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Answer:

(½,0),(1,0)

...............

Answer:

Step-by-step explanation:

To find the x-intercepts of a function, we set y = 0 and solve for x.

For the function 2x² - 3x + 1:

2x² - 3x + 1 = 0

We can use the quadratic formula to solve for x:

x = [ -(-3) ± sqrt( (-3)² - 4(2)(1) ) ] / (2*2)

x = [ 3 ± sqrt(1) ] / 4

x = 1/2 or x = 1

Therefore, the x-intercepts are (1/2, 0) and (1, 0).

For the function y = 2x² + 8x + 6:

2x² + 8x + 6 = 0

We can simplify this equation by dividing both sides by 2:

x² + 4x + 3 = 0

This equation factors as:

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

So the solutions are x = -3 and x = -1.

Therefore, the x-intercepts are (-3, 0) and (-1, 0).

For the coordinates (0.5, [?]).

To find the y-coordinate of the point (0.5, [?]), we can substitute x = 0.5 into the equation for the function:

y = 2(0.5)² + 8(0.5) + 6

y = 2(0.25) + 4 + 6

y = 5.5

Therefore, the coordinates are (0.5, 5.5).

For the coordinates ([ ], [ ]).

Without knowing the specific function, we cannot determine the x-intercepts or any other information about the graph. We would need to know the equation of the function or have additional information about the graph.

the expression cos(x − y) − cos(x + y) simplifies to 2sin(x)sin(y).

what is  expression ?

In mathematics, an expression is a combination of mathematical symbols (such as numbers, variables, and operators) that represents a mathematical object or relationship.

In the given question,

We can use the trigonometric identity cos(a - b) = cos(a)cos(b) + sin(a)sin(b) to simplify cos(x - y), and cos(a + b) = cos(a)cos(b) - sin(a)sin(b) to simplify cos(x + y).

cos(x - y) = cos(x)cos(y) + sin(x)sin(y)

cos(x + y) = cos(x)cos(y) - sin(x)sin(y)

Therefore,

cos(x - y) - cos(x + y) = (cos(x)cos(y) + sin(x)sin(y)) - (cos(x)cos(y) - sin(x)sin(y))

= cos(x)cos(y) + sin(x)sin(y) - cos(x)cos(y) + sin(x)sin(y)

= 2sin(x)sin(y)

So, the expression cos(x − y) − cos(x + y) simplifies to 2sin(x)sin(y).

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simplify the expressions  cos(x − y) − cos(x + y) ?

Answer:

45% = 0.45

(you do this by bringing the decimal over 2 places)

multiply $55 and 0.45 to get $24.75

final answer = $24.75

The synthetic division of (x³ - 12x² + 15x + 7) / (x +4) gives Quotient

x² + 8x -17.

We have to divide.

(x³ - 12x² + 15x + 7) / (x +4)

Now, performing the division we get

              (x + 4) | x³ - 12x² + 15x + 7 | x² + 8x -17

                           x³ - 4x²

                         ________

                                  8x² + 15x

                                   8x² + 32x

                               ___________

                                             -17x + 7

                                               -17x -68

                                             __________

                                                          61

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Mathematical statement  μ = 18000 where μ is the mean, Null hypothesis H₀ : μ = 18000, Alternate hypothesis Hₐ : μ ≠ 18000.

A mathematical statement is a meaningful string of words that can be either true or false.

For instance , 3+4=7 is always true. Consequently, it is a true statement.

Similar to this ,  3+4=8 is never true  Therefore,  it is a false statement.

Here the amusement park makes the claim that the mean daily attendence at the park is 18000 people

∴ μ = 18000 is the statement .

A null hypothesis is known as statistical hypothesis that proposes that no statistical significance exists in a set of given observations. Hypothesis testing is used to assess the credibility of a hypothesis by using sample data. Sometimes referred to simply as the "null," it is represented as H₀.

∴  Here the null hypothesis is μ = 18000

The alternative hypothesis is an assertion used in statistical inference experiment. It is contradictory to the null hypothesis and indicated by Ha or H₁ . We can also say that it is simply an alternative to the null. In hypothesis testing, an alternative theory is a statement which a researcher is testing.

For instance :  A school principal claims that students in her school score an average of seven out of 10 in exams. The alternate hypothesis is μ ≠ 7.0.

Similarly here in this question alternate hypotesis will be μ ≠ 18000.

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Answer: 8x^2 + 2y^2 = 7

Step-by-step explanation:

The equation R = 7/8cosθ + 2sinθ can be rewritten in terms of x and y using the conversions x = Rcosθ and y = Rsinθ.

Substituting R = 7/8cosθ + 2sinθ into these equations, we get:

x = (7/8)cosθ cosθ + 2sinθ cosθ

y = (7/8)cosθ sinθ + 2sinθ sinθ

Simplifying these expressions using trigonometric identities, we get:

x = (7/8)cos^2θ + (4/8)sin2θ

y = (7/8)sinθ cosθ + (4/8)sin2θ

Multiplying both sides of the x equation by 8/7 and simplifying, we obtain:

8x^2 + 2y^2 = 7cos^2θ + 8sin^2θ

Using the identity cos^2θ + sin^2θ = 1, we get:

8x^2 + 2y^2 = 7(1)

Therefore, the Cartesian form of the equation is 8x^2 + 2y^2 = 7.

Answer:y=−4x+7/2

Step-by-step explanation:

Multiply each side of the equation by 8cosθ+2sinθ to get 8rcosθ+2rsinθ=7. Using the relationships x=rcosθ and y=rsinθ, the equation becomes 8x+2y=7. Solving this equation for y shows that y=−4x+7/2.

Start at -2 on the number line and move 7 to the left.

A number line is a visual representation of the real numbers as a straight line. It is a useful tool for understanding and comparing numbers, as well as for performing operations on them.

The number line is typically drawn horizontally, with zero in the center and positive numbers to the right of zero and negative numbers to the left of zero. The distance between any two points on the number line represents the difference between the corresponding numbers.

The number line is also commonly used for representing fractions, decimals, and irrational numbers. For example, fractions can be represented as points on the number line by dividing the line into equal segments, with each segment representing one unit fraction. Decimals can be represented as points on the number line by marking off the appropriate place value.

In addition to basic arithmetic operations such as addition, subtraction, multiplication, and division, the number line can be used to perform more advanced operations such as finding absolute value, calculating distance between two points, and solving linear equations.

Overall, the number line is a powerful visual tool that helps to deepen our understanding of the real numbers and their relationships.

Start at -2 on the number line and move 7 to the left.

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The complete question is:

1.The measure of the central angle is 90°.

2.Equation of x=12.

3.The measure of the angle that bisects the minor arc is 45°.

4.The measure of the major arc is 270°.

The circle in the example illustration has a radius of 10 units and a centre of O. AOB is a central angle that the minor arc AB intercepts.

The fact that the measure of a central angle is equal to the measure of its intercepted arc can be used to determine the measure of the central angle. So, we must determine the minor arc's measure, AB. The circle's diameter is 2r = 20 units because its radius is 10 units. The minor arc AB is one-fourth of the circle's circumference, or (1/4) * 20 = 5 units. As a result, the minor arc's measure is 5 radians.

Radians to degrees conversion

5π * (180/π) = 90° degrees

Therefore, the measure of the central angle AOB is 90° degrees.

To find  Equation of x,

8x=96°

x=96°/8

x=12

Hence, Equation of x will be 12.

The angle that bisects the minor arc AB is half the measure of the central angle AOB. So, the measure of the bisecting angle is:

(1/2) * 90° = 45°

The major arc ACB is the difference between the circumference of the circle and the minor arc AB. So, the measure of the major arc ACB is:

2πr - 5π = 15π

for major arc,

We must multiply by (180/) degrees/radian in order to convert the measure from radians to degrees. The main arc ACB's degree measurement is as follows:

15π * (180/π) = 270°

Therefore, the measure of the major arc ACB is 270°.

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Answer:  The solution to the inequality is x is less than or equal to 4. We can write it in interval notation as (-∞, 4].

Step-by-step explanation: To solve the inequality 1/2x + 8 ≤ 10, we need to isolate the variable x on one side of the inequality sign.

Subtracting 8 from both sides, we get:

1/2x ≤ 2

To isolate x, we need to multiply both sides of the inequality by 2:

x ≤ 4

Answer:3/10

Step-by-step explanation:

Answer:

16.39 square units.

Step-by-step explanation:

The parametric equations x = sin t and y = 3 cos t describe a curve in the xy-plane known as an ellipse.

To see this, we can use the Pythagorean identity for sine and cosine:

sin^2 t + cos^2 t = 1

Multiplying both sides by 9, we get:

9 sin^2 t + 9 cos^2 t = 9

Substituting x = sin t and y = 3 cos t, we get:

9 x^2 + y^2/3 = 9

This is the equation of an ellipse centered at the origin with semi-axes a = 3 and b = sqrt(3), where a is the length of the horizontal semi-axis and b is the length of the vertical semi-axis.

The area of an ellipse is given by the formula:

Area = pi * a * b

Substituting the values of a and b, we get:

Area = pi * 3 * sqrt(3) ≈ 16.39

Therefore, the area of the ellipse described by the parametric equations x = sin t and y = 3 cos t is approximately 16.39 square units.

This line is the horizontal line y = 1. Therefore, the correct answer is "Reflection across y = 1".

How to solve the question?

The line of reflection is the line that serves as the mirror for the original polygon such that each point on the original polygon is reflected to a corresponding point on the reflected polygon such that the distance between the line of reflection and each point is the same as the distance between the line of reflection and its reflection.

In this case, we are given two polygons, one original and one reflected. We need to determine the line of reflection that maps each point of the original polygon to its corresponding point on the reflected polygon.

Looking at the two polygons, we can see that the corresponding vertices are equidistant from a line of reflection that passes through the midpoint of the line segment joining V and V prime. Therefore, the line of reflection is the line that passes through the midpoint of the line segment joining V and V prime.

This line is the horizontal line y = 1. Therefore, the correct answer is "Reflection across y = 1". The other options are incorrect because they do not pass through the midpoint of the line segment joining V and V prime and do not produce the corresponding points for the original and reflected polygons.

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The best description of the figure would be that it is a C. a square.

To find out the type of figure that we have, it would be best to find the lengths of the sides of the figure. We should find AB, BC, CD, and AD.

We can use the distance formula which is:

D=√ ( x 2 - x1 ) ² + ( y2 - y1) ²

Using this formula, we find that AB, BC, CD, and AD are all a distance of 6 units. This therefore means that this figure is a square because all the sides are equal.

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Full question is:

Which best describes the figure that is represented by the following coordinates?

A(-3, 4), B(3, 4), C(3,-2) and D(-3,-2)

a rectangle

a trapezoid

a square

The distance from the center are equal,

x = 6

The value of x is solved using the relationship existing between chords and the bisectors.

It will be noted that the line from the center

In the figure, since the chords are equal and the line from the center are perpendicular bisectors then the line from the center are equal.

we can therefore say that x = 6

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The simplified form of the expression is 71/24.

To simplify the expression 4 - 1/3 - 7/8 + 1/6, we can follow the order of operations, which dictates that we perform multiplication and division before addition and subtraction.

Here's the step-by-step solution:

Find a common denominator for the fractions involved. In this case, the least common denominator (LCD) is 24, which is the least common multiple of 3, 8, and 6.

Convert the fractions to have the same denominator, which is 24:

4 - 1/3 - 7/8 + 1/6

= 4 * 24/24 - 1/3 * 8/8 - 7/8 * 3/3 + 1/6 * 4/4 (Multiplying each fraction by the appropriate form of 1 to get the common denominator)

= 96/24 - 8/24 - 21/24 + 4/24 (Performing the multiplication)

Combine the numerators over the common denominator:

= (96 - 8 - 21 + 4)/24 (Combining numerators)

= 71/24 (Performing the subtraction)

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Answer:

Step-by-step explanation:

you must work in a certain order, usually starting with parentheses, then exponents, then multiplication or division, and finally addition or subtraction.

You can form a right triangle by cutting a square in half diagonally.

A square is a quadrilateral with four equal sides and four right angles. When a square is cut in half diagonally, it forms two congruent right triangles. The two halves of the square, which are the two legs of the right triangle, are equal in length.

The diagonal of the square, which is the hypotenuse of the right triangle, can be found using the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the sum of the squares of the two shorter sides (the legs) is equal to the square of the length of the longest side (the hypotenuse).

Therefore, in a right triangle formed by cutting a square in half diagonally, the length of the hypotenuse can be found by taking the square root of the sum of the squares of the lengths of the two legs.

In summary, cutting a square in half diagonally allows us to form two congruent right triangles with equal leg lengths, making it a suitable shape to form a right triangle.

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Answer:

∠ A = 76°

Step-by-step explanation:

the sum of the 3 angles in a triangle = 180°

sum the 3 angles and equate to 180

9x - 5 - 5 + 6x + 55 = 180

15x + 45 = 180 ( subtract 45 from both sides )

15x = 135 ( divide both sides by 15 )

x = 9

Then

∠ A = 9x - 5 = 9(9) - 5 = 81 - 5 = 76°

Answer:

-72

Step-by-step explanation:

Because -32 + (2 - 6)(10). is -72

The cost of the television and wall mount before discount is $600 + $29.99 = $629.99

After a 30% discount, the subtotal is:

$629.99 x 0.70 = $440.99

The sales tax is 7% of the subtotal:

$440.99 x 0.07 = $30.87

The final total is the subtotal plus the sales tax:

$440.99 + $30.87 = $471.86

The original purchase price before discount is $600.

10% of $600 is $60.

So Jamie decides to tip the installation specialist $60.

After the discount, the subtotal is $440.99 (as calculated in Part A).

The sales tax is 7% of the subtotal:

$440.99 x 0.07 = $30.87

The new total is the subtotal plus the sales tax and the tip:

$440.99 + $30.87 + $60 = $531.86

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Answer: (0,3)

x=0 ; y=3

Step-by-step explanation:

To solve the system of equations:

2x + 4y = 12

3x + y = 3

We can use the method of substitution or elimination. Here we will use the substitution method:

From Equation 2, we can isolate y:

y = 3 - 3x

We can substitute this expression for y into Equation 1:

2x + 4(3 - 3x) = 12

Simplifying and solving for x:

2x + 12 - 12x = 12

-10x = 0

x = 0

Now that we have found the value of x, we can substitute it back into either Equation 1 or Equation 2 to solve for y. Here we will use Equation 2:

3(0) + y = 3

y = 3

Therefore, the solution to the system of equations is (x, y) = (0, 3).

This means that the point (0, 3) is the intersection point of the two lines represented by the given equations. To verify this, we can substitute the values of x and y into both equations and see if they are true.

The procedure to simplify fractions is presented in this answer.

The steps to simplify a fraction are given as follows:

For example, let's say we want to simplify the fraction 12/24:

Another example, let's say we want to simplify the fraction 16/20:

Note that a fraction is in its simplest form when its numerator and denominator have no common factors other than 1.

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The equation of the third linear function is:

y = (-1/3)x + (8/3)

To find a linear function with a rate of change between Function A and Function B, we need to calculate the rates of change for each function.

For Function A, the rate of change is:

(2 - (-4)) / (6 - (-1)) = 6/7

For Function B, we find the rate of change by selecting any two points on the graph, such as (2, 6) and (-4, 7):

(6 - 7) / (2 - (-4)) = -1/6

So the rate of change for Function A is 6/7, and the rate of change for Function B is -1/6.

To find a linear function with a rate of change between these two values, we can select any value between 6/7 and -1/6. Let's choose a rate of change of -1/3.

We can use the point-slope form of a linear equation to write the equation of the line with a rate of change of -1/3 and passing through the point (2, 6):

y - 6 = (-1/3) * (x - 2)

y = (-1/3)x + (8/3)

In conclusion, the equation of the third linear function is:

y = (-1/3)x + (8/3)

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The slope-intercept form of a linear equation with given point (-9,-5) and slope -2/3 is y = (-2/3)x - 11.

The slope of a line is a measure of its steepness or incline, represented by the ratio of the vertical change between two points, known as the rise, to the change in horizontal part between the same two points, known as the run. It describes the rate at which the line is increasing or decreasing as it moves from left to right. The slope of a line can be positive, negative, zero, or undefined, and it plays a critical role in many mathematical applications, including calculus, geometry, and physics. It is commonly denoted by the letter m and is defined as m = (y₂ - y₁)/ (x₂ - x₁), where (x₁, y₁) and (x₂, y₂) are any two points on the line.

The slope-intercept form of a linear equation is y = mx + b, where m represents the slope of the line and b represents the y-intercept.

To find the equation of a line with a given slope and a point on the line, we can substitute the values into the equation and solve for the y-intercept, b.

Given that the line passes through the point (-9, -5) and has a slope of -2/3, we can substitute these values into the equation to find the value of b:

-5 = (-2/3) × (-9) + b

-5 = 6 + b

b = -11

Now that we know the value of b, we can write the equation of the line in slope-intercept form:

y = (-2/3)x - 11

Therefore, the equation of the line in slope-intercept form is y = (-2/3)x - 11.

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Let's say we have a dataset representing the heights (in inches) of 30 students in a class.

Here's an example of data and how we can represent it using a line plot, histogram, and box plot:

Line Plot:

Data: Heights of 30 students (in inches): 60, 62, 61, 63, 64, 65, 63, 62, 64, 63, 61, 60, 61, 63, 62, 64, 65, 64, 63, 62, 61, 63, 65, 64, 63, 62, 61, 60

A line plot would be suitable for visualizing this dataset, as it provides a simple and clear representation of individual data points along a number line. A line plot is useful for showing the distribution of data points and identifying any patterns or trends in the dataset.

Histogram:

Data: Heights of 30 students (in inches): 60, 62, 61, 63, 64, 65, 63, 62, 64, 63, 61, 60, 61, 63, 62, 64, 65, 64, 63, 62, 61, 63, 65, 64, 63, 62, 61, 60

A histogram would be suitable for visualizing this dataset, as it provides a graphical representation of the distribution of data points in different intervals or bins. The heights of the students can be grouped into bins, such as 60-62, 62-64, 64-66, etc., and the frequency of data points falling into each bin can be represented by the height of bars.

Box Plot:

Data: Heights of 30 students (in inches): 60, 62, 61, 63, 64, 65, 63, 62, 64, 63, 61, 60, 61, 63, 62, 64, 65, 64, 63, 62, 61, 63, 65, 64, 63, 62, 61, 60

A box plot, also known as a box-and-whisker plot, would be suitable for visualizing this dataset, as it provides a summary of the data's distribution, including measures of central tendency and variability. The box in the plot represents the interquartile range (IQR), which contains the middle 50% of the data, with the line inside the box representing the median.

Similarities between line plot and box plot:

Differences between line plot and box plot:

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Answer:

Here are two example data sets that meet the given conditions:

Data Set 1:

Values: 10, 12, 14, 16, 18, 20

Mean: (10+12+14+16+18+20) / 6 = 15

MAD: Mean Absolute Deviation = sum(abs(x - mean))/n = ((|10-15| + |12-15| + |14-15| + |16-15| + |18-15| + |20-15|)/6) = 2.5

Story: This dataset may have originated from measuring the time taken to complete a series of tasks by a group of skilled workers. The values represent the time taken in seconds, and the low MAD value indicates that the workers' performance was consistent. The mean value of 15 seconds suggests that the workers were efficient, completing the tasks quickly and accurately.

Data Set 2:

Values: 3, 5, 7, 9, 11, 13

Mean: (3+5+7+9+11+13) / 6 = 8

MAD: Mean Absolute Deviation = sum(abs(x - mean))/n = ((|3-8| + |5-8| + |7-8| + |9-8| + |11-8| + |13-8|)/6) = 2.5

Story: This dataset may have originated from measuring the height of a group of plants grown under different conditions. The values represent the height in inches, and the low MAD value indicates that the plants' growth was consistent across all conditions. The mean value of 8 inches suggests that the conditions were not optimal for plant growth, as the mean height is lower than the expected average for this type of plant.

Both data sets have a similar MAD value of 2.5, indicating that the variation in the data is relatively low, and the differences in the mean values suggest that they came from different sources. In both cases, the means are more than one MAD apart, indicating that there are significant differences between the values in each set.

Psychologist requires a sample size of at least 126 SI scores.

We may use the following calculation to get the minimal sample size required to estimate the mean SI score of smokers with a margin of error of 12 and a 90% confidence level:

[tex]n = [Z * (\sigma / E)]^2[/tex]

Where:

Z = the z-score associated with the confidence level (90%), which can be found using a z-score table or calculator.

For a 90% confidence level, Z is approximately 1.645.

σ = the population standard deviation (82)

E = the desired margin of error (12)

Plugging in the values, we get:

n = [1.645 * (82 / 12)]^2

n = 126.2

We round up to the closest integer as the sample size must be a whole number in order to guarantee that the sample size is sufficient to fulfill the required confidence level and margin of error.

Thus, n = 126 is the required minimum sample size.

In order to estimate the mean SI score of smokers with 90% confidence that the estimate is within 12 of the actual population mean, the psychologist requires a sample size of at least 126 SI scores.

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The justification of the  angles with a combined degree measure of 90⁰ are complementary angles is proved by part 3. ∠1 is complementary to ∠2.

In the figure,

Measure of angle 1 = 40 degrees.

Measure of angle 2 = 50 degrees

Angle 2 is complementary to angle 3.

Proof of the result,

Measure of ∠1 = 40 degrees  ( given  )

Measure of ∠2 = 50 degrees ( given )

Measure of ∠1 + measure of ∠2 = 40° + 50°

⇒ Measure of ∠1 + measure of ∠2 = 90°

⇒ Angle 1 and angle 2 are complementary to each other.

Complementary angles are such pairs of angles whose sum is equal to 90°.

It is given that

Angle 2 is complementary to angle 3.

This implies ,

m ∠1 + m ∠2 = m ∠2 + m ∠3

⇒ m ∠1  = m ∠3

⇒ m ∠1  ≅ m ∠3

Therefore, the part 3 . ∠1 is complementary to ∠2 gives the justification for the proof of complementary angles.

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