HELP PLEASE 30 POINTS
Four transformations of the function f(x)=4x
are given below.

For each transformation, drag the expression that shows the result of that transformation into the box under it.

(f x g)(x) = √(1/x + 2)

(g x f)(x) = 1/(√(x + 2))

To find (f x g)(x), we need to evaluate the composition of functions f and g, which is denoted as f(g(x)).

Similarly, to find (g x f)(x), we need to evaluate the composition of functions g and f, which is denoted as g(f(x)).

Let's calculate (f x g)(x) and (g x f)(x) for the given pair of functions f(x) = √(x + 2) and g(x) = 1/x:

1. (f x g)(x):

We start by substituting g(x) into f(x) wherever we see an x in f(x):

(f x g)(x) = f(g(x)) = f(1/x)

Substitute 1/x into f(x):

(f x g)(x) = f(g(x)) = f(1/x) = √(1/x + 2)

2. (g x f)(x):

We start by substituting f(x) into g(x) wherever we see an x in g(x):

(g x f)(x) = g(f(x)) = g(√(x + 2))

Substitute √(x + 2) into g(x):

(g x f)(x) = g(f(x)) = g(√(x + 2)) = 1/(√(x + 2))

Therefore, we have:

(f x g)(x) = √(1/x + 2)

(g x f)(x) = 1/(√(x + 2))

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By translation, the images of the vertices Q and S are Q'(x, y) = (- 1, 4) and S'(x, y) = (- 3, 2).

In this problem we find the representation of a parallelogram, which is formed by four vertices. The images of the vertices can be found by means of translation, whose formula is introduced below:

C'(x, y) = C(x, y) + T(x, y)

Where:

If we know that Q(x, y) = (4, 1), S(x, y) = (2, - 1) and T(x, y) = (- 5, 3), then the images of the points are:

Q'(x, y) = (4, 1) + (- 5, 3)

Q'(x, y) = (- 1, 4)

S'(x, y) = (2, - 1) + (- 5, 3)

S'(x, y) = (- 3, 2)

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The volume of the solid obtained by rotating the region enclosed by the graphs of y = 18 - x, y = 3x - 6, and x = 0 about the y-axis is 288π cubic units.

To find the volume of the solid obtained by rotating the region enclosed by the given graphs about the y-axis, we can use the method of cylindrical shells.

First, let's sketch the region to visualize it better.

The region is enclosed by the graphs of y = 18 - x, y = 3x - 6, and x = 0.

Let's find the intersection points of these curves by setting them equal to each other:

18 - x = 3x - 6

Simplifying the equation, we have:

4x = 24

x = 6

So, the intersection point is (6, 12).

Now, we can integrate to find the volume of the solid.

The radius of each cylindrical shell is the distance from the y-axis to the curve y = 18 - x.

This can be expressed as x.

The height of each cylindrical shell is the difference between the two curves, which is (18 - x) - (3x - 6).

The volume of each cylindrical shell is given by the formula:

V = 2πrhΔx, where r is the radius, h is the height, and Δx is the width of each shell.

Integrating from x = 0 to x = 6, we can find the total volume:

V = ∫[0,6] 2πx[(18 - x) - (3x - 6)] dx

V = ∫[0,6] 2πx(24 - 4x) dx

V = 2π ∫[0,6] (24x - 4x²) dx

V = 2π [12x² - (4/3)x³] | [0,6]

V = 2π [(12(6)² - (4/3)(6)³) - (12(0)^2 - (4/3)(0)^3)]

V = 2π [(12(36) - (4/3)(216)) - (0 - 0)]

V = 2π [(432 - 288) - (0 - 0)]

V = 2π (432 - 288)

V = 2π (144)

V = 288π

Therefore, the volume of the solid obtained by rotating the region enclosed by the graphs of y = 18 - x, y = 3x - 6, and x = 0 about the y-axis is 288π cubic units.

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Answer: -3 and -17

Step-by-step explanation:

     When completing the square we add and subtract [tex]\frac{b}{2} ^2[/tex] in the form ax² + bx + c.

[tex]\frac{b}{2} ^2 = \frac{-6}{2} ^2=(-3)^2=9[/tex]

x² - 6x - 8 = (x - __)² - __

(x² - 6x) - 8 = (x - __)² - __

(x² - 6x + 9) - 8 - 9 = (x - __)² - __

(x - 3)² - 17 = (x - __)² - __

     The blanks are 3 and 17.

The surface area of the sphere is 98 yd².

To find the surface area of a sphere, we can use the formula:

Surface Area = 4πr²

Given that the radius, r, of the sphere is 7/3.14 yd, we can substitute this value into the formula:

Surface Area = 4 x 3.14 x (7/3.14)²

= 4 x 3.14 x 49/9.86

= 4 x 49/2

= 98 yd²

Therefore, the surface area of the sphere is 98 yd².

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The angle measures of the numbered angles from <1- 8 would be listed below as follows:

<1=147°

<2= 33°

<3= 147°

<4=33°

<5=33°

<6=147°

<7=33°

<8=147°

When two parallel lines a crossed by a transverse line then the following occurs:

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Answer:

Therefore, the volume of the diversion tunnel is approximately 9,839,916,800 cubic feet and the surface area is approximately 1,000,530.9 square feet.

Step-by-step explanation:

To find the volume and surface area of a diversion tunnel, we can use the formulas for the volume and lateral surface area of a cylinder.

The volume of a cylinder is given by the formula:

V = πr^2h

Where:

V is the volume,

π is a mathematical constant approximately equal to 3.14159,

r is the radius of the cylinder, and

h is the height (or length) of the cylinder.

Substituting the given values:

r = 56 feet

h = 4,000 feet

V = π(56^2)(4,000)

V ≈ 3.14159 * 56^2 * 4,000

Calculating the volume:

V ≈ 9,839,916,800 cubic feet

The surface area of the lateral (curved) part of a cylinder is given by the formula:

A = 2πrh

Where:

A is the surface area,

π is a mathematical constant approximately equal to 3.14159,

r is the radius of the cylinder, and

h is the height (or length) of the cylinder.

Substituting the given values:

r = 56 feet

h = 4,000 feet

A = 2π(56)(4,000)

A ≈ 2 * 3.14159 * 56 * 4,000

Calculating the surface area:

A ≈ 1,000,530.9 square feet

Therefore, the volume of the diversion tunnel is approximately 9,839,916,800 cubic feet and the surface area is approximately 1,000,530.9 square feet.

The length AC in the kite is 8.7 cm.

A kite is a quadrilateral that has two pairs of consecutive equal sides and

perpendicular diagonals. Therefore, let's find the length AC in the kite.

Hence, using Pythagoras's theorem, let's find CE.

Therefore,

7² - 4² = CE²

CE = √49 - 16

CE = √33

CE = √33

Let's find AE as follows:

5²- 4² = AE²

AE = √25 - 16

AE = √9

AE = 3 units

Therefore,

AC = √33 + 3

AC = 5.74456264654 + 3

AC = 8.74456264654

AC = 8.7 units

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The dimensions (length and breadth) of the box are 10r x 8r.

We are given that;

π = 3,142

Number of tins=4,5

Now,

To calculate the area of sheet metal needed to make a soup tin, we can use the formula for surface area of a cylinder which is given by:

Surface Area = 2πrh + 2πr^2

where r is the radius of the cylinder and h is the height of the cylinder.

Using the given values, we can calculate the surface area of the soup tin as follows:

Surface Area = 2π(4.5)(8) + 2π(4.5)^2 Surface Area = 226.08 cm^2

To calculate the total surface area of the label, we can use the formula for surface area of a cylinder which is given by:

Surface Area = 2πrh

where r is the radius of the cylinder and h is the height of the cylinder.

Using the given values, we can calculate the surface area of the label as follows:

Surface Area = 2π(4.5)(8) Surface Area = 226.08 cm^2

To find out the dimensions (length and breadth) of the box in which tins are packed, we can use the given information that 4 tins fit in the width of the box and 5 tins fit in the length of the box. Let’s assume that each tin has a diameter of d cm.

4d = width of box 5d = length of box

We know that diameter (d) = 2r where r is radius.

So, width of box = 4d = 8r length of box = 5d = 10r

Therefore, by the area the answer will be 10r x 8r.

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Answer:

  15.  f(-2) = 2

  17.  f(x) = 1 for x = ±1.7

Step-by-step explanation:

You want various values of the function and its inverse relation for f(x)=x²-2.

The value of f(x) is found by locating the value x on the x-axis and following the vertical line until it intersects the graph. Find the y-coordinate of that point.

The value of x for f(x) = k is found by locating k on the y-axis and following the horizontal line to the points of intersection with the graph. The x-coordinates of the points are the values of interest. Interpolation is often required.

The graph intersects the vertical line at x=-2 where y = 2.

  f(-2) = 2

The horizontal line at y=1 intersects the graph in two places, located symmetrically about the y-axis. The leftmost point is approximately (-1.7, 1). The rightmost point is approximately (1.7, 1).

  x ≈ -1.7 or +1.7

__

Additional comment

The instructions are to use the figure to answer the question. We interpret that to mean that you are to read the answers from the graph.

You can also use the figure to determine the equation for the graph (part of our problem statement, above). Then you can find the solutions by using the equation.

  f(x) = 1

  x² -2 = 1

  x² = 3

  x = ±√3 ≈ ±1.732 . . . . the values for problem 17

<95141404393>

Answer: Pretty sure it should be 2.

Step-by-step explanation:

maybe -2 but i dont think so

Hello !

Answer:

[tex]\boxed{\sf V_{hemisphere}=144\pi\ mm^3}[/tex]

Step-by-step explanation:

The volume of a sphere is given by the following formula : [tex]\sf V_{sphere}=\frac{4}{3}\pi r^3[/tex] where r is the radius.

Moreover, we know that the volume of a hemisphere is half the volume of a sphere : [tex]\sf V_{hemisphere}=\frac{1}{2} V_{sphere}[/tex]

We obtain : [tex]\sf V_{hemisphere}=\frac{2}{3}\pi r^3[/tex]

Given :

[tex]\sf r=\frac{1}{2} d=\frac{12}{2} \\\underline{\sf r=6mm}[/tex]

Let's substitue r with it value in the previous formula :

[tex]\sf V_{hemisphere}=\frac{2}{3} \pi\times 6^3\\\boxed{\sf V_{hemisphere}=144\pi\ mm^3}[/tex]

Have a nice day ;)

Answer:

  0.90

Step-by-step explanation:

You want the probability of either event A or event B given the Venn diagram shown.

The probability of an event shown in the diagram is the ratio of counts for that event to the total of all counts in the diagram. That total is 50.

The number of counts that are not part of either event is shown as 5.

  P(A or B) = 1 - P(not (A or B)) = 1 - 5/50

  P(A or B) = 0.90

__

Additional comment

Using the given formula, ...

  P(A or B) = (25+5)/50 +(15 +5)/50 -5/50 = (25 +15 +5)/50 = 45/50

  P(A or B) = 0.90

<95141404393>

Answer:

x = 8

Step-by-step explanation:

Intersecting tangent and secant theorem:

If a tangent and a secant are drawn to the circle from a point from outside, the square of the measure of the tangent is equal to the product of the measures of the secant segment and its external secant segment.

         x² = (4+12)*4

         x² = 16 * 4

         x² = 64

        x = √64

         x = 8

Answer:

Step-by-step explanation:

To solve this problem, we can use the following formula:

(quantity of tea 1 x price of tea 1) + (quantity of tea 2 x price of tea 2) = total quantity x price of mixture

Let x be the number of pounds of black tea that the store owner needs to mix with the oolong tea.

We know that:

The store owner has 35 pounds of oolong tea that sells for $2.40 per pound.

The store owner wants to sell the final mixture for $2.10 per pound.

The black tea is worth $1.80 per pound.

Using the formula above, we can write:

(35 x 2.40) + (x x 1.80) = (35 + x) x 2.10

Simplifying this equation, we get:

84 + 1.8x = 73.5 + 2.1x

0.3x = 10.5

x = 35

Therefore, the store owner needs to mix 35 pounds of black tea with the oolong tea.

I hope this helps! Let me know if you have any other questions.

Answer:

Step-by-step explanation:

Let's assume the store owner needs to mix x pounds of black tea with the 35 pounds of oolong tea.

The cost of the oolong tea is $2.40 per pound, so the total cost of the oolong tea is:

Cost of oolong tea = 35 pounds × $2.40/pound = $84

The cost of the black tea is $1.80 per pound, and the final mixture needs to be sold for $2.10 per pound. To achieve an average price of $2.10 per pound, the total cost of the mixture should be:

Total cost of mixture = (35 + x) pounds × $2.10/pound = $73.5 + $2.10x

Since the cost of the mixture should equal the sum of the costs of the oolong and black teas, we can set up the equation:

$73.5 + $2.10x = $84

Now, let's solve for x to find the amount of black tea needed:

$2.10x = $84 - $73.5

$2.10x = $10.5

x = $10.5 / $2.10

x ≈ 5

Therefore, the store owner needs to mix approximately 5 pounds of black tea with the 35 pounds of oolong tea in order to sell the final mixture for $2.10 per pound.

The perimeter of the trapezoid is 106 meters.

The area of the trapezoid is 1360 square meters.

To calculate the perimeter and area of an isosceles trapezoid, we need to use the given measurements:

The length of the minor base (34 m), the height (20 m), and the length of the oblique side (29 m).

First, let's calculate the length of the major base (the other parallel side). In an isosceles trapezoid, the major base and minor base have the same length.

So, the length of the major base is also 34 m.

The perimeter of a trapezoid is the sum of all its sides. In this case, the perimeter can be calculated as follows:

Perimeter = length of minor base + length of major base + 2 × length of oblique side

Perimeter = 34 m + 34 m + 2 × 29 m

Perimeter = 34 m + 34 m + 58 m

Perimeter = 106 m

To calculate the area of the trapezoid, we can use the formula:

Area = (sum of the lengths of the bases) × height / 2

Area = (34 m + 34 m) × 20 m / 2

Area = 68 m × 20 m / 2

Area = 1360 m²

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The expression √(x²y²)  when simplified is i. xy

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

√(x²y²)

When the expression is expanded, we have

√(x²y²) = √(x² * √(y²)

Evaluae the exponents in the expression

So, we have

√(x²y²) = x * y

Evaluae the products in the expression

So, we have

√(x²y²) = xy

Hence, the expression when simplified is i. xy

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Answer:f(x) = (x-10)^2-49

f(x) = (x-10+7)(x-10-7)

f(x) = (x-3)(x-17)

The zeros of the function are 3 and 17.

Step-by-step explanation:

Answer:

15 °C

Step-by-step explanation:

°C = (°F - 32) * (5/9)

Given that the initial temperature was 77 °F and it dropped by 10 °C, we can calculate the final temperature.

Initial temperature: 77 °F

Converting to Celsius:

°C = (77 - 32) * (5/9)

°C ≈ 25

The temperature dropped by 10 °C, so the final temperature is:

Final temperature = Initial temperature - Temperature drop

Final temperature ≈ 25 - 10 = 15 °C

Therefore, the temperature after the storm was approximately 15 °C.

Given statement solution is :- 60% of the pupils in grade 7 at Mpenzeni Primary School Pass Rate the final examination in 2015.

To find the percentage of pupils who passed the final examination, you can use the following formula:

Percentage = (Number of pupils passed / Total number of pupils) * 100

Given that 90 pupils passed the final examination out of a total of 150 pupils, we can substitute these values into the formula:

Percentage = (90 / 150) * 100

Percentage = 0.6 * 100

Percentage = 60%

Therefore, 60% of the pupils in grade 7 at Mpenzeni Primary School Pass Rate the final examination in 2015.

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Check the picture below.

[tex]\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ c^2=a^2+o^2\implies c=\sqrt{a^2 + o^2} \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{x}\\ a=\stackrel{adjacent}{4}\\ o=\stackrel{opposite}{5.4} \end{cases} \\\\\\ x=\sqrt{ 4^2 + 5.4^2}\implies x=\sqrt{ 16 + 29.16 } \implies x=\sqrt{ 45.16 }\implies x\approx 6.7[/tex]

According to the figure of the trapezoid

angle XMZ = 115 degrees

angle XMY = 102 degrees

Angle YMZ = 78 degrees

The given figure is an isosceles trapezoid, hence

angle XMZ + angle XYZ = 180

angle XYZ = 39 + 26 = 65

angle XMZ + angle XYZ = 180

angle XMZ = 180 - 65

angle XMZ = 115 degrees

angle XMY

angle XMY =  180 - 39 - 39 = 180 - 78 = 102 degrees

Angle YMZ + angle XMY = 180 (angle on a straight line)

Angle YMZ = 180 - angle XMY = 180 - 102 = 78 degrees

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Answer:

17.5

Step-by-step explanation:

You can find the mean of a data set by adding all numbers in the data set together and dividing by the amount of numbers in the given data set.

In this case, your data set is:

15 , 16 , 17 , 23 , 11 , 19 , 20 , 15 , 18 , 22 , 15 , 19   (12 numbers).

Firstly, add all the numbers together: [tex]15 + 16 + 17 + 23 + 11 + 19 + 20 + 15 + 18 + 22 + 15 + 19 = 210[/tex]

Next, divide 210 (total sum) with the amount of terms in total (12):

[tex]\frac{(210)}{(12)} = 17.5[/tex]

17.5 is already in the tenth digit place value, and so you do not need to round.

17.5 is your answer.

~

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Answer:

156yd²

Step-by-step explanation:

area of parallelogram = base X vertical height

= 12 X 13

= 156yd²

Data set: 6, 8, 10, 12, 14, 16, 18

To draw a dot plot representing this data set, we can place a dot above the corresponding value on a number line. Here's the dot plot:

Value    |

---------------------------------

   6    |      o

---------------------------------

   8    |      o

---------------------------------

  10    |      o

---------------------------------

  12    |      o

---------------------------------

  14    |      o

---------------------------------

  16    |      o

---------------------------------

  18    |      o

---------------------------------

In the dot plot, each "o" represents a data point. The values are shown on the left side, and the dots are placed above their respective values on the number line.

Step-by-step explanation:

To find the area of the square all you need to do is to find the length of the hypotenuse of the triangles

this will help us find the length of the square if we are given the values of the shorter lengths as shown up

we can calculate the length of the hypotenuse by using the Pythagorean theorem

[tex] \sqrt{a^{2} + b^{2} } = c[/tex]

we are given the sides of the shorter lengths being 5 and 3 we can then substitute them into the formula

let us label the missing length the hypotenuse as x

[tex] \sqrt{ {3}^{2} + {5}^{2} } = x[/tex]

[tex] \sqrt{34} = x[/tex]

[tex]5.83[/tex]

we get that 5.83 rounded to two decimal places is the length of the hypotenuse

we also know that it is the length of the square so

5.83 × 5.83 = Area of Square

34cm² = Area of Square

In the given expression, 2x³-4x²+2x-x-3, there are five terms. An expression is a mathematical phrase that can be constructed using variables, constants, and operators.

It can include any mathematical operations such as addition, subtraction, multiplication, and division. Additionally, an expression can be made up of one or more terms.In the given expression, 2x³-4x²+2x-x-3, there are five terms. The terms are:2x³: This is the first term in the expression.

It is a cubic term, which means it has an exponent of 3.4x²: This is the second term in the expression. It is a quadratic term, which means it has an exponent of 2.2x: This is the third term in the expression. It is a linear term, which means it has an exponent of 1.-x:

This is the fourth term in the expression. It is also a linear term, but it has a negative coefficient.-3: This is the fifth term in the expression. It is a constant term since it does not have any variable attached to it.In summary, the given expression has five terms, which are 2x³, -4x², 2x, -x, and -3.

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