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The hyperbola has a center of (2, -3)

The equation of the hyperbola is given as

(y + 3)²/9 − (x − 2)²/2 = 1

A hyperbola is generally represented as

(y - k)²/a² − (x − h)²/b² = 1

Where the coordinates of the center of the hyperbola is

Center = (h, k)

Next, we compare (y - k)²/a² − (x − h)²/b² = 1 and (y + 3)²/9 − (x − 2)²/2 = 1

From the comparison, we have

(h, k) = (2, -3)

This means that the center is (2, -3)

Hence, the coordinates of the center is (2, -3)

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Answer:

The number “2” that is a outside the brackets multiplies both of the numbers inside the brackets.

Step-by-step explanation:

3+2(2x-4)

3+4x-8

4x-5

The probability that a random sample of n=40 oil changes results in a sample mean time of less than 20 minutes is 0.00714.

Given,

A random  sample of n = 40  

The mean time μ = 21.4

and, standard deviation is σ =  3.6 min

The z score (z) is given by the equation:

z = (x - μ) / σ / [tex]\sqrt{n}[/tex]

Substituting , the values we get

z = (20 - 21.4) / 3.6 /[tex]\sqrt{40}[/tex]

z = -2.45

Using the z table:

P(x < 20) = P(z < -2.45)= 0.00714

Hence, The probability that a random sample of n=40 oil changes results in a sample mean time of less than 20 minutes is 0.00714.  

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SOLUTION:

The parent function is;

The transformation applied is;

Graphing this, we have;

The period is the time to complete a cycle .

From the graph, the period is;

The asymptotes are those lines for which sec x is undefined. those are lines where;

Formula of simple interest rate:

Where,

For Monica interest rate is:

For Paul interest rate is:

No, Paul interest rate higher then Monic.

Answer: 2/7

Step-by-step explanation:

Substract 7/7 AKA the whole, by 5/7 tp get 2/7

2/7 is the fraction of males.

Based on the vertices of the triangle, the area of the triangle can be found to be 8 cm²

First, find the lengths of JK, KL, and JL. When given vertices, you can find the length of a line by the formula:

= √ ( (x₂ - x₁)² + (y₂ - y₁)²)

The length of JK is therefore 2.83 units

The length of KL is therefore 5.66 units

The length of JL is therefore 6.32 units.

Given these units, the area of the triangle can be found by the formula:

= √ s(s - a) ( s - b) ( s - c)

Where:

s = semi perimeter

a, b, and c are the sides of the triangle which are JK, KL, and JL.

The semi-perimeter can be found by the formula:

= ( a + c + c) / 2

= 15.47 / 2

= 7.74

The area of the triangle is therefore:

= √ s(s - a) ( s - b) ( s - c)

= √ 7.74 (7.74  - 2.83) ( 7.74 - 5.66) ( 7.74 - 6.32)

= 8 cm²

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The categories of the functions are:

The category of the functions are given as

As a general rule, linear functions can take any of the following forms

Where the variables a, A, m, b, B, c and C are real numbers

Any equation that do not have the above form is considered a nonlinear function

Using the above forms as a guide, we have the linear equations to be

(16) y = 7 - x  (17) y = ∛8 - x (19) 2 + y = x + 4 (21) x -y = |-54|

All other equations are nonlinear equations

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The transformation from the graph of f(x) to g(x) is horizontal shift right 0.333 units and vertical shift is up 5 units.

The given functions are f(x) = x² and g(x)= 4(3x-1)²+5.

Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.

The transformation is

To find the transformation, compare the function to the parent function and check to see if there is a horizontal or vertical shift, reflection about the x-axis or y-axis, and if there is a vertical stretch.

Horizontal Shift: Right 0.333 Units

Vertical Shift: Up 5 Units

Reflection about the x-axis: None

Reflection about the y-axis: None

Vertical Compression or Stretch: Stretched

Therefore, the transformation from the graph of f(x) to g(x) is horizontal shift right 0.333 units and vertical shift is up 5 units.

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Answer:

Sum of angles in a triangle add up to 180°.

x = 180 - 64 - 40

= 76°

Answer:

Salton City could have an elevation less than -2 or greater than 2 (depends on what u meant.

Step-by-step explanation:

Usually when u talk abt elevation, when it is lower than sea level, you write it with a negative sign. If you meant that new Orleans is 2 feet below sea level, the Salton City elevation could be anything less than -2. If you meant 2 feet above sea level, the New Orleans elevation could be anything above 2.

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5. How many ways are there to distribute 10 indistinguishable candies among 4 different

children? Children may end up with no candies.

Compound interest formula:

A = P (1+r/n)^nt

Where:

A = total amount

P = principal investment

r= interest rate in decimal form = 2/100 = 0.02

t= years

n= number of compounding periods in a year= 12

Replacing:

A = 30,000 (1+0.02/12)^4x12

A = 30,000 (1.001666667)^48

A= 32,496.45

The length has a value of  9 meters

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

Length = 5 meters less twice it’s width

This means that

Length = 2Width - 5

The perimeter is given as

Perimeter = 38 meters

The perimeter is calculated as

Perimeter = 2 x (Length + Width)

So, we have

2 x (2Width - 5 + Width) = 38

Divide by 2

2Width - 5 + Width = 19

This gives

3Width= 21

Divide

Width - 7

Recall that Length = 2Width - 5

So, we have

Length =  2 * 7 - 5

Evaluate

Length =  9

Hence, the length is 9 meters

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Answer: When you graph part a, it has a negative slope.

Step-by-step explanation:

The amount that can be saved by purchasing ten notebooks at the sale price is 95 cents.

The information stated that the notebook are in sale for 2 at 99 cents. The cost for each notebook will be:

= 99 cents / 2

= 49.5 cents

The amount they can be saved will be:

= (59 × 10) - (49.5 × 10)

= 590 - 495

= 95 cents

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5. The two triangles are similar. The value of x = 12.

6. The information cannot be used to show that the triangles are similar triangles.

Two triangles are similar to each other if they have the same shape but different sizes, in order words, they must have the same corresponding angle measures but different corresponding side lengths that are proportional to each other.

5. In the first figure, we see that there are two pairs of corresponding congruent angles (a pair of right angles and a pair of vertical angles in both triangles), but different corresponding side lengths.

Therefore, based on the AA similarity theorem that says two triangles are similar of they have two pairs of congruent sides, we can prove that both triangles are similar to each other.

Therefore:

x/9 = 20/15

15x = (9)(20)

15x = 180

15x/15 = 180/15

x = 12

6. The second image shows that the two triangles share a common side, which means they have a pair of corresponding sides that are congruent. Therefore, the information given cannot be used to prove they are similar triangles.

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The correct option is D. i.e., Linear Function, Diagonal line which slants upward from left to right.

Given,

The function is :

f(x) = mx + b

and, where m> 0

Described the graph of the function and also write the name of the function:

Now, According to the statement is :
f(x) = mx + b , m > 0

It is an increasing line.

So, The correct option is D. i.e., Linear Function, Diagonal line which slants upward from left to right.

What is a increasing line in a graph?

If a linear graph is increasing then its gradient is positive, since when x increases by 1, y changes by a positive number. If a linear graph is decreasing, the gradient is a negative number.

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The image of the point after the dilation is (-2, -1)

Dilation is the process of altering the side length of a shape or a function

From the question, the given parameters are:

Point =  (-8, -4)

The scale factor of dilation is given as

Scale factor = 1/4

Mathematically, this transformation can be represented as

(x, y) = k(x, y)

Where k = 1/4 i.e. the scale factor

So, we have

(x, y) = (kx, ky)

This gives

(x, y) = (1/4x, 1/4y)

When represented as an equation, we have

Image = 1/4 * Point

Substitute the equation Point =  (-8, -4) in the equation Image = 1/4 * Point

So, we have the following equation

Image = 1/4 * (-8, -4)

Evaluate the product

Image = (-2, -1)

Hence, the image is (-2, -1)

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At this rate, Tommy will earn $211.2 working for 12 hours.

The Unitary Method draws a relation between given data. Following the regular trend, information can be calculated. It is also called the 'Mango Method'.

At this rate, Tommy will earn $211.2 working for 12 hours.

The Unitary Method is only valid for regular increases or decreases. Information about unity is drawn from given data, which is multiplied as required. It is widely used in the calculation of prices, amounts, etc.

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Lines f and g look to be parallel to each other.

Answer:

Lines G and F

Step-by-step explanation:

Parallel means never touching, and they usually run alongside eachother, that's why G and F look parallel.

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The general form of the equation: x2 + y2 − 41 = 0

The Correct option is (B).

Given,

A circle with center O (0,0) has point B (4,5) on its circumference

To find the what is the general form of the equation  for the given circle centered at O(0, 0).

Now, According to the question:

How do you find the equation of a circle with center (0,0)?

x2 + y2 = r2 , and this is the equation of a circle of radius r whose center is the origin O(0, 0). The equation of a circle of radius r and center the origin is x2 + y2 = r2 .

The general form of the equation:

x2 + y2 − 41 = 0

Hence, The general form of the equation: x2 + y2 − 41 = 0

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The value of x that makes the equation 2x+5 = 1.99x + 22 is 1700

The equation is

2x+5 = 1.99x+22

First we have to rearrange the given term and combine the like terms, then we have to find the value of x

Move 1.99x to left hand side of the equation and move 5 to the right hand side of the equation

2x+5 = 1.99x+22

2x-1.99x = 22-5

We have to do the subtraction in like  terms

(2-1.99)x = 22-5

0.01x = 17

Move the number 0.01 to the right hand side of the equation

x = 17/0.01

Division

x = 1700

Hence, the value of x that makes the equation 2x+5 = 1.99x + 22 is 1700.

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Answer:

Step-by-step explanation:

B

The inequalities are solved below

What are inequalities?

A connection in mathematics that compares two numbers or other mathematical functions in an unequal way is known as an inequality. It is most frequently used to compare the sizes of two numbers on the number line. To indicate various sorts of inequalities, a variety of notations are employed. The following characteristics control inequalities. Any of these characteristics are also true if monotonic functions are restricted to strictly monotonic functions and all non-strict inequalities ( and ) are replaced by their equivalent strict inequalities ( and >). On each side of an inequality, a common constant c can be added to or removed from.

The inequalities are solved below

-2x-7>1                                   x-2≥-1

or, -2x>1+7                            or, x≥-1+2

or, -x>8/2                              or, x≥1

or, x<-4

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Note that if the area of any figure is multiplied by a factor of a.

The perimeter will be multiplied by √a

From the problem, the are of the square is multiplied by 1/9, so we need to get the square root of that factor to get the factor for the perimeter.

Therefore, the answer is C. multiplied by 1/3

The system of equations that could be used to determine the number of drinks and the number of tacos that Jordan bought are 2.5x + 2y = 26 and y = x + 4.

Determine the known quantities and designate the unknown quantity as a variable while trying to set up or construct a linear equation to fit a real-world application.

Let's assume that number of drinks that Jordan and his children bought is x while the number of tacos is y.

The cost of drinks = 2.50x

Cost of tacos = 2y

Total cost 2.5x + 2y

2.5x + 2y = 26

Given that,

He bought 4 more tacos than drinks.

Therefore,

y = x + 4.

Hence "The system of equations that could be used to determine the number of drinks and the number of tacos that Jordan bought are 2.5x + 2y = 26 and y = x + 4".

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If two lines are perpendicular, it means that the slope of one line is equal to the negative reciprocal of the slope of the other line. Given a value, a/b, the negative reciprocal of a/b is - b/a.

From the information given, the slope of the red line is 2/5. This means that the slope of the green line which is perpendicular to the red line is - 5/2

Option D is correct

The inequality of the two triangle are 32° < x < 68° and the range of the value x is defined as  x ≥ 4.

Inequality:

Inequality means the relationship between two values that are not equal is defined by inequalities which means they are not equal.

Given,

Here we have the two triangles with some angle values.

Now, we need to find the inequality of these triangle.

To find the inequality of the triangle first we have to write down the values provided, they are,

77, 11x - 33, 68°, 32°

Through this we have identified that, the value of x is lies in between 68° and 32°.

So, it ca be written as,

32° < x < 68°

The next this is to use the triangle inequality theorem, that is,

"The sum of any two sides of a triangle is greater than or equal to the third side; in symbols, a + b ≥ c."

Therefore, based on the given equation we have written it as,

11x - 33 ≥  77

Subtract 33 on both sides then we get,

11x ≥ 44

Therefore, x ≥ 4.

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According to the picture, you can find the area of the figure by susbtracting the area of the segments of the circles to the area of the rectangle. We can observe that these segments are a quarter of a circle, together they would be a complete circle, then to find the area of the figure we can substract the area of one of the circles to the area of the rectangle.

1. Find the area of the circle:

2. Find the area of the rectangle:

To do it, you need to find the length and the width first, do it this way:

Now, find the area of the rectangle:

3. Find the area of the figure:

The area of the figure is 444.76 feet squared.