simplify the following algebric expression X^2-x-12/x^2-4

Answer:

To calculate the total cost of John and his family's meal (including tip and tax), we can follow these steps:

Calculate the tip amount by multiplying the bill amount by 20% (or 0.2): 65.00 x 0.2 = 13.00

Add the tip amount to the bill amount to get the subtotal: 65.00 + 13.00 = 78.00

Calculate the tax amount by multiplying the subtotal by 7% (or 0.07): 78.00 x 0.07 = 5.46

Add the tax amount to the subtotal to get the total cost: 78.00 + 5.46 = $83.46

Therefore, the total cost of John and his family's meal (including tip and tax) was $83.46.

To calculate the price of the suede jacket with a 20% discount and 8% tax, we can follow these steps:

Calculate the amount of the discount by multiplying the original price by 20% (or 0.2): 250 x 0.2 = 50

Subtract the discount amount from the original price to get the sale price: 250 - 50 = $200

Calculate the tax amount by multiplying the sale price by 8% (or 0.08): 200 x 0.08 = 16

Add the tax amount to the sale price to get the total price: 200 + 16 = $216

Therefore, the total price of the suede jacket with a 20% discount and 8% tax is $216.

To calculate the sale price of the bracelet with a 25% discount and 7% tax, we can follow these steps:

Calculate the amount of the discount by multiplying the regular price by 25% (or 0.25): 44 x 0.25 = 11

Subtract the discount amount from the regular price to get the sale price: 44 - 11 = $33

Calculate the tax amount by multiplying the sale price by 7% (or 0.07): 33 x 0.07 = 2.31

Add the tax amount to the sale price to get the total price: 33 + 2.31 = $35.31

Therefore, the sale price of the bracelet with a 25% discount and 7% tax is $35.31.

Therefore, the measure of angle ABC is 35 degrees.

In geometry, a circle is a two-dimensional shape that is defined as the set of all points in a plane that are equidistant from a fixed point called the center. The distance between the center and any point on the circle is called the radius of the circle. A circle has many properties, such as diameter (a line segment passing through the center and having endpoints on the circle), circumference (the distance around the circle), and sector (a region bounded by two radii and an arc of the circle). The circle is one of the most important and frequently studied shapes in geometry and has many applications in mathematics, science, and everyday life.

Here,

Since chord AB is congruent to chord CB, it follows that they subtend congruent angles at the center of the circle.

Therefore, angle AOC is congruent to angle COB.

The sum of the angles at the center of the circle is 360 degrees, so we can find the measure of angle AOC as:

360° - 70° = 290°

Since angles AOC and COB are congruent, they must each measure half of 290°:

290° / 2 = 145°

Finally, angle ABC is an inscribed angle that subtends arc AC. Its measure is half of the measure of arc AC:

70° / 2 = 35°

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According to the given information, the ratio P:O:R is 2√3 : 1 : 2 in its simplest form.

A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0. A proportion is an equation in which two ratios are set equal to each other. For example, if there is 1 boy and 3 girls you could write the ratio as 1 : 3 (for every one boy there are 3 girls).

Since p:q:r = √3:1:1, we can write:

p = √3x

q = x

r = x

where x is a common factor.

We can see that triangle ABC is a 30-60-90 triangle with angle A = 60 degrees, and that angle BOC is a right angle. Therefore, we can use the ratios of sides in a 30-60-90 triangle to find the values of P, O, and R:

P = AB = p = √3x

O = BC/2 = q/2 = x/2

R = AC = r = x

Therefore, the ratio P:O:R is:

P:O:R = √3x : x/2 : x

We can simplify this ratio by multiplying all terms by 2 to get rid of the fraction:

2√3x : x : 2x

We can further simplify by dividing all terms by x:

2√3 : 1 : 2

Therefore, according to the given information, the ratio P:O:R is 2√3 : 1 : 2 in its simplest form.

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The inequality shown on the number line is -3<p<2

Inequalities are simply created through the connection of two expressions. In this case, it should be noted that the expressions in an inequality are not always equal.

Inequalities implies that the expressions are not equal. Here, they are denoted by the symbols ≥ < > ≤.

Based on the information, the inequality shown on the number line is -3<p<2

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Radians are another unit of measurement for angles, and are commonly used in mathematical calculations involving trigonometric functions. In a full circle, there are 2π radians, where π (pi) is a mathematical constant approximately equal to 3.14159.

Degrees are the most commonly used unit of measurement for angles, and a full circle is divided into 360 degrees.

The symbol (∠) represents an angle in geometry, and the letters LMK likely refer to three points on a plane. The backwards "y" symbol is likely the uppercase Greek letter gamma (Γ), which is sometimes used to represent an angle in mathematics.

Therefore, (∠LMK) likely refers to the angle formed by the three points L, M, and K on a plane. The measurement of this angle would depend on the positions of the three points relative to each other and the chosen unit of measurement.

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Answer:

At a recent baseball game of 5,000 in attendance, 150 people were asked what they prefer on a hot dog. The results are shown.

Ketchup Mustard Chili

63 27 60

Based on the data in this sample, how many of the people in attendance would prefer chili on a hot dog?

900

2,000

2,100

4,000

Step-by-step explanation:

The graph of the cubic function y = ∛(x+1) -2 is attached below

A cube root function's graph is a curve that extends to both positive and negative infinity from its origin. An example of a power function is the cube root function, which is described by the equation y = ∛x, where the cube root sign (∛) stands for the inverse of raising a number to the power of three.

The cube root function yields a positive value of y when x is a positive integer. As an illustration, if x = 8, then y = √8 = 2. The cube root function, on the other hand, yields a negative value of y if x is a negative number. As an illustration, if x = -27, y = ∛(-27) = -3

To graph a cube root function, we can create a table of values by choosing several values of x and then calculating the corresponding values of y using the equation y = ∛x. Once we have several points, we can plot them on a coordinate plane and then connect them with a smooth curve to get the graph of the function.

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The apprοximate average rate οf change οf the functiοn f(x)=500(0.5)^x οver the interval x=-2 tο x=2 is apprοximately 105.11.

The average rate οf change οf a functiοn between twο pοints is the same that the slοpe οf the line passes thrοugh these pοints  (secant line).

We need tο calculate the change in the functiοn value and divide it by the change in x.

[tex]f(x=2) - f(x=-2) \\\\= 500(0.5)^2 - 500(0.5)^(-2) \\\\= 420.42[/tex]

x=2 - x=-2 = 4

Average rate οf change = (f(x=2) - f(x=-2)) / (x=2 - x=-2)

Average rate οf change ≈ 420.42 / 4

Average rate οf change ≈ 105.11

Hence, the apprοximate average rate οf change οf the functiοn [tex]f(x)=500(0.5)^x[/tex] οver the interval x=-2 tο x=2 is apprοximately 105.11.

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The expressions k to t are evaluated correctly

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

The expressions k to t

To determine if the expressions are correct, we evaluate each expression and state if it is correct or not

Using the above as a guide, we have the following:

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a. Trigοnοmetric expressiοns 2cοs²(π/8) - 1 is evaluated as √2/2.

b. Trigοnοmetric expressiοns 2tan(11π/12)/(1 - tan²(11π/12)) is evaluated as 1/2.

An expressiοn is cοmbinatiοn οf symbοls  οn numbers that represent quantity οr value. It  cοntain variables, cοnstants, arithmetic οperatiοns, and functiοns. An expressiοn can  be simple οr cοmplex, and it can be written in different fοrms depending οn cοntext and purpοse

a. Tο evaluate 2cοs²(π/8) - 1, we can use the dοuble angle identity fοr cοsine:

cοs(2θ) = 2cοs²(θ) - 1

Where θ = π/8

cοs(2(π/8)) = 2cοs²(π/8) - 1

cοs(π/4) = 2cοs²(π/8) - 1

√2/2 = 2cοs²(π/8) - 1

2cοs²(π/8) = √2/2 + 1

2cοs²(π/8) - 1 = (√2/2 + 1) - 1 = √2/2

Therefοre, 2cοs²(π/8) - 1 = √2/2.

b. We can use the trigοnοmetric identity:

1 + tan²θ = sec²θ

tο rewrite the denοminatοr οf the expressiοn as:

1 - tan²(11π/12) = 1/(1 + tan²(11π/12)) = 1/sec²(11π/12) = sec²(-π/12)

where we have used the fact that secant is an even functiοn, sο sec(-x) = sec(x).

Next, we can use the fοllοwing trigοnοmetric identities:

tan(-x) = -tan(x)

and

sec(-x) = sec(x)

tο rewrite the numeratοr οf the expressiοn as:

2tan(11π/12) = -2tan(-π/12) = -2(-tan(π/12))

Finally, substituting these expressiοns intο the οriginal expressiοn, we get:

2tan(11π/12)/(1 - tan²(11π/12)) = -2(-tan(π/12))/sec²(-π/12)

= 2tan(π/12)cοs²(π/12)

= 2sin(π/12)cοs(π/12)

= sin(π/6)

= 1/2

Therefοre, the value οf the expressiοn is 1/2.

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Option 2 is correct. The lines M and N can be said to be parallel. Yes, because angle 1 and angle 2 form a linear pair so (2) 180-129 = 51 and 2 and 7 are alternate interior angles with the same measure.

A linear pair is a pair of adjacent angles formed when two lines intersect. These angles are called a linear pair because they lie on the same line, and their non-common arms are opposite rays, which means they point in opposite directions. Since the sum of the measures of linear pairs is always equal to 180 degrees, these angles are also known as supplementary angles.

To see if the values are parallel we have that

angle 1 and angle 7 when summed have to be equal to 180 degrees

129 + 51 = 180 degrees

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The tin's actual diameter is 250 mm.

What do you mean by diameter?

A circular object, like a circle or sphere, has a diameter, which is the length of a straight line that runs through its centre. It is the separation between two locations on an object's edge that are the furthest apart and traverse the object's centre.

Here, if the tin's diameter in the illustration is 10 cm, the actual tin's diameter can be determined as follows:

Real Diameter is 2.5 times the image diameter.

2.5 x 10 cm is the actual diameter.

Real diameter is 25 cm.

To translate the actual dimension to millimetres (mm), we can multiply by 10:

Actual Diameter multiplied by 10 to convert to mm

Real Diameter = 25 cm x 10 in mm.

Actual Diameter is 250 millimetres.

As a result, the tin's actual diameter is 250 mm.

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[tex]\textit{area of a rectangle}\\\\ A=Lw ~~ \begin{cases} L=length\\ w=width\\[-0.5em] \hrulefill\\ w=5\\ A=35 \end{cases}\implies 35=L(5)\implies \cfrac{35}{5}=L\implies 7=L[/tex]

Answer:

To find the time it will take to travel 432 kilometers at an average speed of 96 kilometers per hour, we can use the formula:

time = distance / speed

where distance is the distance to be traveled, speed is the average speed of travel, and time is the time taken to travel the distance at the given speed.

Substituting the values given in the problem, we get:

time = 432 km / 96 km/h

time = 4.5 hours

Therefore, it will take 4.5 hours to travel 432 kilometers at an average speed of 96 kilometers per hour.

Answer: x = 2

Step-by-step explanation:

x + (x + 1) + (x + 2) = 9

3x + 3 = 9

3x +(3 - 3) = (9 - 3)

3x = 6

x = 2.

Hope this helps

Answer:

6√2

Step-by-step explanation:

Use trigonometry:

[tex] \cos(45∘) = \frac{x}{12} [/tex]

Use the property of the proportion to find x:

[tex]x = 12 \times \cos(45∘) = 12 \times \frac{ \sqrt{2} }{2} = 6 \sqrt{2}[/tex]

Answer:

David has 25 percent of green pencils and 75percent of purple ones

The correct answer is D. They could file for bankruptcy and discharge some of their debt.

What is bankruptcy?

Bankruptcy is a legal process in which a person or business unable to pay outstanding debts to creditors can get a fresh start. It is a form of debt relief in which a debtor is relieved of some or all of their financial obligations and is protected from creditors.

In order to determine this answer, we first need to calculate the couple's monthly income. With an annual income of $86,000, their monthly income would be $7,166.67 ($86,000/12). If one of them loses their job, their monthly income would be reduced by $3,300, leaving them with a monthly income of $3,866.67.

Next, we need to compare this income to the state requirements based on the number of persons in the household. For a four-person household in Virginia, the monthly income requirement is $7,086.25 ($85,939/12). This means the couple's income is below the state requirement and they could file for bankruptcy and discharge some of their debt.

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The point (0, -5) lies on the graph of the quadratic equation y = x² - 5. The shape of the graph is a parabola.

An equation is an expression containing numbers and variables linked together by mathematical operations such as addition, subtraction, division, multiplication and exponents.

The equation y = x² - 5 represents a quadratic equation. A quadratic equation have the shape of a parabola.

When x = 0;

y = 0² - 5

y = -5

The point (0, -5) lies on the graph of y = x² - 5

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Answer:

B. X

Step-by-step explanation:

the essential rule for a function is that each value of x must have exactly one associated y value.

in other words, if we "feed" the x- value to the function it must be clear what y-value we get as result.

in W 6 has 2 associated y values. no function.

in X all is OK. yes, a function.

in Y again, 6 has 2 associated y values. no function.

in Z 7 has 2 associated y values. no function.

The following numerals in words are as follows:

3 - three, 4 - four, 5 - five

Numbers are symbols or numbers used to represent numbers.

The most common numerals used in everyday life are the Hindu-Arabic numerals, which include the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9.

These numbers can be combined to form any number and are used in mathematical operations such as addition, subtraction, multiplication and division.

Roman numerals, which use a combination of letters, are another example of numerals, but they are not as commonly used today as they were in the past.

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Write the following in numerals in words 3/4/5.

For similar triangle the angle does not change, thus the angle M is 33 degrees.

Triangles that are similar in shape but differ in size are known as similar triangles. Squares with any side length and all equilateral triangles are examples of related objects. In other words, if two triangles are similar, their corresponding sides are proportionately equal and their corresponding angles are congruent.

Both have the same form, although they might be different sizes. All related angle pairs are equal, and corresponding sides have the same ratio.

We can observe that the two triangles are similar.

For similar triangle the angle does not change, thus the angle M is 33 degrees.

Hence, the measure of angle M is 33 degrees.

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Angle M is 147 degrees.

A triangle is a geometric shape that consists of three line segments connected end-to-end to form a closed shape. These line segments are called sides, and the points where the sides meet are called vertices. The sum of the three interior angles of a triangle is always 180 degrees, and the length of each side must be less than the sum of the other two sides. Triangles can be classified based on the length of their sides and the size of their angles. For example, a triangle with all three sides of equal length is called an equilateral triangle, while a triangle with two sides of equal length is called an isosceles triangle. Triangles are used in many areas of mathematics, as well as in physics, engineering, and other sciences, to model and solve problems.

Since triangles XYZ and LMN are congruent, corresponding angles are congruent. Therefore, angle LMN = angle XYZ = 33 degrees.

To find angle NML, we use the fact that the sum of the angles in a triangle is 180 degrees. We have:

angle LNM + angle NML + angle MLN = 180 degrees

Substituting the given values, we get:

124 + angle NML + 33 = 180

Simplifying and solving for angle NML, we get:

angle NML = 180 - 124 - 33 = 23 degrees

Therefore, angle M is the exterior angle of triangle LMN at vertex N, which is equal to the sum of the remote interior angles. We have:

angle M = angle LNM + angle NML = 124 + 23 = 147 degrees

Therefore, angle M is 147 degrees

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6.3. This would be a plot of speed instruction against accuracy instruction as it is shown in the attachment.

6.4) C. . Do not duplicate date in both a figure and table. is consistent with APA style for figures and tables

6.5) D. The section of the APA that the tables and figures are shown is the results

APA style guidelines recommend avoiding duplicating data between figures and tables. Instead, each should complement the other and provide additional information.

Regarding the other options, figures and tables should be embedded within the Results section or the Appendix section, and each figure/table should have its own title that accurately describes its content.

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This two-way table provides a quick and easy way to summarize the data from the Venn diagram and answer the questions.

Diagrams are visual representations of information, processes, or objects. They are used to explain complex topics, show relationships between elements, and to simplify complex processes. Diagrams can be used for anything from showing the structure of an organization to explaining a scientific concept. Diagrams are an effective way to convey information quickly and clearly. They can be used in a variety of contexts, from school projects to professional presentations.

A two-way table is a type of table that summarizes the information from two different variables. In this case, the two variables are the type of bread (sourdough or wheat) and whether or not the sandwich had cheese on it. From the Venn diagram, we can construct a two-way table as follows:

Type of Bread  | With Cheese | Without Cheese | Total
---------------|-------------|---------------|--------
Sourdough      |    +        |       =       |  +
---------------|-------------|---------------|--------
Wheat          |    +        |       =       |  +
---------------|-------------|---------------|--------
Total          |     +       |       =       |  +

From this two-way table, we can see that the total number of people who ordered either sourdough or wheat was +. Of that group, + people chose to add cheese to their sandwich. Additionally, + people chose to not add cheese.

We can also see that of the + people who ordered sourdough, + of them chose to add cheese while + of them did not. For those who ordered wheat, + chose to add cheese while + did not.

This two-way table provides a quick and easy way to summarize the data from the Venn diagram and answer the questions.

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Answer:

27.7°

Step-by-step explanation:

Total angles in any triangle= 180°

Let the missing angle be x°.

Thus,

x°+90°+62.3°=180

x= 180-152.3

x = 27.7°

Hope this helps! :)

Answer: C

Step-by-step explanation:

Every x value can only have one specific y value. You will have to perform the vertical line test. Basically grab a ruler and  slide it across your graphs vertically ( drag the ruler upright from left to right). Look at your x intercepts and their specific y intercepts.

For A, it continously crosses over so it is not a function. For B, it is always crossing over 2 times so it is not a function. For C, every x intercept has a specific y value therefore it is a function. It crosses over at one point only. For D, the vertical is always crossing over 2 times therefore it will not be a function.

Answer:

C.

Step-by-step explanation:

If a vertical line is moved across the graph and, at any time, touches the graph at only one point, then the graph is a function. If the vertical line touches the graph at more than one point, then the graph is not a function.

The vertical parabola is the only graph here that will only touch the graph at one point, so it is the only function.

Answer:

y = 2/3x - 2/3

Step-by-step explanation:

slope m = 2/3, x = 4, y = 2

we have slope-intercept form: y = mx + b

=> 2 = 2/3(4) + b

b = 2 - 8/3 = 6/3 - 8/3 = -2/3

therefore, y = 2/3x - 2/3

Answer: For live plants, Fish-n-Stix Pets is (less expensive) than Fishing For Compliments.

The price per ounce for live plants at Fishing For Compliments is about $2.67.

The price per ounce for live plants at Fish-n-Stix Pets is (about half of) the price per ounce at Fishing For Compliments.

Step-by-step explanation:

Answer: The sales manager, with weekly earnings of $1006.25.

Step-by-step explanation:

To determine who would make the most money in one week, we need to calculate the weekly earnings for each of the four positions.

Let's start with the sales manager, who works 35 hours at a rate of $28.75 per hour:

Weekly earnings for sales manager = 35 hours x $28.75 per hour = $1006.25

Next, let's consider the head mechanic, who works 25 hours. We'll need to know their hourly rate in order to calculate their weekly earnings:

Hourly rate for head mechanic = $35 per hour

Weekly earnings for head mechanic = 25 hours x $35 per hour = $875

Now, let's move on to the assistant mechanic, who works 30 hours:

Hourly rate for assistant mechanic = $20 per hour

Weekly earnings for assistant mechanic = 30 hours x $20 per hour = $600

Finally, let's consider the front desk clerk, who works 40 hours:

Hourly rate for front desk clerk = $15 per hour

Weekly earnings for front desk clerk = 40 hours x $15 per hour = $600

Therefore, the sales manager would make the most money in one week with weekly earnings of $1006.25.

Answer: Sales Manager

Step-by-step explanation:

Let's calculate the total pay for each worker:
Sales manager: $28.75 per hour x 35 hours = $1,006.25

Head mechanic: $32.50 per hour x 25 hours = $812.50
Assistant mechanic: $25.00 per hour x 30 hours = $750.00
Front desk clerk: $20.00 per hour x 40 hours = $800.00