Is the relation a function? {(-3, 4), (6, 0), (-3, 4), (-8, -2)}


yes it is a function


or


no it is not a function

No, the diagonal of a parallelogram cannot be congruent to one of its side.

Given data,

Let the parallelogram be represented as ABCD

Now , the diagonal is AC and BD

The opposing sides of a parallelogram are parallel and congruent. This implies that the length of every pair of opposing sides is the same.

The parallelogram's opposite sides would be equal in length if one of its diagonals were congruent to one of its sides. However, unless it is a rectangle or a rhombus, this goes against the definition of a parallelogram, which calls for opposing sides to be parallel but not equal in length.

Therefore, a parallelogram's diagonal cannot be congruent to one of its sides by definition.

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The algebraic expression for the number of points scored by a football team that makes t touchdowns, f field goals, and e extra points is: 6t + 3f + 1e. Therefore, the team would have scored 15 points in this case.

To calculate the total number of points scored by a football team, we can assign variables to the number of touchdowns, field goals, and extra points. Let's use t for touchdowns, f for field goals, and e for extra points.

The points awarded for each touchdown is 6, for each field goal is 3, and for each extra point is 1. To find the total number of points, we multiply the number of touchdowns by 6, the number of field goals by 3, and the number of extra points by 1, and then add them together.

Hence, the algebraic expression for the number of points scored is: 6t + 3f + 1e.

For example, if a team scores 2 touchdowns, 1 field goal, and 0 extra points, we can substitute the values into the expression:

6(2) + 3(1) + 1(0) = 12 + 3 + 0 = 15.

Therefore, the team would have scored 15 points in this case.

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The end behaviors of the graph of the function are given by:

as x → −∞, f(x) → ∞

as x → ∞, f(x) → ∞

Thus, this is the required answer.

Solution:

The given polynomial function is of degree 2 (quadratic function).f(x) = ax² + bx + c, Where a, b, and c are real numbers with a ≠ 0.

The quadratic function has the general form: f(x) = a(x - r)(x - s)where r and s are the x-intercepts.

The given x-intercepts are (-2,0) and (2,0) which means that:r = -2 and s = 2.

So, the quadratic function can be written as:

f(x) = a(x - (-2))(x - 2)f(x) = a(x + 2)(x - 2), where a is a non-zero constant.The y-intercept is (0,-4).

We know that the y-intercept occurs where x = 0.

Substituting x = 0 and y = -4 in the quadratic function:

f(x) = a(x + 2)(x - 2)

when x = 0,

y = -4.

-4 = a(0 + 2)(0 - 2)

=> -4 = -4a

=> a = 1

The quadratic function is:

f(x) = (x + 2)(x - 2)

The end behaviors of the graph of the function are given by:

as x → −∞, f(x) → ∞

as x → ∞, f(x) → ∞

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Answer:

Step-by-step explanation:

To calculate the upper and lower bounds for the area of the right-angled triangle, we can use the lengths of its two short sides, which are given as 3.7 cm and 4.5 cm to the nearest millimeter.

we need to consider the maximum and minimum possible values within the given ranges. The maximum value for the length of the first short side is 3.75 cm (3.7 cm rounded up), while the minimum value is 3.65 cm (3.7 cm rounded down).

Similarly, the maximum value for the length of the second short side is 4.55 cm (4.5 cm rounded up), and the minimum value is 4.45 cm (4.5 cm rounded down). To calculate the upper bound for the area of the triangle, we can use the maximum values for the lengths of the short sides.

By applying the formula for the area of a triangle (A = 0.5 * base * height), where the two short sides act as the base and height, we obtain the maximum possible area. Similarly, to calculate the lower bound for the area of the triangle, we use the minimum values for the lengths of the short sides and apply the same formula.

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The temperature change per minute during the 20-minute cooling period at a steady rate was -3 degrees Celsius per minute.

To calculate the temperature change per minute, we need to determine the difference in temperature and divide it by the time in minutes. In this case, the initial temperature was +5 degrees Celsius, and the final temperature was -55 degrees Celsius. The temperature change is the difference between these two values: -55 - (+5) = -60 degrees Celsius.

Since the cooling period lasted for 20 minutes, we divide the temperature change by the time: -60 degrees Celsius / 20 minutes = -3 degrees Celsius per minute.

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2 liters per hour is equal to 555.6 millimeters per second.

To convert 2 liters per hour to millimeters per second, you need to follow these steps:

Step 1: Convert liters to milliliters

Since 1 liter = 1000 milliliters, multiply 2 by 1000 to get the number of milliliters per hour.

Therefore, 2 liters per hour is equal to 2000 milliliters per hour.

Step 2: Convert hours to seconds

Since 1 hour = 3600 seconds, divide the number of milliliters per hour by 3600 to get the number of milliliters per second.

Therefore, 2000 milliliters per hour is equal to 0.5556 milliliters per second.

Step 3: Convert milliliters to millimeters

Since 1 milliliter is equal to 1 cubic centimeter (cc) and 1 cc is equal to 1 cubic millimeter, 0.5556 milliliters per second is equal to 0.5556 cubic millimeters per second or 555.6 millimeters per second (since there are 1000 cubic millimeters in a milliliter).

Therefore, 2 liters per hour is equal to 555.6 millimeters per second.

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The amount of lemonade left after the consumption of 280 ml of lemonade by 14 children is 4.08 liters. The given problem can be solved by using basic mathematical operations. In the problem, it is shown that there are 14 children at the birthday party, and each child drinks 280 ml of lemonade.

And, 8 liters of lemonade are also available. The solution of the problem is as follows:

1 litre of liquid = 1000 ml of liquid

8 liters of liquid = 8 × 1000

                   = 8000 ml of liquid

Now, we can calculate the total lemonade consumed by the 14 children as follows:

Total lemonade consumed = 14 × 280

                                          = 3920 ml of liquid

                                      = 3.92liters of liquid

Therefore, the amount of lemonade left after 14 children have consumed 280 ml of lemonade each is given by:

Amount of lemonade left = 8 − 3.92

                                = 4.08liters of liquid

Therefore, 4.08 liters of lemonade is left after the 280 ml of lemonade consumption by 14 children. The problem is calculating the amount of lemonade left after 14 children have consumed 280 ml of lemonade each. To solve the problem, we first need to calculate the total amount of lemonade consumed by the 14 children. We know that each child consumed 280 ml of lemonade.

Now, we can calculate the amount of lemonade left after 14 children have consumed 280 ml of lemonade each. The amount of lemonade left is given by the difference between the total amount of lemonade available and the total lemonade consumed by the 14 children.

Therefore,

Amount of lemonade left = Total lemonade available − Total lemonade consumed

                                     = 8000 − 3920

                               = 4080 ml of liquid

                            = 4.08litres of liquid

Therefore, 4.08 liters of lemonade is left after the 280 ml of lemonade consumption by 14 children.

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The first five terms of the sequence defined by the explicit formula an = (-2)^(n-1) are 1, -2, 4, -8, 16.

To find the first five terms of the sequence defined by the explicit formula an = (-2)^(n-1), we can substitute the values of n from 1 to 5 into the formula and calculate the corresponding terms:

The explicit formula for the sequence is given by an = (-2)^(n-1).

When n = 1: a1 = (-2)^(1-1) = (-2)^0 = 1

When n = 2: a2 = (-2)^(2-1) = (-2)^1 = -2

When n = 3: a3 = (-2)^(3-1) = (-2)^2 = 4

When n = 4: a4 = (-2)^(4-1) = (-2)^3 = -8

When n = 5: a5 = (-2)^(5-1) = (-2)^4 = 16

Therefore, the first five terms of the sequence are:

1, -2, 4, -8, 16

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Ali has hired Mark and Alexis to work for his shipping company, and Mark can load a truck with packages in 120 minutes, while Alexis can load the same number of packages in 240 minutes.

To find out how long they will take to load a truck together, we'll use the formula below:T = (T₁ × T₂) ÷ (T₁ + T₂)Where T is the time it takes for Mark and Alexis to load a truck together, T₁ is the time it takes for Mark to load a truck alone, and T₂ is the time it takes for Alexis to load a truck alone.

We can plug in the given values: T = (120 × 240) ÷ (120 + 240) = 28,800 ÷ 360 = 80Therefore, it would take Mark and Alexis 80 minutes to load a truck together.

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When a straight angle is split into two angles, the sum of those angles is 180 degrees because a straight angle measures 180 degrees.

Let's assume that the smaller angle is represented by x. Since the larger angle is twice as big as the smaller angle, it can be represented as 2x. Therefore, the sum of the two angles can be expressed as:

x + 2x = 180 degrees This simplifies to 3x = 180 degrees.

Dividing both sides by 3, we get: x = 60 degrees.

This means that the smaller angle is 60 degrees and the larger angle is twice as big, or 2(60) = 120 degrees.

Therefore, the two angles are 60 degrees and 120 degrees.

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The probability of rolling at least one six when rolling two standard number cubes is 11/36.

To determine the probability, we first need to find the total number of possible outcomes when rolling two standard number cubes. Each cube has 6 faces, numbered from 1 to 6, so the total number of outcomes is 6 multiplied by 6, which equals 36.

Next, we need to calculate the number of favorable outcomes, which is the number of outcomes where at least one six is rolled. There are three possible scenarios:

Rolling a six on the first cube and any number on the second cube.

Rolling any number on the first cube and a six on the second cube.

Rolling a six on both the first and second cubes.

For each scenario, there is a 1/6 probability of rolling a six on a single cube. Therefore, the number of favorable outcomes is 1 + 1 + 1 = 3.

Finally, we divide the number of favorable outcomes (3) by the total number of possible outcomes (36) to calculate the probability:

Probability = Number of favorable outcomes / Total number of possible outcomes

= 3 / 36

= 1 / 12

= 11 / 36

Therefore, the probability of rolling at least one six when rolling two standard number cubes is 11/36.

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The expression "x - 12" can be modeled in a real world situation where you are trying to find the difference between a number x and 12. Here is an example:Suppose you have a jar containing x marbles.

You give away 12 marbles to your friend. The number of marbles you have left in the jar can be modeled by the expression "x - 12". In this situation, x represents the original number of marbles in the jar, and 12 represents the number of marbles given away to your friend. The expression "x - 12" calculates the number of marbles you have left after giving away 12.

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If angles 1 and 2 are vertical angles, then they are congruent. If angle 1 measures 62 degrees, then angle 2 will also measure 62 degrees.

Vertical angles are formed by the intersection of two lines. They are opposite each other and have equal measures. In this case, if angle 1 measures 62 degrees, angle 2 will also measure 62 degrees because they are vertical angles.

This property of vertical angles can be understood based on the concept of a straight line. When two lines intersect, they form two pairs of vertical angles. Since a straight line measures 180 degrees, each pair of vertical angles will have a total measure of 180 degrees, and thus, each angle within the pair will have the same measure. Therefore, if angle 1 measures 62 degrees, angle 2 will also measure 62 degrees.

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The equation of proportionality is y = 74x

The equation that describes the proportionality is given as follows: y = kx. Here, k is the constant of proportionality. When the equation is multiplied by x, we get y = kx. Here, y represents the dependent variable, and x represents the independent variable. Given that walking at 4 miles per hour, Sue burns about 296 Calories per hour.

Let the independent variable, x, represent the walking rate, which is 4 miles per hour.

Let the dependent variable, y, represent the calories burnt per hour, which is 296 Calories per hour.

To find the constant of proportionality, k, we divide both sides of the equation by x:

y/x = k

Substitute the given values:

(296 Calories per hour) / (4 miles per hour) = k

k = 74

Therefore, the equation of proportionality is y = 74x.

In summary, the equation that represents the proportionality between the walking rate and the calories burnt per hour is y = 74x.

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The listing price for the residence is $158,400. This ensures that the seller will make a 20% profit on the original cost price of $132,000.

To calculate the listing price of the residence, we need to add the 20% profit to the cost price of $132,000.

To find the profit amount, we multiply the cost price by the profit percentage:

Profit = 20% of $132,000 = 0.20 * $132,000 = $26,400

The listing price is obtained by adding the profit to the cost price:

Listing Price = Cost Price + Profit = $132,000 + $26,400 = $158,400

Therefore, the listing price for the residence is $158,400. This ensures that the seller will make a 20% profit on the original cost price of $132,000.


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Based on the scatter plot of car insurance policy cost and ages of twenty-one young men, the following true statements can be made: 1. There is a positive correlation between age and the cost of car insurance policies.2. The cost of car insurance tends to increase as the age of the men increases.

From the scatter plot, we can observe the general trend of the data points. If the points on the scatter plot show an upward trend from left to right, it indicates a positive correlation between the variables. In this case, the scatter plot shows that as the age of the men increases, the cost of car insurance policies tends to increase as well.

This suggests that age is a significant factor in determining the cost of car insurance. Therefore, both statements 1 and 2 are true based on the information provided by the scatter plot.

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The elevation angles that Emma might use to read messages on the billboard are angle A (to see the top of the billboard) and angle B (to see the bottom of the billboard).

In order to determine the elevation angles Emma might use to read messages on the billboard, we need to consider the triangle formed by Emma, the bottom of the billboard (B), and the top of the billboard (T).

Let's label the elevation angle from Emma to the top of the billboard as angle A and the elevation angle from Emma to the bottom of the billboard as angle B.

From the given information, we know that the distance between Emma and the billboard is 20 yards, the bottom of the billboard is 6 yards above the ground, and the top of the billboard is 10 yards above the ground.

Now, let's analyze the possible scenarios:

If Emma's line of sight is parallel to the ground, there will be no elevation angle. This means she will be looking straight ahead and not looking up or down. Therefore, neither angle A nor angle B will be applicable.

If Emma's line of sight is directed toward the top of the billboard, angle A will be the elevation angle. In this case, she will be looking upward, aiming to see the messages at the top of the billboard. Angle B will not be applicable in this scenario.

If Emma's line of sight is directed toward the bottom of the billboard, angle B will be the elevation angle. Here, she will be looking downward, aiming to see the messages at the bottom of the billboard. Angle A will not be applicable in this scenario.

Therefore, the elevation angles that Emma might use to read messages on the billboard are angle A (to see the top of the billboard) and angle B (to see the bottom of the billboard).

Regarding the options provided, "T" represents the top of the billboard, "B" represents the bottom of the billboard, "MILIE" seems unrelated to the question, and "-20 yards" is not a valid elevation angle.

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The algebraic property that could be used to rewrite 4x + 2y as 2y + 4x is option C: Commutative Property of Addition.

From the question. if   a, b and c are any numbers,

Based on Associative Property of Addition, it state that:

a + ( b + c ) = ( a + b ) + c

Based on Associative Property of Multiplication, it state that:

a(bc) = (ab)c

Based on Commutative Property of Addition it state that:

a + b = b + a

Based on Commutative Property of Multiplication it state that:

ab = ba

Note that , 4x + 2y = 2y + 4x

So, Commutative Property of Addition is used in the expression.

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See text below

Which algebraic property could be used to rewrite 4x + 2y as 2y + 4x? A. Associative Property of Addition

B. Associative Property of Multiplication

C. Commutative Property of Addition

D. Commutative Property of Multiplication

The correct expression with the substituted values is −5±√(5^2 - 4(4)(-6)) / (2(4)).

The expression that shows the correct numbers substituted into the quadratic formula to solve the equation 4x^2 + 5x - 6 = 0 is:

−5±√(5^2 - 4(4)(-6)) / (2(4))

In the quadratic formula, the general form is x = (-b ± √(b^2 - 4ac)) / (2a), where a, b, and c are the coefficients of the quadratic equation. In this case, a = 4, b = 5, and c = -6.

Substituting these values into the quadratic formula, we have:

x = (-5 ± √(5^2 - 4(4)(-6))) / (2(4))

Simplifying further:

x = (-5 ± √(25 + 96)) / (8)

x = (-5 ± √121) / 8

x = (-5 ± 11) / 8

Therefore, the correct expression with the substituted values is:

−5±√(5^2 - 4(4)(-6)) / (2(4))

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The cost of one pack of streamers can be calculated by finding the difference in the total cost of the two purchases and dividing it by the difference in the number of packs of streamers. Therefore, one pack of streamers costs $2.75.

Let's denote the cost of one pack of streamers as "x". From the given information, we know that Randy bought 8 packs of streamers for $48.60, and later bought 3 packs of streamers for $34.85.

Using this information, we can set up the following equation to represent the total cost of the two purchases:

8x + 28 balloons = $48.60

3x + 28 balloons = $34.85

To find the cost of one pack of streamers, we need to subtract the second equation from the first equation to eliminate the balloons:

(8x + 28 balloons) - (3x + 28 balloons) = $48.60 - $34.85

Simplifying the equation gives:

5x = $13.75

Dividing both sides by 5, we find that:

x = $2.75

Therefore, one pack of streamers costs $2.75.

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The graph representing the solution set of the compound inequality -4 ≤ 3x - 1 and 2x + 4 ≤ 18 would be a closed interval on the number line, starting from -1 and ending at 7, inclusive.

To determine the graph that represents the solution set of the compound inequality -4 ≤ 3x - 1 and 2x + 4 ≤ 18, we need to solve each inequality separately and then find the overlapping region on a number line.

First, let's solve the first inequality:

-4 ≤ 3x - 1

Add 1 to both sides:

-3 ≤ 3x

Divide both sides by 3 (remembering to reverse the inequality when dividing by a negative number):

-1 ≤ x

So, the solution to the first inequality is x ≥ -1, which means x is greater than or equal to -1.

Now, let's solve the second inequality:

2x + 4 ≤ 18

Subtract 4 from both sides:

2x ≤ 14

Divide both sides by 2:

x ≤ 7

Thus, the solution to the second inequality is x ≤ 7, which means x is less than or equal to 7.

To find the overlapping region on the number line, we need to consider the intersection of the two solution sets.

The first inequality tells us that x is greater than or equal to -1, while the second inequality tells us that x is less than or equal to 7. Therefore, the overlapping region on the number line is between -1 and 7, inclusive.

The graph representing this solution set would be a closed interval on the number line, with a solid dot at -1 and another solid dot at 7, and a line connecting the two dots.

In summary, the graph representing the solution set of the compound inequality -4 ≤ 3x - 1 and 2x + 4 ≤ 18 would be a closed interval on the number line, starting from -1 and ending at 7, inclusive.

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To find the distance between two points in the coordinate plane, we can use the distance formula: Distance = √[(x2 - x1)^2 + (y2 - y1)^2].So the correct answer is C. √113.

Let's apply this formula to the given points in the coordinate plane  (-3, -2) and (5, 5):

Distance = √[(5 - (-3))^2 + (5 - (-2))^2]

= √[(8)^2 + (7)^2]

= √[64 + 49]

= √113

Therefore, the distance between two points in the coordinate plane (-3, -2) and (5, 5) is √113. Others options A. √13  B. √15  D. 5 E. 15

So the correct answer is C. √113.

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Lisa made $841.30 last week after working 35.8 hours and payingpaying $25 for health insurance.

To calculate Lisa's earnings, we need to multiply her hourly rate by the number of hours she worked. Lisa earns $23.50 per hour, and she worked for 35.8 hours. Multiplying these values, we get $23.50 * 35.8 = $841.30.
In addition to her earnings, we need to subtract the amount she paid for health insurance. Lisa pays $25 every week. So, to find her total earnings after deducting health insurance, we subtract $25 from $841.30: $841.30 - $25 = $816.30.
Therefore, Lisa made $816.30 last week after working 35.8 hours and paying $25 for health insurance.

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There were 35 buses and 25 vans, there were 14000 students and teachers who rode to the zoo in buses, and 250 students and teachers who rode to the zoo in vans.

Let b be the number of buses and v be the number of vans. We know that each bus transported 40 students and teachers, each van transported 10 students and teachers, and there were 10 more buses than vans.

We can use this information to write down two equations:

b * 40 + v * 10 = 1400

b = v + 10

We can solve the first equation for v:

v = (1400 - b * 40) / 10

Substituting this into the second equation, we get

b = ((1400 - b * 40) / 10) + 10

Simplifying, we get:

b = 140 - 4b

Solving for b, we get:

b = 35

Now that we know b, we can find v:

v = (1400 - 35 * 40) / 10

v = 25

Therefore, there were 35 buses and 25 vans. There were 1400 * 40 = 14000 students and teachers who rode to the zoo in buses, and 25 * 10 = 250 students and teachers who rode to the zoo in vans.

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The measure of segment QS can be determined by adding the lengths of QR and RS. In this case, since QR is 10 units long and RS is 7 units long, the measure of QS would be 17 units.

To find the measure of segment QS, we need to add the lengths of QR and RS. Given that QR is 10 units long and RS is 7 units long, we can calculate the measure of QS by adding these two lengths together. Therefore, QS = QR + RS = 10 + 7 = 17. Hence, the measure of segment QS is 17 units. By adding the lengths of the two segments that make up QS, we obtain the total length of the segment itself.

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To find the mean and standard deviation of the distribution of excess cleaning solution, we need to calculate the difference between the advertised amount of cleaning solution and the actual amount filled in the bottles.

1 fluid ounce (1 fl oz) is approximately equal to 30 milliliters (30 mL), so we can convert the measurements to milliliters for consistency.

Mean:

The mean of the distribution of excess cleaning solution can be calculated as the difference between the mean amount of filling (33 fl oz) and the advertised amount (32 fl oz), both converted to milliliters:

Mean = (33 - 32) fl oz * 30 mL/fl oz = 30 mL

Therefore, the mean of the distribution of excess cleaning solution is 30 milliliters.

Standard Deviation:

The standard deviation of the distribution can be found using the formula for the propagation of uncertainty. Since the standard deviation of the filling amount is given as 1.5 fl oz, we convert it to milliliters as well:

Standard Deviation = 1.5 fl oz * 30 mL/fl oz = 45 mL

Therefore, the standard deviation of the distribution of excess cleaning solution is 45 milliliters.

In summary, the mean of the distribution of excess cleaning solution is 30 milliliters and the standard deviation is 45 milliliters.

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The best measure of variability for the data is the range because the distribution is scattered.What is the range?The range of data is defined as the difference between the maximum value and the minimum value

. The list of weights is given below:8.7.5, 7.6, 3, 74, 7.9, 81,2,7.7The minimum value in the list is 3, and the maximum value in the list is 81. So, the drange is calculate as follows:Range = Maximum value – Minimum value= 81 – 3= 78The distribution is scattered because the range is relatively large.    

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Andre's proposed rate of 1/350 gallons of paint per square foot is accurate for determining the amount of paint needed for the art project.

Yes, I agree with Andre. The rate of 1/350 gallons of paint per square foot is the correct rate to determine how much paint is needed.

Given that each gallon of paint can cover 350 square feet, we can determine the amount of paint required by dividing the total square footage by the coverage rate:

Amount of paint required = Total square footage / Coverage rate

Amount of paint required = 1750 square feet / (1/350 gallons per square foot)

When we divide by a fraction, we can multiply by its reciprocal:

Amount of paint required = 1750 square feet * (350/1 gallons per square foot)

Amount of paint required = 1750 * 350 gallons

The unit of square feet cancels out, leaving us with gallons as the unit, which is the desired result.

Therefore, Andre's proposed rate of 1/350 gallons of paint per square foot is accurate for determining the amount of paint needed for the art project.

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The midpoint of the line segment connecting two points can be found by averaging their corresponding coordinates. Therefore, to obtain the midpoint of line BC, we add the coordinates of B and C and divide by 2.

Midpoint of line BC is given by:

\[\left(\frac{-1-3}{2},\frac{1-1}{2},\frac{2+0}{2}\right)=(-2,0,1)\]

The length of line AD is found by using the distance formula, which is given as:

\[d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2+(z_2-z_1)^2}\]

Thus, we need to find the coordinates of point D and A to determine the length of AD. The coordinates of D are the average of the coordinates of B and C.

\[\left(\frac{-1-3}{2},\frac{1-1}{2},\frac{2+0}{2}\right)=(-2,0,1)\]The coordinates of A are (1,2,-1).

The distance between A and D is found by substituting these values into the distance formula:

\[d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2+(z_2-z_1)^2}\] \[d=\sqrt{(1-(-2))^2+(2-0)^2+(-1-1)^2}\] \[d=\sqrt{(3)^2+(2)^2+(-2)^2}\] \[d=\sqrt{9+4+4}\] \[d=\sqrt{17}\]

Thus, the distance between points A and D is sqrt(17).Therefore, the midpoint of line BC is (-2,0,1) and the distance between points A and D is sqrt(17).

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