Use transformations of the graph of y=1/x to graph the rational function, and state the domain and range

r(x) = 2x-9/x-4
​

The value of x is given as follows:

x = 2.5 cm.

Similar triangles are triangles that share these two features listed as follows:

The logic for similar triangles can be expanded for any similar polygons, as is the case for this problem.

The proportional relationship for the side lengths is given as follows:

x/5 = 4/8

Applying cross multiplication, the value of x is obtained as follows:

8x = 20

x = 2.5 cm.

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Answer: 1.5

Step-by-step explanation:

To find the constant ratio of successive y-values, we need to divide each y-value by the previous one.

For example, to find the ratio between the second and first y-values:

7.5 ÷ 5 = 1.5

Similarly, we can find the other ratios:

11.25 ÷ 7.5 = 1.5

16.875 ÷ 11.25 = 1.5

25.3125 ÷ 16.875 = 1.5

Since all the ratios are the same, we can conclude that the constant ratio of successive y-values is 1.5.

Therefore, the answer is c. 1.5.

The fraction can be represented as follows:

[tex]\frac{6^8}{6^8} = 6^0[/tex]

Remember the rule for exponents:

[tex]\frac{a^n}{a^m} = a^{n - m}[/tex]

So we just need to subtract the exponents

Here we have the following quotient:

[tex]\frac{6^8}{6^8}[/tex]

Using the rule above, we can rewrite that fraction as follows:

[tex]\frac{6^8}{6^8} = 6^{8 - 8} = 6^0[/tex]

So the exponent at the end is zero, this means that the correct option is B.

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Tatiana is the athlete who trains a weekly amount of kilometers equal to the median of the 11 competitors.

To find the median, we need to first arrange the values in order from lowest to highest:

4, 5, 5, 5, 5.5, 6, 7, 8, 8, 9, 10

Since there are 11 values, the median is the middle value. In this case, the middle value is 5.5. Therefore, the athlete who trains a weekly amount of kilometers equal to the median of the 11 competitors is Tatiana, who trains 5.5 kilometers per week.

None of the other athletes in the table trains exactly 5.5 kilometers per week, so Tatiana is the only correct answer.

It's worth noting that the median is a measure of central tendency that is less sensitive to outliers than the mean. In this case, the values range from 4 to 10, which is a relatively wide range, but the median still provides a useful measure of the typical training distance among the 11 athletes.

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Answer:

a)

[tex] log_{9}(7) - log_{9}(8) = log_{9}( \frac{7}{8} ) [/tex]

b)

[tex] log_{5}(11) + log_{5}(4) = log_{5}(44) [/tex]

c)

[tex] log_{9}(81) = log_{9}( {3}^{4} ) = 4 log_{9}(3) [/tex]

Answer:

The 3rd one or C

Step-by-step explanation:

A       B

C      D

Using the net, the correct surface area of the prism is 216 square units

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

The triangular prism

Using the net, the surface area is

Surface area = Sum of areas of individual shapes

So, we have

Surface area = 2 * 1/2 * 3 * 4 + 17 * 5 + 17 * 4 + 17 * 3

Evaluate

Surface area = 216

Hence, the surface area of the prism is 216 square units

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The inverse function of f(x) = (x - 3)²- 4 is f-1(x) = 3 + √(x + 4)

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

f(x) = (x - 3)²- 4

Rewrite as

y = (x - 3)²- 4

Swap x and y

So, we have

x = (y - 3)²- 4

This gives

(y - 3)² = x +  4

Take teh square roots of both sides

y - 3 = √(x + 4)

So, we have

y = 3 + √(x + 4)

So, the inverse function is f-1(x) = 3 + √(x + 4)

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Answer:

z = 4 , y = 6 , 4 and 13

Step-by-step explanation:

1

8z - 15 = 17 ( add 15 to both sides )

8z = 32 ( divide both sides by 8 )

z = 4

2

22 = 4y - 2 ( add 2 to both sides )

24 = 4y ( divide both sides by 4 )

6 = y

3

3(- 7) + 25 = - 21 + 25 = 4

4

16 - 6 ÷ 2 ← perform division before subtraction

= 16 - 3

= 13

For the middle par, using the answers associated to the colours

13 + (6 ÷ 4) - 4

= 13 + 1.5 - 4

= 14.5 - 5

= 10.5

Answer: 9 and 2/3

Step-by-step explanation:

Answer:  x=3   <W=27

Step-by-step explanation:

<Y is half of the arc XW

<Y=78/2 =39

The sum of all the angles in a triangle is 180

so add all angles ang make =180

114+39+7x+6=180          Simplify

159+7x=180                   Subtract 159 from both sides

7x=21                              Divide 7 to both sides

x=3

plug back in x to find <W

<W=7(3)+6

=21+6

27

The better prediction of x when y = 7, based on the scatter plot, would be A. 11.

When looking at the scatter plot, we see that the potential y values below 10, correspond with potential x values below 20. This is why the only dots in the quadrant y < 10 are also x < 20.

When we have a y value that is 7, this is below 10. What this means therefore is that the most likely value of x is 11 because 52 would be much too high.

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Step-by-step explanation:

This is a composit figure of a 20 x 30 m rectangle and a circle of radius 10m

area of rectangle + area of circle = total area

     l x w                +     pi r^2           = total

       20 x 30         + pi (10^2)   = 914.2 m^2

Answer:

157.08 in.

Step-by-step explanation:

C=2πr=2·π·25≈157.07963

Answer:

A

Step-by-step explanation:

look at pic below.

Here are steps to find the circumference of a circle with a radius of 25 inches:

1. Recall the formula for the circumference of a circle:

C = 2πr

2. Substitute the value of the radius into the formula:

C = 2π(25)

3. Simplify the expression by multiplying 2π by 25:

C = 50π

4. Use the approximate value of π, which is 3.14, to get a numerical answer:

C ≈ 50(3.14)

5. Calculate the product:

C ≈ 157

Therefore, the circumference of a circle with a radius of 25 inches is approximately 157 inches.

Answer:

  (a) ∠7 = 47°. Angles 5 and 7 are vertical angles, hence congruent.

  (b) 47 +(2x -5) = 180

  (c) 69

Step-by-step explanation:

Given angles identified as ∠5, ∠6, ∠7 where two lines cross, and the measure of ∠5 as 47°, you want the measure of ∠7, and an equation and solution when ∠6 is (2x-5).

Angles that share a vertex and are formed from opposite rays are "vertical angles." They are congruent.

Angles 5 and 7 are vertical angles, so the measure of angle 7 is the same as the measure of angle 5.

  ∠7 = 47°

Angles that form a linear pair are supplementary. This means the sum of angles 5 and 6 is 180°.

  ∠5 +∠6 = 180°

  47° +(2x -5)° = 180°

  2x = 138 . . . . . . . . . . . . divide by °, subtract 42

  x = 69

Answer:

x=28

x=-28

Step-by-step explanation:

The lower quartile, the median, and the upper quartile are 22, 31 and 90

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

11, 18, 22, 22, 31, 31, 63, 86, 90, 92, 98

Split the data values into 2

So, we have

11, 18, 22, 22, 31,

31,

63, 86, 90, 92, 98

The middle of each set is the quartiles

So, we have

Lower = 22

Median = 31

Upper = 90

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The graph of the given inequalities is Attached below.

From the given inequalities:

As the first inequality is not strictly true, the graph of it is a straight solid line that passes through the points (0, 2) and (2/3, 0), with the shaded area being further from the origin ( as it fails the zero point test )

As the second inequality is not stringent, the graph of the inequality is a straight solid line that passes through the points (0,-4) and (8,0), with the shaded area pointing in the direction of the origin (since the inequality passes the zero point test)

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Complete question:

Which graph represents the system of inequalities?

y + 3x ≥ 2

y + 4 ≥ 1/2x

The missing side lengths in the triangles are c = 20 ft, b = 17.32 ft and x = y = 6√2

Triangle 1

The side length c is calculated as

sin(30) = 10/c

So, we have

c = 10/sin(30)

Evaluate

c = 20

This also means that the side length b is calculated as

b² = 20² - 10²

b² = 300

Take the square roots

b = 17.32

Triangle 2

Given that the acute angle in the right triangle is 45 degrees and the hypotenuse is 12 meters

The side lengths x and y are calculated as

x = y = 12/√2

Rationalise the expression

x = y = 6√2

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The standard form of the equation of the hyperbola is

[(y + 6)²/4] - [(x - 3)²/16] = 1.08

We have,

To find the standard form of the equation of a hyperbola, we need to know the locations of the vertices and the foci.

In this case, we are given the coordinates of the vertices, but we need to find the foci. However, we are also given that the hyperbola passes through the point (7, −12), which will allow us to find the foci.

First, let's find the center of the hyperbola.

Since the vertices have the same x-coordinate of 3, the center must be the point (3, −6), which is the midpoint of the two vertices.

Next, we can find the distance between the center and one of the vertices. Using the distance formula, we get:

d = √[(3 - 3)² + (-8 - (-6))²] = 2

Since the vertices are vertically aligned, we know that the distance from the center to each vertex is the same.

Therefore, the distance from the center to each vertex is also 2.

We can now use the Pythagorean theorem to find the distance from the center to each focus, which we will call c.

We know that c² = a² + b², where a is half the distance between the vertices (in this case, a = 2), and b is half the distance between the foci.

We want to solve for b.

Since the hyperbola passes through the point (7, −12), we know that the distance from this point to each focus is constant and equal to the distance from this point to the center of the hyperbola.

Using the distance formula, we can set up the following equation:

√[(7 - 3)² + (-12 - (-6))²] = sqrt[(7 - 3)^²+ (-12 - (-8))²] + b

Simplifying this equation, we get:

2 √(37) = 2 √(20) + b

b = √(37) - √(20)

Now that we have the values of a and b, we can write the standard form of the equation of the hyperbola:

[(y + 6)²/4] - [(x - 3)²/16] = 1 + [(√(37) - √(20))²/16]

Simplifying, we get:

[(y + 6)²/4] - [(x - 3)²/16] = 1.08

Therefore,

The standard form of the equation of the hyperbola is

[(y + 6)²/4] - [(x - 3)²/16] = 1.08

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Yes, there are cases where the value of x or a would cause a problem in this equation.

A value of 0 for a would cause a problem because division by zero is undefined.

Therefore, we cannot have a=0 in this equation.

Additionally, if a fraction is being used as a value for a, there could be potential problems with rounding errors or decimal approximations that could cause issues in solving for x accurately.

It is also possible that certain values of x may make the left-hand side of the equation undefined, such as if x = 0 and a = 6.

However, these cases may not necessarily be problematic, depending on the context of the problem and the solutions being sought.

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By simplification we get: [tex]2^4p^8q^1^2[/tex]

Simplify  the expression:

=> [tex](2p^2 q^3)^4[/tex]

We use the property for simplification i.e.,:

[tex](a^m)^n=a^m^n[/tex]

So, We solve by using above property:

[tex]p^2[/tex] raised to the 4 th power = [tex](p^2^.^4) =p^8[/tex]

[tex]q^3[/tex] raised to the 4 th power = [tex](q^3^.^4)=q^1^2[/tex]

Complete simplification, we get:

[tex](2p^2 q^3)^4=[/tex] [tex]2^4p^8q^1^2[/tex]

Hence, By simplification we get: [tex]2^4p^8q^1^2[/tex]

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Answer: Answer

Step-by-step-explanation: 4:2 plays a sport 13:9 does not

The measures the angle 3 is given by 45°.

Hence the correct option is (B).

The quadrilateral which has four equal sides and the adjacent sides of which are in perpendicular that is called Square.

The given figure is a Square.

We know that the angle between two adjacent sides = 90°.

We also know that the diagonal of square divides angles into two equal parts of angles.

So here angle 3 is a one equal part of angle between two adjacent sides of  square.

So angle 3 is given by = (1/2)*90° = 45°.

Hence the correct option will be (B).

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The value of x rounded to 1 decimal place is 15.9 cm.

In Mathematics and Geometry, Pythagorean's theorem is modeled or represented by the following mathematical equation (formula):

x² + y² = z²

Where:

x, y, and z represents the length of sides or side lengths of any right-angled triangle.

First of all, we would determine length of sides or side lengths of the opposite side of the ight-angled triangle as follows;

12.5² + y² = 19.5²

156.25 + y² = 380.25

y² = 224 cm.

y = √224 cm

Now, we can determine value of x;

x² = (√224)² + (5.5)²

x² = 224 + 30.25

x = 15.9 cm.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

The probability that (all 23 are not smokers is 0.0429

P(all 23 are not smokers 0.0429

P(exactly 6 smokers)  ≈ 0.1671

a) If 16% of the population are smokers, then the probability that an individual is not a smoker is 1-0.16=0.84.

P(all 23 are not smokers) = 0.84²³ ≈ 0.0429

b) The probability that any one individual smokes is 0.16, and the probability that any one individual does not smoke is 0.84.

P(all 23 are not smokers) = 0.84²³ ≈ 0.0429 (rounded to four decimal places).

c) Similarly, we can use the binomial distribution to find the probability of exactly 6 smokers in a sample of 23:

P(exactly 6 smokers) = (23 choose 6) * 0.16⁶ * 0.84^17 ≈ 0.1671

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Answer:

Set your calculator to degree mode.

[tex] x = {cos}^{ - 1} \frac{5}{7} = 44.4[/tex]

Angle x measures 44.4 degrees.

The correct option regarding the simplification of the expression is given as follows:

B. [tex]12\sqrt{2} + 4\sqrt{3}[/tex]

The expression in the context of this problem is defined as follows:

[tex]4\sqrt{18} - 2\sqrt{27} + 5\sqrt{12}[/tex]

To simplify the expressions, first we must obtain the simplest radical form of each expression, as follows:

Hence the simplified expression is obtained as follows:

[tex]4(3\sqrt{2}) - 2(3\sqrt{3}) + 5(2\sqrt{3}) = 12\sqrt{2} - 6\sqrt{3} + 10\sqrt{3} = 12\sqrt{2} + 4\sqrt{3}[/tex]

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The area of the decagon with side length 10 is 769.42 square units

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

side length, l = 10

The area of the decagon is calculated as

Area = 5/2l² * √[5 + 2√5]

Where

l = 10

Substitute the known values in the above equation, so, we have the following representation

Area = 5/2 * 10² * √[5 + 2√5]

Evaluate

Area = 769.42

Hence, the area is 769.42

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a. The definite integral ∫₀²f(x)dx = lw

b.  The definite integral ∫₂⁴f(x)dx = πr²/2

A definite integral is an integral evaluated on an interval.

Given the figure, to evaluate the definite integral ∫₀²f(x)dx and ∫₂⁴f(x)dx, we proceed as follows.

a.  The definite integral ∫₀²f(x)dx

Observe the graph, the integral ∫₀²f(x)dx is the area occupied by the square on the interval (0, 2).

So,  ∫₀²f(x)dx = lw

b.  The definite integral ∫₂⁴f(x)dx

Observe the graph, the integral ∫₂⁴f(x)dx is the area occupied by the circle on the interval (2, 4).

So,  ∫₂⁴f(x)dx = πr²/2

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Answer:10

Step-by-step explanation: