4+2√3
4-2-√3
= x +y√3find x and y.

A relationship between sets of real numbers can be accurately represented through mathematical concepts such as subsets, intersections, unions, and equalities.

When comparing sets of real numbers, various mathematical concepts help express the relationship between them. One fundamental concept is the subset. A set A is considered a subset of another set B if every element in A is also an element in B. This relationship is denoted as A ⊆ B. For example, if A = {1, 2} and B = {1, 2, 3}, then A is a subset of B since all the elements in A are also present in B.

Another useful concept is the intersection of sets. The intersection of sets A and B, denoted as A ∩ B, refers to the set of elements that are common to both sets. For instance, if A = {1, 2, 3} and B = {2, 3, 4}, the intersection of A and B would be {2, 3} since those are the elements shared by both sets.

Furthermore, the union of sets provides a way to combine elements from multiple sets. The union of sets A and B, denoted as A ∪ B, represents the set that contains all the elements from both sets without duplication. For example, if A = {1, 2, 3} and B = {3, 4, 5}, the union of A and B would be {1, 2, 3, 4, 5}.

Lastly, the concept of equality between sets implies that two sets have exactly the same elements. If all the elements of set A are present in set B, and vice versa, then A = B. However, it's important to note that the order of elements within a set is irrelevant for equality.

By utilizing these mathematical concepts, one can accurately represent and analyze the relationship between sets of real numbers.

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The angle that is complementary to angle X is 90 degrees minus angle X.

1. Complementary angles are two angles whose sum is 90 degrees.

2. Let's assume that angle X is given.

3. To find the angle that is complementary to angle X, we need to subtract angle X from 90 degrees.

4. The formula to find the complementary angle is: Complementary Angle = 90 degrees - angle X.

5. Substitute the value of angle X into the formula to calculate the complementary angle.

6. For example, if angle X is 45 degrees, the complementary angle would be: 90 degrees - 45 degrees = 45 degrees.

7. Similarly, if angle X is 60 degrees, the complementary angle would be: 90 degrees - 60 degrees = 30 degrees.

8. Therefore, to find the complementary angle to any given angle X, subtract that angle from 90 degrees.

9. The result will be the measure of the angle that is complementary to angle X.

10. Remember that complementary angles always add up to 90 degrees.

11. By using this approach, you can find the complementary angle for any given angle X.

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Answer:

\(\frac{27a^9 * 18b^5 * 4c^2 }{18a^4 * 12b^2 * 2c} = \frac{9}{2}a^5b^3c\)

Step-by-step explanation:

Given

\(\frac{27a^9 * 18b^5 * 4c^2 }{18a^4 * 12b^2 * 2c}\)

Required

Simplify

\(\frac{27a^9 * 18b^5 * 4c^2 }{18a^4 * 12b^2 * 2c}\)

Cancel out 18

\(\frac{27a^9 * b^5 * 4c^2 }{a^4 * 12b^2 * 2c}\)

Divide 4 and 2

\(\frac{27a^9 * b^5 * 2c^2 }{a^4 * 12b^2 *c}\)

Divide 27 and 12 by 3

\(\frac{9a^9 * b^5 * 2c^2 }{a^4 * 4b^2 *c}\)

Apply law of indices

\(\frac{9a^{9-4} * b^{5-2} * 2c^{2-1} }{4}\)

\(\frac{9a^5 * b^3 * 2c }{4}\)

Divide 2 and 4

\(\frac{9a^5 * b^3 * c}{2}\)

\(\frac{9a^5b^3c}{2}\)

Rewrite as:

\(\frac{9}{2}a^5b^3c\)

Hence:

\(\frac{27a^9 * 18b^5 * 4c^2 }{18a^4 * 12b^2 * 2c} = \frac{9}{2}a^5b^3c\)

Answer:

39%

Step-by-step explanation:

Answer:

1/5

Step-by-step explanation:

0.2 is the same as 2/10. you then must reduce the fraction

Step-by-step explanation:

here is the single fraction of it

\( \frac{1}{5} = 0.2\)

Connie's total bill is 9.13$

A game is played using one die. If the die is rolled and shows 1, the player wins $5. If the die shows any number other than 1, the player wins nothing. If there is a charge of $1 to play the game, what is the game's expected value?

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

Let random variable "x" be a count of player gain.

X-values are: 4, -1

P(x=4) = 1/6; P(x= -1) = 5/6

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

E(x) = (1/6)(4) + (5/6)(-1)

E(x) = [4-5]/6

E(x) = -1/6 = -17 cents

=============================

Cheers,

Answer:

It would weigh 30.88 grams

Step-by-step explanation:

\(\frac{8}{13} =\frac{19}{x} \\\\8x = 247\\x=30.875\)

Answer: 14 Units

Step-by-step explanation: Subtract (10-2) and (11-5)

Answer:

4+(3 times x)= height of balloon.   x = seconds

Step-by-step explanation:

The equation which models the height of the balloon as a function of time in seconds is y = 3t + 4.

An equation is the statement of two expressions located on two sides connected with an equal to sign. The two sides of an equation is usually called as left hand side and right hand side.

Given that,

A balloon is 4 feet above the ground.  It is released and floats up 3 feet every second.

So the height balloon will float in every second = 3 feet

Height balloon will float in t seconds = 3t

Initial height of the balloon = 4 feet

Height of the balloon in t seconds will be thus 3t + 4.

Equation to represent the height of the balloon as a function of time in seconds is,

f(t) = 3t + 4.

Hence the function that represents the height of the balloon in t seconds is f(t) = 3t + 4.

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Thus, the number line which shows the graph of Negative 2.75 less-than x is given by option second.

A number line is a visual depiction of numbers on either a straight line in mathematics. A number line's numerals are arranged in a sequential manner at equal intervals along its length. It is often displayed horizontally and can extend indefinitely in any direction.

All sets of numbers, including natural and whole numbers, are included in the numbers on a number line. The natural number ranges from 1 to 6 while a group of whole numbers is represented by (0, 1, 2, 3,4,5,6).

There are three main components to a number line. The origin is typically plotted with zero in the centre. The mnemonic "The origin like most things is nothing" can help you recall that the origin is zero.

The expression for Negative 2.75 less-than x is:

-2.75 < x

So, x > -2.75 in which, -2.75 is not included.

Thus, the number line which shows the graph of Negative 2.75 less-than x is given by option second.

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Answer:

all 3 options are true : A, B, C

Step-by-step explanation:

warning : it has come to my attention that some testing systems have an incorrect answer stored as right answer for this problem.

they say that A and C are correct.

but I am going to show you that if A and C are correct, then also B must be correct.

therefore, my given answer above is the actual correct answer (no matter what the test systems say).

originally the information about the alignment of the point F in relation to point E was missing.

therefore, I considered both options :

1. F is on the same vertical line as E.

2. F is not on the same vertical line as E.

because of optical reasons (and the - incomplete - expected correct answers of A and C confirm that) I used the 1. assumption for the provided answer :

the vertical line of EF is like a mirror between the left and the right half of the picture.

A is mirrored across the vertical line resulting in B. and vice versa.

the same for C and D.

this leads to the effect that all 3 given congruence relationships are true.

if we consider assumption 2, none of the 3 answer options could be true.

but if the assumptions are true, then all 3 options have to be true.

now, for the "why" :

remember what congruence means :

both shapes, after turning and rotating, can be laid on top of each other, and nothing "sticks out", they are covering each other perfectly.

for that to be possible, both shapes must have the same basic structure (like number of sides and vertices), both shapes must have the same side lengths and also equally sized angles.

so, when EF is a mirror, then each side is an exact copy of the other, just left/right being turned.

therefore, yes absolutely, CAD is congruent with CBD. and ACB is congruent to ADB.

but do you notice something ?

both mentioned triangles on the left side contain the side AC, and both triangles in the right side contain the side BD.

now, if the triangles are congruent, that means that each of the 3 sides must have an equally long corresponding side in the other triangle.

therefore, AC must be equal to BD.

and that means that AC is congruent to BD.

because lines have no other congruent criteria - only the lengths must be identical.

Step-by-step explanation:

GDP per capita =

Total GDP / Total Population

\( = \frac{42.29 \times {10}^{9} }{10123540} \\ = 4177.39\)

in dollars.

Note billion = 10^9.

Answer:

x = - 5

Step-by-step explanation:

Given y varies directly as x then the equation relating them is

y = kx ← k is the constant of variation

To find k use the condition y = - 18 when x = 3 , then

- 18 = 3k ( divide both sides by 3 )

- 6 = k

y = -6x ← equation of variation

When y = 30 , then

30 = - 6x ( divide both sides by - 6 )

- 5 = x

Answer:

\(y \: varies \: directly \: as \: x \: mean \\ \: y \: increase \: or \: decrease \: with \: x \\ y = - 18 \: \: \: \: x = 3 \\ y = 30 \: \: \: x = ? \\ - 18 ? = 90 \\ ? = - 5 = x\)

A reflection across the y-axis.

A translation transformation rule describes how to move an object in the plane without changing its shape, size, or orientation. A reflection transformation rule describes how to flip an object across a line or plane. A scaling transformation rule describes how to change the size of an object by multiplying its coordinates by a scalar factor. A rotation transformation rule describes how to rotate an object around a fixed point by a certain angle.

From the graph, we can see,

The coordinates of the figure A are (-2, 0), (-2, 3) and (-5, 2)

The coordinates of the figure A' are (2, 0), (2, 3) and (5, 2)

The reflection across the y-axis, according to the rule is: \((x, y)\) → \((-x, y)\)

We can see, the y-coordinates stay the same values, while the x-coordinates will have the opposite values.

Therefore, the reflection across the y-axis.

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There are 120 different ways can the letters of the word words be rearranged to form a five-letter code word.

The number of different ways that the letters of the word "words" can be rearranged to form a five-letter code word can be found using the formula for permutations.

The formula for permutations is: n! / (n - r)!, where n is the number of items and r is the number of items chosen.

In this case, n = 5 (the number of letters in the word "words") and r = 5 (the number of letters chosen to form a code word).

So, the formula becomes: 5! / (5 - 5)! = 5! / 0! = 5! / 1 = 5! = 5 x 4 x 3 x 2 x 1 = 120

Therefore, there are 120 different ways that the letters of the word "words" can be rearranged to form a five-letter code word.

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a. In an independent-measures design, each treatment condition has its own separate group of subjects.

Therefore, the number of subjects participating in the experiment would be equal to the sum of subjects in both treatment conditions.

In this case, there are 10 scores for each treatment condition, so there would be a total of 10 + 10 = 20 subjects in the experiment.

b. In a repeated-measures design, the same subjects are exposed to both treatment conditions. Therefore, the number of subjects participating in the experiment would be the same as the number of subjects in each treatment condition. In this case, there are 10 scores for each treatment condition, so there would be a total of 10 subjects in the experiment.

c. In a matched-subjects design, each subject is matched or paired with another subject based on specific criteria. The number of subjects participating in the experiment would depend on the matching criteria and the number of matched pairs.

Since the information about the matching criteria is not provided, it is not possible to determine the exact number of subjects in this design. The number of subjects in a matched-subjects design can vary depending on the specific study design and requirements.

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A solid is a three-dimensional figure that encloses a region of space.

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FILL IN THE BLANK. "a __solid___ is a three-dimensional figure that encloses a region of space."

A solid is a three-dimensional figure that encloses a region of space. It can be defined as a geometric shape that has length, width, and height and is made up of atoms, molecules, or ions.

Therefore, a solid can be classified as a polyhedron or a curved surface figure. Examples of solids include cubes, pyramids, spheres, cylinders, and cones.
A polyhedron is a three-dimensional figure that encloses a region of space.

A polyhedron is a solid shape formed by flat polygonal faces, straight edges, and vertices. These faces enclose a three-dimensional region of space, giving the polyhedron its distinct shape.

In summary, the term you are looking for is "polyhedron," which describes a 3D figure composed of flat polygonal faces enclosing a region of space.

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Answer:

x = - 3, x = - 1, x = 6

Step-by-step explanation:

given (x - a) is a factor of f(x) , then the remainder on dividing f(x) by (x - a) is zero.

using Synthetic division to divide f(x) by a = 6

  6 | 1   - 2   - 21   - 18

       ↓    6    24     18

     --------------------------

       1     4      3       0 ← remainder

quotient is x² + 4x + 3 = (x + 3)(x + 1)

then

f(x) = (x + 3)(x + 1)(x - 6)

to find the zeros , equate f(x) to zero , that is

(x + 3)(x + 1)(x - 6) = 0

equate each factor to zero and solve for x

x + 3 = 0 ⇒ x = - 3

x + 1 = 0 ⇒ x = - 1

x - 6 = 0 ⇒ x = 6

In the given diagram, using similar triangles theorem, the value of x is 17

From the question, we are to determine value of x in the given diagram

From the similar triangles theorem, we can write that

JK/KL = UV/VW

From the given information,

JK = 4x - 23

KL = 25

UV = 2x + 2

VW = 20

Thus,

(4x - 23)/25 = (2x + 2)/20

20(4x - 23) = 25(2x + 2)

80x - 460 = 50x + 50

80x - 50x = 50 + 460

30x = 510

x = 510/30

x = 17

Hence, x is 17

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Answer:

1. Angle f and s are supplementary angles, which is equal to 180, so we will: 180-35= 145

So angle f= 145 (degrees)

Angle Q= 180-49 (supplementary angles)

So angle Q= 131

I'm so sorry but I do not know the answer of Q2

I tried.

Answer:

-2

Step-by-step explanation:

We are given the following;

Plug the value of y and x into the expression;

\(\implies 2x - y\)

\(\implies 2(-3) - (-4)\)

Simplify the expression as needed;

\(\implies 2(-3) - (-4)\)

\(\implies -6 + 4\)

\(\implies \boxed{-2}\)

Therefore, -2 is the value of 2x - y, when x = -3 and y = -4.

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The length of a standard pencil is typically around 175 millimeters.

Explanation: The length of a pencil can vary depending on the type and brand, but a standard pencil is typically around 175 millimeters long. Pencils are commonly manufactured in standard sizes to ensure compatibility with pencil sharpeners and other accessories.

The length of a pencil is measured from the tip to the end, excluding any eraser that may be attached to the end of the pencil. The measurement is usually expressed in millimeters, which is a metric unit of length.

It's worth noting that the length of a pencil can differ slightly based on regional preferences or specific pencil designs. Some pencils may be slightly shorter or longer than the standard length, but in general, a length of around 175 millimeters is a common measurement for a standard pencil.

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The scale factor by which the picture has been enlarged is 3.5

It is given that the width of the picture is 5 inches and the length of the picture is 17.5 inches.

Length (l) = 7 inches

Width (b) = 5 inches

The picture is a rectangle, so the area of the picture will be the product of the length and the width, that is Area = 7 * 5 = 35 square inches.

The picture has been enlarged, let k be the scale factor that has been used to enlarge the picture.

The width has been enlarged to 17.5 inches

And the length has been enlarged to 24.5 inches

So, 5 * k = 17.5 and 7* k = 24.5

After solving these two equations, we get

k = 3.5

So, the scale factor by which the picture has been enlarged is 3.5

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Answer:

Step-by-step explanation:

To get a larger image - you multiply the original dimensions.

To find the scale factor - divide each enlarged dimension by its matching original dimension.

17.5 divided by 5 = 3.5

24.5 divided by 7 = 3.5

This is the scale factor for the enlargement.

The answer options are fractions - 17.5/5 = 3.5

so that is the correct choice.

Learning math can be a challenging task, but with persistence, hard work, and effective study strategies, it is definitely possible to improve your math skills.

Start with the basics: Make sure you have a good foundation in basic math concepts before moving on to more advanced topics. Practice basic arithmetic, fractions, decimals, and percentages until you feel comfortable with them.

Focus on understanding, not just memorizing: Math is not just about memorizing formulas and equations; it's about understanding how and why they work. Focus on understanding the underlying concepts and principles.

Practice regularly: The more you practice, the better you will get. Try to set aside some time each day to practice math problems. This will help you build your skills and improve your understanding.

Use multiple resources: Don't just rely on one textbook or resource. Use multiple resources such as online tutorials, videos, practice problems, and textbooks to get a well-rounded understanding of the topic.

Seek help when needed: Don't hesitate to ask for help if you are struggling with a particular topic. You can reach out to a teacher, tutor, or online community for help.

Stay motivated: Math can be challenging, but it's important to stay motivated and not give up. Keep a positive attitude, celebrate your successes, and remember that every mistake is an opportunity to learn and grow.

Remember that learning math takes time and effort, so don't get discouraged if you don't see immediate results. With persistence and hard work, you can become proficient in math.

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a. The equation of the ellipse is x²/900 + y²/400 = 1

b. the foci of the ellipse are at (±10√5,0)

c. Find the graph in the attachment

Since the ellipse is made from a block of wood and centered at the origin, and x- axis major axis.

So, the equation of an ellipse with center at origin and x - axis major axis is

x²/a² + y²/b² = 1 where

Since the rectangular piece of wood  has a length of 60 inches and a width of 40 inches.

The length of the rectangle equals the length of the major axis

So, 2a = 60

a = 60/2

= 30

Also, the width of the rectangle equals the length of the minor axis

So, 2b = 40

b = 40/2

= 20

So, substituting a and b into the equation of the ellipse, we have

x²/a² + y²/b² = 1

x²/30² + y²/20² = 1

x²/900 + y²/400 = 1

So, the equation of the ellipse is x²/900 + y²/400 = 1

The foci of the ellipse are at (±c,0) where c² = a² - b²

= 30² - 20²

= 900 - 400

= 500

c = ±√500

c = ±10√5

So, the foci of the ellipse are at (±10√5,0)

c. Find the graph in the attachment

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Answer:

Decrease

Step-by-step explanation:

It is decreasing because 125 is a bigger number than 75 and it is being subtracted.

125-75=50

decrease.

from 125 to 75= -40

Hoped I help :)

The numerator of the simplified sum x/(x^2) + 3x + 2 is 1/x + 3x + 2.

To simplify the sum x/(x^2) + 3x + 2, we can use the following steps:

1. Combine like terms:

x/(x^2) + 3x + 2 = x/(x^2) + 3x + 2

2. Simplify the fraction x/(x^2):

x/(x^2) + 3x + 2 = 1/x + 3x + 2

3. The numerator of the simplified sum is 1/x + 3x + 2.

So, the numerator of the simplified sum x/(x^2) + 3x + 2 is 1/x + 3x + 2.

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