On a normal curve the center of the range of scores is represented by the what

Reflexive property of congruence CPCTC .

When two objects or figures have the same size and shape, the term "congruence" is used to describe it. Congruence has the transitive property, which states that if two sets of lines, angles, or triangles are congruent with a third pair of lines, angles, or triangles, then the first pair of lines, angles, or triangles are also congruent with the third pair of lines, angles, or triangles. As was previously mentioned, the transitive property creates an equivalence relationship between 3 lines, 3 angles, and 3 triangles. According to the definition of the transitive property of congruence in geometry, if any two angles, lines, or forms are, respectively, congruent with a third angle, line, or shape, then the first two angles, lines, or shapes are likewise congruent with the third angle, line, or shape.

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Answer:

The answer to the first box is SSS criterion, im not sure about the second box, i know it isnt ASA criterion, but i hope this helps!

Step-by-step explanation:

The correct solution to the limits of x in the tiles can be seen below.

The limits of x approaching a given number of a quadratic equation can be determined by knowing the value of x at that given number and substituting the value of x into the quadratic equation.

From the given diagram, we have:

1.

\(\mathbf{ \lim_{x \to 9^+} (\dfrac{|x-9|}{-x^2-34+387}) }\)

So, x - 9 is positive when x → 9⁺. Therefore, |x -9) = x - 9

\(\mathbf{ \lim_{x \to 9^+} (\dfrac{x-9}{-x^2-34+387}) }\)

Simplifying the quadratic equation, we have:

\(\mathbf{ \lim_{x \to 9^+} (-\dfrac{1}{x+43}) }\)

Replacing the value of x = 9

\(\mathbf{ = (-\dfrac{1}{9+43}) }\)

\(\mathbf{ = -\dfrac{1}{52} }\)

2.

\(\mathbf{ \lim_{x \to 8^-} (\dfrac{8-x}{|-x^2-63x+568|}) }\)

Thus |-x²-63x+568| = -x²-63x+568

\(\mathbf{ \lim_{x \to 8^-} (\dfrac{1}{x+71}) }\)

\(\mathbf{=\dfrac{1}{8+71} }\)

\(\mathbf{=\dfrac{1}{79} }\)

3.

\(\mathbf{ \lim_{x \to 7^+} (\dfrac{|-x^2-17x+168| }{x-7}) }\)

\(\mathbf{ \lim_{x \to 7^+} (\dfrac{-x^2-17x+168 }{x-7}) }\)

\(\mathbf{ \lim_{x \to 7^+} (-x-24)}\)

\(\mathbf{ \lim_{x \to 7^+} (-7-24)}\)

= -31

4.

\(\mathbf{ \lim_{x \to 6^-} (\dfrac{|x-6| }{-x^2-86x+552}) }\)

\(\mathbf{ \lim_{x \to 6^-} (\dfrac{-x+6 }{-x^2-86x+552}) }\)

\(\mathbf{ \lim_{x \to 6^-} (\dfrac{1}{x+92}) }\)

\(\mathbf{ \lim_{x \to 6^-} (\dfrac{1}{6+92}) }\)

\(\mathbf{ =\dfrac{1}{98}}\)

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Answer:

63.22⁰

Step-by-step explanation:

the answer is in the picture. please mark mine brainliest.

Answer:

45

Step-by-step explanation:

I think it's 45. Why do I have to have 25 characters

Answer:

5^2 is 5x5=25 25x 2 = 50 minus 5 is 45 so i think its 45

Step-by-step explanation:

Answer:

37

Step-by-step explanation:

180 - 45 - 98 = 37

Answer:

37. ...... yeah.......

Answer:

4'F

Step-by-step explanation:

Answer:

Substitution Property

Step-by-step explanation:

The change from the first equation to the final equation is m∠A has been replaced by m∠B. In other words, m∠B was substituted for m∠A.

Answer:

Substitution property

Step-by-step explanation:

Have a nice day!

Answer:

-------------------------

Let the diagonals be d₁ and d₂.

One of the diagonals has opposite angle 45° and the other one- 135° since adjacent angles of a parallelogram add to 180°.

Use the law of cosines to find diagonals.

Find d₁:

Find d₂:

The lengths of the diagonals of the parallelogram are approximately 12.73 and 15.56 units, respectively.

To determine the lengths of the diagonals of a parallelogram, we can use the law of cosines. Let's denote the lengths of the diagonals as d1 and d2. Given that the sides of the parallelogram are 9 and 8, and one angle is 45°, we can use the following calculations:

For diagonal d1:

d1^2 = 9^2 + 8^2 - 2 * 9 * 8 * cos(45°)

d1 ≈ 12.73

For diagonal d2:

d2^2 = 9^2 + 8^2 - 2 * 9 * 8 * cos(135°)

d2 ≈ 15.56

Therefore, the lengths of the diagonals are approximately 12.73 and 15.56, respectively.

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Answer: 40 inches

Step-by-step explanation:

The woman weight and the seat will be: 145lb + 5lb = 150lb,

her son weight and the seat will be: 95lb + 5lb = 100lb

her daughter weight and the seat will be: 70lb + 5lb = 75lb

Given that the woman is on the left side of the seesaw, 60 inches from the fulcrum. The moment of the woman will be 150 × 60 = 9000

The daughter and son both get on the right side.

If the son sits 60 inches from the fulcrum, his moment will be:

100 × 60 = 6000

The sum of the moment of the son and daughter must be equal to the moment of their mother.

Let the position of the daughter = X

The moment of the daughter will be:

75 × X = 75X

Equate the moment of the mother to the sum of the moment of her children

9000 = 6000 + 75X

Collect the like terms

75X = 9000 - 6000

75X = 3000

X = 3000/75

X = 40

The position the daughter should sit to balance the seesaw is 40 inches away from seasaw to the right.

The money paid to the secretary is $14000 and the money paid to mathematician is $22000.

A mathematical statement that establishes the equality of two mathematical expressions is the called an equation.

Total money available for hiring = $36000

Let the money given to secretary = X

Money given to the mathematician = X + 8000

X + (X + 8000) = 36000

2X = 28000

X = 14000

Money given to secretary is $14000.

Money given to the mathematician is $22000.

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Answer:

x=40

Step-by-step explanation:

2x+7+x-10+63=180

3x=120

x=40

Answer:

12 z

22.5x or 3 meybe

where Y?????

Step-by-step explanation:

Answer:

Step-by-step explanation:

I'm going to assume that y is the length of the red line.

The expression x(dz/dX) - y(dz/dy) can be written as:

x(dz/dX) - y(dz/dy) = x * (x * d/dX[f(XY)]) - y * (x * d/dy[f(XY)])

To express the expression x(dz/dX) - y(dz/dy) in its simplest form, let's differentiate z = x * f(XY) with respect to X and y.

Using the product rule, we differentiate z with respect to X:

dz/dX = x * d/dX[f(XY)] + f(XY) * d/dX[x]

Since f(XY) does not depend on X, the second term on the right-hand side simplifies to zero:

dz/dX = x * d/dX[f(XY)]

Next, we differentiate z with respect to y:

dz/dy = x * d/dy[f(XY)]

Now, we can substitute these derivatives into the expression x(dz/dX) - y(dz/dy):

x(dz/dX) - y(dz/dy) = x * (x * d/dX[f(XY)]) - y * (x * d/dy[f(XY)])

Simplifying further:

x(dz/dX) - y(dz/dy) = x^2 * d/dX[f(XY)] - yx * d/dy[f(XY)]

This is the simplest form of the expression, given the information provided.

However, without knowing the specific form or properties of the function f(XY), we cannot simplify it any further.

Note that the result may vary depending on the specific function f(XY) and the nature of its dependencies on X and y.

Therefore, the expression x(dz/dX) - y(dz/dy) can be written as:

x(dz/dX) - y(dz/dy) = x * (x * d/dX[f(XY)]) - y * (x * d/dy[f(XY)])

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Answer:

11.1667

Step-by-step explanation:

11 1/6

11*6+1

=67/6

=11.1666666666

=11.1667

Answer:

The commutative property is a math rule that says that the order in which we multiply numbers does not change the product.

Step-by-step explanation:

Answer:

Use the formula to find the geometric mean.

√

4

⋅

6

Multiply

4

by

6

.

√

24

Rewrite

24

as

2

2

⋅

6

.

Tap for more steps...

√

2

2

⋅

6

Pull terms out from under the radical.

2

√

6

Approximate the result.

4.89897948

The geometric mean should be rounded to one more decimal place than the original data. If the original data were mixed, round to one decimal place more than the least precise.

4.9

Answer:

When you add polynomials, you combine only like terms together. When you multiply polynomials, you multiply all pairs of terms together.

Step-by-step explanation:

.

Answer:

adding, subtracting and multiplying polynomials are, basically, the same as adding, subtracting and multiplying numbers. They only difference is that we have a pesky variable to worry about

The surface with the given vector equation, r(s, t) = (s cos(t), s sin(t), s), is a circular cone.

The vector equation r(s, t) = (s cos(t), s sin(t), s) represents a surface in three-dimensional space. Let's analyze the equation to determine the nature of the surface.

In the equation, we have three components: s, cos(t), and sin(t). The presence of s indicates that the surface expands or contracts radially from a central point. The trigonometric functions cos(t) and sin(t) determine the angle at which the surface extends in the x and y directions.

By observing the equation closely, we can see that as s increases, the radius of the surface expands uniformly in all directions, while the height remains constant. This behavior is characteristic of a circular cone. The circular base of the cone is defined by s cos(t) and s sin(t), and the vertical component is determined by s.

Therefore, the surface described by the vector equation r(s, t) = (s cos(t), s sin(t), s) is a circular cone.

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We can write A = PAP where 1 P= and A= where P is an invertible matrix that maps the null space of A to itself.  

To find the matrix P, we need to solve the following system of linear equations:

λ_1 1 = 1

λ_2 (-4) 1 = 1

λ_3 (-1) 1 = 1

The eigenvalues are real and non-negative, so they can be written as λ = λ_1, λ_2, λ_3 = λ_1, -4, -1 respectively.

Using Cramer's rule, we have:

\(λ_1 * 1^T = 1 * 1^T = 1\)

\(λ_2 * (-4)^T = -4 * 1^T = -4\)

\(λ_3 * (-1)^T = (-1) * 1^T = -1\)

Multiplying the first and third equations, we get:

\(-λ_1 * λ_3 = -4 * (-1) = 4\)

Multiplying the second and third equations, we get:

\(-λ_2 * λ_3 = -4 * (-1) = 4\)

Subtracting the second equation from the first, we get:

\(λ_1^2 - λ_2^2 = 1^2 - (-4)^2 = 5\)

Multiplying the first and third equations, we get:

\(-λ_1 * λ_2 = -4 * (-1) = 4\)

Dividing the third equation by the second equation, we get:

\(-1/λ_2 = -1/λ_3\)

Taking the reciprocal of both sides, we get:λ_2 = λ_3

Substituting this into the second equation, we get:

-\(λ_1 * λ_3 = -4 * (-1) * λ_3 = -4\)

Simplifying, we get:

-4 = -4

This equation has no solution, so the matrix A cannot be written in the form A = PAP where 1 P= and A= Thus, the answer is no.  

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Full Question: the matrix, A, has eigenvectors and whose eigenvalues are 1, –4 and – 1 respectively. Then, using the same order, A can be written in the form A = PAP where 1 P= and A=

The two ratios that are equivalent to 15/36 are expressed as: B.) 5/12 and 30/72.

If two ratios are said to be equivalent, it means that they will have the same value when simplified or expressed in their simplest form.

Given the ratio, 15/36, simplify in its simplest form:

15/36 = 5 * 3 / 12 * 3 = 5/12

So also, we have:

30/72 = 5 * 6 / 6 * 12 = 5/12

Therefore, 5/12 and 30/72 are equivalent to the ratio, 15/36.

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Range: All real numbers greater than or equal to 3. The Option C.

To find the range of the function, we need to determine the set of all possible y-values that the function takes.

Since the line crosses the y-axis at (0, 2), we know that the function's range includes the value 2. Also, since the line turns at (-1, 3), the function takes values greater than or equal to 3.

Therefore, the range of the function is all real numbers greater than or equal to 3.

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Answer:

A E F

Explanation:

Rules to know:

Triangles = 180 degrees

Straight lines = 180 degrees (example z + w = 180)

Therefore: angles of straight line = angles of triangle

A : w is an obtuse angle (greater than 90) and x is acute (less than 90)

E : w is obtuse whereas y is acute.

F : Since triangle = 180 = x + y + z

Straight line = 180 = z + w

Equate the two:

z + w = x + y + z  (subtract z from both sides)

w = x + y

Equate the two z + w = x + y + z  (subtract z from both sides) w = x + y

Answer:

f = (N² - H)/6

Step-by-step explanation:

Step 1: Write equation

N² = 6f + H

Step 2: Solve for f

The series of transformations shows that pentagon A is congruent to pentagon B is

A. Reflect pentagon A over the y-axis, rotate it 180° clockwise about the origin, and translate it 3 units up.

To determine which series of transformations shows that pentagon A is congruent to pentagon B, we need to study the transformations that maps A to B

Reflect pentagon A over the y-axis, brings the image to the 2nd quadrant

Also, rotate it 180° clockwise about the origin, this movement brings the pentagon to the 4th quadrant

Then translate it 3 units up maps it to pentagon B

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Answer:

D

Step-by-step explanation:

I believe its D due to the fact when lined up from the point both wrenches align

Answer:

H

Step-by-step explanation:

sorry if im wrong

Answer:

H

Step-by-step explanation:

A translation from the point (3,2) 1 unit to the left and two units down leaves you at (2,0). A reflection across the y-axis leaves you at point (-2, 0). A 90 degree counterclockwise rotation about the origin leaves you at point (0,-2), which is also point H.

Answer: 279.43

Step-by-step explanation:

The area of the tent that she will need to waterproof is 279.43 feet².

The area of a three dimensional object on it's outer surface is called the surface area of the object.

Given a tent in the form of a triangular prism as given.

We have to find the surface area of the tent excluding the base.

There are 2 triangular faces and 2 rectangular faces.

Area of the prism that needs to waterproof = area of 2 rectangles + area of 2 triangles

Area of rectangles = 2 × 14 × 8 = 2 × 112 feet² = 224 feet²

Height of the triangular face = √(8² - 4²) = √48

Area of 2 triangles = 2 × 1/2 × 8 × (√48) = 8√48 feet²

Area needed to be waterproofed = 224 feet² + 8√48 feet² = 279.43 feet²

Hence the area of the tent is 279.43 feet².

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Answer: the speed of the elevator is 4.6 miles per hour.

Step-by-step explanation:

Given, The elevator in the Washington Monument takes 75 seconds to travel 506 feet to the top floor.

Since 1 hour = 3600 seconds

⇒ 1 second = \(\dfrac{1}{3600}\) hour

⇒ 75 seconds = \(\dfrac{75}{3600}\) hour \(=\dfrac{1}{48}\) hour

1 mile = 5280 feet

1 feet = \(\dfrac{1}{5280}\) mile

506 feet = \(\dfrac{506}{5280}\) miles \(=\dfrac{23}{240}\) miles

Speed = \(\dfrac{Distance}{Time}\)

\(=\dfrac{\dfrac{23}{240}}{\dfrac{1}{48}}\\\\=\dfrac{23\times48}{240}\\\\=\dfrac{23}{5}\\\\=4.6\text{ miles per hour}\)

Hence, the speed of the elevator is 4.6 miles per hour.