which the parameters are given as follows:

The function touches the y-axis at y = 100, meaning that the intercept b is defined as follows:

b = 100.

When x increases to six, y decays to 94, hence the slope m is obtained as follows:

m = (94 - 100)/(6 - 0)

m = -1.

Hence the function that predicts the amount of hot cocoa sold for a high temperature of x ºF is given as follows:

y = -x + 100.

The estimate if the high temperature was of 42 ºF is given as follows:

y = -42 + 100

y = 58.

The graph of the linear function is given by the image presented at the end of the answer.

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Answer:

3 green apples and 7 red apples.

Step-by-step explanation:

1. Start with the ratio of green apples to red apples, which is 3 to 7.

2. Multiply 3 (the number of green apples) by any number to get a number that is divisible by 7 (the number of red apples).

3. In this case, multiplying 3 by 2 gives 6, which is divisible by 7.

4. Since 6 is divisible by 7, that means that the solution is 3 green apples and 7 red apples.

The height is 2 and radius is √2 of the largest right circular cylinder that can be put into a sphere of radius √3.

A cylinder whose bases are circular in shape and parallel to each other is called the right circular cylinder. It is a three-dimensional shape.

Given that the radius of a sphere R = √3

Let the radius of the cylinder is r and the height of the cylinder is h.

than.

r² = R² − h²/4

and Vc = πr²h

⇒ Vc = π(R² − h²/4)h

⇒ Vc = πR²h − πh³/4

dVc/dh = πR² − 3πh²/4  

(dVc/dh)R=√3 = 3π − 3πh²/4

For maximum or minimum volume,

dVc/dh = 0

⇒ 3π − 3πh²/4 = 0

⇒ 3πh²/4 = 3π

⇒ 3πh² = 3π*4

⇒ h² = 4

⇒ h=2

Also,  dVc/dh changes sign from positive to negative in the neighborhood of h=2. Hence, h=2 is a maximum point.

r² = R² − h²/4

⇒ r² = (√3)² - 2²/4

⇒ r² = 3 - 1

⇒ r² = 2

​⇒ r = √2

So, the height is 2 and radius is √2 of the largest right circular cylinder

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(8, 3) is the point that is two-thirds segment of the way from point $r$ to point $s$, we can use the following method:

initially to get the difference between the x-coordinates of points $r$ and $s$, and multiply the values  by 2/3. let us consider that value as  $dx$.

and to get the difference between the y-coordinates of points $r$ and $s$, and multiply it by 2/3. let us assume the value as  $dy$. then add $dx$ to the x-coordinate of point $r$ and $dy$ to the y-coordinate of point $r$.on doing certain operations we get as:

hence the  coordinates of the point at two-thirds of the way from $r$ to $s$ is $(x,y)$ can be established as

x = -6 + (15 - (-6))(2/3) = -6 + 21(2/3) = -6 + 14 = 8

y = 19 + (-5 - 19)(2/3) = 19 - 24(2/3) = 19 - 16 = 3

therefore  the point two-thirds of the distance from point $r$ to point $s$ is (8, 3).

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So on solving the provided question, we can say that by unitary method task done of 15 days done = 7/5 X 15hours = 21 hours

The unit technique is an approach to problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value. The unit method, to put it simply, is used to extract a single unit value from a supplied multiple. For instance, 40 pens would cost 400 rupees, or the price of one pen. The process for doing this may be standardized. a single country. anything that has an identity element. (mathematics, algebra) (Linear algebra, mathematical analysis, mathematics of matrices or operators) Its adjoint and reciprocal are equivalent.

here,

task done of 5 days done = 7 hours.

task done of 1 days done = 7/5 hours.

task done of 15 days done = 7/5 X 15hours = 21 hours

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The null hypothesis would be H0: p <= 0.25 and the alternative hypothesis would be Ha: p > 0.25

The null hypothesis represents the default assumption that there is no significant difference between the proportion of high school couples who believe they will marry their high school sweetheart and the researcher's claim that more than 25% of high school couples believe they will marry.

The alternative hypothesis represents the claim that the researcher wants to test, which is that the proportion of high school couples who believe they will marry their high school sweetheart is greater than 25%.

So, the null hypothesis would be:

H0: p <= 0.25 (where p is the proportion of high school couples who believe they will marry their high school sweetheart)

The alternative hypothesis would be:

Ha: p > 0.25 (where p is the proportion of high school couples who believe they will marry their high school sweetheart)

The researcher would then use statistical methods to test if the sample data provide enough evidence to reject the null hypothesis in favor of the alternative hypothesis.

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Answer:

Step-by-step explanation:

Total Student in a class = 80

No. of students passed = 80*80% = 64

No. of students failed = Total Students in a class - No. of students passed

No. of students failed  = 80-64 =16

The air pressure at the center of the hurricane when the mean sustained wind velocity is 54.5 meters per second is 1011.5 millibars.

Equations whose variables have a power of one are called linear equations. One example with one variable is where ax+b = 0, where a and b are real values and x is the variable.

Given:

In a hurricane,

the mean sustained wind velocity v (in meters per second) can be modeled by v(p) = 6.3/(1013-p)

The mean sustained wind velocity = 54.5 M/s

To find the air pressure at the center of the hurricane when the mean sustained wind velocity is 54.5 meters per second:

That means,

the equation

54.5 = 6.3/(1013-p)

63 = (1013 - p)54.5

63 = 55208.5 - p54.5

p = 55145.5 / 54.5

p = 1011.844

Therefore, the air pressure is 1011.844 millibars.

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The answer provided illustrates the concept of implied and express warranties, unilateral and bilateral contracts, voidable and void contracts, and executory consideration. It also provides number of  examples of each of these concepts.

1. O fit for the ordinary purpose for which such goods are used.

2. A enforce the contract against Olive.

3. C An express warranty must be in writing and signed by the parties.

4. C supported by consideration.

5. O is void.

6. C enforceable.

7. O is a rejection and counteroffer.

8. O A promise to do something in the present in exchange for something else in the future.

9. A An offer to pay a reward for the return of lost property.

10. C An offer to do something in the future in exchange for something else in the present.

The answer provided illustrates the concept of implied and express warranties, unilateral and bilateral contracts, voidable and void contracts, and executory consideration. It also provides number of examples of each of these concepts.

The complete question is :

Question 1 (1 point) Home Remodelers, Inc., and Imogen enter into a contract for a sale of cabinets and countertops. Home Remodelers merchant who deals in goods of the kind sold, notes that its goods come with an implied Under the UCC, this means that the goods are reasonably warranty of merchantabilit fit for the buyer's particular purpose. O fit for the ordinary purpose for which such goods are used. O suitable for resale at an acceptable price. C the best quality that money can buy Save Question 2 (1 point) Olive, an agent for Precision Paving Corporation, enters into an unauthorized contract with Quality Asphalt, Inc. Quality Asphalt may, at its option, A enforce the contract against Olive. O enforce the contract against Precision Paving. C void the contract. Save Question 3 (1 point) Which of the following statements about an express warranty is true? A An express warranty does not need to be in writing. O An express warranty does not need to be signed by the parties. C An express warranty must be in writing and signed by the parties. Save Question 4 (1 point) In order to be enforceable, a contract must be A fair and equitable to both parties. O signed by both parties. C supported by consideration. Save Question 5 (1 point) A contract that is void because of a mistake by one of the parties O is voidable. A is void. C is still enforceable. Save Question 6 (1 point) A contract between two individuals is generally A voidable. O void. C enforceable. Save Question 7 (1 point) Phil makes an offer to sell a house to Sally for $200,000. Sally responds by saying that she will buy the house for $200,000, but wants to add a condition that the house must pass an inspection. This response A is an acceptance of the offer. O is a rejection and counteroffer. C is a condition of acceptance. Save Question 8 (1 point) Which of the following is an example of Executory consideration? A A promise to do something in the future in exchange for something else in the present. O A promise to do something in the present in exchange for something else in the future. C A promise to do something in the future in exchange for something else in the future. Save Question 9 (1 point) Which of the following is an example of a unilateral contract? A An offer to pay a reward for the return of lost property. O An offer to do something in the present in exchange for something else in the future. C An offer to do something in the future in exchange for something else in the present. Save Question 10 (1 point) Which of the following is an example of an implied contract? A An offer to pay a reward for the return of lost property. O An offer to do something in the present in exchange for something else in the future. C An offer to do something in the future in exchange for something else in the present. Save

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m = the slope of the curve at x=3 and b = the y-intercept at x=3. Therefore, the approximate value of y at x=2

We can use the local linearization of the curve to approximate the value of y at x=2.

The local linearization of the curve is given by the equation y = mx + b, where m is the slope of the curve at x=3 and b is the y-intercept at x=3.

Let m be the slope of the curve at x=3 and b be the y-intercept at x=3.

The slope of the curve at x=3 can be found by calculating the derivative of the curve at x=3.

The y-intercept at x=3 can be calculated by substituting x=3 into the equation of the curve and solving for y.

Therefore, m = the slope of the curve at x=3 and b = the y-intercept at x=3.

Substituting the values of m and b into the equation of the local linearization, we get the equation y = mx + b.

Substituting x=2 into the equation, we get y ≈ 0.5 + 1 = 1.5.

Therefore, the approximate value of y at x=2

The local linearization of the curve can be used to approximate the value of y at x=2. Substituting x=2 into the equation, we get y ≈ 1.5, which is the approximate value of y at x=2.

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Answer:540

Step-by-step explanation:

Answer:

540

Step-by-step explanation:

When multiplying two numbers and one is a decimal you multiply both of them by 10 to keep whole number denominators.

[tex]\frac{324}{0.6}[/tex]

[tex]10* \frac{324}{0.6}[/tex]

[tex]\frac{3240}{6}[/tex]

[tex]\frac{3240}{6} = 540[/tex]

It takes 10 minutes for the two lines to have filled an equal number of barrels

Each line will have filled 90 barrels

Let “x” be the number of minutes

The old conveyer line has filled 20 barrels of paint, and is filling more at a rate of 7 barrels per minute

Thus, a equation is framed as follows:

Old conveyor: 20 + 7(number of minutes)

Old conveyor: 20 + 7x ------- eqn 1

A worker just switched on a newer line that can fill 9 barrels per minute

Thus, a equation is framed as follows:

New conveyor: 9(number of minutes)

New conveyor: 9x -------- eqn 2

In a little while, the two lines will have filled an equal number of barrels.

Thus, eqn 1 must be equal to eqn 2

Thus it takes 10 minutes for the two lines to have filled an equal number of barrels

Substitute x = 10 in any one of equations

Substitute in eqn 2

9x = 9(10) = 90

Thus each line will have filled 90 barrels

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The given point has been plotted on the graph as (-3.5, 4.75).

Coordinate, is represented as the values on the x-axis and y-axis of the graph. while the coordinate x is called abscissa and the coordinate of the y is called ordinate.

Here,
Given coordinate,
(−3 1/2, 4 3/4}
x = -[3 1/2]
x = -3.5

y = 4 3 /4
y = 4 + 0.75
y = 4.75

So, the coordinates of (x, y) is shown,

Thus, the given point has been plotted on the graph as (-3.5, 4.75).

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Answer:

in the picture below

Step-by-step explanation:

It can be concluded that Gym city membership fee is less than Jane’s current gym membership fee.

Given is that the equation C = 50m, that represents the monthly cost of membership at Jane’s current gym. The equation C = 35m represents the monthly cost of membership at a different gym, named Gym City

The equation for direct variation is -

y = Kx

where -

{K} denotes the rate of change

Now -

Therefore, it can be concluded that Gym city membership fee is less than Jane’s current gym membership fee.

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Using the Fundamental Counting Theorem, it is found that 6 different possible outcomes are there.

What is the fundamental principle of counting?

The total number of times an event can occur is m n if there are m possible ways for one event to happen and n various ways for another. A rule used to determine the total number of potential outcomes in a circumstance is known as the fundamental counting principle.

                        It states that there are n m times m n times m methods to do both of these activities if there are n ways to perform one action and m ways to perform another action after that.

For the coin, there are two outcomes, hence . n₁ = 2

For the spinner, there are three outcomes, hence n₂ = 3

Then, the number of outcomes is given by:

N = 2 x 3 = 6.

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The total amount in an account to the nearest cent after 3 years if the interest is compounded annually on an investment of $5600 at 7.65% is $6,986.02

To find the total amount in the account after 3 years, we need to use the formula for compound interest:

A = P(1 + r/n)^(nt)

where A is the total amount, P is the initial investment (principal), r is the annual interest rate (expressed as a decimal), n is the number of times the interest is compounded per year, and t is the number of years.

In this case, P = $5600, r = 0.0765, n = 1 (because the interest is compounded annually), and t = 3. Plugging these values into the formula gives:

A = 5600(1 + 0.0765)^3

A = $6,986.02

So, the total amount in the account after 3 years, to the nearest cent, would be $6,986.02

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The dependent variable in this case would be the total number of hot dogs needed for the cookout.

In mathematics, a variable is a symbol, usually a letter, used to represent a quantity in an equation or in a mathematical expression. It can be thought of as a placeholder that can take on different values in a given equation or expression. Variables are essential for mathematics because they allow us to explore different scenarios and solve problems.

This is dependent on the number of guests attending, which is the independent variable. Depending on how many people show up, the individual will need to adjust the amount of hot dogs to accommodate the guests.

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The probability that Esteban wins the game is 29/49.

Probability can be defined as the ratio of the number of favourable outcomes to the total number of outcomes of an event.

We know that, probability of an event = Number of favourable outcomes/Total number of outcomes

Given that, Esteban is playing a matching card game.

If the cards are identical, he wins the game.

Probability of getting cross on both the cards

2/7 × 2/7

= 4/49

Probability of getting star on both the cards

5/7 × 5/7

= 25/49

Probability to win the game is

4/49 + 25/49

= 29/49

Therefore, the probability that Esteban wins the game is 29/49.

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The least positive integer value of x is 1

We can start by expressing the expression (2x)^2 2372x 37^2 as a multiple of 47.

47 | (2x)^2 2372x 37^2

Since 47 is a prime number, we can use the property that a multiple of a prime number is a number that can be divided by that prime number without leaving a remainder.

So, we need to find the least positive integer value of x such that (2x)^2 2372x 37^2 is divisible by 47.

We can start by assuming (2x)^2 2372x 37^2 as (2x)^2 2372x 37^2 = 47*k, where k is any integer.

We can start testing values of x starting from 1,

x=1 : (21)^2 * 23721 * 37^2 = 4 * 74 * 1369 = 47 * 2028,

x=2 : (22)^2 * 23722 * 37^2 = 16 * 148 * 1369 = 47 * 6912,

and so on.

So the least positive integer value of x such that (2x)^2 2372x 37^2 is a multiple of 47 is x=1.

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Answer:

A rhombus is a four-sided shape with all sides equal in length, and opposite angles equal. The diagonals of a rhombus bisect each other at right angles and they are equal in length.

In this case, the length of one diagonal of the rhombus is 6 times the length of the other diagonal. Let's call the length of the shorter diagonal "d", and the length of the longer diagonal "6d".

To find the perimeter of the rhombus, we can add up the lengths of all four sides. Since all sides of a rhombus are equal, we can find the perimeter by multiplying the length of one side by 4.

To find the length of one side, we can use the Pythagorean theorem to find the length of the side in terms of d, the shorter diagonal.

We know that d^2 + (3d)^2 = s^2, where s is the length of one side.

After simplifying, we get: d^2 + 9d^2 = s^2

s = √10d^2

so the perimeter is 4s = 4 √10d^2

Therefore, the perimeter of the rhombus can be represented by the expression 4* √10d^2 where d represents the length of the shorter diagonal.

Answer:

14d

Step-by-step explanation:

First the short diagonal is d, so we can mark it as d:

d

Second we have 6 times that, so 6d:

d+6d

Then we multiply it by two since a rhombus has 4 sides:

2d+12d

Then we simplify:

14d

Voila!

The equation showing the total cost for purchasing x tickets is given as y = 12.5x + 7

An equation is a expression that shows the relationship between numbers and variables.

The standard form of a linear equation is:

y = mx + b

Where m is the rate of change and b is the y intercept

Let y represent the total cost for x tickets.

From the table, using the points (2, 32) and (6, 82):

y - 32 = [(82 - 32)/(6 - 2)](x - 2)

y - 32 = 12.5(x - 2)

y = 12.5x + 7

The equation is given as y = 12.5x + 7

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The symbol of absolute value is two vertical bars (||).

The absolute value of a number is the distance between that number and zero on a number line. The absolute value of a number is always positive, regardless of the sign of the original number. For example, the absolute value of -5 is 5 and the absolute value of 5 is also 5.

In mathematical notation, the absolute value of a number is represented by placing the number between the vertical bars, like this: |x|. When the absolute value is applied to a variable or an expression, the result is the positive value of that variable or expression. For example, |-5| = 5, and |5| = 5.

The absolute value is used in many branches of mathematics, including algebra, calculus and geometry, and it is used to represent the magnitude of a number, regardless of its sign, and also it is used to define the distance between two points on a number line.

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Answer:

To solve this problem, we will use the following steps:

Step 1: Convert the amount of roast beef used in each sandwich to a decimal by dividing the numerator by the denominator: 3/8 pound = 0.375 pound

Step 2: Subtract the amount of roast beef that Marisa has left from the amount of roast beef that she started with to find the amount of roast beef used: 5 - 2.75 = 2.25 pounds

Step 3: Divide the amount of roast beef used by the amount of roast beef used in each sandwich: 2.25 pounds / 0.375 pounds = 6

Final Answer: Marisa made 6 deli sandwiches.

The coach can select the 6 starting players in 20 different ways, as probability are 6 players to choose from and they must consist of 3 boys and 3 girls. There are 7 boys and 6 girls, so each player is eligible to play each position. To calculate this, the formula 6! / (3! * 3!) is used.

1. Calculate 6 factorial (6!) which is 6*5*4*3*2*1 = 720

2. Calculate 3 factorial (3!) which is 3*2*1 = 6

3. Calculate 3 factorial (3!) again which is also 6

4. Divide 6! by (3! * 3!) which is 720 / (6 * 6) = 20

When selecting a starting lineup for an indoor soccer team consisting of 6 players who must be 3 boys and 3 girls, there are 20 possible combinations. To calculate this, the coach must use the formula 6! / (3! * 3!). This formula is used to calculate the number of possible combinations when selecting a certain number of items from a set of items, where all items are unique. 6! is 6 factorial, which is calculated by multiplying the numbers from 6 down to 1 (6*5*4*3*2*1). 3! is 3 factorial, which is calculated by multiplying the numbers from 3 down to 1 (3*2*1). When 6! is divided by the product of 3! multiplied by 3!, the result is 20. This shows that the coach can select the 6 starting players in 20 different ways, as there are 6 players to choose from and they must consist of 3 boys and 3 girls. There are 7 boys and 6 girls, so each player is eligible to play each position.

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Therefore , solving the provided quadrilateral  question we can say that - (x,y) -&gt; (x,y) is the formula for a reflection across the y-axis.

In geometry, a four-sided object having four corners is referred to as a quadrilateral. The word comes from either the Latin quad or portfolio of innovative (meaning "side"). Four corners, four states, and four corners are the three dimensions of a rectangle. Concave and convex surfaces come in essentially two varieties. Convex quadrilaterals also include the subclasses of trapezoids, parallelograms, angles, rhombuses, and squares.

Here,

The ordinate and abscissa are other names for the y-axis and x-axis, respectively.

The Y-axis is a line drawn from the bottom to the top of the graph. This axis runs parallel to the coordinates that need to be measured.

The numbers on the y-axis are referred to as y-coordinates.

When writing sorted pairs, the x-coordinate and then the y-coordinate are included in parenthesis.

(x, y).

A' ( -1, 1 ) ⇒ A"(-1, -1)

B' (-2, 2) ⇒ B"(-2, -2)

C' (-2, 3) ⇒ C"(-2, -3)

and D' (-1, 4) ⇒ D" (-1, -4)

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The solution to the system does not exist

From the question, we have the following parameters that can be used in our computation:

y = −2x + 1

4x + 2y = −3

Divide the first equation by 1

So, we have

y = −2x + 1

By substitution, the second equation becomes

Substitute y = −2x + 1 in the second equation

4x + 2(-2x + 1) = -3

So, we have

4x - 4x + 2 = -3

Evaluate the like terms

2 = -3

This equation is false

Hence, the system has no solution

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Complete question

What is the solution to the system of equation? (Page 84, #1b)

y = −2x + 1

4x + 2y = −3

QC ≅ Q'C'  and ∠AQC  is a right angle.

What is the transformation?

A transformation is a general term for four specific ways to manipulate the shape and/or position of a point, a line, or a geometric figure. The original shape of the object is called the Pre-Image and the final shape and position of the object is the Image under the transformation.

Given: A reflection is a transformation that maps point Q in a figure over a line, AB, such that for point C at the intersection of AB and QQ'.

We know that reflection creates an image equidistant from the line of reflection.

Thus,  QC ≅ Q'C'

Also in reflection, a line drawn from the point is perpendicular to the line of reflection.

Therefore,  ∠AQC is a right angle.

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Answer:

Step-by-step explanation:

Given that w=5 and x=9, we can substitute these values into the expression to find the value of the expression:

7w-x

= 7(5) - 9

= 35 - 9

= 26

So the value of the expression when w=5 and x=9 is 26