Use f(x) = 1
2
x and f -1(x) = 2x to solve the problems.

The new graph after the given transformations would have an equation; y = -f (x + 2).

It follows from the task content that the pre-image graph; y = f (x) is to be translated 2 units to the left and afterwards reflected across the X axis.

First, when a function, f (x) is translated k units to the left, the resulting function is; f (x + k).

Hence, when the graph is translated w units to the left, the resulting function is; y = f (x + 2).

Additionally, when a function, f (x) is reflected across the x-axis, the resulting function is; -f (x).

Ultimately, the resulting graph upon reflection over the x-axis is; y = -f (x + 2).

Complete question: The graph is reflected over the x-axis.

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The simplest form of monomial rational expressions are

17. 4x,         18. xy²,        19. 2xy      

20. 3xy,      21. 3x²y⁶,    22. 13x⁶ y

23. 8x⁶y²,   24. 19x⁹y⁵,   25. 5y

26. -5x¹¹y⁴,  27. -8x⁵y³.

A polynomial with only one term is called a monomial. An algebraic expression known as a "monomial" has a single term but can also include several variables and a higher degree.

Given Monomial Rational expressions can be solved as follows

17.  [tex]\frac{4x^{2} y^{3} }{xy^{2} } = \frac{4 \times x \times x \times y \times y \times}{x \times y\times y} = 4\times x[/tex]  

=>  [tex]\frac{4x^{2} y^{3} }{xy^{2} } = 4x[/tex]  

18.  [tex]\frac{2x^{4}y^{3} }{2x^{3} y } = \frac{2 x^{3} \times x\times y^{2} \times y }{2x^{3} y}[/tex]  

=>  [tex]\frac{2x^{4}y^{3} }{2x^{3} y } = x y^{2}[/tex]    

19.  [tex]\frac{8x^{2} y^{2} }{4xy} = \frac{2xy (4xy)}{4xy}[/tex]  

=>  [tex]\frac{8x^{2} y^{2} }{4xy} = 2xy[/tex]  

20.  [tex]\frac{6x^{3} y^{4} }{2x^{2} y^{3} } = \frac{3xy (2x^{2} y^{3} )}{2x^{2} y^{3} }[/tex]  

=>  [tex]\frac{6x^{3} y^{4} }{2x^{2} y^{3} } = 3xy[/tex]  

21.  [tex]\frac{12x^{6} y^{8} }{4x^{4} y^{2} } = \frac{3x^{2} y^{6} (4x^{4} y^{2})} {4x^{4} y^{2} }[/tex]

=> [tex]\frac{12x^{6} y^{8} }{4x^{4} y^{2} } = 3x^{2} y^{6}[/tex]  

22. [tex]\frac{26x^{9} y^{5} }{2x^{3} y^{4} } = \frac{13x^{6} y (2x^{3} y^{4})}{2x^{3} y^{4}}[/tex]  

=>  [tex]\frac{26x^{9} y^{5} }{2x^{3} y^{4} } = 13x^{6} y[/tex]  

23.  [tex]\frac{80x^{12}y^{9} }{10 x^{6}y^{7} } = \frac{8x^{6}y^{2}(10 x^{6}y^{7})}{10 x^{6}y^{7} }[/tex]  

=>  [tex]\frac{80x^{12}y^{9} }{10 x^{6}y^{7} } = 8x^{6}y^{2}[/tex]  

24.  [tex]\frac{95x^{18}y^{7} }{5x^{9}y^{2} } = \frac{19x^{9}y^{5}(5x^{9}y^{2}) }{5x^{9}y^{2} }[/tex]  

=>  [tex]\frac{95x^{18}y^{7} }{5x^{9}y^{2} } = 19x^{9}y^{5}[/tex]    

25.  [tex]\frac{200x^{3}y^{8} }{40x^{3}y^{7} } = \frac{5y (40x^{3}y^{7}) }{40x^{3}y^{7}}[/tex]  

=>   [tex]\frac{200x^{3}y^{8} }{40x^{3}y^{7} } = 5y[/tex]  

26.  [tex]\frac{- 15x^{17} y^{13} }{3x^{6} y^{9} } = \frac{-5x^{11}y^{4} (3x^{6} y^{9} )}{3x^{6} y^{9} }[/tex]  

=>  [tex]\frac{- 15x^{17} y^{13} }{3x^{6} y^{9} } = -5x^{11}y^{4}[/tex]  

27.  [tex]\frac{-64x^{8}y^{10} }{8x^{3}y^{7} } = \frac{ -8x^{5}y^{3} (8x^{3}y^{7} )}{8x^{3}y^{7} }[/tex]  

=> [tex]\frac{-64x^{8}y^{10} }{8x^{3}y^{7} } = -8x^{5}y^{3}[/tex]  

Therefore,

The simplest form of monomial rational expressions are

17. 4x,         18. xy²,        19. 2xy      

20. 3xy,      21. 3x²y⁶,    22. 13x⁶ y

23. 8x⁶y²,   24. 19x⁹y⁵,   25. 5y

26. -5x¹¹y⁴,  27. -8x⁵y³.

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On solving the provided question, we can say that form an equation = area of the figure = x = 1/2*9*9 + 6*18 = 40.5 + 48 = 88.5

A mathematical equation is a formula that joins two statements and uses the equal symbol (=) to indicate equality. A mathematical statement that establishes the equality of two mathematical expressions is known as an equation in algebra. For instance, in the equation 3x + 5 = 14, the equal sign places the variables 3x + 5 and 14 apart. The relationship between the two sentences on either side of a letter is described by a mathematical formula. Often, there is only one variable, which also serves as the symbol. for instance, 2x – 4 = 2.

here,

to find the area

we have to form an equation =

area of the figure = x = 1/2*9*9 + 6*18 = 40.5 + 48 = 88.5

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The relationship between x and y in the equation y = x + 6. the relationship is Linear because the value of y is can be represented in a straight line

An equation consists of numbers and variables linked together by mathematical operations to form an expression.

A linear equation is in the form:

y = mx + b

Where m is the rate of change and b is the initial value

Given the equation:

y = x + 6

This is a linear equation.

The slope (rate of change) is 1 and the initial value (y intercept) is 6

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The value of the composite function h(1) is 24

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

f(x) = -5x, g(x) = x + 3 and

h(x) = -2f (x + 2) - 2g(x - 1)

The above are individual functions

This means that

h(x) = -2(-5(x + 2)) - 2(x + 3 - 1)

For h(1), we have

h(x) = -2(-5(1 + 2)) - 2(1 + 3 - 1)

Evaluate

h(x) = 24

Hence, the value of the composite function is 24

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Find 10% of 50 by dividing 50 by 10. Then multiply the result by 4 is how to determine 40% of 50 which is denoted as option A.

This is referred to as the process of splitting a number or an amount into equal parts.

40% of 50 = 40/100 × 50 = 2000/100 = 20

Another method is finding the 10% of 50 by dividing 50 by 10 which will be 50/10 = 5. Then multiplying the result by 4 to get 20 which is why option A was chosen as the correct choice.

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The image of point Q under a translation by 4 units to the right and 1 unit up is Q'(5, 5).

Two-dimensional figures can be transformed mathematically in order to travel about a plane or coordinate system.

Dilation: The preimage is scaled up or down to create the image.

Reflection: The picture is a preimage that has been reversed.

Rotation: Around a given point, the preimage is rotated to create the final image.

Translation: The image is translated and moved a fixed amount from the preimage.

Given, A point Q with coordinates (1, 4).

Now, The translation of point Q  4 units to the right and 1 unit up would be,

Q'(1 + 4, 4 + 1).

= Q'(5, 5).

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The height of the roof is 21 inches.

Any triangle with any two sides that have the same length is known as an isosceles triangle. An isosceles triangle has two equal-sized angles that are opposite from one other and have equal sides. In other terms, an isosceles triangle is a triangle with two congurrent sides.  

Here we have,

Tony is building a doghouse, and the front view of the roof is an isosceles triangle.  

As we consider, the front view as an isosceles triangle

Side of the triangle = 29 inches

Base of the triangle = 40 inches

When we draw a line along the height of the triangle, it will divide the base equally and forms two right-angle triangles.

Let 'x' be the height of the triangle  

If we apply the Pythagorean theorem,

=> 29² = 20² + x²  

=> 841 = 400 + x²

=> x² = 441

=> x² = (21)²    

Hight of the triangle = 21

Therefore,

The height of the roof is 21 inches.

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Answer: 1.5 dollars

Step-by-step explanation: 24 times 1.5 is 36

Answer: 3/2 or 1.5 dollars per cupcake

Step-by-step explanation:

Use ratios:

$36 : 24 cupcakes

Divide by 24 on each side:

$36/24 : 1 cupcake

36/24 = 3/2 or 1.5 dollars per cupcake

The quadratic equation represented by the table is

y = x² + 6x - 9.

A function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

The domain of a function f(x) is the set of all values for which the function is defined, and the range of the function is the set of all values that function takes.

Given is a quadratic function in tabular form as -

(x)   :   1     2   3   4

f(x)  :   -2  -5  -6  -5

The general form of a quadratic function is -

y = ax² + bx + c

For the point (1, - 2), we can write -

- 2 = a + b + c

For the point (2, - 5), we can write -

- 5 = 4a + 2b + c

For the point (3, - 6), we can write -

- 6 = 9a + 3b + c

Now, let's assume that -

a = x

b = y

c = z

Now, we can write the equations as -

- 2 = x + y + z             ... (1)

- 5 = 4x + 2y + z          ... (2)

- 6 = 9x + 3y + z           ... (3)

Subtracting Eq(1) from Eq(2) -

4x + 2y + z - (x + y + z) = - 5 + 2

4x + 2y + z - x - y - z = - 3

3x - y = - 3                       ... (4)

Subtracting Eq(2) from Eq(3) -

9x + 3y + z - (4x + 2y + z) = - 6 + 5

5x - y = - 1                          ... (5)

From the graph, we get -

x = 1

y = 6

Then, we can write {z} as -

- 2 = x + y + z

z = - 2 - x - y

z = - 2 - 1 - 6

z = - 9

So, we get -

x = 1

y = 6

z = - 9

Now, we can write -

a = x = 1

b = y = 6

c = z = - 9

So, we will get the quadratic equation as -

y = x² + 6x - 9

Therefore, the quadratic equation represented by the table is

y = x² + 6x - 9.

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Answer:

[tex]\frac{281}{6}[/tex] or 46 [tex]\frac{5}{6}[/tex]

Step-by-step explanation:

First lets find out the parentheses. ( The first thing we always do ):

89+9=98 ( Lets keep this aside )

Now lets find out what is : [tex]12^{2}[/tex] =

12 x 12 = 144.

Now lets add 144+98 = 242

Now subtract 78 from 242 =

164

Now lets add 398 =

562.

Now divide it by 12.

[tex]\frac{281}{6}[/tex] or 46 [tex]\frac{5}{6}[/tex]

The number of terms in the sequence is 10.

It is a sequence where the difference between each consecutive term is the same.

Example:

2, 4, 6, 8, 10 is an arithmetic sequence.

We have,

First term = -10

Last term = 26

Sum of all the terms = 80

We need to find how many terms are in the sequence.

Now,

Sum of n terms of an arithmetic sequence = n/2 x (First term + Last term)

So,

80 = (1/2)n (-10 + 26)

2 x 80 = n x 16

n = 10

Thus,

The value of n is 10.

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A thermometer's accurate reading of the air's average temperature for a specific time frame, typically a day, a month, or a year.

The temperature for a month as a whole is known as the mean monthly temperature. The thermometer used to record it is well exposed. The average daily temperature for the month is added up and divided by the total number of days in the month to determine the mean monthly temperature.

By adding up the daily mean temperatures for each day of the month, multiplying that total by the number of days in the month, and then subtracting that result, you can find the mean monthly temperature. Add up the 31 mean daily temperatures for January, for instance, and divide the result by 31.

The average air temperature over a specific time period, typically a day, a month, or a year, as measured by an accurately exposed thermometer. In climatological tables, the average temperature is typically determined for each.

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25 hours, 12 dollars an hour.

How can we set this up?

25 hours, 12 dollars per hour.  So 12 dollars per each hour, adding up to 25 hours in total.

12 (1 hour), 12 (1 hour), 12 (1 hour)..

Or you could do 12 x 25 to find it, just to make things a little more simple. 25 x 12 = 50
             250
= $300

The histogram's graph of her number of handkerchiefs, y, in relation to the length of weeks since she last used one, x, is accurate.

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The family buys around 19 cases of sparkling water in 30 days

lnequality is relationship between two expressions or values that are not equal to each other.

Let the total number of sparkling cans of water used in a day be =x

As mentioned, the family uses more than 15 cans each day so inequality becomes , ×> 15

As they buy cases of water with 24 cans in each case. So less than 1 case is used in a day.

Number of cans used in a day is more than 15, so approx number of cans used in 30 days will be = 30 x 50 =450

As each case contains 24 cans, so the number of cases that will contain 450 cans will be,  450÷24 =18.75 cases. Rounding this off to nearest whole number, we get 19 cases.

Hence, the family buys around 19 cases of sparkling water in 30 days

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The common difference will be equal to 3.

The sequence in which every next number is the addition of the constant quantity in the series is termed the arithmetic progression. A series of numbers called an arithmetic progression or arithmetic sequence has a constant difference between the terms.

Given that the data for the arithmetic sequence is a₁= -10, an = 26, Sn = 80, and the total number is n = 13.

The common difference will be calculated as,

an = a₁ + d ( n - 1 )

26 = -10 + d ( 13 - 1 )

d = 36 / 12

d = 3

Hence, for the arithmetic progression, the common difference is 3.

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Answer:

$7.50

Step-by-step explanation:

The price of a hot dog today is $0.75 * (1 + 220%) = $2.38.

In another 45 years, the price will be $2.38 * (1 + 220%) = $7.50.

Answer: only y=3x+4 is a function

Step-by-step explanation:

vertical line test. basically a function has to have one output (y) for every input (x)

The graph of the trigonometry function g(x) = 4 cos πx is plotted and attached,

The graph is made by picking some x values say 0, 0.5, 1, 1.5, 2 .... and solve for the output y.

For x = 0, y = 4 cos π * 0 = 4

For x = 0.5, y = 4 cos π * 0.5 = 0

For x = 1, y = 4 cos π * 1 = -4

For x = 1.5, y = 4 cos π * 1.5 = 0

For x = 2, y = 4 cos π * 2 = 4

Table of value

x     y

0     4

0.5  0

1      -4

1.5    0

2      4

The graph is plotted by tracing each x and y value and joining the intercepts to form a curve

It can be deduced that the amplitude of the graph is 4 and it completes a revolution in 2 units

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The number of years after which the population of North Dakota equals the population of South Dakota is 150.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

North Dakota:

Population in 2012 = 0.3 million

Growth rate per year = 0.017 million

The population after x years.

= 0.3 + 0.017x

South Dakota:

Population in 2012 = 0.9 million

Growth rate per year = 0.013 million

The population after x years.

= 0.9 + 0.013x

Now,

The number of years after which the population is equal.

0.3 + 0.017x = 0.9 + 0.013x

Solve for x.

0.017x - 0.013x = 0.9 - 0.3

0.004x = 0.6

x = 0.6/0.004

x = 150

Thus,

After 150 years, the population will be the same.

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The respective exterior angles are 155°, 55°, 150°

The angle sum property of a triangle states that the sum of interior angles of a triangle is 180°

Given here: The angles of the triangle as 30°, 25°, and 125°

We know that sum of an exterior angle is the sum of the two non-adjacent angles

Thus we have ∠DBC= 30+125=155°

∠ECA=30+25=55°

∠FAD=25+125=150°

Hence, The respective exterior angles are 155°, 55°, 150°

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Answer:

In real world context, h(10) would represent the height of the balloon above the ground. To find the value of h(10), substitute t with 10 in the equation

height = 210-15t

height = 210-15(10)

height = 210-150

height = 60

Answer:

A = 811.84 centimeters squared

Step-by-step explanation:

I cut the shape in half (two trapezoids)

I did the area for one trapezoid:

A = 22.3+46.5/2 (11.8)

A = 68.8/2 (11.8)

A = 34.4 (11.8)

A = 405.92 centimeters squared

Since this is only half of the shape, I multiplied the area by 2.

A = 405.92 (2)

A = 811.84 centimeters squared

The relative frequency for Point 3 will be 28.57 and cumulative frequency will be 28.

What is relative and cumulative frequencies?

Relative frequency can be defined as the number of times an event occurs divided by the total number of events occurring in a given scenario.

To calculate the relative frequency two things must be known:

Number of total events/trials

Frequency count for a category/subgroup.

Relative frequency = subgroup frequency/ Total frequency

Cumulative frequency-

In statistics, the frequency of the first-class interval is added to the frequency of the second class, and this sum is added to the third class and so on. Frequencies that are obtained this way are known as cumulative frequency (c.f.).  

Now,

For Relative frequency

subgroup frequency for point 3=8

Total frequency = 28

Therefore,

Relative frequency=8/28

=2/7

=0.2857

Relative frequency=28.57 (upto two decimal points)

For cumulative frequency,

add all the subgroup frequency and that will be 28.

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Answer:

10 dollars for adult tickets and 6 dollars for student tickets

Step-by-step explanation:

a=adult tickets

s=student tickets

4a+2s=52              3a+5s=60

5(4a+2s=52)         2(3a+5s=60)

20a+10s=260        6a+10s=120

-6a+10s=120

14a=140

a=10

10 dollars per adult ticket

4(10)+2s=52

40+2s=52

2s=12

s=6

6 dollars per student ticket

Answer:

Step-by-step explanation: Inverse property of addition

The expression equivalent to (p - q)(x) is (x² - 1) - 5(x - 1).

An expression in math is a sentence with a minimum of two numbers or variables and at least one math operation. This math operation can be addition, subtraction, multiplication, or division.

It is given that

p(x) = x² - 1

q(x) = 5(x - 1)

We have to find (p - q)(x)

We know that

(p - q)(x) = p(x) - q(x)

Substituting the values

= (x² - 1) - 5(x - 1)

Therefore, the expression equivalent to (p - q)(x) is (x² - 1) - 5(x - 1).

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Answer:

It is given that

p(x) = x² - 1

q(x) = 5(x - 1)

We have to find (p - q)(x)

We know that

(p - q)(x) = p(x) - q(x)

Substituting the values

= (x² - 1) - 5(x - 1)

Step-by-step explanation: