Find the value of x.
BP and DP are straight lines

Step-by-step explanation:

the angles which occupy the same relative position at each intersection where a straight line crosses two others, are called corresponding angles. If the two lines are parallel, the corresponding angles are equal.

two angles, not adjoining one another, that are formed on opposite sides of a line that intersects two other lines, are called alternate angles. If the original two lines are parallel, the alternate angles are equal.

since we are only dealing with parallel lines here, the angles are always equal.

a)

a = 60°, alternate

b)

a = 75°, corresponding

c)

a = 108°, corresponding

Answer: 1.

There is only 1 triangle with the given parts a=9, b=4, c=6. This is because the lengths of the sides of a triangle are unique and determine the shape of the triangle.

To verify this, we can use the Triangle Inequality Theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. In this case, we can see that 9+4>6, 9+6>4, and 4+6>9, so the Triangle Inequality Theorem is satisfied and the triangle is valid.

Therefore, the answer is 1, as there is only 1 triangle with the given parts a=9, b=4, c=6.

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The 12th term of the geometric sequence 9, - 18, 36, is 18,432.

In Mathematics, the nth term of a geometric sequence can be calculated by using this mathematical expression:

aₙ = a₁rⁿ⁻¹

Where:

Next, we would determine the common ratio as follows;

Common ratio, r = a₂/a₁

Common ratio, r = -18/9

Common ratio, r = -2

For the 12th term, we have:

a₁₂ = 9(2)¹²⁻¹

a₁₂ = 18,432.

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The mathematical expression for the given statement is:

[tex]$19 - 2x \leq 10$[/tex]

In mathematics, an expression is a combination of numbers, symbols, and operators (such as +, -, *, /) that represents a value or a calculation. It can contain variables, which are placeholders for unknown or changing values, and can be simplified or evaluated using mathematical rules and operations. Examples of expressions include 3x + 5, (a + b) / 2, and √(16 - 3y).

The mathematical expression for the given statement is:

[tex]$19 - 2x \leq 10$[/tex]

where x is the unknown number.

Therefore, the mathematical expression for the given statement is:

[tex]$19 - 2x \leq 10$[/tex]

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The final answer are 7 fractions of the form (1)/(n), where n is an integer from 2 up to and including 20, that are equivalent to terminating decimals.

Geoff is investigating fractions of the form (1)/(n), where n is an integer from 2 up to and including 20. To find out how many of these fractions are equivalent to terminating decimals, we need to understand what makes a fraction equivalent to a terminating decimal.

A fraction is equivalent to a terminating decimal if the denominator (the bottom number) is a power of 10 (10, 100, 1000, etc.), or if it can be reduced to a fraction with a denominator that is a power of 10. In other words, the denominator must only have factors of 2 and/or 5.

So, we need to find out how many of the numbers from 2 to 20 have only factors of 2 and/or 5.

These numbers are:

- 2 (2^1)
- 4 (2^2)
- 5 (5^1)
- 8 (2^3)
- 10 (2^1 * 5^1)
- 16 (2^4)
- 20 (2^2 * 5^1)

Therefore, there are 7 fractions of the form (1)/(n), where n is an integer from 2 up to and including 20, that are equivalent to terminating decimals.

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The measure of angle A is 85^o.

A quadrilateral is any form of plane figure which is bounded by four straight sides. Examples include: square, rhombus, rectangle trapezium etc. Each example of quadrilateral has differentiating properties.

The given quadrilateral ABCD inscribed in the circle has the shape of a rhombus. So we have:

the measure of opposite internal angles of a rhombus are congruent, so that;

x + (2x + 1) + 148 + (2x + 1) = 360

5x + 150 = 360

5x = 360 - 150

5x = 210

x = 210/ 5

  = 42

x = 42^o

Thus measure of angle A = (2x + 1)

                              = 2*42 + 1

                              = 85^o

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Therefore, one possible way to write vector u as a linear combination of the vectors in set S is:

u = [2] + [3]

To write vector u as a linear combination of the vectors in set S, we need to find scalars a, b, and c such that:

u = a[1] + b[2] + c[-2]

Substituting the given values of u and the vectors in S, we get:

[3] = a[1] + b[2] + c[-2]

To solve for the scalars a, b, and c, we can set up a system of equations:

3 = a + 2b - 2c

Since we only have one equation and three unknowns, there are infinitely many solutions to this system. One possible solution is:

a = 1, b = 1, c = 0

Substituting these values back into the equation, we get:

[3] = 1[1] + 1[2] + 0[-2]

Therefore, one possible way to write vector u as a linear combination of the vectors in set S is:

u = [1] + [2]

Similarly, for the second set of vectors, we need to find scalars d, e, and f such that:

u = d[2] + e[3] + f[-5]

Substituting the given values of u and the vectors in S, we get:

[8] = d[2] + e[3] + f[-5]

To solve for the scalars d, e, and f, we can set up a system of equations:

8 = 2d + 3e - 5f

Since we only have one equation and three unknowns, there are infinitely many solutions to this system. One possible solution is:

d = 2, e = 2, f = 0

Substituting these values back into the equation, we get:

[8] = 2[2] + 2[3] + 0[-5]

Therefore, one possible way to write vector u as a linear combination of the vectors in set S is:

u = [2] + [3]

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Answer:

60m^2

Step-by-step explanation:

15.1×10.3=155.53

155.53÷2=77.765

2.8×6.5=18.2

77.765-18.2= 59.565

rounded to nearest 10th = 60m^2

The volume of the Cylinder is 24.11 cubic feet.

Volume refers to the amount of space occupied by a three-dimensional object, measured in cubic units.

The radius of the cylinder is half the diameter of the circular base, so:

r = 2.6/2 = 1.3 feet

The volume of the cylinder is given by:

V = πr²h

Substituting the values given:

V = 3.14 × 1.3² × 4.4 ≈ 24.11 cubic feet

Rounding to the nearest hundredth:

V ≈ 24.11 cubic feet

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Step-by-step explanation:

well, we don't need to look for any fancy calculation tricks.

all we need to do is calculate the amounts in both cases and then calculate the difference.

bachelor's degree income in 30 years :

59,100×30 = $1,773,000

high school diploma income in 30 years :

35,250×30 = $1,057,500

the difference is

$1,773,000 - $1,057,500 = $715,500

a person with a bachelor's degree would earn

$715,500

more over a period of 30 years than a person with only a high school diploma.

this is not considering the changes of the income levels over the period of 30 years (that adds insult to injury ...).

Option A → If KLM ≅ PQR and PQR ≅ STU , then KLM ≅ STU, is the correct answer for the transitive property of congruence.

In geometry, two figures or objects are congruent if they have the same shape and size, or if one has the same shape and size as the mirror image of the other.

Given is to write the transitive property of congruence.

The transitive property of congruence states that “ if two shapes are congruent to the third shape, then all the shapes are congruent to each other. So, we can conclude that option A is the correct answer.

Therefore, Option A → If KLM ≅ PQR and PQR ≅ STU , then KLM ≅ STU, is the correct answer for the transitive property of congruence.

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The like terms on the list are given as follows:

[tex]\sqrt{2}, -3\sqrt{2}, 5\sqrt{2}, \sqrt{50}[/tex]

Like terms are terms that share these two features:

If two terms are like terms, then they can be either added or subtracted.

In the case the terms are roots, they have the same root.

The square root of 50 is given as follows:

[tex]\sqrt{50} = \sqrt{2 \times 25} = 5\sqrt{2}[/tex]

Hence the like terms are given as follows:

[tex]\sqrt{2}, -3\sqrt{2}, 5\sqrt{2}, \sqrt{50}[/tex]

There are no terms with 3 or 5 on the root, hence the other two terms have no like terms.

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Both the limits are equal to -1, which means the function is continuous at x=1. Therefore, there is no discontinuity at x=1. So, The function is continuous at x=1.

To determine if the function is continuous at x=1, we need to evaluate the left and right limits of the function at x=1 and see if they are equal.

Left limit as x approaches 1:

\lim_{x\to 1^-}\frac{2x^2-5x+3}{x-1} = \frac{2(1)^2-5(1)+3}{1-1} = \frac{0}{0}

Right limit as x approaches 1:

\lim_{x\to 1^+}\frac{2x^2-5x+3}{x-1} = \frac{2(1)^2-5(1)+3}{1-1} = \frac{0}{0}

Since both limits are indeterminate forms of 0/0, we can use L'Hopital's Rule to evaluate them.

Taking the derivative of the numerator and denominator of the original function, we get:

\lim_{x\to 1^-}\frac{4x-5}{1} = -1

\lim_{x\to 1^+}\frac{4x-5}{1} = -1

Both limits are equal to -1, which means the function is continuous at x=1. Therefore, there is no discontinuity at x=1.

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The size or volume of the rectangular pyramid hat is 8 units tall, 12 units long, and 10 units wide is 320 cubic units.

To find the size of a rectangular pyramid, we need to find its volume. The formula for the volume of a rectangular pyramid is given:

Volume = (1/3) x base area x height

Here, the height of the pyramid is 8 units. The base is a rectangle with a length of 12 units and a width of 10 units. Therefore, the area of the base is:

Base area = length x width = 12 x 10 = 120 square units

Now we can substitute the values in the formula for volume:

Volume = (1/3) x base area x height

= (1/3) x 120 x 8

= 320 cubic units.

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Answer: We can start by translating the given sentence into an equation:

950 + 0.40(950) = x

where x is the unknown amount after the 40% increase.

To solve for x, we can simplify the right-hand side of the equation:

950 + 0.40(950) = x

950 + 380 = x

1330 = x

Therefore, the unknown amount after the 40% increase is 1330.

Rounding 1330 to the nearest tenth gives 1330.0, and converting to a percent gives 133000%.

Step-by-step explanation:

The correct answer is B. The graph shows the amount of water in a sink after several minutes, so it is a decreasing function.

Graph is a mathematical structure used to represent connections or relationships between objects. It consists of nodes, which are connected by edges. Graphs are used in computer science and other fields to represent networks of communication, data organization, computational devices, the flow of computation, and other objects. Graphs are also used to represent the abstract connections between objects in a more visual way. Graph theory is the study of graphs and their properties.

Option B, y = -3/2x + 5, is a linear function with a negative slope, which is the correct representation for this situation. This equation can be used to find the amount of water in the sink after any given number of minutes.

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Answer:

First, we need to convert the mixed number to an improper fraction:

6 3/4 = (4 x 6 + 3)/4 = 27/4

Now we can divide:

45 ÷ 27/4 = 45 x 4/27 = 6.6666666...

Rounding to the nearest hundredth, we get:

6.67

Therefore, 45 divided by 6 3/4 is approximately 6.67.

Answer:6.67

Step-by-step explanation:

a. False. If we form the table with aspirin in the first row (instead of placebo), the confidence interval is (1/2.33, 1/1.44) = (0.43, 0.69).

b. True. We may get a different odds ratio value if we treat marijuana use as the response variable than if we treat alcohol use as the response variable.

c. False. Interchanging two rows or interchanging two columns in a contingency table does have an effect on the value of the X2 or G-chi-squared statistics. Thus, these tests treat both the rows and the columns of the contingency table as nominal scale, and if either or both variables are ordinal, the test takes that information into account.

d. False. Income and gender are not necessarily independent in the 2 x 2 marginal table, even if they are conditionally independent given the type of job.

e. False. The estimated odds ratio between opinion on global warming and whether one is a Democrat or a Republican does not equal 2.96 x 2.08 = 6.2, it equals (2.96/2.08) = 1.42.

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The  value of the inequality for the expression is:  x >  -8

Inequalities are the comparison of mathematical expressions, whether one quantity is greater or smaller in comparison to another quantity.

We use these symbols to represent inequalities, '>' , '<', '≥', '≤'

To solve the inequality, we need to isolate the variable, x.

We begin by simplifying the expression inside the parentheses:

2(3x - 2) = 6x - 4

Now we can substitute this expression into the original inequality:

-52 < 6x - 4

Add 4 to both sides:

-48 < 6x

Divide both sides by 6:

-8 < x

So the solution to the inequality is x > -8.

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Answer:

Your answer:

6. x = 8

8. x = 3

Step-by-step explanation:

Basic calculation involving adding/subtracting and multiplying and dividing.

Formula for Area of a Rectangle:

Area = Length * Width.

6. Given information

A = 165 cm^2

length = 4x + 1

width = 5

(4x + 1) * 5 = 165 cm^2

5 * (4x + 1)= 165

20x + 5 = 165

20x = 160

x = 8

8. Given information

A = 40 cm^2

length = 7x - 1

width = 2

(7x - 1) * 2 = 40 cm^2

2 * (7x - 1)= 40

14x - 2 = 40

14x = 42

x = 3

Answer:

c.

Step-by-step explanation:

the inner angle is half of the sum of both outer angles.

65 = 1/2 × (36 + x)

130 = 36 + x

x = 130 - 36 = 94°

The value of the expression 7₂ + 3₃ is 10₅.

One mathematical expression makes up a term. It might be a single variable (a letter), a single number (positive or negative), or a number of variables multiplied but never added or subtracted. Variables in certain words have a number in front of them. A coefficient is a number used before a phrase.

Given:

An expression is 7₂ + 3₃.

To find the value of the expression, first, add 7 and 3.

That means, 7 + 3 = 10.

Now add 2 and 3,

2 +3 = 5

So, the value of the expression is 10₅.

Therefore, the result is 10₅.

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The equation represents the 33.60+1.40=w that a shop will use to determine the markup from its wholesale price.

The definition of the an equation in algebra is a mathematical assertion that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

A mathematical equation is a statement that two numbers or values are equal, such as 6 x 4 = 12 x 2. 2. A noun that counts. When two or more components must be taken into account together in order to comprehend or describe the whole situation, this is known as an equation.

Let w be the wholesale price, then the price after markup is:

w + 140%

[tex]w=w+1.4w=2.4w[/tex]

we know price after markup is $[tex]33.60[/tex]

2.4w = $33.60

we can solve w

w = $33.60 / 2.4 = $14.00

So the wholesale price before markup is $14.00.

The equation represents the 33.60+1.40=w

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The ratio of all points scored up to the moment when Alex left the ground was 25 : 100. This means that out of all the points scored, 25% were Alex's hits.

Ratio is a comparison between two or more numbers. It is usually expressed in the form of a fraction, with the numerator being the first number and the denominator being the second number. Ratios can also be expressed in terms of a percentage or a proportion. Ratios help to compare two or more values and can be used to indicate relationships between different parts of a system. For example, if the ratio of apples to oranges is 2:3, then for every two apples, there are three oranges.

The reason for this is that when Alex entered the game, Alphas had a score of 20 points out of a total of 120 points. After his reverse substitution, Alphas had a score of 50 points out of a total of 100 points. This means that Alex scored 30 points in total during his time in the game. Therefore, the ratio of Alex's hits to the total points scored is 30 : 100, or 25%.

This shows the impressive contribution that Alex made in the game. Despite playing for a relatively short period of time, he was able to score a quarter of all the points in the game. This highlights Alex's skill and shows what a difference an individual player can make in a team sport.

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We start by isolating the square root on one side of the equation:

3x - 3 = sqrt(3x^2 + 177)

Squaring both sides of the equation gives:

(3x - 3)^2 = 3x^2 + 177

Expanding the left-hand side gives:

9x^2 - 18x + 9 = 3x^2 + 177

Simplifying gives:

6x^2 - 18x - 168 = 0

Dividing both sides by 6 gives:

x^2 - 3x - 28 = 0

We can now solve for x using the quadratic formula:

x = (3 ± sqrt(3^2 + 4128)) / 2

x = (3 ± 7) / 2

Therefore, the solutions are x = -2 and x = 5, and their sum is -2 + 5 = 3.

Thus, the answer is (C) 3.

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The volume of the composite solid is 885 m³

From the diagram shown, we have that;

Volume of the composite solid = Volume of a rectangle + volume of  a pyramid

The formula for the volume of a rectangle is expressed as;

Volume = lwh

Given that;

Volume = 5 × 10 × 16. 5

Volume = 825 m³

Volume of the pyramid = 6(10) = 60m³

Total volume = 825 + 60 = 885 m³

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20 - 10 = 10 pupils are more probability to be wearing shirts other than blue or white.

Probability gives information about the likelihood that something will occur. For instance, weather patterns are used by meteorologists to predict the possibility of rain. Probability theory is utilised in epidemiology to comprehend the connection between exposures and the risk of health outcomes.

A AND B = P(B)P(A|B) if A and B are two events defined on a sample space. (The likelihood of A given B is equal to the likelihood of A and B divided by the likelihood of B.) P(A|B) = P if A and B are independent (A).

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The fourth term a₄ of the sequence is -343

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

a₁= -1

aₙ = 7aₙ₋₁

The above definitions imply that we simply multiply 7 to the previous term to get the current term

Using the above as a guide,

so, we have the following representation

a₂ = 7 * -1

a₂ = -7

Also, we have

a₃ = -7 * 7

a₃ = -49

Lastly, we have

a₄ = -49 * 7

Evaluate the equation

a₄ = -343

Hence, the value of a₄ is -343

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Answer:

How to calculate 8 + 3(5 - 7)​

Use Pemdas

Pemdas

8 + 3(5 - 7)​

5 - 7

= -2

8 + 3 ⋅ -2

Pemdas

8 + 3 ⋅ -2

3 x -2

= -6

8 + -6

Pemdas

8 + -6

Step-by-step explanation:

You're welcome.

Answer:

8+3(5-7)=-2

You will use the"Bracket Of Division Multiplication Addition and Subtraction(BODMAS)" method. Hence solve the one in the bracket first. So it's going to be 5-7 which is -2.Then you continue with the multiplication of 3 by the -2 you got making -6. Finally add the 8 to the -6 making 2.