Which piecewise function represents the graph?

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

The rewritten rational expression with the indicated denominator of  (6x^2) is (10x) / (6x^2). This is because when we multiply both the numerator and denominator of a rational expression by the same quantity, the value of the expression remains the same.

In this case, by multiplying the numerator and denominator of the original expression (5) / (2x) by 5, we get (10x) / (6x^2). We multiplied both the numerator and denominator by 5 because the denominator of the target expression (6x^2) is twice the denominator of the original expression (2x).

This means that the numerator of the target expression should be double the numerator of the original expression. Hence, by multiplying the numerator and denominator of the original expression by 5, we get the target expression.

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Answer:3

Step-by-step explanation:

The HCF of 3 and 9 is 3. To calculate the HCF (Highest Common Factor) of 3 and 9, we need to factor each number (factors of 3 = 1, 3; factors of 9 = 1, 3, 9) and choose the highest factor that exactly divides both 3 and 9 . i.e 3.

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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65. Find cos tetha, given that sin tetha = 3/5 and tetha is in quadrant II.

We can use the identity cos^2 tetha + sin^2 tetha = 1 to find cos tetha.

cos^2 tetha = 1 - sin^2 tetha

cos^2 tetha = 1 - (3/5)^2

cos^2 tetha = 1 - 9/25

cos^2 tetha = 16/25

cos tetha = ±√(16/25)

cos tetha = ±4/5

Since tetha is in quadrant II, cos tetha is negative. So, cos tetha = -4/5.

66. Find sin tetha, given that cos tetha = 4/5 and tetha is in quadrant IV.

We can use the same identity to find sin tetha.

sin^2 tetha = 1 - cos^2 tetha

sin^2 tetha = 1 - (4/5)^2

sin^2 tetha = 1 - 16/25

sin^2 tetha = 9/25

sin tetha = ±√(9/25)

sin tetha = ±3/5

Since tetha is in quadrant IV, sin tetha is negative. So, sin tetha = -3/5.

67. Find csc tetha, given that cot tetha = -1/2 and tetha is in quadrant IV.

We can use the identity csc^2 tetha = 1 + cot^2 tetha to find csc tetha.

csc^2 tetha = 1 + (-1/2)^2

csc^2 tetha = 1 + 1/4

csc^2 tetha = 5/4

csc tetha = ±√(5/4)

csc tetha = ±√5/2

Since tetha is in quadrant IV, csc tetha is negative. So, csc tetha = -√5/2.

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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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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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Answer:

1= b to the second power, 2=a to the second power, 3=b to the fourth power, 4=a to the fourth

Step-by-step explanation: your welcome

Answer: 2)b^2+a^2

Step-by-step explanation:

x and y would have to be the same value since y(sin) and x(cos) of x and y on the unit circle is the same meaning it's the same point. Thus, cos(x-y) = cos(0) = 1. b^2+a^2=cos^2(x)+sin^2(x)= 1.

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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Using the slope-intercept form, the equation that represents the amount of battery charge y, in miles, after traveling for x hours is: y = -23x + 410

Equation of straight line can be defined as y = mx+b where m is slope of a line.

To create the equation in slope-intercept form, we need to find the slope and y-intercept.

The slope represents the rate at which the battery charge decreases, which is 46 miles every 2 hours. This can be expressed as:

slope = -23 miles/hour

The negative sign indicates that the battery charge decreases over time.

The y-intercept represents the initial battery charge when the car is fully charged, which is 410 miles.

Using the slope-intercept form, the equation that represents the amount of battery charge y, in miles, after traveling for x hours is: y = -23x + 410

where x is the number of hours the car has been traveling and y is the remaining battery charge in miles.

Therefore, Using the slope-intercept form, the equation that represents the amount of battery charge y, in miles, after traveling for x hours is:

y = -23x + 410

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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 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:

Infinitely Many Solutions

Step-by-step explanation:

We can start by simplifying both sides of the equation:

2(12-w) = -2(w-17)-10

Expanding the brackets:

24 - 2w = -2w + 34 - 10

Simplifying:

24 - 2w = -2w + 24

At this point, we can see that both sides of the equation are equivalent, so we can conclude that the equation is an identity and has infinitely many solutions. Any value of w will satisfy the equation.

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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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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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: 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 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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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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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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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 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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There are infinitely many rational numbers between 0 and 5. This is because the set of rational numbers is dense in the set of actual numbers.

To peer why, remember that a rational quantity can be expressed as a fraction p/q, where p and q are integers and q isn't always the same as 0. Considering there are infinitely many integers, there are infinitely many feasible values of p and q.

Consequently, there are infinitely many viable fractions among any given rational number. To locate the whole range of rational numbers among 0 and 5, we will use the truth that any rational wide variety in this program can be expressed as p/q, in which p and q are integers and 0 <= p <= 5q.

That is because any rational wide variety extra than 5 can be written as a sum of a whole range and a fragment, with the intention to be greater than 5/q.

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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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Answer:

La ecuación punto-pendiente de la recta que pasa por los puntos P1 (1,6) y P2 (4,0) es:

Primero, encontramos la pendiente de la recta utilizando la fórmula:

m = (y2 - y1) / (x2 - x1)

m = (0 - 6) / (4 - 1) = -2

Luego, utilizamos la fórmula punto-pendiente de la recta:

y - y1 = m(x - x1)

y - 6 = -2(x - 1)

y - 6 = -2x + 2

y = -2x + 8

Por lo tanto, la ecuación punto-pendiente de la recta que pasa por los puntos P1 (1,6) y P2 (4,0) es y = -2x + 8.

Step-by-step explanation:

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 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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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: