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The vertex of function is (2, 0).

In mathematics, a graph is defined as a graphical representation or diagram that organises facts or values. The graph's points frequently reflect the relationship between two or more things.

A graph is a non-linear data structure composed of nodes (vertices) and edges. The edges in the graph connect any two nodes, which are also known as vertices.

Given:

y = |x - 2|

When we plot the graph as y = |x - 2|.

we get the vertex of the function y = |x - 2| at (2, 0).

Also, the function y = |x - 2| cuts the y axis at (0, 2).

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The value of x is 11.

A square is a two dimensional shape which consist of four sides and four angles, where each angle is 90 degrees.

Given is a square PQRS.

PR and QS are diagonals of the square.

Square has the property that the diagonals bisect the interior angles.

So, ∠Q will be bisected by diagonal QS.

So, ∠PQS = ∠SQR = (6x - 21)°

∠Q is the interior angle of a square, thus it is 90°.

∠Q = ∠PQS + ∠SQR

90 = 6x - 21 + 6x - 21

90 = 12x - 42

12x = 90 + 42

12x = 132

x = 11

Hence the value of x is 11.

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The tax owed by a person in 2021 who had a single filling status with a taxable income of $ 62, 000 is $ 9, 388. 50.

In 2021, the Internal Revenue Service issued rates such that a person with a single filling status and earning $ 62, 000 per year would be subject to tax of ;

= 4, 664 + 22 % of the amount over $ 40, 525

This means that the tax owed by this taxpayer with a $ 62, 000 gross income is :

= 4, 664 + ( 22 % x ( 62, 000 - 40, 525 ) )

= 4, 664 + ( 22 % x 21, 475 )

= 4, 664 + 4, 724. 50

= $ 9, 388. 50

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Answer:

The formula for the function g(x) obtained when the graph of f(x) = √x is shifted up 1 unit and to the left 6 units is g(x) = √(x + 6) + 1.

Step-by-step explanation:

To obtain the formula for the function g(x) when the graph of f(x) = √x is shifted up 1 unit and to the left 6 units, we can use the following transformations:

A vertical shift up by 1 unit is represented by adding 1 to the function: f(x) + 1

A horizontal shift to the left by 6 units is represented by replacing x with (x + 6): f(x + 6)

Therefore, the formula for the function g(x) is:

g(x) = f(x + 6) + 1

Substituting the expression for f(x), we get:

g(x) = √(x + 6) + 1

So, the formula for the function g(x) obtained when the graph of f(x) = √x is shifted up 1 unit and to the left 6 units is g(x) = √(x + 6) + 1.

The area of the rhombus is, A = (x² + 2x - 8) m².

A quadrilateral with all equal sides is a rhombus.

Rhombuses are a particular kind of parallelogram in which all of the sides are equal since the opposite sides of a parallelogram are equal.

A rhombus has 360° of interior angles total.

A rhombus's adjacent angles add up to 180°.

A rhombus's diagonals are perpendicular to one another and cut each other in half.

We also know That the area of a rhombus is, Half times the product of the two diagonals.

Given, A rhombus, with d₁ = (2x + 8) m and d₂ = (x - 2) m.

Therefore, The area of the rhombus is,

= (1/2)×(2x + 8)(x - 2) m².

= (1/2)(2x² - 4x + 8x - 16) m².

= (1/2)(2x² + 4x - 15) m².

= (x² + 2x - 8) m².

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Answer:

The solution to the equation 7x [6+10(1+1)] = 4 x 5 is x = 10/91.

Step-by-step explanation:

o solve the equation 7x [6+10(1+1)] = 4 x 5, we can use the order of operations, which tells us to first perform the operations inside the parentheses, then the multiplication and finally the multiplication by 7x.

So, we have:

7x [6+10(1+1)] = 4 x 5

7x [6+10(2)] = 20

7x [6+20] = 20

7x [26] = 20

182x = 20

To solve for x, we can divide both sides by 182:

182x/182 = 20/182

x = 20/182

Simplifying the fraction by dividing both the numerator and denominator by their greatest common factor, we get:

x = 10/91

Therefore, the solution to the equation 7x [6+10(1+1)] = 4 x 5 is x = 10/91.

Answer:

[tex]625m^{2}[/tex]

Step-by-step explanation:

Answer:

See below.

Step-by-step explanation:

For this problem, we are asked for the value of x.

Let's use a Proportion to identify x.

A Proportion is a comparison of two equivalent fractions, or ratios.

An example of a proportion can be; [tex]\frac{x}{16} =\frac{16}{32}[/tex], where the value of x is 8.

For this example, we can find x by dividing the Numerator and Denominator by 2.

Let's use the example as a guide for our problem.

We can set up our problem as a ratio, or a fraction. Both represent the same data.

[tex]\frac{x}{8} = \frac{21}{24}[/tex]

We should know that 24 is 3 times bigger than 8, hence we should divide both the Numerator and Denominator by 8.

[tex]\frac{21 \div 8}{24 \div 8} = \frac{7 \ (x)}{8}[/tex]

The value of x is 7.

Answer: x = 7

Step-by-step explanation:

   Given:

x:8 = 21:24

   Rewrite as fractions:

[tex]\displaystyle \frac{x}{8} =\frac{21}{24}[/tex]

   Cross-multiply:

x * 24 = 8 * 21

24x = 168

   Divide both sides of the equation by 24:

x = 7

The radical expression (6–√4)3 written in exponential form is 612.

Expression is a term used to describe the process of making clear or conveying one's thoughts, ideas, and feelings. It is a way of communicating with others and expressing oneself in a meaningful and effective manner. Expression can be done through verbal and non-verbal communication, including writing, art, music, dance, and other creative outlets. It can also be used to express emotions such as joy, sadness, fear, anger, and love. Expression is essential to healthy communication and can be a powerful tool for self-expression, personal growth, and development.

This is because raising a number to an exponent is the same as multiplying that number by itself the number of times specified by the exponent. In this case, the base number is 6, and the exponent is 12. When a number is multiplied by itself 12 times, it is referred to as an exponential expression. To convert the radical expression to an exponential expression, the radical needs to be converted to an exponent. The radical of 4 is 2, so the exponent is 12. This results in the answer 612.

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Answer:

A reciprocal function can be written in the form of f(x) = a / (x-h) + k, where a is a constant, h is the x-value of the vertical asymptote, and k is the y-value of the horizontal asymptote.

Given that the vertical asymptote is located at x = -2 and the horizontal asymptote is located at y = 5, we can write:

f(x) = a / (x - (-2)) + 5

Simplifying this expression, we get:

f(x) = a / (x + 2) + 5

Therefore, an equation that could represent this reciprocal function is:

f(x) = a / (x + 2) + 5

Step-by-step explanation:

Answer:

After the reverse stock split, Gene will own 120 shares of XYX Corporation.

To calculate the post-split market price per share, we can start by finding the total value of Gene's shares before the split:

Total value before split = 1,200 shares * $1.20 per share = $1,440

Since the reverse stock split is 1 for 10, the total number of shares outstanding will be reduced by a factor of 10, and the price per share will be increased by a factor of 10:

Total value after split = 120 shares * $12.00 per share = $1,440

Therefore, the post-split market price per share is $12.00.

Step-by-step explanation:

After using the dimensions (length and width) of the pool to determine an expression that gives the perimeter of the rectangular pool is  P = 2 (5x- 4)

What is perimeter?

When defining a length in one dimension or a form in two dimensions, a perimeter is a closed path. The perimeter of a two-dimensional figure is the region that surrounds it. It provides the length of the shape, whether it is a circle, triangle, square, or rectangle. Area and perimeter are a 2D shape's two main properties.

The area of a given rectangular pool is

6x²−11x+3

⇒6x²− (9 + 2) x + 3

⇒ 6x²− 9x - 2x + 3

⇒ 3x(2x - 3) - 1 (2x - 3)

⇒ (3x - 1) (2x - 3)

An expression that gives the perimeter of the rectangular pool is,

P = 2 [ (3x - 1) + (2x - 3) ]

P = 2 [ 3x - 1 + 2x - 3 ]

P = 2 (5x - 4)

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Answer:

Step-by-step explanation:

200,000 square kilometers is a good estimate for the area of South Dakota because the actual area of South Dakota is approximately 199,729 square kilometers according to the United States Geological Survey (USGS).

This means that the estimate is only off by about 0.1% of the actual area. This level of accuracy is generally considered to be very good for an estimate, especially when dealing with large areas like states or countries.

Additionally, 200,000 square kilometers is a round number and easy to remember, making it a useful estimate in contexts where a precise value is not necessary. It also allows for quick comparisons with other areas or states that may be roughly similar in size.

Overall, 200,000 square kilometers is a good estimate for the area of South Dakota because it is reasonably close to the actual value, easy to remember, and useful for rough comparisons with other areas.

ALSO:

South Dakota is approximately 383 miles long (east to west) and 237 miles wide (north to south).

It has the approximate shape of a rectangle, its Area = (Base x Height)= (383 x 237)= 90,771.00 miles ^2 which are 235,095.81 Km^2. So by this geometric reasoning we can have a correct approximation of the area of ​​South Dakota.

Answer:

17,714.7

Step-by-step explanation:

a_n = 3^(2 n - 1) 10^(5 - n) (for all terms given)

{30000, 27000, 24300, 21870, 19683, 177147/10, 1594323/100, 14348907/1000, 129140163/10000, 1162261467/100000, 10460353203/1000000, 94143178827/10000000, 847288609443/100000000, 7625597484987/1000000000, 68630377364883/10000000000, 617673396283947/100000000000}

The correct inequality that represents how many video games he could buy is C. 15.99x + 9.99 ≤ 100.

Inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are not equal.

Let x be the number of video games Manny wants to buy.

The total cost will be the sum of the cost of the video games and the shipping charges:

Total cost = (number of video games) × (cost per game) + (shipping charges)

Total cost = 15.99x + 9.99

Since Manny can spend at most $100, we can write the inequality:

Total cost ≤ 100

15.99x + 9.99 ≤ 100

Therefore, the correct inequality that represents how many video games he could buy is C. 15.99x + 9.99 ≤ 100.

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Answer:

2x(1700%x4)+2=138

Step-by-step explanation:

2x2.00=4 2x17=34 34 per month plus the 2 that they already had. 34x4=136 there will be 136 plus 2 after the 4 months

Answer:

The APY would be D, 3.92%

Step-by-step explanation:

Attached Image

By using the properties of the diagonal of the parallelogram, we found the values of x and y as 2 and 7 respectively.

A parallelogram is a straightforward quadrilateral with two pairs of parallel sides in Euclidean geometry. A parallelogram's facing or opposing sides are of equal length, and its opposing angles are of similar size. A parallelogram has adjacent angles that add up to 180 degrees.

A parallelepiped is a three-dimensional shape with parallelogram-shaped faces. The base (one of the parallel sides) and height (the distance from top to bottom) of the parallelogram determine its area. A parallelogram's perimeter is determined by the lengths of its four sides.

Here the diagonal of the parallelogram intersects each other.

According to the properties of the paralleogram, the diagonal bisects each other.

So,

2x = x + 2

x = 2

and

5y -5 = y + 23

4y = 28

y = 7

Therefore by using the properties of the diagonal of the parallelogram, we found the values of x and y as 2 and 7 respectively.

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The Tape diagram for 7/8 is shown below.

A tape diagram is a visual model that students can use to show a mathematical connection or to help them grasp a math idea. Tape diagrams can be used to solve a variety of arithmetic problems, although they are most typically employed to solve word problems.

Tape diagrams are graphic representations that use rectangles to depict the portions of a ratio. Drawing them requires attention to detail because they are a visual model. They simplify complex mathematical word problems by breaking them down.

Given:

Here we can divide the fraction 7/8 as

7/8

= 2/8 + 5/8

= 2/8 + 2/8 + 3/8

So, the tape diagram will have 8 out tapes out of which 7 are shaded.

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Answer:

Terri paid $71.14

Step-by-step explanation:

$34.35+$15.50+$45.00=$94.85

$94.85-25%=$71.14

$94.85 is over $50, so Terri can get a 25% discount. After the 25% discount, Terri paid $71.14

By answering the above question, we may infer that Thus, 12 is the result equation of 1/4 times 48.

A mathematical equation links two statements and utilises the equals sign (=) to indicate equality. In algebra, an equation is a mathematical assertion that proves the equality of two mathematical expressions. For instance, in the equation 3x + 5 = 14, the equal sign separates the numbers by a gap. A mathematical formula may be used to determine how the two sentences on either side of a letter relate to one another. The logo and the particular piece of software are usually identical. like, for instance, 2x - 4 = 2.

You can multiply 1/4 by 48 using the following formula:

1/4 x 48 = (1/4) * 48

The numerator (1) is first multiplied by the integer being multiplied (48):

1 * 48 = 48

Divide the result by the denominator (4) after that:

48 / 4 = 12

Thus, 12 is the result of 1/4 times 48.

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Answer:

60%

Step-by-step explanation:

Answer:

3 Burrito Bowls

Step-by-step explanation:

32.46 - 12.96 = 19.5

6.5 x 3 = 19.5, so 3 bowls

Answer:

the customer ordered 3 burrito bowls

Step-by-step explanation:

32.46=6.5x+12.96

-12.96 -12.96

19.5=6.5x

3=x

x=# of burrito bowls ordered

The solution is, the expression is -3+0i, so, a = -3 & b = 0.

In mathematics, a complex number is an element of a number system that extends the real numbers with a specific element denoted i, called the imaginary unit and satisfying the equation {\displaystyle i^{2}=-1}; every complex number can be expressed in the form a + bi, where a and b are real numbers.

here, we have,

So we have:

given that,

(2+6i) - (5+6i)

First, distribute:

2+6i - 5 -6i

Combine like terms:

2 - 5 + 6i - 6i

Add:

-3 + 0

So, in the a+bi format, we will have:

-3 + 0i

Hence, The solution is, the expression is -3+0i, so, a = -3 & b = 0.

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We can write the terms of the sequence as -

a(1) = 5

a(2) = 18

a(3) = 26

a(10) = 500

The nth term of a arithmetic progression is given by -

a{n} = a + (n - 1)d

Given is to find 1st, 2nd, 3rd and 10th term of the sequence function -

a{n} = 4n² + n

a{n} = n(4n + 1)

a(1) = 1 x (4 + 1) = 5

a(2) = 2 x (8 + 1) = 18

a(3) = 3 x (12 + 1) = 26

a(10) = 10 x (40 + 10) = 500

Therefore, we can write the terms of the sequence as -

a(1) = 5

a(2) = 18

a(3) = 26

a(10) = 500

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Answer:

I do not have access to drawing tools. However, I can describe how to plot the function on a graph.

To plot the function h(x) = {-4, x < -3 and x+5, x > -3, you would start by drawing the x-y axes on a coordinate plane. Then, you would mark a point at x=-3 on the x-axis. At this point, the value of h(x) changes from -4 to x+5. So, you would draw a solid dot at (-3, 2) on the graph.

Next, you would draw a horizontal line at y=-4 to the left of x=-3, indicating that h(x) is always equal to -4 for x values less than -3.

Finally, you would draw a diagonal line starting from the dot at (-3, 2) and continuing to the right. This line represents the equation x+5 for x values greater than -3.

The resulting graph should have a horizontal line at y=-4 to the left of x=-3, a solid dot at (-3, 2), and a diagonal line extending to the right from the dot.

Step-by-step explanation:

By answering the above question, we may infer that Thus, the 159 feet that make up the perimeter of the area used for the new playground.

A limit is a closed path that encircles, separates, or encompasses a one-dimensional length, a two-dimensional shape. A circle's or an ellipse's perimeter refers to its outermost region. Many practical uses may be made of the perimeter calculation. The radius of an edge is used to calculate a shape's perimeter. Get the circle's radius by multiplying the lengths of the sides of irregular shapes. Every form's perimeter may be determined by multiplying its side lengths. The area around an object is called its perimeter. Your home's walled garden serves as a wonderful example of this. A thing's perimeter is the area surrounding it. A 200 foot barrier will be needed to contain a 50 by 50 foot yard.

Current playground size is 1,575 square feet, or 35 feet by 45 feet.

The difference between the old and new playgrounds is 1,575 square feet.

New playground length = 1,575 square feet / 42 feet 37.5 feet, where new playground width equals new playground area.

We can calculate the perimeter now that we know the new playground's width is around 37.5 feet:

The new playground's perimeter is equal to 2 (length + width).

The new playground's perimeter is 2 (42 feet plus 37.5 feet).

2 is the new playground's perimeter (79.5 feet)

The new playground's perimeter is 159 feet.

Thus, the 159 feet that make up the perimeter of the area used for the new playground.

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Answer:

Will is 122% of Wandas height.

Step-by-step explanation:

The length of the rope swing is approximately 98.9 feet (rounded to the nearest tenth of a foot).

Algebraic expressions are used to represent mathematical relationships and formulas, and can be used to solve equations and manipulate equations in order to isolate variables or solve for unknown quantities. They are used extensively in algebra, calculus, and other branches of mathematics.

We are given that the time for one swing is given by the formula:

t = 2√(L/32.2)

where L is the length of the rope swing in feet, and 32.2 is the acceleration due to gravity in feet per second squared.

We are also given that one swing takes 3.5 seconds, so we can write:

3.5 = 2√(L/32.2)

Squaring both sides, we get:

12.25 = 4(L/32.2)

Multiplying both sides by 32.2/4, we get:

L = 32.2 × 12.25/4

L ≈ 98.9 feet

Therefore, the length of the rope swing is approximately 98.9 feet (rounded to the nearest tenth of a foot).

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The interest rate of the saving account is 2.71%

Simple interest is the amount of interest charged on a specific principal amount at a specific interest rate. Compound interest, on the other hand, is the interest that is computed using both the principal and the interest that has accumulated over the preceding period.

Given, the interest rate of a savings account is represented by the formula such that:

r = [tex]\sqrt{\frac{V_2}{V_0} } - 1[/tex]

Where V₀ is the initial investment,

and V₂ is the balance of the account after 2 years.

In our case,

V₂ = 422

V₀ = 400

So the interest rate,

r = [tex]\sqrt{\frac{422}{400} } - 1[/tex]

r = 1.0271 - 1

r = 0.0271

therefore, the interest rate of the saving account is 2.71%

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Complete question:

The average annual interest rate r (in decimal form) of a savings account is V₂ represented by the formula r = [tex]\sqrt{\frac{V_2}{V_0} } - 1[/tex], where Vo is the initial investment, and V₂ is the balance of the account after 2 years. Find the average annual interest rate r of a savings account with an initial investment of $400 and a balance of $422 after 2 years.