What are the proofs to this triangle? There has to be a minimum of 6 Proofs.

The number 7 will be placed in the middle circle.

To place the numbers 2, 6, 7, 8, and 9 in the circles so that the sums across and down are equal, you can use the following method:

1. Place the median number (7) in the middle circle.

2. Place the two smallest numbers (2 and 6) on either side of the median number.

3. Place the two largest numbers (8 and 9) in the top and bottom circles.

Here is a list of them. Each group of three numbers makes up a side of the triangle. Of course, within a side you can replace round numbers that are not on a corner, but that does not really give any new solutions.

So, the final arrangement would be:

6 2 7

9 8 7

6 2 7

Therefore, the number 7 will be placed in the middle circle.

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The chart fits the functional equation for all values of x, according to the claim made.

The Geometric Mean (GM) in mathematics is the average or mean that, by calculating the product of the values of the collection of numbers, denotes the central trend of the numbers. In essence, we combine the numbers collectively and calculate their nth root, in which n is the entire amount of data values.

We can use the given functional equation f(x+1) = 4(f(x)) to find the values of f(x) for each value of x, given that we know f(1) = 4. We start by computing:

f(2) = 4(f(1)) = 4(4) = 16

f(3) = 4(f(2)) = 4(16) = 64

f(4) = 4(f(3)) = 4(64) = 256

f(5) = 4(f(4)) = 4(256) = 1024

Now, we have determined all the values of f(x) for x=1 to 5. Since the table has 5 rows, we can write:

x f(x)

1 4

2 16

3 64

4 256

5 1024

We can check that the table satisfies the given functional equation f(x+1) = 4(f(x)). For example, when x = 3, we have:

f(x+1) = f(4) = 256

4(f(x)) = 4(f(3)) = 4(64) = 256

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The probability of randomly selecting a girl from Ms. Garcia's class is 5/9.

Which means that for every 5 students in the class, 4 of them are boys and 5 of them are girls.

To calculate the probability of selecting a girl from the class, we need to divide the number of girls by the total number of students:

Number of girls: 5 students

Total number of students: 4 students + 5 students = 9 students

Probability of selecting a girl: 5 students / 9 students = 5/9

So the probability of randomly selecting a girl from Ms. Garcia's class is 5/9.

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Answer: 174 miles

Step-by-step explanation: 14.5 (14 1/2) times 12 is 174

The distance around the track along its outer edge is  238 + 100 x π metres and the area of the track is  1250 x π  + 2380 square metres.

The racetrack is divided by two parallel sections and two semi-circular endpoints. The two parallel segments are 119 metres long, and the track is 10 metres wide. The inner length of the two parallel sections is 70 metres.

To calculate the distance around the track's outer edge, multiply the lengths of the two parallel segments by the diameter of the two semi-circular ends. C = 2 x π x r, where r is the radius of the semi-circle, may be used to compute the circumference of each semi-circular end.

The radius of each semi-circle is calculated by subtracting the track width (10 metres) from half the inner distance between the two parallel sections (70 metres / 2 = 35 metres). So, the radius of each semi-circle is 35 metres - 10 metres = 25 metres.

As a result, the circumference of each semi-circle is 2 x π x 25 = 50 x π  metres. As a result, the circumference of the track along its outside border is 119 metres + 119 metres + 50 x π  metres + 50 x π  metres = 238 + 100 x π metres.

To calculate the area of the track, first calculate the areas of the two semi-circular ends and the two parallel segments, then add them. A = π[tex]r^{2}[/tex], where r is the radius of the semi-circle, may be used to compute the area of each semi-circular end.

Each semi-circle has an area of π x [tex]25^2[/tex] = 625 x π  square metres. The size of the two parallel lengths is 1190 square metres (119 metres x 10 metres). The track's total area(A) = 625 x π  + 625 x π  + 1190 + 1190

A= 1250 x π  + 2380 square metres.

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Answer:

12000

Step-by-step explanation:

4500:12=470

425:125=100

1000×12=12000

Step-by-step explanation:

For the first question, let's add the %'s

37% + 13% + 25% + 25% = 100%

So it looks like you have a 100% chance to win a prize.

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For the second question

It cost $2 to play

Soda - $1

Candy Bar - $1

Toy - $3

Mega Win - $40

It looks like 2 out of 4 (50%) cost more than the price to play.

So we add the % of the Toy and Mega since those are the ones more than $2

25% + 13% = 38% chance to win a prize more than the cost to play

Answer:

-3(x+0.5)^2-181/4 (if I calculated correctly)

Step-by-step explanation:

f(x)=-3x^2-3x-46

=-3(x^2+x+46/3)

=-3(x+0.5)^2-(0.5)^2+46/3

=-3(x+0.5)^2+181/12

=-3(x+0.5)^2-181/4

The principal amount of $5,000 deposited for 8 years with simple interest gives amount $7,880 at the annual interest of 7.2%.

Total amount 'A' in the Macy account after 8 years = $7,880

Time 't' = 8 years

Principal amount 'P' = $5,000

Let 'r' be the rate of interest given in saving account with annual simple interest.

Simple interest = Amount - Principal

                         = $7,880 - $5,000

                         = $2,880

Simple interest = ( P × r × t ) / 100

Substitute the value we get,

⇒ $2,880 = ( 5,000 × r × 8 ) / 100

⇒ r = ( 2,880 × 100 ) / ( 5,000 × 8 )

⇒ r = 7.2%

Therefore, the annual interest rate for the given amount as per simple interest is equal to 7.2%.

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"Every linear transformation is a matrix transformation." This is false. Not all linear transformations are matrix transformations, even if all matrix transformations are linear transformations.

A point, line, or geometric object can be changed in four different ways that are all referred to as transformations. The Pre-Image refers to the object's initial shape, and the Image, after transformation, refers to the object's ultimate shape and location.

Bring out the pattern blocks, tangrams, and geoboards for another low-prep, high-engagement method of teaching geometric transformations. Students can produce an original design and then hand it off to a partner so that they can add a reflection, rotation, or translation to it.

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The value of m for which the equation will have two equal solutions is given as follows:

m = -2.5.

A quadratic equation is modeled by the rule presented as follows:

y = ax² + bx + c

The discriminant of the quadratic function is given as follows:

Δ = b² - 4ac.

The numeric value of the coefficient and the number of solutions of the quadratic equation is defined as follows:

For this problem, the discriminant is given as follows:

Δ = 2m + 5 (it is the term that goes inside the root during the solution).

Hence, to have two equal solutions, the condition is:

Δ = 0.

Hence:

2m + 5 = 0

2m = -5

m = -5/2

m = -2.5.

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The length and the width are 21cm and 16cm respectively.

The formula for calculating the perimeter of a rectangle is expressed as;

P = 2(l +w)

Given that;

But we have that;

Length = 5 + w

Substitute the value

74 = 2(5 + w + w)

collect like terms

74=2 (5 + 2w)

expand the bracket

64 = 4w

Make 'w' the subject of formula

w = 16cm

Then, length = 5 + 16 = 21cm

Hence, the values are 16cm and 21cm

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The solution for this equation system is x= 29, y=53, (29, 53).

[tex](1)y=3x-34\\ \\(2)y=2x-5[/tex]

[tex](2x-5)=3x-34\\\\2x-5=3x-34[/tex]

[tex]2x-5+5=3x-34+5\\ \\2x=3x-29[/tex]

[tex]2x-3x=3x-29-3x\\ \\-1x=-29\\ \\-x=-29[/tex]

[tex]-x(-1)=-29(-1)\\ \\x=29[/tex]

To find a value of "y", use the calculated value of "x" (29), and substitute in any of the two equations to find the value of "y". For this solution, we're going to use equation 2.

[tex]y=2(29)-5\\ \\y=58-5\\ \\y=53[/tex]

On step 6 we proved that the value of "x=29" returns a value of "53" when evaluating with equation 2. Now, if equation 1 returns the same "y" value when evaluating "x=29", then the calculated values of both "x" and "y" are correct. Let's verify!

[tex]y=3(29)-34\\ \\y=87-34\\ \\y=53[/tex]

Both of the equations return the same value of "y" (53) when evaluated with "x=29". Therefore, the solution for this equation system is x= 29, y=53, (29, 53).

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Simultaneous equation is a finite set of equations for which common solutions are soughtThe equivalent expression is 5x + 7y = 37

A finite set of equations for which common solutions are sought is referred to as a set of simultaneous equations, often known as a system of equations or an equation system.

Given the simultaneous equation below:

-2x - y = -4

7x + 8y = 41

In order to compress the equation into 1, we need to add the equation or subtract the equation

On adding, we will have:

(-2x + 7x) + (-y + 8y) = -4 + 41

5x + 7y = 37

Hence the equivalent expression is 5x + 7y = 37

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The length of the arc is 42.98 inches, so the correct option is A.

For an arc defined by an angle θ on a circle of radius r the length of the arc is given by:

L = (θ/360°)*2*pi*r

Where pi = 3.1416

Here we know that:

r = 10.26 inches

θ = 240°

Then we can replace that in the formula above, we will get:

L = (240°/360°)*2*3.1416*10.26 in

L = 42.98 inches

The correct option is A.

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Answer:

Let's first convert 1/6 mile into minutes by multiplying the distance by the number of minutes per mile:

1/6 mile * (1 minute/1/6 mile) = 6 minutes/mile

Next, let's convert the 7/9 minutes into miles:

7/9 minutes * (1/6 mile/minute) = 7/9 * 1/6 mile = 7/54 miles

Now that we have the distance and time in the same units, we can calculate Ed's speed as:

Speed = Distance / Time = 7/54 miles / 7/9 minutes = 7/54 miles / (7/9 * 1 minute) = 7/54 miles / (7/9) minutes = 7/54 miles / (7/9) = 54/7 miles/minute

So, Ed's speed is 54/7 miles per minute.

Step-by-step explanation:

The plane is travelling at a speed of 424.26 mph.

Velocity of an object is the speed of the object with a given direction. Therefore velocity is a vector quantity and speed is a scalar quantity.

Given that,

A plane is traveling Northeast.

If the plane is travelling northeast, then the angle that the plane makes with the horizontal component will be 45°.

The eastern component of it's velocity is 300 mph.

Vector v can be represented as v cos (θ) i + v sin(θ) j.

Here v cos (θ) is the eastern component and v sin(θ) is the northern component.

v cos (θ) = 300

v cos(45°) = 300

v = 300 / cos(45°)

  = 300 / (1/√2)

  = 424.26 mph

Hence the speed of the plane is 424.26 mph.

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Answer:

8b + 4 = 6

Step-by-step explanation:

8b + 4 = 6

It didn't say you have to solve for b, but just in case...

8b = 6 - 4 = 2

b = 2/8 = 1/4

A public event or celebration, typically held outdoors and involving stalls, entertainment, and processions.

In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.

Multiplication is often referred to as repeated addition because what the multiplication problem is telling you is that you have a certain number of groups of something, all containing a specific number. Confused yet? Here's an example.

You have 3 bags of candy, and each bag contains 5 pieces of candy. How many pieces of candy do you have?

There are two ways to solve this problem. The first is by adding up the pieces of candy:

5 + 5 + 5 = 15

The other way to solve this problem is to use multiplication, because you have 3 groups of candy with 5 pieces of candy in each bag.

3 * 5 = 15

The answer to this multiplication problem is the product, which in this case is 15.

Here's another example. The classroom has 8 rows of chairs and each row has 7 chairs in it. How many chairs are there?

Again, you could add:

7 + 7 + 7 + 7 + 7 + 7 + 7 + 7 = 56

Or, you can find the product by multiplying:

7 * 8 = 56

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CORRECT QUESTION FORMAT IS GIVEN BELOW -----

Q. What is the Product in Math?

Step-by-step explanation:

So to start

Perpendicular lines are lines that form 90 degree angles when they meet.

Parallel lines will never touch, no matter how far they go.

So

Top left

A vertical line and a horizontal line

This would be perpendicular

Lines that intersect to form right angles

As mentioned above this would be perpendicular

Two nonvertical lines that have a product of -1 for their slopes.

Parallel lines always have the same slope, so this goes for parallel.

Equations that can be written in slope intercept form

This would be both as all lines can be written in this form

Non vertical lines that have the same slope and different y-intercepts

As they have the same slope this would make it parallel

You can determine the relationship between two lines by comparing their slopes and y-intercepts.

This is both as this is a way to compare all lines

Lines in the same plane never intersect

This would be parallel

Slopes are opposite reciprocals

This is perpendicular as the slopes of perpendicular lines are reciprocals

Vertical lines that have different x-intercepts

This would be parallel

Sorry this is a lot

Hope this helped though :)

Since triangle ABC with vertices at A(−3, −3), B(3, 3), C(0, 3) is dilated to create triangle A′B′C′ with vertices at A′(−15, −15), B′(15, 15), C′(0, 15), the scale factor used is: A. 5.

In Geometry, the scale factor of a geometric figure can be calculated by dividing the dimension of the image (new figure) by the dimension of the pre-image (original figure):

Scale factor = Dimension of image (new figure)/Dimension of pre-image(actual figure)

Substituting the given parameters into the scale factor formula, we have the following;

Scale factor = Dimension of image (new figure)/Dimension of pre-image(original figure)

Scale factor = -15/-3

Scale factor = 5.

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Answer: its 5

Step-by-step explanation: I did it in a test and got it right

The number of bacteria after 3 months is 7500.

The equation is y = 60,000 x [tex]0.5^3[/tex].

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 3 = 8 is an equation.

We have,

Number of bacteria initially = 60,000

After one month,

The number of bacteria = 30,000

This means,

60,000 - 30,000 = 30,000

The percentage decreased.

= 30,000 / 60,000 x 100

= 1/2 x 100

= 50%

Now,

The equation for the number of bacteria after x months.

y = 60,000 x [tex]0.5^x[/tex]

For x = 3,

y = 60,000 x [tex]0.5^3[/tex]

y = 60,000 x 0.125

y = 7500

Thus,

The number of bacteria after 3 months is 7500.

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The required value of x, if the side length of Terrarium A is four times the side length of Terrarium B is 3.63.

A terrarium is a glass container with soil and plants inside of it that can be opened for maintenance purposes. Terraria, however, can be exposed to the atmosphere rather than being sealed. Terraria are usually kept as decorative or ornamental items.

The volume of Terrarium B is 2 m³, so its side length is the cube root of 2, which is approximately 1.26.

The side length of Terrarium A is 4 times that, or approximately 5.04. The volume of Terrarium A is [tex]2^x[/tex] cubic meters, so we can set up the equation:

(5.04)³ = [tex]2^x[/tex]

Taking the cube of both sides, we get:

125.7376 = [tex]8^x[/tex]

Taking the log base 8 of both sides:

x = log(125.7376) / log(8)

x is approximately 3.63.

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Answer:

b=95; c=85

Step-by-step explanation:

B is equivalent to 85 degrees because of the vertical angle theorem. B is equivalent to 95 degrees because b and c lie along a straight line; a straight line is 180 degrees, so 180-85=95.

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Answer:

b equals 95 c equals 85 that's what I think and I have straight A's so I think I'm right

Answer:

3.1.1) There are four terms in this expression.

3.1.2) The coefficient of x^3 is 0.5.

3.1.3) The constant term is 8.

3.1.4) The degree of the expression is 5.