What is the distance between the pair of points 2 3 and 4 1?

The area, in square inches, of the floor in the scale drawing is, 300 inches²

Scale factor is a mathematical term, which we use to scale 2-dimensional and 3-dimensional shapes. Scale factor is a measure of similar figures. Those figures who look the same but are in different sizes.

For example, Two spheres look similar but could have different radii.

Given that,

The rectangular floor of a classroom is 40 feet in length

And 38 feet in width

length in scale drawing  =  20 inches

The area, in square inches = ?

Scale factor  = length in scale drawing/ length of floor

length in scale drawing = 20 inches

length of floor =  40 feet = 480 inches

Scale factor  =  20/480

                      =   1/24

Dimensions in scale drawing,

length of scale drawing =   length of floor x  Scale factor

                                       =   480 x 1/24

                                       =   20 inches

Width of scale drawing =  width of floor x  Scale factor      

                                       =   30 x 12 x 1/24

                                       =    15 inches

Area of scale drawing =  20 x 15

                                     =  300 inches²

Hence, the area is 300 inches²

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A line is parallel to x = -3 if and only if it has the same slope. The slope of a line perpendicular to x = -3 is undefined, because x = -3 is a vertical line, which has no slope. A vertical line is always parallel to itself.

Slope is 4 and represents the rate at which the water flows into the tank in liters per minute.

The correct option is B.

A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation.

Given,

Tank has 9 liters water already

By the table

Amount of water is 17 liters in 2 minutes

But there was 9 liters of water already

So, the tank filled in 2 minutes = 17 - 9 = 8 liters

Tank filled per minute = 8/2 = 4 liters

Amount of water in the tank can be written as

y = 4x + 9

where x is number of minutes

comparing it with slope form of equation

y = m x + c

slope m = 4

Hence, 4 is the slope that represents rate of the flow of water into the tank in liters per minute.

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Therefore, for the given quadratic equation, k has values of 0 and 12.

Any equation in algebra that can be written in standard form as where x stands for an unknown value, where a, b, and c stand for known numbers, and where a 0 is true is known as a quadratic equation.

Here,

A quadratic equation 3x² -k x + k = 0 has equal roots.

The value of k such that the equation has equal roots is,

1. The given quadratic equation is   3x² - kx + k = 0.  

2. For an equation to have equal roots the value of the discriminant is 0,  

=> The discriminant of a quadratic equation ax² + b x + c = 0 is given by the formula,  

=> Discriminant ( D ) =√(b²-4ac)

=> For equal roots D = 0.  

3. Substitute the values in the above formula,  

=>  D = 0,  

=> √[(-k)² - 4(3)(k)] = 0,

=> k² -12k = 0,

=> k(k-12) = 0,

=> k = 0 (OR) k =12.

Therefore, the values of k are 0 and 12 for the given quadratic equation.

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Complete question:

What is the value of K for which the quadratic equation 3x2-kx+k=0 has equal roots?

Answer: When two variables vary inversely, the product of their values is constant. This means that x * y = k, where k is a constant.

We are given that y = 14 when x = 3, so we can use this information to find the value of k:

k = x * y = 3 * 14 = 42

Now that we know the value of k, we can use it to find the value of y when x = 7:

y = k / x = 42 / 7 = 6

So, y = 6 when x = 7.

Step-by-step explanation:

x= -17

y=5

——-

I had this question on a quiz and got it right

The angle in the capital letter "L" measures 90°, making it a right angle.

A right angle is one that is exactly 90 degrees, or half of a straight angle. There is usually a quarter turn in it. The fundamental geometric forms, rectangle, and square, each have four angles that measure 90 degrees.

When two lines cross, and there is a 90-degree angle between them, the lines are said to be perpendicular. A few examples of 90-degree angles in real life include the angle between the hands of a clock at 3 o'clock, the angles between two neighboring sides of a rectangular door or window, etc.

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Answer:

x= 3     y= 1

Step-by-step explanation:

4 * 3 (x)= 12 + 1 (y)= 13

5 * 3 (x)= 15 - 3*1 (y)= 15 - 3 (y)= 12

Both scenarios are now proven true.

Answer: 24

Step-by-step explanation:

Divide the 1,320 by the rate which is 55, and you get your answer.

The coach can use this information to help determine the uniform size for each player based on their height. For example, if a player's height is 78 inches, they would need a Size Medium uniform. If a player's height is 82 inches, they would need a Size Large uniform. This correlation between height and uniform size will make it easier for the school to purchase the correct sizes for each player and ensure that they are comfortable and properly fitted in their uniforms.

The axis of symmetry for f(x) = 3x^2 + 12x - 6 is x = -2. To find the axis of symmetry for a parabola, you need to find the vertex.

To find the axis of symmetry for a parabola, you need to find the vertex. The formula for the vertex is:

Vertex = (-b/2a, f(-b/2a))

where

a = the coefficient of x^2

b = the coefficient of x

In this equation,

a = 3

b = 12

So the vertex is:

(-12/2(3), f(-12/2(3)))

(-12/6, f(-12/6))

(-2, f(-2))

Therefore, the axis of symmetry is x = -2.

The axis of symmetry for f(x) = 3x^2 + 12x - 6 is x = -2.

The axis of symmetry for f(x) = 3x^2 + 12x - 6 can be found by calculating the vertex of the parabola. The formula for the vertex is (-b/2a, f(-b/2a)), where a is the coefficient of x^2, and b is the coefficient of x. In this equation, a = 3 and b = 12, so the vertex is (-12/2(3), f(-12/2(3))), or (-2, f(-2)). Therefore, the axis of symmetry is x = -2.

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There are 134596 ways to distribute 24 slices between 6 people

Since pizza slices are the same hence order doesn't matter and also people are distinct so it is a case of combination.

Combination in mathematics is a way of choosing or distributing selected items from a list of the total set with distinct values. It is used when there is no repetition and order doesn't matter. It can also be depicted as permutation/r!

combination = nCr =n!/(r!(n-r!)

where n is the total number of objects

r is the number of chosen objects from the total.

Now, 24c6=24!/6!18!

=24x23x22x21x20x19x18!/6!18!

=24x23x22x21x20x19/6x5x4x3x2x1

=134596

Therefore, There are 134596 ways to distribute 24 slices between 6 people

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P(t)=20t+3660 is the formula for the moose population.

We will consider x on the graph to be years since 1990 and y on the graph to be the number of Moose.

We have two points on the graph:(0,3560) and (5,3460)

Using the slope formula, we can find the slope of this line:

m=(y2 - y1)/(x2 - x1)  

Substituting the points in the slope formula:      

m=(3560-3460)/(5-0)

m=100/5                        

m=20                            

Now that we have the slope of the line, we can use the point-slope formula to find the equation for the line:

y - y1 = m(x - x1)                              

y - 3560=-20(x-5)                            

y-3560=20x+100                  

y =20x+3660

Since the formula that is being sought is supposed to be in terms of P and t, we get:

P(t) =20t+3660

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The slope of the line with the given coordinates A(-2,2) and B(0,4) is 1.

Slope is simply expressed as change in y over the change in x.

Slope m = ( y₂ - y₁ )/( x₂ - x₁ )

Given the data in the question;

Point A (-2,2)

Point B (0,4)

Plug the given x and y values into the slope formula and simplify.

Slope m = ( y₂ - y₁ )/( x₂ - x₁ )

Slope m = ( 4 - 2 )/( 0 - (-2) )

Slope m = ( 2 )/( 2 )

Slope m = 1

Therefore, the slope of the line is 1.

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The answer choice which correctly represents the value of cos B as required is; Choice B; Cosine B = StartFraction 40 Over 41 EndFraction.

It follows from the task content that the ratio which represents cos B is to be identified among the given answer choices.

Recall from trigonometric ratios that the cosine of an angle is the ratio of its opposite and hypothenuse.

Hence, it can be inferred that;

cos B = 80 / 82

cos B = 40 / 41.

Ultimately, the cosine of angle B following from trigonometric ratios as requested is; cos B = 40 / 41.

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Answer: you need to be more specific like give numbers how can i solve for x if i don't know what the problem is

Step-by-step explanation:

The rowers travelled 7.5 miles upstream.

We can define relative speed as the speed of a moving body with respect to another. When two bodies move in the same direction, their relative speed is computed by their difference. But when two bodies are moving in the opposite direction, the relative speed is calculated by adding the speed of both the bodies.

Given here: The speed of the rowers in still water as 4 mph but since they are rowing upstream their relative speed will be equal to 4-3= 3 mph and while in downstream their speed is 5 mph

Now the distance they travelled on both ends of the river is equal

let they reach the upstream end in x hours and travel downstream for 4-x hours then we have

3x=(4-x )× 5

3x+5x=20

x=20/8

x=2.5 hours

Thus the distance travelled is 2.5×3=7.5 miles

Hence, The rowers travelled 7.5 miles upstream.

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To ensure that the frame is a rectangle, the carpenter needs to make sure that opposite sides of the frame have the same length.

In other words, the two 6-foot-long boards must be opposite to each other and the two 8-foot-long boards must be opposite to each other.

This way, the carpenter can ensure that opposite sides of the frame are parallel and that the angles between these sides are right angles, which are characteristics of a rectangle.

Additionally, the carpenter could use a square or a measuring tape to check that the angles between the two sides of each length are 90 degrees. This will confirm that the frame is indeed a rectangle.

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Answer:

In the problem, we are told that Amelie completed 56 sit-ups, and this is 7 times the number of sit-ups that Kiki completed.

We can use this information to create an equation that models the problem.

Let k represent the number of sit-ups Kiki completed.

One equation that models this problem is:

k = 56/7

Another equation that models this problem is:

56 = 7k

Both equations represent the same information, the first one is solved for k, and the second one is solved for the number of sit-ups Amelie completed.

So either k = 56/7 or 56 = 7k is the equation that models the problem.

Answer:

k=8

Step-by-step explanation:

If Amelie completed 56 sit-ups and its 7 times more you would divide

y=kx

k=56 divided by 7

k=8

k is the constant of proportionality

Answer: x=-3, y=-4

Step-by-step explanation:

System of equations is actually pretty simple.

Let me explain the two methods of solving a system of equations problem.

1. Elimination method

y-2x=2

-y=-x+1

In this approach, we will subtract or add the two equations together to eliminate one variable.

So in this problem, we'll organize -y=-x+1 like this:

x-y=1

Now we have

-2x+y=2

x-y=1

All we have to do now is add the two equations together and:

-x=3

x=-3

As you can see, the y variable is gone and we can find x by simply solving the rest.

Now we know that x=-3, let's plug in the value to get y.

x-y=1

-3-y=1

-y=4

y=-4

Therefore, x=-3, and y=-4

2. Substitution method

Let's go back to the problem.

y-2x=2

-y=-x+1

Now let's say that we will solve the problem using the substitution method.

In this approach, we will express one variable with the other.

So what we do is express y with x:

-y=-x+1

y=x-1

Now that we went through that process, we can plug in the y in the other equation:

x-1-2x=2

-x-1=2

-x=3

x=-3

Now that we now x=-3, let's plug that in to get y.

y=-3-1

y=-4

So the answer: x=-3, y=-4

Do you see the pattern?

System of equations problems are all about eliminating one variable and using the value of one to find the other.

Please let me know if there is anything else you're confused about.

Good luck with your exams!

Answer:

left 4(B)

Step-by-step explanation:

When the number is (x+4) or (×-4)

The plus one moves left.

The minus one moves right.

Since the natural log function, ln(x), is a logarithmic function with base e, the inverse of lnx exists since logarithmic functions are one-to-one. In actuality, an exponential function with the same base is the inverse of a logarithmic function. As a result, [tex]e^x[/tex] is the inverse of function lnx.

There aren't always inverse functions for functions. An inverse function can only exist if certain requirements are met.

1. If and only if a function is a one-to-one function, it has an inverse.

2. There exists an inverse over that confined domain if a function is not one-to-one but the domain may be restricted to an interval where the function is one-to-one.

3. Logarithmic relationships are 1:1.

4. Exponential relationships are 1:1.

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The dilation center is at C. The scale factor is 5/12. The value of x is 5/2.

What is dilation?

Meaning of Dilation in Math. Dilation is a transformation that allows you to resize an object. Dilation is a technique for making objects larger or smaller. This transformation yields an image that is identical to the original shape. However, there is a size difference in the shape.

Given that the length of the original rectangle is 12. The length of the new rectangle is 5.

The scale factor is the ratio of the dimension of the new rectangle to the dimension of the original rectangle = 5:12 = 5/12

The width of the new rectangle is the product of the original width by the scale factor = 5/12 × 6 = 5/2

The value of x is 5/2.

The vertex of the triangles is at C.

The dilation center is at C.

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Answer: z = 133

Step-by-step explanation:  From the question

126 + z = 259

Make z the subject

z = 259 - 126

z = 133

Answer:

Step-by-step explanation:

Momentum = mass x velocity

Elephant Momentum = 6300 x 0.11

                                    = 693 kg m/s

Dolphin momentum = 66 x 10.5

                                 = 693 kg m/s

The momentum of the dolphin and the elephant are the same.

Answer:

f(2) = -1

f(x) = 1 the x value is equal to 0

Step-by-step explanation:

at f(2) we evaluate what the y value of the x is at the number given so when x =2 the y value is -1 so therefore f(2) = -1

For f(x) = 1 we do the opposite as we look for the x value for when y = 1 giving us the x value of 0.

Hope this helps

Answer:4/7

Step-by-step explanation: The question isn't very clear, so I just did 1/2 divided by 7/8

The inequality is 13 + 39x ≤ 325 and the solution is x ≤ 8

Let's call the number of people in the group "x".

The total cost of parking and admission is no more than $325, so we can write the inequality:

13 + 39x ≤ 325

Subtracting 13 from both sides:

39x ≤ 312

Dividing both sides by 39:

x ≤ 8

So the group can have no more than 8 people if they want to stay within their budget of $325 for parking and admission.

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The width of Todor's area model is 5+3=8

The width of Todor's area model can be determined by factoring 10x² - 5x + 15. 10x², -5x, and 15 can be factored into

5(2x² - x + 3).

Since the greatest common factor of these terms is 5, Todor's area model can be represented as 5 multiplied by two rectangles.

The first rectangle would have a length of 2x² and a width of 5, and the second rectangle would have a length of x and a width of 3. Therefore, the total width of Todor's area model would be 5 + 3 = 8

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Correct question should be:

Todor was trying to factor 10x^(2)-5x+15. He found that the greatest common factor of these terms was 5 and made an area model: What is the width of Todor's area model?