To be able to walk to the center $C$ of a circular fountain, a repair crew places a 16-foot plank from $A$ to $B$ and then a 10-foot plank from $D$ to $C$, where $D$ is the midpoint of $\overline{AB}$ . What is the area of the circular base of the fountain

2x 11 is congruent to 13 mod 16, if 3x 7 is congruent to 2 mod 16.

If 3x 7 is congruent to 2 mod 16, then 2x 11 is congruent mod 16 to what integer between 0 and 15, is inclusive.

To find the solution of 2x 11 congruent mod 16, given 3x 7 congruent to 2 mod 16, we can first use the given equation to find the value of x and then substitute it into the second equation.

First, we can solve for x in the given equation:

3x 7 is congruent to 2 mod 16

3x is congruent to 2 mod 16

x is congruent to 6 mod 16

Now that we know that x is congruent to 6 mod 16, we can substitute it into the second equation:

2x 11 is congruent to 2(6) 11 which is congruent to 13 mod 16

So the solution is that 2x 11 is congruent to 13 mod 16.

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Answer:

x = 2[tex]\sqrt{6}[/tex]

Step-by-step explanation:

[tex]\sqrt{24}[/tex] = [tex]\sqrt{(2)(2)(2)(3)}[/tex]  We can pull out a pair of 2's

2[tex]\sqrt{(2)(3)\\}[/tex] = 2[tex]\sqrt{6}[/tex]

We require median, interquartile range, outliers, minimum and maximum value.

What are statistics?

Statistics is a branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of data.

From the upper box plot representing the top 12 men's long jumpers at the U.S. Qualifying meet, we can gather the following pieces of information:

The median (middle value) of the data is around 7.6 meters, as indicated by the line in the center of the box.

The interquartile range (IQR), which is the range between the first and third quartiles, is approximately 0.4 meters, as indicated by the height of the box.

There are some outliers or values that fall outside the range of the box, which is represented by the dots or asterisks outside the box.

The minimum and maximum values for the data are around 7.3 meters and 8.0 meters, respectively, as indicated by the lower and upper ends of the whiskers.

From the lower box plot representing the distances achieved in the men's long jump at the 2012 Olympic games, we can gather the following pieces of information:

The median (middle value) of the data is around 8.0 meters, as indicated by the line in the center of the box.

The interquartile range (IQR), which is the range between the first and third quartiles, is approximately 0.5 meters, as indicated by the height of the box.

There are some outliers or values that fall outside the range of the box, which is represented by the dots or asterisks outside the box.

The minimum and maximum values for the data are around 7.5 meters and 8.4 meters, respectively, as indicated by the lower and upper ends of the whiskers.

The main difference between the two box plots is the median value, which is 0.4 meters apart and the IQR for the Olympic games is slightly bigger than the Qualifying meet.

Hence, we require median, interquartile range, outliers, and minimum and maximum values.

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We require median, interquartile range, outliers, and minimum and maximum values.

What are statistics?

Statistics is a branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of data.

From the upper box plot representing the top 12 men's long jumpers at the U.S. Qualifying meet, we can gather the following pieces of information:

The median (middle value) of the data is around 7.6 meters, as indicated by the line in the center of the box.

The interquartile range (IQR), which is the range between the first and third quartiles, is approximately 0.4 meters, as indicated by the height of the box.

There are some outliers or values that fall outside the range of the box, which is represented by the dots or asterisks outside the box.

The minimum and maximum values for the data are around 7.3 meters and 8.0 meters, respectively, as indicated by the lower and upper ends of the whiskers.

From the lower box plot representing the distances achieved in the men's long jump at the 2012 Olympic games, we can gather the following pieces of information:

The median (middle value) of the data is around 8.0 meters, as indicated by the line in the center of the box.

The interquartile range (IQR), which is the range between the first and third quartiles, is approximately 0.5 meters, as indicated by the height of the box.

There are some outliers or values that fall outside the range of the box, which is represented by the dots or asterisks outside the box.

The minimum and maximum values for the data are around 7.5 meters and 8.4 meters, respectively, as indicated by the lower and upper ends of the whiskers.

The main difference between the two box plots is the median value, which is 0.4 meters apart and the IQR for the Olympic games is slightly bigger than the Qualifying meet.

Hence, we require median, interquartile range, outliers, and minimum and maximum values.

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x     y   is the two-step function table of the given linear equation

0    -4

1     0

A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."

given an equation y  = 4x -4

Use the slope-intercept form to find the slope and y-intercept.

y = mx + c

m =4

c = -4

Slope = 4

The slope of the line is the value of m, and the y-intercept is the value of b.

y-intercept  : (0, -4)

x-intercept where y = 0 : (1, 0)

Therefore, the table of the two-step functions is Written below.

x     y  

0    -4

1     0

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The y-intercept in this situation means A. When the cab travels 0 miles, the total fee will be $14.00.

The formula to find the y-intercept is y = f(x), where x = 0, and then solve for y.

The equation for a linear relationship is y = mx + b, where x is the independent variable, y is the dependent variable, m is the slope of the line, and b is the y-intercept.

Cab Fare

Number of Miles Total Fee

2                             $17.00

5                             $21.50

7                            $24.50

10                          $29.00

15                          $36.50

Difference between 7 and 5 = 2

Difference between $24.50 and $21.50 = $3

Variable cost per mile (Slope) = Rise/Run

= $1.50 ($3/2)

y = mx + b

y-intercept, b = 24.50 - 7(1.5)

= 14

= $14.00

Thus, the y-intercept in this situation means Option A while the slope shows that for every additional mile, the total fee increases by $1.50.

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Answer:

The y-intercept in this situation means A. When the cab travels 0 miles, the total fee will be $14.00.

Step-by-step explanation:

Answer:

β, α, γ

Step-by-step explanation:

The figure only shows us the side lengths of the triangle, but is asking for the angles.

Thus, we have to use the angle relationships of a triangle to answer the question.

⭐What are the angle relationships of a triangle?

α° is opposite of the side length with 9 cm.

β° is opposite of the side length with 12 cm.

γ° is opposite of the side length with 5 cm.

∴ The angles from highest to the least are β, α, γ

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Answer:

Step-by-step explanation:

The answer should be BAY but if i check it don't work

Answer:

Without being able to see the graph, it is not possible for me to accurately compare the two functions. Is it possible for you to provide more information about the functions or the graph?

Answer:

Step-by-step explanation:

graph please

The relationship between xzw and wzv on the vertical angle is as follows:

∠ xzw + ∠ wzv = 180

Vertically opposite angles are angles that are opposite one another at a specific vertex and are created by two straight intersecting lines. Vertically opposite angles share the same vertex and they are congruent to each other.

Therefore,

∠vzy ≅ ∠wzx(vertical angles)

Hence, the relationships between angles xzw and wzv  is as follows:

∠ xzw + ∠ wzv = 180 (sum of angles on a straight line)

3x + 17 + x - 9 = 180

4x + 8 = 180

4x = 180 - 8

4x = 172

x = 172 / 4

x = 43

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The number of units that tile will he need to surround his pool is 19.82units.

this question is of quadratic equation ,

The number of units of tile simply refers to the perimeter.

So, we need to find all the sides of the rectangle.

Now, we have,

AB = 4.24 units

BD = 7.07 units.

So, we can find AD using pythagoras theorem.

So,

(AD)² + 4.24² = 7.07²

(AD)² + 17.978 = 49.985

(AD)² = 49.985 - 17.978

AD = √32.007

AD = 5.66 units

AD = BC = 5.66 units

Likewise, AB = DC = 4.24 units

Thus,

perimeter = 2(5.66) + 2(4.24) = 19.8 units.

The number of units that tile will he need to surround his pool is 19.82units.

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The number of calories Jina is burning per minute is 0.1 and the slope is 0.1

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

Points, (x, y) = (0, 0) and (150, 15)

The burning rate per minute can then be calculated as

Burning rate per minute = (y₂ - y₁)/(x₂ - x₁)

Substitute the known values in the above equation, so, we have the following representation

Burning rate per minute = (15 - 0)/(150 - 0)

Evaluate the quotient

Burning rate per minute = 0.1

In (a), we have

Burning rate per minute = 0.1

This rate is the same as the slope

Hence, the slope is 0.1

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Jackie spends 15 minutes running every day.

Part A: The relationship between the number of minutes Jackie runs (x) and the number of minutes she dances (y) every day can be represented by the following pair of linear equations:

Equation 1: x + y = 55 (This equation represents the total amount of time Jackie spends running and dancing every day, which is 55 minutes)

Equation 2: y = x + 25 (This equation represents the relationship between the number of minutes Jackie runs and the number of minutes she dances, which is that she dances 25 minutes longer than she runs)

Part B: To find out how much time Jackie spends running every day, we can substitute the second equation into the first equation:

x + (x + 25) = 55

2x + 25 = 55

2x = 30

x = 15

Therefore, Jackie spends 15 minutes running every day.

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A line's x-intercept as well as y-intercept are the points at which the x- and y-axes, respectively, are crossed.

Now, According to the question:

Let's know:

Definition of Intercept

The term "intercept" refers to the location where a line and curve crosses an graph's axis. The x-intercept would be the point at which the x-axis gets crossed. The y-intercept would be the point at which the y-axis becomes crossed.

The x- as well as y-axis intersection point gets what is meant when a line has an intercept. The y-axis was often taken into account if indeed the axis is also not stated. The letter "b" can be typically used to represent it.

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The answer will start with 500 USD. For every hour, 75 USD is charged. We can multiply 'x' to 75 USD which will represent the amount of hours. The equation will now become, 'y = 75x + 500'. In most cases, like this one, y will represent the total cost. Here are the answers.

a. 75USD

b. x (amount of hours)

c. y (total cost)

d. y = 75x + 500

Hope I understood what you were asking and if not I'm really sorry <3

The shaded region has a surface area of 7π.

The size of a region on a surface is measured in area. Surface area refers to the area of an open surface or the border of a three-dimensional object, whereas area of a plane region or plane area refers to the area of a form or planar lamina. The total space occupied by a flat (2-D) surface or the form of an item is defined as its area. Draw a square on a sheet of paper using a pencil. It is a two-dimensional figure. The area of the form on the paper is referred to as its Area. Consider your square to be made up of smaller unit squares.

Here,

find the area of the circle with radius =3 cm,

then subtract the areas of the two circles with radius 1 cm

pir^2 = the area of a circle with radius = r

=pi(3)^2 -pi(1)^2 - pi(1)^2

= 9pi -pi-pi

= 9π-2π

= 7π

The area of shaded region is 7π.

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The value of the given expression 4x(3-x)+5x(x-2) when x = -3 is 3.

A phrase is considered a mathematical expression if it contains at least two numbers or variables and one or more mathematical operations.

A number is 6 more than half of the other number, which is x.

This statement is represented by the mathematical equation x/2 + 6.

So, we have the expression:

4x(3-x)+5x(x-2)

Now, the value of the expression when x = -3.

Insert values and calculate as follows:

4x(3-x)+5x(x-2)

4(-3)(3-(-3))+5(-3)((-3)-2)

-12(6)-15(-5)

-72 + 75

3

Therefore, the value of the given expression 4x(3-x)+5x(x-2) when x = -3 is 3.

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Correct question:

What is the value of the expression 4x(3-x)+5x(x-2) for x=(-3)​?

If no payments are made then the then after 1 year the interest will go by 5% , therefore the amount to be paid will become ,   P + 25 = 525 $.

Principle + 5% of 500

Therefore, the equation becomes ,

Amount = P + 25

To calculate the interest ,

interest = principal × interest rate × term

             = 500 x 5 x 1

              = 2500.

A loan is defined as a thing or money which is borrowed, especially a sum of money that is expected to be paid back with an interest rate which is fixed by both the parties.

Loans are typically taken or granted by by corporations, financial institutions, and governments. They allow for growth in the overall money supply in an economy and open up competition by lending to new businesses.

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a) Each person would receive 1/6 of the cake

b) If there are 49 balls in total and each person is to get seven balls, How many persons can share the balls?

We know that we can be able to make us of the principles of algebra so as to be able to obtain the problems that we have to deal with in the question that appears in the image that is attached.

Given that we have the total amount of the cake as 2 1/2 and then we are told that there are 15 persons in the class thus the amount that everyone should receive would be x.

2 1/2 = 15 x

5/2 = 15x

5 = 2 * 15x

x = 5/2 * 15

x = 1/6

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Answer:

610.75

Step-by-step explanation:

48.86 divided by 0.08

Answer: A

Step-by-step explanation:

Based on the graph, we know that it is negative if it is under the x-axis. It is also indicated by the negative labels.

A: correct

Looking at choice A, it says the interval is from -4<x<-2. This means we have to find x=-4 and x=-2. On the graph, that interval is below the x-axis, so it is negative.

B: incorrect

Looking at choice B, it says the interval is from -1<x<1. This means we have to find x=-1 and x=1. On the graph, that interval is above the x-axis, so it is positive, not negative.

C: incorrect

Looking at choice C, it says the interval is from 2<x<4. This means we have to find x=2 and x=4. On the graph, that interval is above the x-axis, so it is positive, not negative.

Therefore, A is the correct answer.

The side length of each square represent for the rectangle to correctly represent (0, 3) · (0, 5) is 1 units.

A rectangle represented by (0, 3) · (0, 5) has length 3 units and breadth 5 units. To represent that rectangles with minimum number of squares of same size, we calculate the highest common factor.

Highest Common Factor is a mathematical concept used to find the greatest number that divides two or more numbers without leaving a remainder. It is also known as the greatest common divisor (GCD) or the greatest common factor (GCF).

Highest common factor of 3 and 5 is 1 as both are prime numbers. So squares with side length 1 unit best represent the rectangle to correctly represent (0, 3) · (0, 5).

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Answer:

9 days

Step-by-step explanation:

We know

Elizabeth has 214 gallons of milk; she drinks 23 of the quantity each day.

We take

214 / 23 = 9 days

So, she can drink in 9 days

Answer:The Surface Area of Pyramid is 105 cm².

Step-by-step explanation:

What is Surface Area of Pyramid?

If “P” is the base perimeter, “l” is the slant height, and “B” is the base area, then the total surface area of the regular pyramid formula is given by (½)Pl + B Square units.

Given:

slant height, l= 8 cm

So, the base Perimeter = 4 x 5

                                     = 20 cm

Now, area of the base = 5 cm x 5 cm

                                    = 25 cm²

Then,  surface area of a square pyramid

= 1/2 x slant height x base perimeter + area of base

= 1/2 x 8 x 20 + 25

= 80 + 25

= 105 cm²

Yes, if the value of y = 0 then it makes the horizontal line.

The term horizontal line is defined as one that goes from left to right.

And here we also know that they are parallel to the x –axis in the coordinate plane.

And the horizontal line has a slope of zero.

While we looking into the move along the right of the line, then it does not rise or fall at all.

Here we have to the that the following factors are also included in feature:

In as the horizontal line is parallel to the x-axis and it is parallel to the horizon.

Where as the horizontal line is a sleeping line and it is also defined as can be a sleeping, standing, or a slanting line.

Where the horizontal line is perpendicular to the y-axis.

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Following is the graph of two given equations.

The mapping of functions of two variables onto a Cartesian coordinate system, which is made up of a horizontal x-axis, or abscissa, and a vertical y-axis, or ordinate, is done analytically through the use of graphs. The intersection of each axis, which is a real number line, at its zero point is known as the origin.

On solving the two equations,

2x-3y=-6                              ....(1)

7x-3y=9                               .....(2)

Firstly we will find common points by elimination -

The common points are - (3,4)

Then We can find all the values of equation (1)

2x-3y=-6                          

x    0      3    -3

y    2      4     0

7x-3y=9

x    0      3    10

y   -3      4    20.33

The respective graph is attached below

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Angle sum of three angles of ABC triangle must be equal to 180 degrees.

Angle is the space between two intersecting lines or surface or at close to the point where there ends point meet.

A triangle is a polygon that has three straight sides and three angles.

Let, ABC is a triangle. The angles in this triangle can be different types.

All angles in ABC can be lies between 90 degrees and that time triangle is called acute triangle. If ABC has one right angle, then this is termed as right-angled triangle.

If one of the angles is measured greater than 90 degrees, the triangle is called obtuse triangle.

if we find all angles in ABC triangle is equal to 60 degrees, this is termed as equilateral triangle.

But for each triangle, the sum of three angles must be equal to 180 degrees.

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Answer:

Step-by-step explanation:

1) 1,15,29,43,57,.....

here, 15-1 =14 and 29-15=14

therefore,it is an arithmetic sequence with common difference = 14

2) 3,6,9,15,17,....

here, 6-3=3, 9-6=3 , 15-9=6

therefore,it is not an arithmetic sequence.

3) 93,86,79,72,65,......

here, 86-93=-7 , 79-86=-7 and 72-79=-7

therefore,it is an arithmetic sequence with common difference = -7

4) 37,34,31,29,26,......

here, 34-37 = -3,31 - 34 = -3,29 - 31 =-2

therefore,it is not an arithmetic sequence.

8x-12+3x+5=180(sum of straight angles)

8x+3x-12+5=180

11x-19=180

11x=180-19

11x=161

x=161÷11

Step-by-step explanation:

sum of straight angles are 180

Answer:

B) 2 + 3x = 8

Step-by-step explanation:

Option B is not an expression as expressions do not have equal signs.

Based on the data, the statement that is most likely correct is D. In Grade 9, 18% of students liked running.

The ratio (fraction or proportion) of the number of times a data value appears in the set of all outcomes to the total number of outcomes is known as the relative frequency.

From the information, the Dean collected data on the favorite sports of the students of two grades.

Here, the table shows the relative frequencies of rows for the data collected:

Swimming      Running Volleyball Row     totals

Grade 8          0.17       0.24              0.05     0.46

Grade 9           0.14       0.18             0.22      0.54

Column totals 0.31      0.42              0.27        1

In the table, Grade 9, 18% of students liked running. This is Illustrated above. The correct option is D.

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