Could someone help me figure this out.?

Answer:

Its D Dude!

Step-by-step explanation:

To prove that two functions are inverses of each other, it is necessary to show that both of the conditions f(g(x)) = x and g(f(x)) = x hold, but this does not necessarily mean that the two functions are equal.

We have,

This statement is not entirely correct.

To prove that two functions are inverses of each other, it is indeed necessary to show that both of the following conditions hold:

f(g(x)) = x for all x in the domain of g

g(f(x)) = x for all x in the domain of f

Now,

This does not necessarily mean that the two functions are equal to each other.

For example,

Consider the functions f(x) = x + 1 and g(x) = x - 1.

It can be shown that f(g(x)) = x and g(f(x)) = x for all values of x, which satisfies the conditions for being inverses of each other.

However, it is clear that f(x) and g(x) are not the same functions.

Thus,

To prove that two functions are inverses of each other, it is necessary to show that both of the conditions f(g(x)) = x and g(f(x)) = x hold, but this does not necessarily mean that the two functions are equal.

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(a) | Masses (kg) | Frequency | Cumulative Frequency |

|-------------|-----------|---------------------|

| 15-24       | 14        | 14                  |

| 25-34       | 54        | 68                  |

| 35-44       | 24        | 92                  |

| 45-54       | 26        | 118                 |

| 55-64       | 2         | 120                 |

(b) The cumulative frequency curve starts from the origin (0, 0) and moves upward and to the right, indicating that the mass of logs is increasing as we move right on the x-axis.

To construct the cumulative frequency table for the distribution of masses of 120 logs of wood, we need to add up the frequencies of each class and all the classes before it.

(b) To draw a cumulative frequency curve, we plot the cumulative frequency values against the upper class limits. The plot shows how the cumulative frequency increases with the increase in the mass of the log.

We use the same class intervals as in part (a):

- x-axis = Masses (kg)

- y-axis = Cumulative frequency

To plot the cumulative frequency curve, we mark the upper limit of each class on the x-axis, and its corresponding cumulative frequency on the y-axis. Then, we join the plotted points with a smooth curve, as shown in the graph.

The steeper the curve, the more rapid the increase in cumulative frequency, indicating that a larger number of logs fall in higher mass categories.

In the given distribution, the plot of the cumulative frequency curve shows that the majority of logs fall in the mass range of 25-34 kg, closely followed by the range of 45-54 kg.

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Answer:

it would be solved by it mom

Substituting in the above expression,

we get:dy/dx = 4(1-5x) - 20x(4x - 4)= 16(1-x5)(4x - 4) - 20x4 (1 - x) (4x - 4) -

-Therefore, the required differentiation is given by

dy/dx = 16(1-x5)(4x - 4) - 20x4 (1 - x) (4x - 4).

The given function is

y

= (4x - 4)4(1-5x)

Differentiating with respect to x we get the following result.

dy/dx

= d/dx [ (4x - 4)4(1-5x) ]

= [d/dx (4x - 4)] 4(1-5x) + (4x - 4) [d/dx (4(1-5x))]

Using the chain rule for differentiation:

d/dx (4x - 4)

= 4d/dx (x - 1)

= 4 (1)

= 4d/dx (4(1-5x))

= -4×5

= -20

Substituting in the above expression,

we get:dy/dx

= 4(1-5x) - 20x(4x - 4)

= 16(1-x5)(4x - 4) - 20x4 (1 - x) (4x - 4) - -

Therefore, the required differentiation is given by

dy/dx

= 16(1-x5)(4x - 4) - 20x4 (1 - x) (4x - 4).

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Answer:

answer is ABCD

Step-by-step explanation:

I took the quiz

Step-by-step explanation:

100% is 24. divided by 2 giving you 50% which is 12. divided by another giving you 25% which is 6 so meaning you will subtract 6 out of 24 which is 18 so your answer is 18

Answer:

18

Step-by-step explanation:

Answer:

$20,000=4x

Step-by-step explanation:

First if we want to find out how much the price of the car went down we would have to find out how much the price went down by subtracting $20,000 by $8,000. I got 12,000. Then we have to find out how much the price went down every year. So, $12,000 ÷ 4 = $3,000. So, in 4 years the price went down $3,000 dollars every year

Answer:

The point (0,-2) is the solution to the problem. Substitue 0 into x, the answer is -2 which matches f(x), or y value.

Step-by-step explanation:

The number of bows a student can make is 8 and centimeter of ribbon left over is 14 cm

According to the question we have been given that student had

            Total length of the ribbon = 174 cm

            Length of each bow  = 20 cm

We need to find the number of bows that can be made from the given total length of the ribbon.

The formula to find the number of bows is  = \(\frac{Total length}{Length of each bow}\)

Putting the required values we get,

                             = 174/20

                             = 8.7 = 8 + 0.7

Hence the number of bows a student can make is 8.

Ribbons left over will be 14 cm.

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If a divides b and a divides c, then a divides (bm + cn).

To prove that if a divides b and a divides c, then a divides (bm + cn), we can use the properties of divisibility.

Given:

a|b, which means b is divisible by a.

a|c, which means c is divisible by a.

We want to show that a|(bm + cn), which means (bm + cn) is divisible by a.

By definition, if a divides b, then there exists an integer k₁ such that b = ka. Similarly, if a divides c, there exists an integer k₂ such that c = ka.

Now, let's substitute these expressions into (bm + cn):

(bm + cn) = (ka)m + (ka)n

= kam + kan

= a(km + kn)

We can see that (bm + cn) can be written as a times the integer (km + kn). Since (km + kn) is an integer, this implies that (bm + cn) is divisible by a.

Therefore, if a divides b and a divides c, then a divides (bm + cn).

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a. D. magna is an effective grazer of the G. semen alga. b. a very strong negative correlation between the number of grazers and the net growth rate of G. semen.

a. The scatterplot of the data shows a clear negative correlation between the number of D. magna grazers and the net growth rate of G. semen. As the number of grazers increases, the net growth rate of G. semen decreases. This suggests that D. magna is an effective grazer of the G. semen alga.

b. The correlation coefficient between the number of grazers and the net growth rate is -0.996. This indicates a strong negative correlation between the two variables, which supports the interpretation that D. magna is an effective grazer of G. semen. The closer the correlation coefficient is to -1, the stronger the negative correlation between the two variables. In this case, the correlation coefficient is very close to -1, which indicates a very strong negative correlation between the number of grazers and the net growth rate of G. semen.

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Answer:The answer is B.

Step-by-step explanation: He has to spend 10 dollars to get into the fair and each ride cost 1.50. We don’t know how many rides he’s going to get on so that is an unknown variable multiplied by 1.50 (r). He also has to spend less than or equal to $40. So Daniel’s total of 1.50r + 10 has to be less than or equal to $40.

The quadratic equation that represents the solution is F: p(x) = x² - 49.

The term "quadratic" refers to functions where the highest degree of the variable (in this example, x) is 2. A quadratic function's graph is a parabola, which, depending on the sign of the leading coefficient a, can either have a "U" shape or an inverted "U" shape.

Algebra, geometry, physics, engineering, and many other branches of mathematics and science all depend on quadratic functions. They are used to simulate a wide range of phenomena, including population dynamics, projectile motion, and optimisation issues.

Given that the solution of the quadratic function are x = -7 and x = 7 thus we have:

p(x) = (x + 7)(x - 7)

Solving the parentheses we have:

p(x) = x² - 7x + 7x - 49

Cancelling the same terms with opposite sign we have:

p(x) = x² - 49

Hence, the quadratic equation that represents the solution is F: p(x) = x² - 49.

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Answer:

The temperature on the top of the mountain that is 4900 m high is approximately -13.85°C.

Step-by-step explanation:

The temperature decreases with height at a rate of approximately 6.5°C per 1000 meters. Therefore, to calculate the temperature on the top of a mountain that is 4900 m high, we can use the following formula:

Temperature at the top of the mountain = Temperature at sea level - (Rate of temperature decrease x Number of 1000 meters)

Plugging in the values we get:

Temperature at the top of the mountain = 18°C - (6.5°C/1000 m x 4.9)

Temperature at the top of the mountain = 18°C - (31.85°C)

Temperature at the top of the mountain ≈ -13.85°C

Answer:

shhshshshs

hshdhsnsnjsjdje

Step-by-step explanation:

bshsjsnsjjsusjsjsjs

The range at which Dan's car can go is 3.33 miles

A car's range is the distance it can travel with the current amount of fuel in the tank.

The vehicle calculates the range based on the amount of fuel, how the accelerator and brakes are used, and how quickly the car is travelling.

The range of a car can be measured in the unit of distance.

Therefore the range of a car can be calculated as;

R = distance per gallon/ number of gallon.

Dan's car is 40mpg and has 12 gallons in it's tank.

Therefore it's range = 40/12

= 3.33miles.

therefore the range of Dan's car is 3.33miles

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A comprehensive understanding of the graph of △ABC, including its vertices, side lengths, and angles.

When you have a graph of △ABC, consider the following steps:
Identify the coordinates: Locate the coordinates of each vertex (A, B, and C) on the graph. Write them down as ordered pairs (x, y).
Calculate side lengths: Using the distance formula, calculate the length of each side (AB, BC, and CA) of the triangle. The distance formula is:

√((x₂ - x₁)² + (y₂ - y₁)²)
Determine the type of triangle: Based on the side lengths, determine if the triangle is equilateral (all sides are equal), isosceles (two sides are equal), or scalene (no sides are equal).
Calculate angles: Using the Law of Cosines, find the angles between each pair of sides.

The Law of Cosines states that c² = a² + b² - 2ab × cos(C),

where a, b, and c are the side lengths, and C is the angle between sides a and b.
Determine the triangle's classification by angles: Based on the angles, determine if the triangle is acute (all angles < 90°), obtuse (one angle > 90°), or right-angled (one angle = 90°).

Once you have completed these steps, you should have a comprehensive understanding of the graph of △ABC, including its vertices, side lengths, and angles.

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The algebraic expression for the scenario is 15 + x = 60

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

Amount saved up = $15

Cost of item = $60

Amount gifted by your grandma = x

The above parameters means that the mathematical statement is an equation statement

So, we have the following representation

Amount saved up + Amount gifted by your grandma = Cost of item

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

15 + x = 60

Hence, the algebraic expression is 15 + x = 60

The question does not require that the equation be solved

However, when it is solved, we have:

15 + x = 60

Subtract 15 from both sides

x = 45

So, the amount is 45

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Answer:

top right :3

Step-by-step explanation:

Based on the diagram, there are 8 triangles in total

A triangle is a polygon with three sides and three angles.

Therefore, there are 8 triangles in the diagram.

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Answer:

In the exponential function y = C(a)^x, the value of a is the base of the exponent, which determines how fast the function grows or decays. If a were equal to zero, then any value of x would result in y being equal to zero, which would make the function flat and unchanging. Therefore, a cannot be equal to zero in an exponential function, as this would result in an undefined or meaningless expression. Additionally, any number raised to the power of zero is equal to 1, so an exponential function with a base of zero would also violate this mathematical rule.

The remaining chocolate slices is 1/12th and the remaining vanilla slices are 1/24th. so the remaining vanilla cake is double of the remaining chocolate cake. here the concept of fraction word problem is used.

There was 1/4th of the chocolate cake left over and there was 3/8th of the vanilla cake left over. Steven divided the remaining chocolate cake into 3 equal slices and the remaining vanilla cake into 9 equal slices.

For the chocolate cake,

Chocolate Cake Remaining 1/4 is divided by 3

            = (1 /4) / 3 = 1 / (4x3) = 1/12

For the Vanilla Cake, Remaining 3/8 is divided by 9

            = (3/8) / 9 = 3 /(8 x 9 ) = 3 / 72 = 1 /24

so from this we conclude that the remaining chocolate slices are twice the size of the remaining vanilla slices because 1/24th Vanilla is half of 1/12th Chocolate. Here the concept of Fraction word problem is used. In word problems on fraction we will solve different types of problems on multiplication of fractional numbers and division of fractional numbers.

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9514 1404 393

Answer:

Step-by-step explanation:

Locate the digit to the right of the place you're rounding to. If that digit is 5 or more, add 1 to the digit in the place you're rounding to. Drop all digits to the right of the one you're rounding to, unless it is left of the decimal point. In that case, zero any digits between the one you rounded and the decimal point. (See problem 3 for an example of this.)

If you're rounding to the ones place (nearest whole number), and that digit ends up being 0, then put a decimal point after it to indicate it is a significant digit.

The second attachment shows the names of the number places, if you need a reminder.

Answer:

x = 7

Step-by-step explanation:

Given

7x + 4(- 3x + 6) = - 7x + 38 ← distribute and simplify left side

7x - 12x + 24 = - 7x + 38

- 5x + 24 = - 7x + 38 ( add 7x to both sides )

2x + 24 = 38 ( subtract 24 from both sides )

2x = 14 ( divide both sides by 2 )

x = 7

Answer:

Step-by-step explanation:

Here you go mate

Use PEMDAS

Parenthesis

Exponent

Multiplication

Division

Addition

Subtraction

Step 1

7x+4(-3x+6) =-7x+38  Equation/Question

Step 2

7x+4(-3x+6) =-7x+38  Remove parenthesis

-5x+24=−7x+38

Step 3

-5x+24=−7x+38  Add 7x

2x+24=38

Step 4

2x+24=38  Subtract 24

2x=14

Step 5

2x=14  Divide by 2

answer

x=7

Hope this helps

Answer:

x = -5 and x = 1

Step-by-step explanation:

4( x2 + 4x + 4 ) = 36

4x2 + 16x + 16 = 36

4x2 + 16x - 20 = 0

x2 + 4x - 5 = 0

Answer:

C. x = -5, and x = 1

Step-by-step explanation:

You have the equation 4(x + 2)2 = 36

You then isolate 4 out of the equation using division on both sides

You are left with (x+2)2 = 9

Next, take square roots

\(\sqrt({x} +2) ^{2}\) = \(\sqrt{9}\)

This leaves you with x + 2 ± 9

So, x = -2 + 3 = 1

or

x = -2 - 3 = -5

Answer:

Step-by-step explanation:

To find the area of a trapezium with parallel sides AB and CD, we can use the formula:

Area = (AB + CD) * height / 2

In this problem, we know that:

AB = 30 cm

CD = 20 cm

DA = 9 cm

We can use these measurements to find the height of the trapezium:

height = DA = 9 cm

Now we can substitute these values into the area formula:

Area = (30 + 20) * 9 / 2

Area = 50 * 9 / 2

Area = 450 / 2

Area = 225 sq cm

So the area of the trapezium is 225 sq cm.

Note that this is only one of the ways to calculate the area of a trapezium and you could have also used the height(in this case 17cm) and the breadth to calculate the area of the trapezium as well.

The coordinates of the vertices of the image of the trapezoid are A'(x, y) = (- 4, 1), B'(x, y) = (- 2, 1), C'(x, y) = (- 5 / 2, 5 / 2) and D'(x, y) = (- 7 / 2, 5 / 2).

In this question we have a representation of a trapezoid, whose image has to be generated by a kind of rigid transformation known as dilation, whose equation is described below:

P'(x, y) = O(x, y) + k · [P(x, y) - O(x, y)]

Where:

If we know that k = 1 / 2, A(x, y) = (- 5, - 2), B(x, y) = (- 1, - 2), C(x, y) = (- 2, 1), D(x, y) = (- 4, 1), O(x, y) = (- 3, 4), then the coordinates of the vertices of the image are:

Point A'

A'(x, y) = O(x, y) + k · [A(x, y) - O(x, y)]

A'(x, y) = (- 3, 4) + (1 / 2) · [(- 5, - 2) - (- 3, 4)]

A'(x, y) = (- 3, 4) + (1 / 2) · (- 2, - 6)

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

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

Point B'

B'(x, y) = O(x, y) + k · [B(x, y) - O(x, y)]

B'(x, y) = (- 3, 4) + (1 / 2) · [(- 1, - 2) - (- 3, 4)]

B'(x, y) = (- 3, 4) + (1 / 2) · (2, - 6)

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

B'(x, y) = (- 2, 1)

Point C'

C'(x, y) = O(x, y) + k · [C(x, y) - O(x, y)]

C'(x, y) = (- 3, 4) + (1 / 2) · [(- 2, 1) - (- 3, 4)]

C'(x, y) = (- 3, 4) + (1 / 2) · (1, - 3)

C'(x, y) = (- 3, 4) + (1 / 2, - 3 / 2)

C'(x, y) = (- 5 / 2, 5 / 2)

Point D'

D'(x, y) = O(x, y) + k · [D(x, y) - O(x, y)]

D'(x, y) = (- 3, 4) + (1 / 2) · [(- 4, 1) - (- 3, 4)]

D'(x, y) = (- 3, 4) + (1 / 2) · (- 1, - 3)

D'(x, y) = (- 3, 4) + (- 1 / 2, - 3 / 2)

D'(x, y) = (- 7 / 2, 5 / 2)

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According to the calculations, $ 3200 of the rebate is taxable.

Given that Carol is an unmarried mother of two dependent children, and she received a $ 4,200 recovery rebate in 2021, to determine how much of the rebate is taxable if she has a $ 1,000 tax liability, the following calculation must be performed:

Therefore, $ 3200 of the rebate is taxable.

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