write an equation of the line passing through (-1,3) and (2,4). give the answer in standard form.

the equation of the line in standard form is

[tex]\:\: \:\: \:\star[/tex] We are asked to find out the distance between (1,5) and (-6,-2).We know the formula to find the distance between two points is given by -

[tex] \:\: \star \underline{ \sf{ Distance = \sqrt{ (y_2 -y_1)^2 + (x_2-x_1)^2}}}\\[/tex]

As per question, points are -

Now that we are given the points, so we can put them into the formula and solve for distance between them.Which is -

[tex]\:\: \:\: \:\star \underline{ \sf{ Distance = \sqrt{ (y_2 -y_1)^2 + (x_2-x_1)^2}}}\\[/tex]

[tex] \longrightarrow \sf Distance_{(AB)} = \sqrt{ (-2-5)^2 + (-6-1)^2 }\\[/tex]

[tex]\:\:\:\:\:\longrightarrow \sf Distance_{(AB)}= \sqrt{ (-7)^2 + (-7)^2 }\\[/tex]

[tex]\:\:\:\:\longrightarrow \sf Distance_{(AB)} = \sqrt{ 49+49 }\\[/tex]

[tex]\: \:\:\:\: \:\longrightarrow \sf Distance _{(AB)}= \sqrt{ 98}\\[/tex]

[tex]\: \:\:\: \:\longrightarrow \sf Distance_{(AB)} = \sqrt{49 \times 2}\\[/tex]

[tex]\:\: \:\: \:\:\longrightarrow \sf\underline{ Distance_{(AB)} = 7√2}\\[/tex]

[tex]\: \:\:\: \:\:\longrightarrow \sf Distance_{(AB) }= 9.89949......\\[/tex]

[tex]\: \:\:\: \:\:\longrightarrow \sf \underline{Distance_{(AB) }= 9.9\:(Approx)}\\[/tex]

Therefore, the distance between (1,5) and (-6,-2) is 7√2 or, 9.9 ( Approx).

Answer:

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Step-by-step explanation:

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Answer:

54

Step-by-step explanation:

║∦⇵π⇅⇵⇅⇵⇅⇵⇵⇵⇵⇵⇵⇄⇆⇄⇆

The constant of variation and write a direct variation equation relating s and t direct variation s= (1/2)t and t=32.

Direct Variation is that in which there is a  relationship between two variables in which one is a constant multiple of the other. For example, when one variable changes the other also changes, then they are said to be in proportion. If y is directly proportional to x then the equation is of the form y = k x (where k is a constant).

Given that,

s varies directly as t

i.e. s∝ t

   ⇒s= kt [ where k is the variational constant] -------------(1)

Given that s=8 when t= 16

putting these values in equation (1) we get,

8= k× 16

k= 8/16

k= 1/2

so, s= (1/2)t

If s= 16 then t= 16×2=32

Hence, s= (1/2)t and t=32

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The total width of the maze is 51.5+2=53.5 yards and the total length of the maze is 105 yards.

Equations are mathematical statements with two algebraic expressions on either side of an equals (=) sign. It illustrates the equality between the expressions written on the left and right sides. To determine the value of a variable representing an unknown quantity, equations can be solved. A statement is not an equation if there is no "equal to" symbol in it. It will be regarded as an expression.

The total area of the maze and walkway is equal to the area of the maze plus the area of the walkway. The area of the walkway is equal to the length of the maze plus twice its width since the walkway is one yard wide on both sides of the maze.

Let x be the width of the maze. So, (x+2) is the width of the maze and walkway, and (2x+2) is the length of the maze and walkway.

length×width=area

(2x+2)(x+2)=5616

2x²+6x+4=5616

2x²+6x=5612

Write in the form x2+bx=d by dividing both sides by 2:

x²+3x=2806

Complete the square by adding (23)2=2.25 to each side:

x²+3x+2.25=2806+2.25

(x+1.5)²=2808.25

Take the square root of both sides:

x+ 1.5 = ±√2808.25

x = −1.5±√2808.25

x ≈ −54.5 or x ≈ 51.5

A negative solution does not make sense so we take x≈51.5.

Hence, the total width of the maze is 51.5+2=53.5 yards and the total length of the maze is

2(51.5)+2

= 105 yards.

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Answer: it is one of the last two

Step-by-step explanation:

The information inferred from the graphs includes the overall trend, frequency of responses, and distribution of data, and predicting what the graphs would look like if we polled 100 people depends on factors such as sample population, question being asked, and range of possible responses.

From the graphs created, we can infer several things such as the overall trend, frequency of responses, and distribution of the data. For instance, if the graphs depict a bell-shaped curve, we can conclude that the responses were normally distributed, and that most people fell within the average range of responses. Conversely, if the graphs show a skewed distribution, it can indicate that a particular response was more common among the participants. We can also deduce from the graphs which response was the most popular and which was the least popular.

As for predicting what the graphs would look like if we polled 100 people, it would depend on various factors such as the sample population, the question being asked, and the range of possible responses. However, we can assume that with a larger sample size, the graphs would provide a more accurate representation of the population as a whole, and the distribution of responses would be more normal.

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The surface area of the rectangular prism is 348 square meters.

Hello! I'd be happy to help you find the surface area of a rectangular prism with dimensions 6 m by 4 m by 15 m. The surface area can be calculated using the formula:

Surface Area = 2lw + 2lh + 2wh

where l = length, w = width, and h = height.

Given the dimensions 6 m (length), 4 m (width), and 15 m (height), we can plug in the values

The surface area can be calculated using the formula:

Surface Area = 2(6)(4) + 2(6)(15) + 2(4)(15)
Surface Area = 48 + 180 + 120
Surface Area = 348 m²

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The two types of errors you might make in conducting hypothesis test is type I error occurs when we conclude that the new marketing campaign does not increase sales when it actually does, This would lead to missed opportunities for increased sales and revenue for the company. Type II error occurs when we conclude that the new marketing campaign does not increase sales when it actually does, This would lead to missed opportunities for increased sales and revenue for the company. So, the correct option is A) and D).

Type I error is also known as a "false positive" error, where we reject the null hypothesis (i.e., conclude that the marketing campaign does increase sales) when it is actually false (i.e., the campaign does not have an effect on sales). This would lead to missed opportunities for increased sales and revenue for the company.

Type II error is also known as a "false negative" error, where we fail to reject the null hypothesis (i.e., conclude that the marketing campaign does not increase sales) when it is actually false (i.e., the campaign does have an effect on sales). This would also lead to missed opportunities for increased sales and revenue for the company.

Therefore, it is important to choose an appropriate significance level (alpha) and calculate the power of the test to minimize the risk of both types of errors in a hypothesis test. The correct answers are (A) and (D).

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--The given question is incomplete, the complete question is given

"Suppose you are conducting a hypothesis test to determine if a new marketing campaign increases sales for a particular product. What are the two types of errors you might make in conducting this test? (select all that apply)

a) A type I error occurs when we conclude that the new marketing campaign does not increase sales when it actually does. This would lead to missed opportunities for increased sales and revenue for the company.

b) A type II error occurs when we conclude that the new marketing campaign increases sales when it actually does not. This would lead to wasted resources on the marketing campaign and potentially lost sales if the company shifts resources away from a successful strategy.

c) A type I error occurs when we conclude that the new marketing campaign increases sales when it actually does not. This would lead to wasted resources on the marketing campaign and potentially lost sales if the company shifts resources away from a successful strategy.

d) A type II error occurs when we conclude that the new marketing campaign does not increase sales when it actually does. This would lead to missed opportunities for increased sales and revenue for the company."--

Answer:

To solve this problem, we need to set the equation of the line and the equation of the given curve equal to each other and then solve for x. Once we find the value of x, we can substitute it back into either equation to find the corresponding y-coordinate. Here are the steps:

1. Set the equations equal to each other:

4 - 2x = 1

2. Solve for x:

4 - 2x - 1 = 0

3 - 2x = 0

3 = 2x

x = 3/2

2. Substitute x back into either equation to find y:

y = 4 - 2(3/2)

y = 1

Therefore, the point where the graph of y=4-2x crosses the line y=1 is at (3/2, 1).

Ans:-

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Solution:-

[tex] \: [/tex]

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The value of x is 2 !

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hope it helps:)

The value of solution of expression is,

⇒ x = 2

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The expression is,

⇒ 7 + 4x - 9 = 6

Now, We can simplify as;

⇒ 4x - 2 = 6

⇒ 4x = 4 + 2

⇒ 4x = 8

⇒ x = 2

Thus, The value of solution of expression is,

⇒ x = 2

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For a total of $2,400, the coach purchased 30 hoodies and 15 long sleeve shirts. A hoodie costs $60 and a long sleeve shirt is $45.

Let x represent the number of hoodies ordered and y represent the number of long sleeve shirts ordered. To describe the provided data, we may construct the following system of two equations:

x + y = 45 (because there are 45 players) (since there are 45 players)

60x + 45y = 2400 (the total cost of the order) (the total cost of the order)

We may determine that x = 30 and y = 15 by solving for x and y. As a result, the coach placed orders for 15 long sleeve jerseys and 30 hoodies. We can confirm that the total price is $2400: (30 x $60) + (15 x $45) = $1800 + $675 = $2400

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According to the given expression some are shortlisted factored expressions are [tex]4(3a^3 + 2a) for 12a^3 + 8a , 6(4a^4 + 3) for 24a^4 + 18, 4a^3(4a^2 - 5) for 16a^5 - 20a^3.[/tex]

Expressions in mathematics are numerical, variable, and operation combinations that are used to indicate a quantity or a relationship between values.

One or more variables or numbers are combined with one additional operation to form an expression. An illustration of an expression is X + 1.

The completely factored expressions are:

[tex]4(3a^3 + 2a) for 12a^3 + 8a\\\6(4a^4 + 3) for 24a^4 + 184a^3(4a^2 - 5) for 16a^5 - 20a^3[/tex]

So the correct answers are:

[tex]12a^3+8a=4(3a^3+2a)24a^4+18=6(4a^4+3)16a^5−20a^3=4a^3(4a^2−5)[/tex]

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Answer:a) r >= -20
             b) -10 <= x, or x >=-10
             c) q<= 5

Step-by-step explanation:
a)-11r >=220
 -11r/-11 >= 220/-11
  r>=-20

b) -8<=-7+x/10
   -8+7<=x/10
   -1 <=x/10
    -10 <=x

c) -1-6(5q-2)>=-139
  -1 -30q +12 >= -139
   -30q+12-1>=-139
   -30q+11>=-139
   -30q >= -139-11
   -30q>= -151
    -30q/-30 >= -151/-31
    q <= 5,

u will notice the sign has changed from >= to <= it is coz when the negative signs erase themselves.
   

Answer:

A

Step-by-step explanation:

because I took the test

Answer: I think it's a. 84 cubic units

Hope it helped : D

To find the area of a triangle, the correct formula is Area = (base x height) / 2.

A triangle is a 2-dimensional shape with three sides and three angles. It does not have a total surface area like a 3-dimensional shape such as a cube or a sphere.

However, you can find the area of a triangle using the following formula:

Area = (base x height) / 2

where "base" refers to the length of one of the sides of the triangle, and "height" refers to the perpendicular distance from the base to the opposite vertex.

Once you have calculated the area of the triangle, you can use this value to find other quantities such as the perimeter or the length of other sides using various formulas.

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To find when the daily ticket sales will peak, we need to find the maximum value of the quadratic equation [tex]N &= -0.3x^2+9x+13[/tex].

How to calculate no. of ticket solds and peak ticket sales?

Part 1:

The maximum value of a quadratic equation of the form [tex]y &= ax^2 + bx + c[/tex] occurs at [tex]x = \frac{-b}{2a}[/tex]. So in our case, the peak day will be at:

[tex]x &= \frac{-9}{2(-0.3)} = 15[/tex]

Therefore, the peak will be reached 15 days after the concert was first announced.

Part 2:

To find the number of tickets sold on that day, we substitute x=15 into the equation [tex]N &= -0.3x^2+9x+13[/tex]:

[tex]N &= -0.3(15)^2 + 9(15) + 13 = 67[/tex]

So the number of tickets sold on the day of the peak will be 67.

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The area of the rectangle is 40 square inches.

For a rectangle that is 8 inches long, 3 inches on the bottom, and 5 inches on the side, there are a few things you can do.

The perimeter of a rectangle is the sum of the lengths of all four sides.

To calculate the perimeter, add the lengths of the top and bottom sides (8 + 3 = 11) and the lengths of the two side lengths (5 + 5 = 10).

To find the area of a rectangle with an 8-inch long side, a 3-inch bottom side, and a 5-inch side, follow these steps:
Identify the dimensions of the rectangle.
The dimensions are given as 8 inches long, 3 inches on the bottom, and 5 inches on the side.

However, a rectangle only has two different side lengths, so we can assume that the 3-inch measurement is irrelevant.
Confirm the side lengths.
In this case, the side lengths are 8 inches and 5 inches. The 8-inch side is the length, and the 5-inch side is the width.
Calculate the area of the rectangle.
To find the area, multiply the length by the width. In this case, that is 8 inches (length) multiplied by 5 inches (width).
Area = Length × Width
Area = 8 inches × 5 inches
Area = 40 square inches

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The correct answer is "The slope is 4 over 5, which means for each additional donut sold, the shop is predicted to earn $0.80."

The slope of the line of fit represents the rate of change in the dependent variable (total cost, y) with respect to the independent variable (number of donuts, x). In other words, it represents the amount by which the total cost increases or decreases for each unit increase in the number of donuts sold.

In this case, the slope of the line of fit is 4/5, which means that for each additional donut sold, the total cost is predicted to increase by $0.80. This indicates that the donut shop should expect to make a profit of $0.80 for each donut sold, assuming that all other factors remain constant. This information can be used by the donut shop to determine the optimal price to sell its donuts and maximize its profits.

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Since lines l and m are parallel, we know that angles 1 and 5 are corresponding angles and are therefore congruent. Also, angles 4 and 8 are corresponding angles and are congruent.

We also know that angles 1 and 4 are vertical angles, so they are congruent, and angles 2 and 3 are vertical angles, so they are congruent.

Thus, we can set up the following equation:

m∠7 = m∠8 - m∠5 = m∠4 - m∠5

We are given that m∠2 = 120°, so we can use this to find m∠1:

m∠1 + m∠2 = 180° (since angles 1 and 2 are supplementary)

m∠1 + 120° = 180°

m∠1 = 60°

Since angles 1 and 5 are congruent, we know that m∠5 = 60°.

We are also given that angles 1 and 3 are complementary, so we can use this to find m∠3:

m∠1 + m∠3 = 90°

60° + m∠3 = 90°

m∠3 = 30°

Now we can find m∠4:

m∠1 + m∠4 = 180° (since angles 1 and 4 are supplementary)

60° + m∠4 = 180°

m∠4 = 120°

Finally, we can use these values to find m∠7:

m∠7 = m∠4 - m∠5

m∠7 = 120° - 60°

m∠7 = 60°

Therefore, m∠7 is 60°.

We can write √a⁵ as √a⁴ × a.Therefore, a factor out of each square root  of √a⁵ = a²√a.

A factor in mathematics is an algebraic expression or number that divides another expression or number without producing a residue.

For instance, 1, 2, 3, 4, 6, and 12 are factors of 12 because they can divide 12 equally.

Then, using the property of square roots that √ab = √a × √b, we can simplify this to:

√a⁴ × a = (√a²)² × √a = a²√a

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Answer:

$750

Step-by-step explanation:

.8x = $600, so x = $750

This statement is false. Therefore, the original equation has no solution.

How to solve an equation?

To solve the equation 5x + 3x = 2(4x - 5) - 2, we need to simplify each side of the equation using the order of operations (PEMDAS).

First, we simplify the left side of the equation by combining like terms. 5x + 3x equals 8x, so we have:

8x = 2(4x - 5) - 2

Next, we simplify the right side of the equation using the distributive property of multiplication. We multiply the 2 by each term inside the parentheses:

8x = 8x - 10 - 2

We can simplify further by combining like terms on the right side of the equation:

8x = 8x - 12

Now we have an equation with variables on both sides. To solve for x, we want to isolate the variable on one side of the equation. We can do this by subtracting 8x from both sides:

0 = -12

This statement is false. Therefore, the original equation has no solution.

The equation 5x + 3x = 2(4x - 5) - 2 is an example of a contradiction. It means that there is no value of x that makes both sides of the equation equal. In this case, we can see that the left side of the equation is always greater than or equal to the right side, no matter what value of x we choose. Therefore, the equation has no solution.

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Answer: To solve the quadratic equation, we can start by simplifying the left side of the equation:

9(x^2 −10)−3 = 7

9x^2 - 90 - 3 = 7

9x^2 - 93 = 7

Next, we can isolate the x^2 term by adding 93 to both sides:

9x^2 = 100

Finally, we can solve for x by taking the square root of both sides and considering both the positive and negative square roots:

x = ±√(100/9)

x = ±(10/3)

Therefore, the solutions to the quadratic equation are:

x = 10/3 or x = -10/3.

Step-by-step explanation:

Answer: x=10/3

Step-by-step explanation:

9(x^2-10)-3=7

=>9(x^2-10)=7+3

=>x^2-10=10/9

=>x^2=10/9+10

=>x^2=100/9

=>x=10/3

The volume of the right rectangular prism with dimensions length = 7 feet, width = 2 feet, and height = 3.5 feet is 49 cubic feet.

What is volume ?

Volume is a physical quantity that refers to the amount of space occupied by an object or a substance. In mathematical terms, volume can be defined as the measure of the three-dimensional space enclosed by a closed surface or shape.

It is usually expressed in cubic units such as cubic meters, cubic feet, or cubic centimeters, depending on the system of measurement being used.

the length of the prism is 7 feet, the width is 2 feet, and the height is 3.5 feet.

Volume = Length x Width x Height

Volume = 7 ft x 2 ft x 3.5 ft

Volume = 49 cubic feet

So, the volume of the right rectangular prism with dimensions length = 7 feet, width = 2 feet, and height = 3.5 feet is 49 cubic feet.

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After dividing the given expression 4×10²/4×10¹, we have the resultant answer which is 10.

An expression, often known as a mathematical expression, is a finite collection of symbols that are well-formed in accordance with context-dependent principles.

Algebraic expressions contain both numbers and variables in terms, separated by operators, whereas mathematical expressions only contain numbers and operators.

So, we have the expression:

= 4×10²/4×10¹

Now, solve as follows:

= 4×10²/4×10¹

= 4×100/4×10

= 400/40

= 10/1

= 10

Therefore, after dividing the given expression 4×10²/4×10¹, we have the resultant answer which is 10.

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Step-by-step explanation:

y ( 2y + 5 )   + 4 ( 2y+3)

2y^2 + 5y     +  8y + 12  

 2y^2   + 13 y   + 12

Answer:

Step-by-step explanation:

i would say 45cm

The answer is  3u•v = 3(-6) = -18. So, the result is a Scalar

In physics, a scalar quantity is a physical quantity that has only magnitude, but no direction. Examples of scalar quantities include mass, time, temperature, energy, and distance. Scalar quantities are represented by a single numerical value, and they can be added, subtracted, multiplied, and divided like regular numbers.

On the other hand, a vector quantity is a physical quantity that has both magnitude and direction. Examples of vector quantities include displacement, velocity, acceleration, force, and momentum. Vector quantities are represented by a magnitude (the size or amount of the quantity) and a direction (the orientation of the quantity in space), and they are usually written as boldface letters or with an arrow above them. Unlike scalar quantities, vector quantities cannot be added, subtracted, multiplied, or divided like regular numbers. Instead, they must be combined using vector operations such as vector addition, dot product, and cross product.

The dot product of two vectors u and v is defined as:

u•v = (u1 * v1) + (u2 * v2)

where u1 and u2 are the components of vector u, and v1 and v2 are the components of vector v.

Using this formula, we can calculate:

u•v = (7 * -2) + (2 * 4) = -14 + 8 = -6

So, 3u•v = 3(-6) = -18.

Therefore, the result is a scalar.

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