Calculate the length of IG. *
3
square root 20
square root 50
square root 10
square root 25

Answer: Correct answer is pie/2 or A

Step-by-step explanation:

r = -5sinθ + 4θ has symmetry with respect to the line θ = π/2.

To demonstrate this, we can apply the third symmetry test for polar equations:

Symmetry with respect to the line θ = π/2: Replace θ by π - θ and see if the equation remains the same. If it does, the equation has symmetry with respect to the line θ = π/2.

r = -5sin(π/2 - θ) + 4(π/2 - θ) = 5cosθ + 2π - 4θ

r = 5cosθ + 2π - 4θ is the same as the original equation, so there is symmetry with respect to the line θ = π/2.

Therefore, the correct answer is θ = π/2.

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.

Answer: The negative sign in front of 7/8 indicates that the fraction is negative. To find an equivalent fraction, we can keep the same value but change the sign. Therefore, an equivalent fraction that is positive would be (-(7/8)) = (-7)/8.

Step-by-step explanation:

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) ?

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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Answer:

-72

Step-by-step explanation:

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

Answer:3/10

Step-by-step explanation:

As a result, the triangle formed by the vertices A(0,0), B(3,8), and C(9,0) has an area of 18 square units.

A triangular is a three-sided, tri-geometric shape. It is a double figure that is frequently represented by the character "." A triangle's angles can never add up to more than 180 degrees. Triangles can be categorized into equilateral, elliptic, and scalene varieties according to the length of their sides and the dimensions of their angles. Three equal edges and three equal, 60-degree angles make up an equilateral triangle. Equal size ends and equal size angles make up an isosceles triangle. The sides and angles of a scalene triangle are not equal.

Given a triangle's vertices in the coordinate plane, we can apply the following formula to get its area:

A is equal to [tex]|(x1(y_2 -y_3) + x_2(y_3 -y_1) + x3(y_1 -y_2)) / 2|.[/tex]

where the triangle's vertices' coordinates are [tex](x_1, y_1), (x_2, y_2), and (x_3, y_3).[/tex]

We obtain: by substituting the coordinates of the specified vertices.

[tex]A = |(0(8 - 0) + 3(0 - 0) + 9(0 - 8)) / 2| = |-36| / 2 = 18[/tex]

As a result, the triangle formed by the vertices A(0,0), B(3,8), and C(9,0) has an area of 18 square units.

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The answer on shape of house is , (1) A rectangle for the main structure of the house. (2) A triangle for the roof. (3) A rectangle for the front porch. (4) Two trapezoids for the roof of the front porch. (5) A rectangular door.

A trapezoid is a four-sided geometric shape with two parallel sides, called the bases, that are of different lengths, and two non-parallel sides that connect the bases. The non-parallel sides are also called legs, and they may or may not be equal in length.

Trapezoids are often encountered in geometry and in real-life situations, such as in construction and architecture. They can be classified as either right trapezoids or oblique trapezoids depending on whether one of the angles formed by the bases and a leg is a right angle or not.

Based on the image provided, the shapes that make up the front of the house are:

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If Laurel received a 1099 form from her bank for her savings account interest in the amount of $690 and a 1099 form from an employer that she did some consulting work for in the amount of $2,600, then Laurel's taxable income is calculated as  $98,580.

Taxable income refers to the base upon which an income tax system imposes tax.

We deduct the following;

Wages reported on W-2 =  $100,750

Interest income reported on 1099=  $690

Consulting income reported on 1099= $2,600

Therefore, her total income = $100,750 + $690 + $2,600 = $104,040

Laurel's allowable deductions include:

FSA contributions: $30 per week x 52 weeks = $1,560

Retirement plan contributions: $75 per week x 52 weeks = $3,900

Total deductions = $1,560 + $3,900 = $5,460

Laurel's taxable income  is found as

= Total income - Total deductions

= $104,040 - $5,460

= $98,580

In conclusion, Laurel's taxable income is $98,580.

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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 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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1) The graph of function g is graph W because it is result of a vertivcal compression applied to graph f.

2)  The graph of function g is graph X because it is result of a horizontal shift applied to graph f.

3)  The graph of function g is graph Y because it is result of a reflection over y-axis applied to graph f.

4)  The graph of function g is graph Z because it is result of a horizontal compression applied to graph f.

Here, a transformation applied to function f where f(x) = (1/2)^x

Consider graph W. We can observe that when the the graph of f(x) is compressed vertically then it will results in the graph of g(x)

Consider graph X. We can observe that if the the graph of f(x) is shifted horizontally right by 2 units then it will results in the graph of g(x)

Consider graph Y. We can observe that the the graph of g(x) is nothing but the reflection of f(x) over x-axis.

Consider graph Z. We can observe that when the the graph of f(x) is compressed horizontally then it will results in the graph of g(x)

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Answer:

yes it is if you bisect 5m on a 12m line

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

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:

8. mArc ED = 38°

9. mArc EA = 142°

10.mArc BDC = 308°

Step-by-step explanation:

The measure of an a central angle and it's intercepted arc are equal

So if the measure of the angle for the angle that intercepts Arc ED is 38° the arc is also 38°

Same thing with Arc EA, the central angle that intercepts it is 142° so the measure of Arc EA is 142°

Arc BDC is a major arc so it is greater than 180°. It goes around the circle from point B to point C and point D is one of the points on the arc.

We could find the value of the arc two ways. We could add all the angles  the that make up the central angle it is intercept by or we could simply subtract the 52° that isn'tt a part of the arc and subtract that from 360°

360 - 52 = 308

So the central angle intercepting Arc BDC is 308° so the arc also has a measure of 308°.

The area of the irregular shape is 34m²

The area of a shape is the space occupied by the boundary of a plane figures like circles, rectangles, and triangles

The shape above can be divided into three rectangles and the sum of the area of this rectangles is the area of the shape.

Area of rectangle 1

= l× w

= 7×2 = 14 m²

Area of rectangle 2

= l× w

= 5×2 = 10 m²

Area of rectangle 3

= l×w

= 5×2 = 10m²

Therefore , the area of the irregular shape is

14+10+10 = 34m²

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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:

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.

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:

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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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:

∠ 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°

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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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 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