on a coordinate plane,point A is located at (7,4), and point B is located at (-8,4). What is the distance between the two points ?

A go-fuel kart's and maintenance costs are calculated as follows: c=10x+1200, where x is the number of rides. $40 is the cost per ride. it takes x = 40 to break even.

The cost function given here is

c(x) = 10x + 1200

Where x = number of rides

c(x) is the total cost including the fixed cost.

Also it is given that each ride costs $40

So Revenue function for x number of rides shall be

R(X) = 40x

For break even

the cost must be equal to the revenue

Hence

R(x) = C(x)

40x = 10x + 1200

Subtracting 10x from both sides we get

30x = 1200

Dividing by 30 on both sides

We get

x = 40

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Answer: a = 1, b = -11, and c = -42.

Step-by-step explanation:

The solutions to the equation x² - 11x - 42 = 0 are x = -6 and x = 7.

You can find the solutions by factoring the equation, or by using the quadratic formula: x = (-b ± √(b² - 4ac)) / 2a.

In this case, a = 1, b = -11, and c = -42.

The rate of change of function is {r} = (1/8)(B - A).

Given is a function f(x).

The given interval is - (2, 10). Since the table is not given, we can assume that -

f(10) = A

f(2) = B

Then, we can write the rate of change of functions as -

{r} = {f(b) - f(a)}/{b - a}

{r} = (B - A)/8

{r} = (1/8)(B - A)

Therefore, the rate of change of function is {r} = (1/8)(B - A).

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Nico, Raj and Sandra are correct.

And the explanation is given.

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:

An equation,

2/5(5 +x) = 8.

Nico, Aditi, Erick, Raj, and Sandra are solving the equation.

Approach 1:

Multiply by 5/2.

(5/2)(2/5)(5 +x) = 8(5/2)

5 + x = 20

x = 15.

Approach 2:

Multiply by 1/2 both sides

(1/2)(2/5)(5 +x) = 8(1/2)

5 + x = 4(5)

x = 15.

Approach 3:

Simplifying,

2 + 2/5x = 8

2x/5 = 6

x = 30/2

x = 15.

Therefore, Nico, Raj and Sandra are correct.

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We can still simplify the fraction by dividing the numerator and denominator by 5 one more to obtain the final result, which is 29/40.

As the fraction's numerator, you should first write 725 because that is how the number appears after the decimal point.

We will take 1,000 as the fraction's denominator because there are three digits following the decimal point, allowing us to add three zeros and a one before it.

725/1000 is not the lowest word for the fraction.

The result of dividing the numerator and denominator by 5 is

145/200.

We can still simplify the fraction by dividing the numerator and denominator by 5 one more to obtain the final result,

which is 29/40.

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The equation y = [tex]ax^2[/tex] + bx + c is in factored form when it is written as

y = a(x - [tex]r_{1}[/tex])(x - [tex]r_{2}[/tex]).

The term "factored form" refers to a quadratic expression that is the product of two factors, each of which is a linear expression.

When an equation is in factored form, it can be expanded, which entails multiplying out the factors, to rewrite it in standard form. Factoring is the process of representing a given number or algebraic statement as the sum of its components.

The equation y = [tex]ax^2[/tex] + bx + c is in factored form when it is written as

y = a(x - [tex]r_{1}[/tex])(x - [tex]r_{2}[/tex]).

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Answer:

Step-by-step explanation:here is a example:Recall that the volume of a regular prism is given by the area of the base times the height.

Given that the base of the prism is a regular pentagon with an apothem of 2.8 centimeters.

The pentagon consist of 5 isosceles triangles with the apothem as the height and the side of the pentagon as the base.

Recall that the are of a triangle is given by 1/2 base times height.

Thus the area of of the pentagon base of the prism is given by

Therefore, the volume of the prism is given by volume=7x(2x+1)=14x2+7x

Answer: 35

Step-by-step explanation: 41 - 6 = 35

Answer:

Step-by-step explanation:

That equals 4/6 which is 2/3. Hope that was helpful!!!

If the seed sprouted and grew [tex]\frac{2}{3}[/tex] foot in 3 months , then the growth rate of the plant is   [tex]\frac{2}{9}[/tex] foot per month .

the time in which the seed sprouted and grew  [tex]\frac{2}{3}[/tex]  feet = 3 months ,

to find the growth rate of the plant , we have to divide the length of plant grown by the time required for the growth .

that means , Growth Rate = [tex]\frac{\frac{2}{3} }{3}[/tex] ;

simplifying , we can write the fraction as : [tex]\frac{2}{9}[/tex] ;

So , the growth rate of the plant is [tex]\frac{2}{9}[/tex] foot per month , that means that there will be a [tex]\frac{2}{9}[/tex] foot increase in the length of the plant .

The given question is incomplete , the complete question is

A seed sprouted and grew 2/3 of a foot in 3 months. What was its rate of growth ?

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Answer:

37⁰

Step-by-step explanation:

180⁰ - 106⁰ =74⁰

74⁰ ÷ 2= 37⁰

The ratio comparing the 6 bowls to all the dishes will be 6 over 26. The correct option is B.

An ordered pair of numbers a and b, represented as a / b, is a ratio if b is not equal to 0. A proportion is an equation that sets two ratios at the same value. The numerical relationship between two values demonstrates how frequently one value contains or is contained within another.

Given that Jaidon counted dishes in the kitchen cabinet. The table shows what was found. Plates 8 Bowls 6 Cups 12.

The ratio will be calculated as,

Ratio = 6 / ( 6 + 12 + 8 )

Ratio = 6 / 26

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Answer:

0-a/c-0 = -a/c

Step-by-step explanation:

Orthocenter: Solve system of 3 eqs. using 3 altitudes' equation & vertices' coordinates.

What is coordinate ?

Coordinate is a value or set of values that identify the position of a point in a certain space. Represented by ordered pair or triple of numbers (x,y) or (x,y,z) respectively.

The orthocenter of a triangle is the point where the three altitudes of the triangle intersect. To find the orthocenter of a triangle with coordinates, you can use the following steps:

1) Find the equation of the three altitudes of the triangle. To do this, you will need the coordinates of the three vertices of the triangle, as well as the slope of the line perpendicular to the side opposite each vertex.

2) Once you have the equations of the three altitudes, you can use them to find the coordinates of the orthocenter. To do this, you will need to solve a system of three equations with three variables (the x and y coordinates of the orthocenter, and the y-intercept of the altitude).

3) Once you have the coordinates of the orthocenter, you can use them to check your work by verifying that the point is indeed on each of the three altitudes.

Orthocenter: Solve system of 3 eqs. using 3 altitudes' equation & vertices' coordinates.

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The ratio of the central angle measure to the circumference of a circle is called the "arc measure" and it is given by the formula:

arc measure = central angle measure / circumference

For a given central angle measure in degrees, the formula will be:

arc measure = (central angle measure in degrees) / 360

It's worth noting that this ratio is equal to the fraction of the circumference that the arc of the central angle measures.

For example, if the central angle measure is 90 degrees, the arc measure will be 90/360 = 1/4, meaning that the arc that is formed by the central angle measure is 1/4 of the circle's circumference.

It's also important to note that this ratio is also equal to the fraction of the total area of the circle that the sector formed by the central angle measures.

It's also worth noting that this ratio is always less than 1, since the central angle can't be greater than 360 degrees.

Therefore, The ratio of the central angle measure to the circumference of a circle is called the "arc measure" and it is given by the formula: arc measure = central angle measure / circumference

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The probability that you select a greater proportion of orange peanut M&M's than of orange M&M's milk chocolate candies is 0.7881

We have to use the available data to solve this problem

We have The probability 1 = P1 = 20%

= 0.20

We have the probability 2 = p2 = 23%

= 0.23

The difference between p1 - p2

0.20 - 0.23

= - 0.03

n1 = 240

n2 = 240

[tex]\sqrt{\frac{p1 (1-p1)}{n1} +\frac{p2(1-p2)}{n2} } \\\\\sqrt{\frac{0.20 (1-0.20)}{240} +\frac{0.23(1-0.23)}{240} }[/tex]

= 0.0375

Then Z value = -0.03 / 0.0375

= -0.80

We have to find the p value

The p value = 1 - p(z ≤ -0.80)

= 1 - 2119

= 0.7881

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Answer:

75.25

Step-by-step explanation:

to find the area of the square you multiply 5.5×5.5

you then add that to the are of the trapezoid using the formula a=a+b/2 h

you plug it all in and get (5.5×5.5)+((5.5+9.5/2)6)

the answer to that is 75.25

A line segment whose endpoint are on the circle is called a __________ of a circle.

Chord

Radius

Tangent

Diameter

Answer: Chord

In the end, Moe played 51 games, while  Meeny played 17 games and Miny played 35 games.

We can start solving the problem by using algebra. Let x be the number of games Moe played. Then, since Meeny and Miny played 17 and 35 games respectively, the total number of games played is 17 + 35 + x = x + 52.

We know that in the second game and on, the one who sat out the preceding game would replace the loser of that game. Therefore, the number of games played by Moe is one less than the number of games played by Meeny and Miny combined.

x = (17 + 35) - 1 = 51.

So, Moe played 51 games.

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The complete question is -

Meeny, Miny and Moe were playing tennis. From the second game on, the one who sat out the preceding game would replace the loser of that game. In the end, Meeny played 17 games and Miny played 35 games. How many games did Moe play?

Expressing 1.9 as a quotient of integers is 19/10.

An integer is a whole number (not a fractional number) that can be positive, negative, or zero. It is not a fraction, a decimal, or a percentage. A number such as 7, -11, or 0 is an integer. Integers are used in everyday life and are also used in computer programming.

This is equivalent to 1 9/10 which is a fraction. To write it as a quotient of integers, 19 is the numerator and 10 is the denominator. This means that if you take 19 parts of a whole and divide it into 10 equal parts, each part will be equal to 1.9.

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Given the above image, the estimated scale factor used in the dilation are given as follows:

Dilation A -  3/4

Dilation B - 1/4

Dilation C - 1/2

The scale factor is a metric for figures with similar appearances but differing scales or measurements. Assume two circles appear identical but have different radii. The scale factor specifies how much larger or smaller a figure is than the original figure.

When the new and original dimensions are specified, the scaling factor may be determined. The fundamental formula for determining a figure's scale factor is: Scale factor = Dimension of the new shape ÷ Dimension of the old shape.

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The graphs of absolute value functions are called "V-shaped" or "V-graphs" because their graph is in the shape of a "V".

The graph of an absolute value function is a V-shape that opens upward or downward, depending on the function.

The vertex of the V is the point where the absolute value function equals zero. The two arms of the V extend out from this point, going in opposite directions along the number line.

The absolute value function is defined as |x| where x is any real number and |x| represents the distance of x from zero on the number line, i.e., always non-negative.

Example of an absolute function is f(x) = |x + 3|. The vertex is where

x + 3 = 0

That is at x = -3.

Here the function opens upward, but if the function was -|x + 3|, it will open downward.

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The equation of the tangent to the circle, whose equation is given below, at the point (0,4).

(x−2)² + (y−3)² = 5 is y = -x + 4

The equation of a circle is (x-a)^2 + (y-b)^2 = r^2, where (a,b) is the center of the circle, and r is the radius. So given equation is of circle whose center is (2,3) and radius is √(5)

To find the equation of the tangent to the circle at point (0,4) we have to find the slope of tangent and point of tangent.

The slope of tangent is equal to the derivative of the equation of the circle.

y = mx + c

m = (y2 - y1) / (x2 - x1)

where (x1, y1) = (0, 4) and (x2, y2) = (2, 3)

so, m = (3-4) / (2-0) = -1

Now, we know the slope of the tangent line is -1, we can substitute this value in the point slope form of line equation,

y - y1 = m(x - x1)

y - 4 = -1(x - 0)

y = -x + 4

So, the equation of the tangent to the circle at the point (0,4) is y = -x + 4

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To multiply two numbers, use the multiplication operator (*) between them. The product is the answer you get when you multiply the two numbers. For example, if you wanted to multiply 3 and 5, you would write 3 * 5 and the product would be 15.

1. Choose the two numbers to be multiplied.

2. Place the multiplication operator (*) between the two numbers.

3. Calculate the product of the two numbers.

4. The product is the answer you get when you multiply the two numbers.

To multiply two numbers, use the multiplication operator (*) between them. The product is the answer you get when you multiply the two numbers. For example, if you wanted to multiply 3 and 5, you would write 3 * 5 and the product would be 15.

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On solving the provided question, we can say that from graph we have a equation ,[tex]y = 4x^2[/tex]  because it's a parabola

Mathematicians use graphs to logically convey facts or values using visual representations or charts. A graph point will typically reflect a relationship between two or more things. Nodes, or vertices, and edges make form a graph, a non-linear data structure. Glue together the nodes, often referred to as vertices. This graph has vertices V=1, 2, 3, 5, and edges E=1, 2, 1, 3, 2, 4, and (2.5), (3.5). (4.5). Statistical charts (bar charts, pie charts, line charts, etc.) graphical representations of exponential growth. a logarithmic graph in the shape of a triangle

here,

On solving the provided graph

we have a equation , [tex]y = 4x^2[/tex]

because it's a parabola

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The scale factor showing the view of the original building as a dilation of the toy is 0.00111.

The scale factor is a smaller or bigger representation of an object or shape.

The scale factor shows the ratio of the bigger or smaller scale to the original scale.

The scale factor shows the dilation of the toy when the new scale is reduced.  It can also show the larger transformation of the toy when the original scale is increased by the scale factor.

The area of the scale model of the front side of the toy building = 1 ft²

The area of the front side of the original building = 900 ft²

The scale factor = 0.00111 (1 ft²/900 ft²)

Thus, we can conclude that the toy train's scale model is dilated by a scale factor of 0.00111.

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Answer:

y = 5/2 x - 13

Step-by-step explanation:

A line perpendicular to y=-2/5x-1 has a slope equal to the negative reciprocal of -2/5. The slope of the line passing through (2,-8) can be calculated as follows:

m = -(-5/2) = 5/2

The equation of the line in point-slope form is:

y - (-8) = (5/2)(x - 2)

Expanding the equation gives:

y + 8 = 5/2 x - 5

Solving for y:

y = 5/2 x - 5 - 8

y = 5/2 x - 13

The equation of the line is:

y = 5/2 x - 13

To make 3.5 batches of salad dressing, 7.875 cups of salad dressing are required.

A mathematical equation is a formula that uses the equals sign to express the equality of two expressions. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two expressions 3x + 5 and 14, which are separated by the 'equal' sign. a formula that expresses the connection between two expressions on either side of a sign. Typically, it has a single variable and an equal sign. Like this: 2x - 4 = 2.

Here,

1.5 cups of olive oil and .75 cups vinegar for 1 batch of salad dressing.

1.5+0.75=2.25 cups for 1 batch of dressing

3 1/2=3.5 batch

Total amount of cups=3.5*2.25

=7.875 cups of salad dressing

7.875 cups of salad dressing will be be needed to make 3.5 batches of salad dressing.

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The surface area that minimizes the weight of the storage bin is:

70x cm^2

To minimize the weight of an open-top storage bin in the shape of a rectangular prism, we need to minimize its surface area.

The volume of the storage bin is given as 3500 cm^3. Since the base of the bin is a square, we can let the length of one side of the base be x cm.

Therefore, the area of the base is x^2 cm^2.

          V = x^2 * h

where V is the volume and h is the height of the bin

So, we can substitute the value of V in the above equation to get:

3500 = x^2 * h

To minimize the surface area of the bin, we must minimize the sum of the areas of all its faces. The surface area of the rectangular prism is given by the formula:

           2lw + 2lh + 2wh

where l, w, and h are the length, width, and height of the prism respectively.

Since the base of the bin is a square, we can let the length and width be equal to x. Therefore, we can use the equation of the height of the bin and the formula of the surface area of the rectangular prism to get:

     2x^2 + 2xh = 2x^2 + 2x(3500/x^2)

Now, we can simplify the above equation to:

       2x^2 + 2x(3500/x^2) = 2x^2 + 70x

To minimize the surface area, we need to minimize the value of x. We can see that the second term of the equation is a linear function of x and has a negative slope, which means that as x increases, the surface area decreases. Therefore, the surface area will be minimized when x is at its maximum value.

   Therefore, the surface area that minimizes the weight of the storage bin is 70x cm^2.

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