Pleases help ASAP!!!

Consider the function f(x)=sqrt x-4+9 for the domain [4, infinity).
Find f^-1(x), where f^-1 is the inverse of f.
Also state the domain of f^-1 in interval notation.

The first step to solve this exercise is to write the Mixed number as a decimal number. You can do it by dividing the numerator by the denominator of the fractional part and adding the quotient to the Whole number part, as follows:

So:

Knowing that Positive numbers are greater than zero and knowing that Negatives numbers are less than zero, we can order the given numbers from greatest to least, as you can see below:

The maximum distance that block of wood fly backward as per given mass and velocity is equal to 2.759 × 10⁻⁴ m.

As given in the question,

Mass of the person 'M' = 74.9kg

1kg = 1000grams

Mass of the bullet 'm'= 10 gram

                                  = 0.01 Kg

Initial velocity 'u₁' = 0m/s

Velocity of bullet (initial velocity) 'u₂' = 391m/s

Angle formed with the horizontal = 45°

Apply conservation of Momentum:

M u₁  + m u₂= ( M + m ) V

74.9 x 0 + 0.01 x 391 = (74.9+ 0.01) V

⇒ 3.91 = 74.91V

⇒V = 3.91 /74.91

⇒V = 0.052m/s

acceleration due to gravity 'g' = 9.8m/s²

Maximum distance that block of wood fly

= V²sin²θ/ g

= ( 0.052)² × sin² 45° / 9.8

= 0.002704 × 1 / 9.8

= 0.0002759

= 2.759 × 10⁻⁴ m

Therefore, the maximum distance block of wood fly backward is equal to  2.759 × 10⁻⁴ m.

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The values of Z such that e² = 2 + i√3 are Z = ln(2 + i√3) + 2πik, where k is an integer.

To find the values of Z, we can start by expressing 2 + i√3 in polar form. Let's denote it as re^(iθ), where r is the modulus and θ is the argument.

Given: 2 + i√3

To find r, we can use the modulus formula:

r = sqrt(a^2 + b^2)

= sqrt(2^2 + (√3)^2)

= sqrt(4 + 3)

= sqrt(7)

To find θ, we can use the argument formula:

θ = arctan(b/a)

= arctan(√3/2)

= π/3

So, we can express 2 + i√3 as sqrt(7)e^(iπ/3).

Now, we can find the values of Z by taking the natural logarithm (ln) of sqrt(7)e^(iπ/3) and adding 2πik, where k is an integer. This is due to the periodicity of the logarithmic function.

ln(sqrt(7)e^(iπ/3)) = ln(sqrt(7)) + i(π/3) + 2πik

Therefore, the values of Z are:

Z = ln(2 + i√3) + 2πik, where k is an integer.

The values of Z such that e² = 2 + i√3 are Z = ln(2 + i√3) + 2πik, where k is an integer.

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The line that intersects the curve at (8, p(8)) represents the secant line to the curve at that point. The statement is true.

A straight line that crosses a curve at two or more points is known as a secant line. The given point (8, p(8)) in this instance is on the curve and the line. As a result, the secant line to the curve at that point is the line that intersects the curve at (8, p(8)).

Let's think of an example to help further clarify this idea. Let's say we wish to locate the secant line to a curve at the point (8, p(8)) where the equation \(y = x^2\) defines the curve.

We must first determine the secant line's slope. The following formula determines the slope of a line via the points (x1, y1) and (x2, y2):

slope= (y2 - y1) / (x2 - x1).

The two points in this case are the curve's second point and (8, p(8)). We can select a different point on the curve, such as (4, p(4)), to get the slope.

slope = (p(4)-p(8)) / (4 - 8)

Next, we evaluate the function at these points:
\(p(4) = 4^2 = 16\\p(8) = 8^2 = 64\)

Substituting these values into the slope formula:
slope = (16 - 64) / (4 - 8)
     = -48 / -4
     = 12

Now that we have the slope, we can write the equation of the secant line using the point-slope form:
y - y1 = m(x - x1)

Substituting the values (8, p(8)) and slope = 12 into the equation:
y - p(8) = 12(x - 8)

Simplifying the equation:
y - p(8) = 12x - 96

This is the equation of the secant line to the curve at the point (8, p(8)).

In conclusion, the statement is true. The line that intersects the curve at (8, p(8)) represents the secant line to the curve at that point.

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Transformations are operators that can act on functions, modifying them in different ways. In this particular problem, we see the translations.

The correct option is B:

g(x) can be graphed by translating the basic rational function ƒ(x)=  1∕x left by 3 units and downward by 5 units.

Let's describe the transformations:

Horizontal translation:

For a general function f(x), a horizontal translation of N units is written as:

g(x) = f(x + N)

If N is positive, the shift is to the left.

If N is negative, the shift is to the right

Vertical translation:

For a general function f(x), a vertical translation of N units is written as:

g(x) = f(x) + N

If N is positive, the shift is upwards.

If N is negative, the shift is downwards.

Now that we know this, let's see the problem.

We have:

\(g(x) = \frac{1}{x + 3} - 5\)

So, the original function is:

\(f(x) = \frac{1}{x}\)

Now from f(x) we can apply translations to create g(x).

If first, we apply a translation of 3 units to the left, we get:

\(g(x) = f(x + 3) = \frac{1}{x + 3}\)

If now we apply a translation of 5 units downwards, we get:

\(g(x) = f(x + 3) - 5 = \frac{1}{x + 3} - 5\)

So we can conclude that the correct option is B:

g(x) can be graphed by translating the basic rational function ƒ(x) 1∕x left by 3 units and downward by 5 units.

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The x-axis should be labeled quartz of yogurt.

The y-axis should be labeled total cost.

The slope of each line represents the cost of yogurt ($/qt).

The y-intercept of each line represents the initial equipment cost.

In Mathematics, the y-intercept is also known as an initial value and the y-intercept of any graph such as a linear function, generally occur at the point where the value of "x" is equal to zero (x = 0).

Based on the graph above, the initial equipment cost represents the y-intercept of each line.

In Mathematics, a slope is also referred to as gradient or rate of change and it is typically used to describe both the ratio, direction and steepness of the function of a straight line.

Therefore, the slope of each line represents the rate of change of the total cost with respect to the quartz of yogurt ($/qt).

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A cross-sectional effect diagram, also known as an axial force-shear force-bending moment diagram or simply an internal force diagram, is a graphical representation that shows the distribution of internal forces (axial force, shear force, and bending moment) along the length of a structural member, such as a beam or column.

To draw the cross-sectional effect diagrams for the beam whose loading condition is given in the figure, we need to follow these steps:

Step 1: Identify the type of loadingFor this question, the loading conditions are {N}, {T}, {M}. So, the loading types are axial force, shear force, and bending moment.

Step 2: Draw the cross-sectional diagram of the beam. We need to draw the diagram of the cross-section of the beam in the direction of the forces acting on the beam. In this case, it will be a rectangular beam.

Step 3: Draw the effect diagrams After drawing the cross-sectional diagram, we need to draw the effect diagrams for each loading condition.

The effect diagrams are as follows: 1. Axial force diagram (N):In this case, the axial force is positive (+) which means it is a tensile force. 2. Shear force diagram (T):The shear force is negative (-) from x = 0 to x = 1, which means the shear force is acting downward. It is zero at x = 1 and then becomes positive (+) from x = 1 to x = 2, which means the shear force is acting upward. 3. Bending moment diagram (M):The bending moment is zero at x = 0, becomes negative (-) from x = 0 to x = 1, reaches a minimum at x = 1, and then becomes positive (+) from x = 1 to x = 2.

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Answer:

Step-by-step explanation:

Sean drank at a rate of 5 milliliters per second. It took Sean 55 seconds to drink all the slushy.

Answer:

5 millimeters per second

Step-by-step explanation: 55 seconds

The approximate length of a side of the rhombus is 10.67 cm.

A rhombus is a quadrilateral with all sides of equal length.

The diagonals of a rhombus bisect each other at right angles.

Let's label the length of one diagonal as d1 and the other diagonal as d2.

In the given rugby-shaped figure, the length of d1 is 14 cm, and the length of d2 is 12 cm.

Since the diagonals of a rhombus bisect each other at right angles, we can divide the figure into four right-angled triangles.

Using the Pythagorean theorem, we can find the length of the sides of these triangles.

In one of the triangles, the hypotenuse is d1/2 (half of the diagonal) and one of the legs is x (the length of a side of the rhombus).

Applying the Pythagorean theorem, we have \((x/2)^2 + (x/2)^2 = (d1/2)^2\).

Simplifying the equation, we get \(x^{2/4} + x^{2/4} = 14^{2/4\).

Combining like terms, we have \(2x^{2/4} = 14^{2/4\).

Further simplifying, we get \(x^2 = (14^{2/4)\) * 4/2.

\(x^2 = 14^2\).

Taking the square root of both sides, we have x = √(\(14^2\)).

Evaluating the square root, we find x ≈ 10.67 cm.

Therefore, the approximate length of a side of the rhombus is 10.67 cm.

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Answer:

When flipping a coin, there are two possible outcomes: heads or tails. The probability of getting heads on any one flip is 1/2, and the probability of getting tails is also 1/2.

To find the probability that all three coins will land on the same side (either all heads or all tails), we can use the multiplication rule of probability, which states that the probability of two independent events occurring together is the product of their individual probabilities.

So, for each coin flip, there are two possible outcomes, and the probability of getting either outcome is 1/2. To find the probability that all three coins will land on the same side, we need to find the probability of getting either all heads or all tails.

The probability of getting all heads is:

(1/2) x (1/2) x (1/2) = 1/8

Similarly, the probability of getting all tails is also 1/8.

So, the probability of all three coins landing on the same side is:

1/8 + 1/8 = 2/8 = 1/4

Therefore, the probability that Matrix will flip 3 coins and all three coins will land on the same side is 1/8 or 0.125, which can also be written as a fraction or percentage.

Answer:

4|−12| = 48 dollars.

Step-by-step explanation:

The question asks for the total decrease after 4 weeks. Since there is no such thing as negative weeks, A and C are disqualified. Since D is simply wrong math (-4x12=-48), it is also wrong.

Answer:

HAHAHAH SORRY WHAT?

Step-by-step explanation:

im dead

Technically, you'd be able to touch all colors. Colors are all around us, whether it be white (If all three primary colors of light are mixed in equal proportions, the result is neutral which is gray or white) or black (The absence of light of any color) or any other shades, etc.

Answer:

dydx=−1x√x2−1.

Step-by-step explanation:

Then, differentiating simplicity gives: cosydydx=−x−2 ∴dydx=−1x2cosy.

The error of Fatima is: C. She applied the exponent -2 to "4(-2) instead of only to "(-2).

An exponent in any expression is the letter or number on the right of a base in an expression.

In the evaluated expression shown, the base that the exponent "-2" applies to is "m", and does not include 4. If we substitute the value of m = -2, into the evaluated expression, the base that the exponent "-2" applies to is "-2" and does not include "4".

Therefore, Fatima's mistake is: C. She applied the exponent -2 to "4(-2) instead of only to "(-2).

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The function ƒ(x) is integrable on [0, 1], and the value of the integral ∫ƒ(x) dx is equal to 1.

To determine if the function ƒ: [0, 1] → R is integrable and to find the value of the integral, we need to analyze the upper and lower sums.

Given that the upper sum Un = 1+ and lower sum Ln = 1/2n, we can compare their values as n approaches infinity.

(i) To find Ln as a function of n:

Ln = 1/2n

(ii) To find Un as a function of n:

Un = 1+

As n approaches infinity, Ln approaches 0, and Un approaches 1.

(iii) Now, let's calculate the integral of g(x) dx using the upper sum and lower sum:

∫g(x) dx = Lim(n→∞) Un

Since Un approaches 1 as n approaches infinity, the integral of g(x) dx is equal to 1.

Therefore, the function ƒ(x) is integrable on [0, 1], and the value of the integral ∫ƒ(x) dx is equal to 1.

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If Kayla can pay off up to $175 monthly for the purchase of a new television for $487.89, the interest she will pay at 23.5% compounded monthly is D. $18.87.

The compound interest payable on the credit card for the purchase of a new television can be computed using an online finance calculator as follows:

N (# of periods) = 3 months

I/Y (Interest per year) = 23.5%

PV (Present Value) = $487.89

PMT (Periodic Payment) = $-175

Results:

FV = $18.23

Sum of all periodic payments = $525.00

Total Interest = $18.87

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Answer:

\(\Huge \boxed{\£55}\)

________________________________________________________

A 17% reduction means that the dress cost 83% (100 - 17) of the original amount.

\(\large \fbox{\begin{minipage}{8.1 cm}83\% of the original price = \£45.65\\\\$\Rightarrow$1\% of the original price = $\frac{45.65}{83}$\\\\$\Rightarrow$1\% of the original price = 0.55\\\\$\Rightarrow$100\% of the original price = 0.55 \times 100\\\\$\Rightarrow$100\% \text{ of the original price = \£55}\end{minipage}}\)

To work out 83% of the original price, you multiply by 0.83. We can do the inverse, which is dividing by 0.83.

                                 ×0.83

Original Price →→→→→→→→→→→→→ Sale Price

        £?           ←←←←←←←←←←←←←     £45.65

                                ÷0.83

\(\large \boxed{\begin{minipage}{7 cm}Original Price = $\frac{\text{Sale Price}}{0.83}$\\\\$\Rightarrow$Original Price = $\frac{45.65}{0.83}$\\\\$\Rightarrow$Original Price = \£55\end{minipage}}\)

Therefore, the original price of the dress is £55.

________________________________________________________

There are 2 pictures.

1. (x,y)=(-1,5),(0,2),(1,-1),(2,-4). Option -3 is correct.

2. The slope of the line is 4/3. Option-1 is correct.

Given that,

There are 2 pictures.

In the first picture we have to find which table satisfy the equation.

In the second picture we have to find slope of the given graph.

First,

The given equation is y=-3x+2

In every option the x values are same that is -1,0,1,2.

Substitute x value as -1,0,1,2

Taking x as-1

y=-3(-1)+2

y=3+2

y=5

Taking x as 0

y=-3(0)+2

y=2

Taking x as 1

y=-3(1)+2

y=-3+2

y=-1

Taking x as 2

y=-3(2)+2

y=-6+2

y=-4

Therefore, we got (x,y)=(-1,5),(0,2),(1,-1),(2,-4). Option -3 is correct.

Now, We see the second picture.

Given line point are (2,2) and (-1,-2)

Slope of the line formula is \(\frac{y_{2} -y_{1} }{x_{2} -x_{1} }\)

Slope =(-2-2)/(-1-2)

Slope=-4/-3

Slope=4/3

Therefore, the slope of the line is 4/3. Option-1 is correct.

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Answer:

it is Greater than because blue and green combined equal to 12

\( \: \: \: \: \: \: \)

\(1 + w\)

Step-by-step explanation:

\(1 - w + w2\)

\(1 - w + 2w\)

\( = \: \: 1 + w\)

The range of this data set is 1 to 5 inches of rainfall, as indicated by the dots on the graph.

Rainfall is the precipitation that falls from the sky, usually in the form of drops of water. It is a major component of the water cycle, and is responsible for replenishing the earth’s water supply. Rainfall can be light or heavy, and it can occur as a drizzle, shower, or downpour. Rainfall is produced when warm, moist air rises and cools, forming clouds and eventually releasing the water in the form of rain. The amount of rainfall an area receives depends on the global climate, topography, and other local conditions. Rainfall is a vital part of the environment, providing water for plants, animals, and humans. It also helps to keep the temperature of the earth in balance, and can help prevent or lessen the effects of drought.

The lowest value is 1 inch of rainfall in Week 3, and the highest value is 5 inches of rainfall in Week 5.

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The answer is option 4: The range of the given data is 4, as the difference of the highest observation 5 inches and the lowest observation 1 inch is 4 inches.

There are various ways to represent data. It can be tabular form, grouped or ungrouped form of data or the visual representation of data. The types of visual representation can be pictographs, bar graphs, histogram, scatter plot, leaf plots, pie charts etc. Line graph is also a kind of data representation in which the frequency dots are connected using line segments. It is also called a line plot or line chart. Line graphs are used to show the changes in data with time. They have horizontal(x-axis) and vertical(y-axis) to represent the data. The measurements are represented on y-axis.

Here as per the data given about the Amount of Rainfall over 6 weeks, let’s arrange it in a frequency distribution table.

Range of any set data = Highest observation - Lowest observation(frequency)

                                   =5 - 1

                                   =4

Range of set data=4

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The frequency table and graph attached below,

Answer:

18 ft^2

Step-by-step explanation:

This quadrilateral is a parallelogram.

Area = base × height

= 6 × 3

= 18 ft^2

The natural breaks, quantile, and equal interval classification schemes are methods used to categorize data for the purpose of creating thematic maps. Each scheme has its own approach and considerations: Natural Breaks, Quantile, Equal Interval.

Natural Breaks (Jenks): This classification scheme aims to identify natural groupings or breakpoints in the data. It seeks to minimize the variance within each group while maximizing the variance between groups. Natural breaks are determined by analyzing the distribution of the data and identifying points where significant gaps or changes occur. This method is useful for data that exhibits distinct clusters or patterns.

Quantile (Equal Count): The quantile classification scheme divides the data into equal-sized classes based on the number of data values. It ensures that an equal number of observations fall into each class. This approach is beneficial when the goal is to have an equal representation of data points in each category. Quantiles are useful for data that is evenly distributed and when maintaining an equal sample size in each class is important.

Equal Interval: In the equal interval classification scheme, the range of the data is divided into equal intervals, and data values are assigned to the corresponding interval. This method is straightforward and creates classes of equal width. It is useful when the range of values is important to represent accurately. However, it may not account for data distribution or variations in density.

In summary, the natural breaks scheme focuses on identifying natural groupings, the quantile scheme ensures an equal representation of data in each class, and the equal interval scheme creates classes of equal width based on the range of values. The choice of classification scheme depends on the nature of the data and the desired representation in the thematic map.

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Answer: . . . . . . Step-by-step explanation:

Answer:

2/6b-7

Step-by-step explanation:

Answer:

1/3(b-21)

hope it helps :)

Answer:

for first three terms of this pattern

n=1,2,3

Tn= 52,48,44

Step-by-step explanation:

18 is not the term because let's say

18=56-4n

4n=56-18

4n= 38

n=9.5

but n should be a whole no. that's why 18 is not the term of this sequence

Answer:

Number 2

Step-by-step explanation:

Predation refers to a flow of energy between two organisms, predator and prey. In this interaction, the prey loses energy, and the predator gains energy

The probability of getting at least one head is 15/16.

What is probability?

The ratio of positive outcomes to all possible outcomes of an event is known as the probability.

Formula for probability = favourable outcomes/ total outcomes

Main body:

if 4 coins are tossed , total no. of outcomes = 2⁴ = 16

In a toss there are 2 outcomes T or H

so, Probability of getting Head = 1/2

The probability of getting at least 1 head = 1- probability of getting no heads

⇒1 - Probability of getting tail in 4 tosses

⇒ 1 - (1/2)⁴

⇒ 1 - 1/16

⇒ 15/16

So the probability of getting at least one head is 15/16.

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Answer:

1/50

Steps:

Recall 2 can divide 100

therefore

2/100 = 1/50