T is the midpoint of KL. K has coordinates (2,−6), and T has coordinates (−4,2). Identify the coordinates of L.

The correct option for the given sum is option B. The point (2,-9) paired with (2, 3), will make a side equal to this length.

Let the other point of the pentagon will be M(n, o).

The given point be A (a, b)

Also given one of the sides of a pentagon has length 12.

Now, we need to find the distance between the two points,

Distance between two points: |AM| = √\((a-n)^2+(b-o)^2\)

Now,

\(12 = \sqrt{(2-n)^2+(3-o)^2}\)

\((12)^2\) = \((2-n)^2+(3-o)^2\)

\((2-n)^2+(3-o)^2\) = 144 ----------------------------- eq (1)

Now, check every point for the values to match with equation (1)

Option A: \((2-14)^2+(3-15)^2\) = 288. So the option is false.

Option B:

\((2-2)^2+(3-(-9))^2\) =114

0+114 =114

Therefore option B is correct. The other point is (2,-9).

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The factors of the polynomial function f(x) must be x, x + 6  and x + 3

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

The graph (see attachment)

On the graph, we have the zeros of the function to be

x = -6, x = -3 and x = 0

Set the equations to 0

So, we have the following representation

x + 6 = 0, x + 3 = 0 and x = 0

This means that the factors are

x, x + 6  and x + 3

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The area of the figure is 51.4 unit²

Figure ABCDEF is shown. A is located at 5, negative 8. B is located at 11, negative 8. C is located at 11, 0. D is located at 6

See attachment for the figure

The figure can be divided into the following shapes:

The area of the trapezoid is:

Area = 0.5 * (Sum of opposite sides) * height

So, we have:

Trapezoid 1 = 0.5 * (8 + 5) * 5 = 32.5

Trapezoid 2 = 0.5 * (5 + 4.8) * 2 = 9.8

The area of the triangle is:

Area = 0.5 * Base * Height

This gives

Triangle = 0.5 * 4.8 * 4 = 9.6

Add the individual areas

Area = 32 + 9.8 + 9.6

Evaluate the sum

Area = 51.4

Hence, the area of the figure is 51.4 unit²

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The independent variable in this data is the speed of the car. This is because the congressman is trying to determine whether or not the gas mileage improves at lower speeds.

The dependent variable is the gas mileage, because it is the variable that is being measured and that is affected by the independent variable.

The other variables in this data are the weight of the car, the type of engine, and the year of the car. However, these variables are not being changed in this experiment, so they are not considered to be independent variables.

The data shows that the gas mileage of the Toyota Camry improves as the speed of the car decreases. This supports the claim of the supporters of the bill to reduce the speed limit.

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Answer:

Step-by-step explanation:

Since order does not matter \(_{12}C_3\\ \\ \frac{12!}{3!9!}\\ \\ 220\)

Answer: 1

Step-by-step explanation:

The equation of line which passes through (-2, 8) and perpendicular to the line conatining (0, 1) and (4, 5) is y = -x + 6 .

Let the equation of line passes through the point (-2, 8) be y = mx + b.

Where m is the slope of the line and b is the y intercept of the line.

According to the given question.

A line passes through the points (-2, 8).

And it is also perpendicular to the line containing (0, 1) and (4, 5).

Since, the line is perpendicualr to the line conatining (0, 1) and (4, 5).

So, the slope of the line whose equation is to be find is given by

m = -1/(5 - 1/4-0)

⇒ m = -1/4/4 = -1

Thereofre, the equation of line with slope -1 is

y = -1x + b

Also, it passes through (-2, 8)

So,

8 = -1(-2) + b

⇒ 8 - 2 = b

⇒ b = 6

Thereofore, the equation of line which passes through (-2, 8) and perpendicular to the line conatining (0, 1) and (4, 5) is y = -x + 6 .

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Answer:

what the heck question is this

The area of both the top face and the bottom face of the cuboid is 63 square centimeters (cm²).

To find the area of each face of the cuboid, we'll use the formulas for finding the area of a rectangle (which is the shape of each face of the cuboid).

Given dimensions:

Length (L) = 9 cm

Width (W) = 7 cm

Height (H) = 4 cm

a) Area of the top face of the cuboid:

The top face is a rectangle with dimensions 9 cm (length) and 7 cm (width).

Area = Length × Width

Area = 9 cm × 7 cm

Area = 63 square centimeters (cm²)

b) Area of the bottom face of the cuboid:

The bottom face is also a rectangle with dimensions 9 cm (length) and 7 cm (width).

Area = Length × Width

Area = 9 cm × 7 cm

Area = 63 square centimeters (cm²)

Therefore, the area of both the top face and the bottom face of the cuboid is 63 square centimeters (cm²).

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Answer:

C. 3:1

Step-by-step explanation:

Ive done this lesson before.

Answer:

C. 3:1

Step-by-step explanation:

They are only asking about the bones  and the one stuffed animal. Also it is 3 nes to 1 stuffed animal, erefore 3:1

The minimum amount of wrapping paper Sarah will need to cover the present is; 351.68 square inches and one gallon of filtered water is not enough because the capacity of fish tank will be 2.17 gallons.

WE are Given that, the dimensions of cylindrical fish tank are height=10 inches and radius = 8/2 = 4 inches.

Now the total surface area of a cylinder is 2πr(r + h).

Here, the required wrapping paper = 2×3.14 ×4(4+10)

= 2×3.14×4×14

= 351.68 square inches

We know that, the volume of cylinder = πr²h

= 3.14 × 4² × 10

= 502.4 cubic inches

Thus, 1 gallon is equal to 231 cubic inches

Number of gallons of filtered water required = 502.4/231

= 2.17 gallons

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Answer:

m= -125/176

Step-by-step explanation:

Answer:

x=37°

y=6

Step-by-step explanation:

(ASSUMING BD is a perpendicular bisector of AC, otherwise answers maybe be wrong)

Consider the triangle ABC:

AB is the same length as BC (marked), meaning ABC is an isosceles triangle.

Since ABC is isosceles, ∠BAC=∠BCA=53

All angles in a triangle add up to 180:

180=∠ABC + ∠BAC + ∠BCA

180= ∠ABC + 53 +53

∠ABC = 180 - 106

∠ABC = 74

Assuming BD bisects ∠ABC perfectly, x is half of ∠ABC.

x=74/2=37

If BD bisects AC perfectly, AD=DC=y=6

The value that would have the most dots on a line plot is given as follows:

4.25.

The dot plot gives a dot to each measure for each time that it appears, hence it says the same thing as a table, in a different format.

A line plot is built from the dot plot, in which:

Hence the value 4.25 is the value in this problem that would have the most dots in a line plot, as it is the value that appears the most times in the data-set (only value to appear three times).

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The presented system of linear equations has no solution.

The final form of the augmented matrix suggests that the system of linear equations has no solution, as the last row represents an equation with 0 = 0, which is always true but doesn't provide any information about the variables.

To see this more clearly, let's use the augmented matrix to write out the system of linear equations:

1x - 1y + 2z = 4

2y + 1z = -1

z = 1

The first two equations are consistent and have a unique solution, but the last equation is trivial and provides no information about x and y. In other words, infinitely many pairs of x and y satisfy the first two equations, but none satisfy the third equation. Therefore, the given system of linear equations has no solution.

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Answer:

You would have 10 more legos than your sister.

Step-by-step explanation:

20-10=10

Answer is - 2 \(\sqrt{3}\) / 13

Cosecant Given a point P(x, y) on the terminal side of an angle θ in standard position

cosθ = cos (π + d) (d is the inner angle of the tringle)

       = - cos 2

       = - 4 / - \(\sqrt{(- 6^{2} + (- 4^{2} )\)

       = - 4 / - \(\sqrt{36 + 16 }\)

      = - 4 / -\(\sqrt{52}\)

      = - 4 / 2\(\sqrt{13}\)

      = - 2 / \(\sqrt{13}\)

multiply by \(\sqrt{13}\)

we get,

      = -  \(\frac{2 \sqrt{13} }{13}\)

Formulae :

Arc cosecant      y = arcs(x) = csc-1(x). Another way to write x = csc(y).

Arccosine      y = arcos(x) = cos-1(x). Another way to write x = cos(y).

Arc cotangent    y = arcos(x) = cot-1(x). Another way to write x = cot(y).

Arc secant       y = arcsec(x) = sec-1(x). Another way to write x = sec(y).

Arcsine       y = arcsine(x) = sin-1(x). Another way to write x = sin(y).

Arctangent   y = arctan(x) = tan-1(x). Another way to write x = tan(y).

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The measure of the angle ABC given that the bisector is ABP is 12n degrees

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

Angle measures

The angle measures and the relationships are given as

Using the above as a guide, we have the following:

The above statements mean that

ABC = 2 * ABP

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

ABC = 2 * 6n

Evaluate the products

ABC = 12n

Hence, the measure is 12n degrees

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Answer:

3.5 hours

Step-by-step explanation:

use this linear equation

y = 45x + 55     y is the amount earned and x is the hours worked

plug in 212.50 for y then solve for x

212.50 = 45x + 55

157.5 = 45x

3.5 = x

so he worked for 3.5 hours or 3 hours and 30 minutes

hope this helps <3

Answer:

Step-by-step explanation:

Solve for y:

Add - 2x to both sides

or

Answer:

a = 150

Step-by-step explanation:

Sum to infinity of a geometric series

\(S_{\infty}=\dfrac{a}{1-r}\:\textsf{ for }|r| < 1\)

where:

Given:

Substitute the given values into the formula and solve for a:

\(\begin{aligned}S_{\infty} & =\dfrac{a}{1-r}\\\\\implies 100 & =\dfrac{a}{1-\left(-\frac{1}{2}\right)}\\\\ 100 & =\dfrac{a}{1+\frac{1}{2}}\\\\100 & = \dfrac{a}{\frac{3}{2}}\\\\a & = \dfrac{3}{2} \cdot 100\\\\a & = 150\end{aligned}\)

The equation of p(x) in vertex form is;

p(x) = 9.67(x + 1.04)² - 10.25

The closest answer choice is:

p(x) = 3(x - 1)²  - 2, which is not correct.

In the context of a quadratic function, the vertex is the highest or lowest point on the graph of the function. It is the point where the parabola changes direction. The vertex is also the point where the axis of symmetry intersects the parabola.

To find the vertex form of the quadratic function p(x), we need to first find the vertex, which is the point where the function reaches its maximum or minimum value.

To find the vertex, we can use the formula:

x = -b/2a, where a is the coefficient of the x²  term, b is the coefficient of the x term, and c is the constant term.

Using the table, we can see that the highest value of p(x) occurs at x = 5, and the value is 46.

We can then use the formula to find the vertex:

x = -b/2a = -5/2a

Using the values from the table, we can set up two equations:

46 = a(5)² + b(5) + c

1 = a(0)²  + b(0) + c

Simplifying the second equation, we get:

1 = c

Substituting c = 1 into the first equation and solving for a and b, we get:

46 = 25a + 5b + 1

-20 = 5a + b

Solving for b, we get:

b = -20 - 5a

Substituting b = -20 - 5a into the first equation and solving for a, we get:

46 = 25a + 5(-20 - 5a) + 1

46 = 15a - 99

145 = 15a

a = 9.67

Substituting a = 9.67 and c = 1 into b = -20 - 5a, we get:

b = -20 - 5(9.67) = -71.35

Therefore, the equation of p(x) in vertex form is:

p(x) = 9.67(x - 5)²  + 1

Simplifying, we get:

p(x) = 9.67(x²  - 10x + 25) + 1

p(x) = 9.67x²  - 96.7x + 250.85 + 1

p(x) = 9.67x²  - 96.7x + 251.85

Rounding to the nearest hundredth, we get:

p(x) = 9.67(x - 5²  + 1 = 9.67(x + 1.04)²  - 10.25

Therefore, the answer is:

p(x) = 9.67(x + 1.04)² - 10.25

The closest answer choice is:

p(x) = 3(x - 1)²  - 2, which is not correct.

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A 95% confidence interval that the t population mean number of books  is between 9.89 and 11.11 books.

What is confidence interval ?

A confidence interval is a statistical range that provides an estimate of the likely range of values for a population parameter (such as a mean, proportion, or standard deviation) based on a sample of data. It is calculated using a specific level of confidence, which represents the probability that the true population parameter falls within the calculated range.

Confidence intervals are typically expressed as a range of values with a margin of error or standard error. The margin of error represents the amount of random variation that is expected due to sampling error, while the standard error reflects the variability of the sample data.

According to the question:
C. There is 95% confidence that the population mean number of books read is between a lower bound of approximately 9.89 books and an upper bound of approximately 11.11 books.

To construct the confidence interval, we can use the formula:

\(CI =\bar x \± z* (s/\sqrt{n})\)

substitute the values, we get:

CI = 10.5 ± 1.96 * (16.6/√1015)

CI = (9.89, 11.11)

This means that we are 95% confident that the  population mean number of books is between 9.89 and 11.11 books.

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The number would you add to both sides of x² + 7x = 4 to complete the square option C 7²/2.

Suppose the considered quadratic equation is of the form

ax^2 + bx + c = 0

Then, completing the squares method tries to make a squared term in terms of x in the left side, so that x comes in linear form, instead of quadratic.

The given quadratic equation is

x² + 7x = 4

add  7²/2 to both sides of x² + 7x = 4 to complete the square

7²/2 = 49/4

x² + 7x + 49/4 = 4+ 49/4

(x + 7/2)² = 4+ 49/4

Thus, option C 7²/2 is correct.

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Answer:

.125 should be your answer. Have a Great Day!

Step-by-step explanation:

Answer:

5 to 8, 5/8, 5:8

Step-by-step explanation:

if you have 5 triangles then TO 8 rectangles it will be (5 to 8, 5/8, or 5:8) those are all 3 ways to write it and it has to be # TO # in the right order it says in the sentence

Equation:

Replace d with 10, b with 9 , c with 5, and a with 1/3.

Solve: