For f(x)=6x+8 and g(x)= 5x, find the following composite functions and state the domain of each (a) fog (b) gof (c) fof (d) gog (a) (fog)(x) = _____ (Simplify your answer.)

The inverse of f(x)=−8x+9 is y = (-x + 9)/8.

The inverse of a function is found by switching the x and y variables and solving for y. This is done to find the function that will undo the original function.

To find the inverse of f(x)=−8x+9, we will follow these steps:

1. Switch the x and y variables: x = -8y + 9
2. Solve for y by isolating the y variable on one side of the equation:
x - 9 = -8y
(x - 9)/-8 = y
3. Simplify the equation by dividing the numerator and denominator by -1:
y = (-x + 9)/8

Therefore, the inverse of f(x)=−8x+9 is y = (-x + 9)/8.

Note that we do not need to use parentheses around the denominator since it is a single term. We also do not need to use the term "inverse" in our answer since we are simply finding the inverse of the function. The terms "denominator" and "parentheses" are also not needed in our answer since they do not apply to this specific problem.

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The plane will end up flying 1.7 degrees off course.
The plane's speed relative to the ground will be 729.1 km/hr.

To determine the plane's speed and direction relative to the ground, we need to use vector addition to combine the velocity of the plane and the velocity of the wind.

First, let's find the components of the wind velocity. Since the wind is blowing from the southeast, its x-component is -30cos(45) = -21.2 km/hr and its y-component is -30sin(45) = -21.2 km/hr.

Next, let's find the components of the plane's velocity. Since the plane is heading north, its x-component is 0 km/hr and its y-component is 750 km/hr.

Now, we can add the components of the plane's velocity and the wind's velocity to find the plane's velocity relative to the ground:

x-component: 0 + (-21.2) = -21.2 km/hr

y-component: 750 + (-21.2) = 728.8 km/hr

Finally, we can use the Pythagorean theorem to find the magnitude of the plane's velocity relative to the ground:

speed = sqrt((-21.2)^2 + (728.8)^2) = 729.1 km/hr

And we can use the inverse tangent function to find the direction of the plane's velocity relative to the ground:

direction = tan^(-1)(-21.2/728.8) = -1.7 degrees

So, the plane will end up flying 1.7 degrees west of north, and its speed relative to the ground will be 729.1 km/hr.

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Shape A is Convex and Hexagon.

Shape B is Concave and Hexagon.

Shape C is Convex and Pentagon.

Shape D is Concave and Hexagon.

Shape E is Concave and Pentagon.

Shape F is Convex and Pentagon.

Polygons are closed figures which has at least three set of line segments joined together.The polygon with the least number of sides is a triangle.

As per the given data:

The shape of the figures is given.

The shapes can be classified as:

Concave, Convex, Hexagon, Pentagon.

Concave polygons are the one with alteast one of the vertices pointing inwards toward the shape.

Convex polygons are the one with all the vertices pointing outwards from the shape.

A Hexagon can be defined as a closed two-dimensional polygon with six sides.

A Pentagon can be defined as a closed two-dimensional polygon with five sides.

Consider the shape A:

It has 6 sides and all vertices pointing outwards.

Shape A is Convex and Hexagon.

Consider the shape B:

It has 6 sides and some vertices pointing inwards.

Shape B is Concave and Hexagon.

Consider the shape C:

It has 5 sides and all vertices pointing outwards.

Shape C is Convex and Pentagon.

Consider the shape D:

It has 6 sides and one vertice pointing inwards.

Shape D is Concave and Hexagon.

Consider the shape E:

It has 5 sides and one vertice pointing inwards.

Shape E is Concave and Pentagon.

Consider the shape F:

It has 5 sides and all vertices pointing outwards.

Shape F is Convex and Pentagon.

Hence, Shape A is Convex and Hexagon. Shape B is Concave and Hexagon. Shape C is Convex and Pentagon. Shape D is Concave and Hexagon. Shape E is Concave and Pentagon. Shape F is Convex and Pentagon.

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The inequality's solution set can be described by inspection as x <= 8.

Inequality is the unequal treatment of people based on factors such as race, gender, class, or other social characteristics. It is often seen as unfair and can lead to social and economic disparities.

This is because the inequality (x-8)^(6)<=0 is asking when the quantity (x-8) raised to the 6th power is less than or equal to zero.

Since any number raised to an even power will always be positive or zero, the only way for this inequality to be true is when (x-8) is equal to zero. This occurs when x = 8. Therefore, the solution set is x <= 8.

To summarize, the inequality's solution set is:
x <= 8

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Answer: As the two cylinders have the same height, the cylinder with the greater radius will have the greater volume. Therefore, the statement "The cylinder with radius has a greater volume than the cylinder with radius /2" is true.

Step-by-step explanation:

The values of the length and angle are;

AD = 22 units

m < ADC = 106 degrees

The properties of a kite are given as;

From the information given, we have that;

AB = 8x - 2

AD = 6x + 4

Equate the sides

8x - 2 = 6x + 4

collect like terms

2x = 6

x = 3

AD = 22 units

Also,

m < ABC = m < ADC

Substitute the values

12x + 10 = 15x - 14

collect like terms

-3x = -24x

x = 8

m < ADC = 106 degrees

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Answer: AD = 22 units

Step-by-step explanation:

m < ADC = 106 degrees

AB = 8x - 2

AD = 6x + 4

Equate any sides

8x - 2 = 6x + 4

Collect terms

2x = 6

x = 3

AD = 22 units

m < ABC = m < ADC

Substitute the values

12x + 10 = 15x - 14

Collect terms

-3x = -24x

x = 8

m < ADC = 106 degrees

Answer:

Step-by-step explanation:

[tex]\frac{-1}{12}[/tex]

Answer:

a

Step-by-step explanation:

- [tex]\frac{1}{4}[/tex] × [tex]\frac{2}{3}[/tex] × [tex]\frac{1}{2}[/tex] ( cancel the 2 on the numerator/ denominator of last 2 fractions )

= - [tex]\frac{1}{4}[/tex] × [tex]\frac{1}{3}[/tex] × 1

multiply values on numerators and values on denominators )

= - [tex]\frac{1(1)}{4(3)}[/tex] × 1

= - [tex]\frac{1}{12}[/tex]

The equation for the line that passes through the point (-1,4) and that is parallel to the line with the equation y=2 is y=4.

To find the equation for the line that passes through the point (-1,4) and that is parallel to the line with the equation y=2, we need to use the concept of slope. The slope of a line is the ratio of the vertical change to the horizontal change between any two points on the line.

The equation y=2 is a horizontal line, which means that its slope is 0. Since the line we are looking for is parallel to this line, its slope will also be 0.

Now that we know the slope, we can use the point-slope form of an equation to find the equation of the line. The point-slope form of an equation is [tex]y-y1=m(x-x1)[/tex], where m is the slope and [tex](x1,y1)[/tex] is a point on the line.

Plugging in the values we know, we get:

[tex]y-4=0(x-(-1))[/tex]

Simplifying the equation, we get:

[tex]y-4=0[/tex]

Adding 4 to both sides of the equation, we get:

[tex]y=4[/tex]

So the equation for the line that passes through the point (-1,4) and that is parallel to the line with the equation y=2 is [tex]y=4[/tex].

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The is no solution of the  equation  (1)/(x-1)-1=(x)/(x-1).

To solve for all values of x in the equation (1)/(x-1)-1=(x)/(x-1), we can follow these steps:

1. Multiply both sides of the equation by (x-1) to eliminate the denominators:
1 - (x-1) = x

2. Simplify the left side of the equation:
- x + 2 = x

3. Add x to both sides of the equation to isolate the variable on one side:
2 = 2x

4. Divide both sides of the equation by 2 to solve for x:
x = 1

Therefore, the solution for x is 1.

When we plug x = 1 back into the original equation, we get a denominator of 0, which is undefined. This means that there are actually no solutions for this equation.

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The probability that the distance between them is more than the radius of the circle is given as follows:

0.5 = 50%.

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes.

For the circle, we have that the radius is the distance between any point on the circumference of the circle, and the center.

The largest distance is the diameter, which is the distance between two points on the circumference of the circle, passing through the center.

The diameter is twice the radius, hence the probability is given as follows:

p = r/2r

p = 1/2

p = 0.5 = 50%.

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The intersection point of ℓ and Q is (1, 1, 2.5) is not in any of the option.

To find the intersection point of ℓ and Q, we need to find a point that lies on both the line and the plane. We can do this by finding the equation of the line and the equation of the plane, and then solving for the point where they intersect.

First, let's find the equation of the line ℓ. We can use the formula for a line passing through two points:

(x - x1) / (x2 - x1) = (y - y1) / (y2 - y1) = (z - z1) / (z2 - z1)

Plugging in the points (1, 1, 1) and (2, 0, 1), we get:

(x - 1) / (2 - 1) = (y - 1) / (0 - 1) = (z - 1) / (1 - 1)

Simplifying, we get:

x - 1 = -y + 1 = 0

So the equation of the line is x + y = 2.

Next, let's find the equation of the plane Q. We can use the formula for a plane passing through three points:

| x - x1  y - y1  z - z1 |
| x2 - x1  y2 - y1  z2 - z1 | = 0
| x3 - x1  y3 - y1  z3 - z1 |

Plugging in the points (0, 0, 0), (1, 2, 2), and (1, 0, 1), we get:

| x   y   z |
| 1   2   2 | = 0
| 1   0   1 |

Expanding the determinant, we get:

x(2 - 0) - y(2 - 1) + z(0 - 2) = 0

Simplifying, we get:

2x - y - 2z = 0

So the equation of the plane is 2x - y - 2z = 0.

Now we can solve for the intersection point of the line and the plane by substituting the equation of the line into the equation of the plane:

2(x + y) - y - 2z = 0

2x + 2y - y - 2z = 0

2x + y - 2z = 0

Since x + y = 2, we can substitute 2 for x + y:

2(2) + y - 2z = 0

4 + y - 2z = 0

y - 2z = -4

Now we can solve for y in terms of z:

y = 2z - 4

And substitute this back into the equation of the line:

x + (2z - 4) = 2

x = 2 - 2z + 4

x = 6 - 2z

Now we have two equations with two unknowns:

y = 2z - 4
x = 6 - 2z

We can solve for z by setting the two equations equal to each other:

2z - 4 = 6 - 2z

4z = 10

z = 2.5

And then solve for x and y:

y = 2(2.5) - 4 = 1
x = 6 - 2(2.5) = 1

So the intersection point of ℓ and Q is (1, 1, 2.5).

The correct answer is none of the options given.

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I think  it would be 56%

Answer:56.06%

Step-by-step explanation:

Divide 37 by 66 to get it in decimal form

37 ÷ 66 ≈0.5606

Then multiply the answer from the previous step by 100 to get an answer as %

0.5606 x 100 = 56.06%

The proof answer is correct by taking 56.06 % of 66 to get 37

(66 x 56.06) ÷ 100 ≈ 37

All of Four table shows the proportionality.

Proportionality refers to any relationship that always has the same ratio. For example, the amount of apples in a crop is proportionate to the number of trees in the orchard, with the proportionality ratio being the average number of apples per tree.

To the proportionality we have to find the rate change of each table

Table 1:

Rate of change

= (4-2)/ (4-0)

= 2/4

= 0.5

Again, (6-4)/ (8-4)

= 2/4

= 0.5

As, the rate of change is constant then the table shows the proportionality.

Table 2:

Rate of change

= (1-0)/ (2-0)

= 1/2

= 0.5

Again, = (2-1)/ (4-2)

= 1/2

= 0.5

As, the rate of change is constant then the table shows the proportionality.

Table 3:

Rate of change

= (3-1)/ 5-0)

= 2/5

= 0.4

Again, (5-3)/ (10-5)

= 2/ 5

= 0.4

As, the rate of change is constant then the table shows the proportionality.

Table 4:

Rate of change

= (7-3)/ (3-0)

= 4/3

Again, (11-7)/ (6-3)

= 4/3

As, the rate of change is constant then the table shows the proportionality.

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Answer:

It is not clear what you mean by "pre-image" in this context. However, based on the given information, we can say that the second triangle is a dilation of the first triangle.

A dilation is a transformation that changes the size of an object, but not its shape. In this case, the second triangle has the same shape as the first triangle, but its sides are scaled up by a factor of 8/3, which is greater than 1. Therefore, the second triangle is an enlargement (or a magnification) of the first triangle.

Answer: Your welcome!

Step-by-step explanation:

The transformation of the triangle is a reduction. This is because the side of the triangle that was 3 cm has been reduced to 8 cm, while the other two sides have stayed the same. This reduction has resulted in the triangle being smaller than the original triangle.

One possible set of values that would make the inequality true is:

g = 5

g = 0

g = -1

When we substitute these values into the inequality, we get:

4 + 5 ≥ 9 (true)

4 + 0 ≥ 9 (false)

4 + (-1) ≥ 9 (false)

Therefore, the values that make the inequality true are g = 5, g = 0, and g = -1.

The solution of the equation 1/2x² + 3/8x - 2 using completing the square method are: 1.66 or -2.41.

To solve the equation 1/2x² + 3/8x -2 using completing the square method, follow these steps:

Step 1: Move the constant term to the right-hand side

1/2x² + 3/8x = 2

Step 2: Multiply both sides by 2 to clear the fraction

x² + 3/4x = 4

Step 3: Add the square of half of the coefficient of x to both sides of the equation

x² + 3/4x + (3/8)² = 4 + (3/8)²

The left-hand side is now a perfect square, specifically (x + 3/8)².

Step 4: Simplify the right-hand side of the equation

x² + 3/4x + 9/64 = 256/64 + 9/64

x² + 3/4x + 9/64 = 265/64

Step 5: Take the square root of both sides

x + 3/8 = ±√(265)/8

Step 6: Solve for x

x = -3/8 ± √(265)/8

x = 1.66 or - 2.41

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Answer:

13,860 egyptian pounds

Answer:

Step-by-step explanation:

1 USD = 18.48 Egyptian pounds

∴ 750 USD = 750 × 18.48 Egyptian pounds

                  = 13860 Egyptian pounds

The sales price of the item after the 15% discount is $850.

The original price of the item is $1,000 and the discount rate is 15%. To find the amount of the sales price, we need to calculate the amount of the discount and subtract it from the original price.

Step 1: Calculate the amount of the discount by multiplying the original price by the discount rate.
Discount = Original Price x Discount Rate
Discount = $1,000 x 0.15
Discount = $150

Step 2: Subtract the amount of the discount from the original price to find the sales price.
Sales Price = Original Price - Discount
Sales Price = $1,000 - $150
Sales Price = $850

Therefore, the sales price of the item after the 15% discount is $850.

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The common tangent of the compound curve is parallel to its long chord. This means that the angle between the common tangent and the long chord is 0°. The long chord makes an angle of 18° with the shorter tangent and 12° with the longer tangent. We can use the law of sines to determine the length of the common tangent.

Let's call the length of the common tangent x, the length of the long chord L, the angle between the common tangent and the long chord θ, the angle between the long chord and the shorter tangent α, and the angle between the long chord and the longer tangent β.

Using the law of sines, we have:

x/sin(θ) = L/sin(α+β)

Substituting the given values, we have:

x/sin(0°) = 546/sin(18°+12°)

Simplifying the equation, we get:

x = 546*sin(0°)/sin(30°)

Since sin(0°) = 0 and sin(30°) = 0.5, we have:

x = 546*0/0.5

x = 0

Therefore, the length of the common tangent is 0m.

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The percent of each response are 20%, 30%, 15%, 20%, and 15%, respectively.

What is Percentage?

By dividing the value by the entire value and multiplying the result by 100, one may get the percentage. A figure or ratio stated as a fraction of 100 is called a percentage. Often, it is indicated with the percent symbol, "%".

To find the percent of each response, we need to divide the number of responses for each choice by the total number of responses, and then multiply by 100.

Let's assume the total number of responses received for the survey was 500.

The choices and number of responses received for each were:

100 people responded "Too expensive": (100 / 500) x 100% = 20%

150 people responded "Poor service quality": (150 / 500) x 100% = 30%

75 people responded "Too far away": (75 / 500) x 100% = 15%

100 people responded "Long wait times": (100 / 500) x 100% = 20%

75 people responded "Other": (75 / 500) x 100% = 15%

Therefore, the percent of each response are 20%, 30%, 15%, 20%, and 15%, respectively.

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The solution to the equation |9a+5|=68 is a = 7, -8.111. To solve the equation |9a+5|=68, we can use the property of absolute value that states that |x| = x or |x| = -x. This means that we can set up two equations to solve for a:

9a+5 = 68 or 9a+5 = -68

Now we can solve each equation separately:

9a+5 = 68
9a = 63
a = 7

9a+5 = -68
9a = -73
a = -8.111

So the solutions are a = 7 and a = -8.111. We can write these solutions separated by a comma as follows:

a = 7, -8.111

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The multiplied the binomials of

Multiplying binomials involves using the distributive property to multiply each term in one binomial by each term in the other binomial.

(i) 2a-9 and 3a+4
(2a-9)(3a+4) = 2a(3a) + 2a(4) - 9(3a) - 9(4) = 6a²+ 8a - 27a - 36 = 6a² - 19a - 36

(ii) x-2y and 2x-y
(x-2y)(2x-y) = x(2x) + x(-y) - 2y(2x) - 2y(-y) = 2x² - xy - 4xy + 2y² = 2x^(2) - 5xy + 2y²

(iii) kl+lm and k-l
(kl+lm)(k-l) = kl(k) + kl(-l) + lm(k) + lm(-l) = k^(2)l - kl²+ lmk - l²m = k²l - l²m - kl² + lmk

(iv) m²-n² and m+n
(m²-n²)(m+n) = m²(m) + m²(n) - n²(m) - n²(n) = m³ + m²n - mn² - n²

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Answer:

18cm^2

Step-by-step explanation:

3×2=6cm^2

2×6=12cm^2

6+12=18cm^2

Therefore , the solution of the given problem of function comes out to be Nolan dropped the ball from a height of 12 units at the beginning.

The study of mathematics includes numbers, symbols, and their parts, as well as anatomy, building, and both actual and hypothetical geographic locations. The relationships between different components, each of which has a corresponding result, are described by a function. A function is made up of a variable of distinct components that, when put together, produce specific results for each input.

Here,

Assume that h represents the original height at which Nolan threw the ball. The object bounces once and rises to a height of 4, so after the bounce it has a height of h + 4.

=> h = k f(1) (1)

where k is a constant that denotes how much energy the object retains after each bounce.

=> h = k(4) (4)

The knowledge that the ball returns to a height of 4 on the first bounce must be used to determine the value of k:

=> 4 = k f(1) (1)

=> 4 = k (4/3)

=> k = 3

When we put this number of k back into the equation as a replacement for h, we get:

=> h = k(4) = 3(4) = 12

Nolan dropped the ball from a height of 12 units at the beginning.

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Vertical Line (1, 0, 0, 10)

Each augmented matrix has 4 basic variables. The augmented matrix above is written as
\[ \left[\begin{array}{rrrr|r}1 & 0 & 0 & 10 & -9 \\ 0 & 1 & 0 & 0 & 4 \\ 0 & 0 & 1 & 0 & -6\end{array}\right] \]
where the 4 basic variables are the columns of the matrix before the vertical line (1, 0, 0, 10).

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For 175÷2, the quotient is 87 and remainder is 1

When dividing 175 by 2, we can use long division to find the quotient and remainder.

First, we will divide 2 into the first digit, 1. Since 2 does not go into 1, we will move to the next digit, 7. 2 goes into 7 three times, so we will write 3 above the 7.

Next, we will multiply 3 by 2 to get 6, and subtract this from 7 to get a remainder of 1.

We will then bring down the next digit, 5, and divide 2 into 15. 2 goes into 15 seven times, so we will write 7 above the 5.

Finally, we will multiply 7 by 2 to get 14, and subtract this from 15 to get a remainder of 1.

Therefore, the quotient is 87 and the remainder is 1.

The final answer is:

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The equations that represent functions are:

  1) 2x + 3y = 10

  2) 3y = 18

Functions are relations which give a particular output for each input.  The characteristic that every input is associated with exactly one output defines a function as a relationship between a set of inputs and a set of allowable outputs. Specific input is supplied to a function in order to produce a specific result. To determine if a curve is a function or not, apply the vertical line test. Any curve that intersects a vertical line at more than one point is not a function.

Let us look into each equation.

1)  2x + 3y = 10

Here for each input of x, we get only one output y.

So this is a function.

2)  4x = 16

 This is not a function because there can be multiple values of y for a single value of x.

3) 2x − 3 = 14

 This is also not a function because there can be multiple values of y for a single value of x.

4)  3y = 18

 This is a function because there is only one value of y for exactly one value of x. Also, considering the vertical line test, the curve is a straight horizontal line which intersects with a given vertical line only once. So it is a function.

5)14.6 = 2x

  This is also not a function because there can be multiple values of y for a single value of x.

Therefore the equations that represent functions are:

  1) 2x + 3y = 10

  2) 3y = 18

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The distance between London and Cardiff is approximately 241.4 kilometers.

A conversion factor is a ratio in mathematics that is used to change a quantity's unit of measurement. We may represent the same quantity in many units thanks to this link between the two units of measurement. For instance, 1 mile equals 1.60934 kilometres, thus we may multiply the number of miles by this conversion ratio to find the corresponding distance in kilometres. In science, engineering, and daily life, conversion factors are frequently employed to translate units of length, volume,

We know that,

1 mile = 1.60934 kilometers

Thus,

150 miles x 1.60934 kilometers/mile = 241.4 kilometers

Hence, the distance between London and Cardiff is approximately 241.4 kilometers.

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