Slope of y=-5.5
Slope of 4x-4y=22

The diagonal length of the figure, to make sure the base of his tree house is a rectangle, is given as follows:

15 feet.

We want for the figure in this problem to represent a rectangle. For a rectangle, the diagonal is the hypotenuse of a right triangle in which the side lengths are the same as the side lengths of the triangle, and there is an angle of 90º between them.

Hence the Pythagorean Theorem can be used to obtain the diagonal, which states that the length of the hypotenuse squared is equals to the sum of each of the sides of the triangle squared.

Then the diagonal length is calculated as follows:

d² = 12² + 9²

d = square root (12² + 9²)

d = 15 feet.

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The area of the triangle and the square are the same = 4 square units

How to determine the area?

You should know that the area talks about the floor space occupied by each shape.

The square occupies 2 units on the base and two units on the height

The triangle occupies two grids on the base and four grids on the height

Area of square is S² and Area of a triangle is 1/2base*height

⇒Area of square is = 2² = 4 ²square units

Area of triangle = 1/2 * 2 * 4 = 4 square units.

In conclusion the area of the triangle is equal to the area of the square with 4 units square each

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Answer:

x = 71

y = 71

Step-by-step explanation:

The value of x and y would be the same because this is an isosceles triangle.

38 + x + y = 180

x + y = 142

142/2 = 71

x = 71

y = 71

The expression 6wy-2wz+3xy-xz can be factorized into (2w+x) ( 3y-z). The value of a and b are 2 and 3 respectively

To factorize an algebraic expression, the highest common factors of the terms of the given algebraic expression are determined and then we group the terms accordingly. In another word, the reverse process of expansion of an algebraic expression is its factorization.

to factorize 6wy-2wz+3xy-xz , we firstly collect like terms, 6wy + 3xy -2wz - xz

The next step is to group the expression into two

(6wy+3xy)(-2wz-xz)

bringing out the factors in each parentheses

3y( 2w+x) -z(2w+z)

therefore 6wy-2wz+3xy-xz = (3y-z)(2w+z)

comparing the expression (aw+x)(by-z)

Therefore a = 2 and b= 3

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The multiples of 8 are 8, 16, 24, 32, 40, 48, 56, 64, 72, 80… and so forth.

A multiple of 8 is a sequence where the difference among each next number and the previous number is 8. In other words, multiples of 8 are numbers which can be divided exactly by 8. Multiples of 8 are found by counting up in eights.

We also can see that the multiples of 8 are in the table of 8. The first multiples of 8 are 8, 16, 24, 32, 40. And the prime factorization of 8 is 8 = 2 × 2 × 2 = 2³.

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Answer:

-6.2

Step-by-step explanation:

1.4-3.1-4.5

=-1.7-4.5

=-6.2

The equation y=ax^b, where a and b are constants. If the points follow this equation, then the set of points is an exponential function.

An exponential function is a function in which the output is proportional to the exponent of the input. Exponential functions follow the equation y=ax^b, where a and b are constants. To determine if a set of points is an exponential function, you must look for a pattern in the points that follows the equation. If the points follow the equation, then the set of points is an exponential function. If the points do not follow the equation, then the set of points is not an exponential function. An example of an exponential function is y=2^x, where the output, y, is proportional to the exponent of the input, x. Exponential functions can be used to model a variety of real-world phenomena, such as population growth, radioactive decay, and compound interest.

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The process of identify the exponential function coordinates are explained below.

The term coordinates in math is defined as a set of numbers or numbers and letters together that show you a position on a map.

Here we have to identify that whether the a set of points is an exponential function.

In order to find this one, first we must know the definition of exponential function,

The term exponential function is defined as defined by the formula f(x) = aˣ where the input variable x occurs as an exponent. and the exponential curve depends on the exponential function and it depends on the value of the x.

Now, the steps to identify whether the set of points are exponential function or not is listed below:

If we plot the points on the graph passes through the point (0,1).

If the domain of the points is in real numbers.

Whether the range of the points is y>0.

If we plot the points on the graph is continuous and increasing.

Whether we plot the points on the graph is asymptotic to the x-axis as x approaches negative infinity.

If we plot the points on the graph increases without bound as x approaches positive infinity.

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The required measures of the angles of parallelogram ABCD as are follows m∠A = 66°,  m∠B = 114°, and m∠C = 66°.

A parallelogram is defined as a special type of quadrilateral that has both pairs of opposite sides parallel and equal.

Given parallelogram ABCD,

m∠D = 114°

In a parallelogram, the opposite angles are congruent, so m∠A is congruent to m∠C. This means that m∠A and m∠C have the same measure.

If m∠D = 114°, then m∠A must be equal to 180° - 114° = 66°, since the measures of the adjacent angles of a parallelogram add up to 180°.

So, m∠A = m∠C = 66°

So, m∠B = 114°

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In the worst case, it will take 125.7 more hours for all of the oil to leak out. In the best case, it will take 104.17 more hours for all of the oil to leak out.

Worst case:

25,000 gallons of oil / (720 gallons/hour) = 34.72 hours

25,000 gallons of oil - (720 gallons/hour * 34.72 hours) = 8,640 gallons of oil remaining

8,640 gallons of oil / (720 gallons/hour) = 12.04 hours

34.72 hours + 12.04 hours = 46.76 hours

46.76 hours x (720 gallons/hour) = 33,360 gallons of oil

25,000 gallons of oil - 33,360 gallons of oil = -8,360 gallons of oil

-8,360 gallons of oil / (720 gallons/hour) = -11.56 hours

46.76 hours + (-11.56 hours) = 35.2 hours

35.2 hours x (720 gallons/hour) = 25,440 gallons of oil

25,000 gallons of oil - 25,440 gallons of oil = 560 gallons of oil

560 gallons of oil / (720 gallons/hour) = 0.78 hours

35.2 hours + 0.78 hours = 36.0 hours

36.0 hours x (720 gallons/hour) = 25,920 gallons of oil

25,000 gallons of oil - 25,920 gallons of oil = 80 gallons of oil

80 gallons of oil / (720 gallons/hour) = 0.11 hours

36.0 hours + 0.11 hours = 36.11 hours

36.11 hours x (720 gallons/hour) = 25,952 gallons of oil

25,000 gallons of oil - 25,952 gallons of oil = 48 gallons of oil

48 gallons of oil / (720 gallons/hour) = 0.07 hours

36.11 hours + 0.07 hours = 36.18 hours

36.18 hours x (720 gallons/hour) = 25,976 gallons of oil

25,000 gallons of oil - 25,976 gallons of oil = 24 gallons of oil

24 gallons of oil / (720 gallons/hour) = 0.03 hours

36.18 hours + 0.03 hours = 36.21 hours

Best case:

25,000 gallons of oil / (720 gallons/hour) = 34.72 hours

25,000 gallons of oil - (720 gallons/hour * 34.72 hours) = 8,640 gallons of oil remaining

8,640 gallons of oil / (720 gallons/hour) = 12.04 hours

34.72 hours + 12.04 hours = 46.76 hours

46.76 hours x (720 gallons/hour) = 33,360 gallons of oil

25,000 gallons of oil - 33,360 gallons of oil = -8,360 gallons of oil

-8,360 gallons of oil / (720 gallons/hour) = -11.56 hours

46.76 hours + (-11.56 hours) = 35.2 hours

35.2 hours x (720 gallons/hour) = 25,440 gallons of oil

25,000 gallons of oil - 25,440 gallons of oil = 560 gallons of oil

560 gallons of oil / (720 gallons/hour) = 0.78 hours

35.2 hours + 0.78 hours = 36.0 hours

36.0 hours x (720 gallons/hour) = 25,920 gallons of oil

25,000 gallons of oil - 25,920 gallons of oil = 80 gallons of oil

80 gallons of oil / (720 gallons/hour) = 0.11 hours

36.0 hours + 0.11 hours = 36.11 hours

36.11 hours x (720 gallons/hour) = 25,952 gallons of oil

25,000 gallons of oil - 25,952 gallons of oil = 48 gallons of oil

48 gallons of oil / (720 gallons/hour) = 0.07 hours

36.11 hours + 0.07 hours = 36.18 hours

Therefore, in the worst case it will take 125.7 more hours for all of the oil to leak out and in the best case it will take 104.17 more hours for all of the oil to leak out.

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a) Another name of plane p  is parallelogram.

b) Z and X are distinct points that are collinear.

c) Y, X, Z, and T are distinct points that are coplanar.

d) Then QT and ST are distinct lines that are intersect.

One particular type of quadrilateral that is created by parallel lines is a parallelogram. A parallelogram can have any angle between its adjacent sides, but it must have parallel opposite sides in order to be considered one. If two opposite sides of a quadrilateral are parallel and congruent, it will be a parallelogram. As a result, a parallelogram is a quadrilateral with two pairs of opposite sides that are both parallel and equal.

The Greek word "parallelogrammon," which means "bounded by parallel lines," is where the word "parallelogram" comes from. A quadrilateral that has parallel lines enclosing it is referred to as a parallelogram.

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Answer:

b = 138⁰ (Being alternate angles)

The total number of girls and the total number of boys in the club are

number of girls = 58

number of boys = 25

The total number of girls and the total number of boys in the club is solved using the equation generated as follows

The number of girls in the Middle School Cyber Club was 8 more than double the number of boys

let the number of girls be x and the number of boys be y

x = 8 + 2y

total there were 83 middle school students in the Cyber Club

x + y = 83

substituting for x in x + y = 83

x + y = 83

plugging in x = 8 + 2y

8 + y + y = 83

8 + 2y = 83

solving for y

3y = 83 - 8

3y = 75

y = 25

solving for x

x = 8 + 2y

x = 8 + 2 * 25

x = 58

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Answer:

A quadrilateral is a parallelogram if and only if opposite angles are equal.

So, to make the quadrilateral a parallelogram, we can set the following equalities:

(4x + 13) deg = (5x - 12) deg

(4y + 7) deg = (3x - 8) deg

Solving the first equation,

4x + 13 = 5x - 12

x = -5

Solving the second equation,

4y + 7 = 3(-5) - 8

4y + 7 = -17

4y = -24

y = -6

So, the values of x and y that make the quadrilateral a parallelogram are x = -5 and y = -6

Answer:

27

Step-by-step explanation:

Answer:

don't know if I am correct but,

18<n<20

so must be 19.

Each student must work 14 hours on the project.

To solve this problem, we need to isolate the variable x on one side of the equation.

First, we can get rid of the fraction on the left side of the equation by multiplying both sides by 5:

5 * (x + 28) / 5 = 5 * (3x) / 5

This simplifies to:

x + 28 = 3x

Then, we can subtract x from both sides to get:

x + 28 - x = 3x - x

This simplifies to:

28 = 2x

Finally, we can divide both sides by 2 to find the value of x:

28 / 2 = 2x / 2

This simplifies to:

14 = x

Therefore, each student must work 14 hours on the project.

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Each student must work 14 hours on the project.

this is a question of set of equations, the solution is as follows,

we can get rid of the fraction on the left side of the equation by multiplying both sides by 5:

5 * (x + 28) / 5 = 5 * (3x) / 5

x + 28 = 3x

Then, we can subtract x from both sides to get:

x + 28 - x = 3x - x

28 = 2x

2x=28

Finally, we can divide both sides by 2 to find the value of x:

2x/2 = 28/2

x = 14

Therefore, each student must work 14 hours on the project.

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Answer: Don't use this if it is a test!

Step-by-step explanation:

Hello! An equation for this to represent the number of dogs that are not yellow is 12 dogs - yellow dogs = dogs that are not yellow.  Make an expression out of this with numbers and variables! I hope this helps you!

Yes, the distribution given is a discrete probability distribution.

A discrete probability distribution is a distribution that assigns probabilities to individual values or discrete outcomes. In other words, it is a distribution that consists of a set of discrete values, each with an associated probability.

In the given distribution, the values x = 10, 20, 30, 40, and 50 are all discrete values, and each has an associated probability P(x) = 0.2. This satisfies the definition of a discrete probability distribution.

On the other hand, a continuous probability distribution is a distribution that assigns probabilities to intervals of values rather than individual values.

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The minimum cost per unit is obtained for an order of 8 units.

Since the total cost is modeled by;

We'll solve this by unitary method

The unitary method is a technique for solving a problem by finding the value of a single unit, I.e.,1,(by dividing), and then finding the necessary value by multiplying the single unit value.

C(x)=5x²+320

Then;

1 unit costs; C(x)=5(1)²+320 = 325

cost per unit 325/1 = 325

8 units costs; C(x)=5(8)²+320 = 640

cost per unit = 640/8 = 80

80 units costs; C(x)=5(80)²+320 = 32320

Cost per unit = 32320/80 = 404

The minimum cost per unit is obtained for an order of 8 units.

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Answer:

width: 8 ft

length: 24 ft

Length of fence whole garden: 2 (8 + 24) = 64 ft

Step-by-step explanation:

x * 3x = 192

3x² = 192

x² = 192 / 3

x² = 64

x = 8

width: 8 ft

length: 3 * 8 = 24 ft

Length of fence whole garden: 2 (8 + 24) = 64 ft

Answer:

x = -19/7 z

z = -7/19 x

Lets solve for x in 21x + 39z = (7x+z):

Step 1: Add -7x to both sides.

21x+39z+−7x=7x+z+−7x

14x+39z=z

Step 2: Add -39z to both sides.

14x+39z+−39z=z+−39z

14x=−38z

Step 3: Divide both sides by 14.

14x/14 = −38z/14

x = −19/7 z

Lets solve for z in 21x 39z = (7z+z):

Step 1: Add -z to both sides.

21x+39z+−z=7x+z+−z

21x+38z=7x

Step 2: Add -21x to both sides.

21x+38z+−21x=7x+−21x

38z=−14x

Step 3: Divide both sides by 38.

38z/38 = −14x/38

z = −7/19 x

Hope this helps!!

The range of probability is:

​c. ​zero to one

Probability is a measure of the likelihood of an event occurring. It is a value that ranges between 0 and 1, where 0 represents an impossible event, and 1 represents a particular event. In other words, a probability of 0 means that an event will not happen, and a probability of 1 means that an event will happen. Any probability value between 0 and 1 can be written as a decimal or a percentage. For example, a probability of 0.5 can also be written as 50%.

It is important to note that probability values cannot be negative or greater than 1. In probability theory, events that are impossible to happen have a probability of 0, and events that are certain to happen have a probability of 1. For example, a probability value of 0.5 means a 50% chance of an event and a 50% chance of it not happening. Therefore, the range of probability is between 0 and 1, as any value outside of this range would not be a valid probability.

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If the dot plot is converted to a box plot, the first quartile would be drawn at 61 and the third quartile would be drawn at 63.

In Mathematics, a dot plot can be defined as a type of line plot that is typically used for the graphical representation of a data set above a number line, especially through the use of dots.

Based on the dot plot, the average daily temperatures include the following:

Temperature                  frequency            

  59                                   0

  60                                   2

  61                                    3

  62                                   3

  63                                   4

  64                                   2

  65                                   1

Total                                 15

By grouping the average daily temperatures, we have:

(60, 60, 61), 61, (61, 62, 62), 62, (63, 63, 63), 63, (64,64,65)

First quartile = 61.

Median = 62.

Third quartile = 63.

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Answer:

Step-by-step explanation:

I got you. ( It's basically just y is double x.)

y  x

2  1

4  2

6  3

8  4

10  5

Compare the costs for the two programs and results are when the number of classes are more, canoeing is less expensive and when the number of classes are less, fishing is less expensive.

The division in mathematics is one kind of operation. In this process, we split the expressions or numbers into the same number of parts.

Given:

The graph and the table show the total costs of two different summer programs, y, as functions of the two different summer programs, y, as a function of the number of classes, x.

For canoeing program,

And number of class 1 then cost is $32.

The number of classes 2 then y = 44

For each, 44/2 = $22

The number of classes 3 then y = 56

For each, 56/3 = $18.67

The number of classes 2 then y = 68

For each, 68/4 = $17

So,

When the number of classes are more, canoeing is less expensive.

And number of class 1 then cost is $20.

The number of classes 2 then y = 40

For each, 40/2 = $20

The number of classes 3 then y = 60

For each, 60/3 = $20

The number of classes 2 then y = 80

For each, 80/4 = $20

So,

When the number of classes are less, fishing is less expensive.

Therefore, when the number of classes are more, canoeing is less expensive and when the number of classes are less, fishing is less expensive.

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Answer:

it is a one-to-one function

Step-by-step explanation:

Answer:

b

production of pancakes depends on batter

Answer:

b, because they are asking how much batter(b) they will need to make pancakes(p), which the dependent variable is what happens as a result of the independent variable, which in this case it is, b, or the batter to make the pancakes, so the dependent variable would be b.

Step-by-step explanation:

Hope it helps!

It is impossible to determine with certainty which number of pushups Bucky will never do in any game, as this depends on Bucky's physical abilities, training, and determination.

It is possible that Bucky may be able to do a very large number of pushups in a game, or he may not be able to do very many. It is also possible that there may be certain numbers of pushups that Bucky finds more challenging or difficult to do than others, but this would depend on his individual physical abilities and strengths. Ultimately, the number of pushups that Bucky will be able to do in any given game will depend on a variety of factors, and it is not possible to predict with certainty which numbers he will never do.

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Number of push-ups Bucky will never perform in any game is impossible to predict with confidence because it relies on Bucky's physical prowess, training, and willpower.

In a game, Bucky might be able to perform a lot of push-ups or he might not be able to perform many at all. It's also likely that Bucky will find some numbers of push-ups harder or more difficult to complete than others; however, this will depend on his particular physical prowess and capabilities.

In the end, Bucky's ability to do a certain number of push-ups throughout a game will rely on a multitude of variables, and it is impossible to say with certainty certain numbers he will never complete.

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