Which function is represented by the graph?
A nonlinear function starts at the point (minus 2, minus 1) and also passes through (0, minus 2.4), (2, minus 3), and (7, minus 4)
Answers
The option range of a function is (-∞, ∞), x-intercept of (0.1, 0), and the vertical asymptote is x = 0.
What is a function?
It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
As we can see in the picture, we have given a function:
We have a function:
g(x) = 4log(x) + 4
To find x-intercept plug g(x) = 0
0 = 4logx + 4
x = 0.1
(0.1, 0)
The vertical asymptote:
x = 0
The range of a function:
(-∞, ∞)
Thus, the option range of a function is (-∞, ∞), x-intercept of (0.1, 0), and the vertical asymptote is x = 0.
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Related Questions
Determine if the columns of the matrix form a linearly independent set. Justify your answer. Select the correct choice below and fill in the answer box within your choice. (Type an integer or simplified fraction for each matrix element.) A. If A is the given matrix, then the augmented matrix represents the equation Ax =0. The reduced echelon form of this matrix indicates that Ax =0 has only the trivial solution. Therefore, the columns of A do not form a linearly independent set. B. If A is the given matrix, then the augmented matrix represents the equation Ax =0. The reduced echelon form of this matrix indicates that Ax =0 has more than one solution. Therefore, the columns of A form a linearly independent set. C. If A is the given matrix, then the augmented matrix represents the equation Ax =0. The reduced echelon form of this matrix indicates that Ax =0 has more than one solution. Therefore, the columns of A do not form a linearly independent set. D. If A is the given matrix, then the augmented matrix represents the equation Ax =0. The reduced echelon form of this matrix indicates that Ax =0 has only the trivial solution. Therefore, the columns of A form a linearly independent set.
Answers
The correct answer is (D) If A is the given matrix, then the augmented matrix represents the equation Ax =0. The reduced echelon form of this matrix indicates that Ax =0 has only the trivial solution. Therefore, the columns of A form a linearly independent set.
What is a matrix?A collection of numbers lined up in rows and columns to form a rectangular array is called a matrix. The elements, or entries, of the matrix are the integers. In addition to numerous mathematical disciplines, matrices find extensive use in the fields of engineering, physics, economics, and statistics. In computer graphics, where they have been used to describe picture rotations and other transformations, matrices have vital applications as well.
Mathematically, assume that B = {v₁, v₂, v₃, ........} is the set of vectors. Then B will be linearly independent if the vector equation
y₁v₁ + y₂v₂ + y₃v₃ + ........ = 0 possesses the trivial solution such that
y₁ = y₂ = y₃ = ........ = 0.
Let A be a matrix, then columns of A will be linearly independent if the equation Ax = 0 possesses the trivial solution. In other words, The row space of matrix A is the span of its rows. The column space denoted by
C(A) is the span of A’s columns. The dimension of the row and column spaces is always the same, which is known as the rank of A.
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A marathon runner travels 2/3 in 10 minutes. What is the runners rate in miles per hour ?
Answers
The runner's rate in miles per hour is D * 4/3 miles per hour.
Describe Distance?Distance is a measure of the physical space between two objects or points. It is the length of the shortest path between two points in space. Distance can be measured in different units, such as meters, kilometers, miles, feet, or inches, depending on the scale of the objects or the purpose of the measurement.
In geometry, the distance between two points in a Euclidean space can be calculated using the Pythagorean theorem or the distance formula. The distance formula is expressed as:
d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
where d is the distance between two points (x1, y1) and (x2, y2) in a two-dimensional plane. This formula can be extended to three dimensions by adding a third term to the equation.
Distance can also be calculated using other methods, such as GPS (Global Positioning System) or by measuring the time it takes for an object to travel from one point to another, using the speed of light or sound.
In everyday life, distance is a fundamental concept used in various contexts, such as navigation, transportation, sports, and communication. It plays a significant role in determining the time and effort required to travel between two points and is often used as a basis for making decisions.
We can use the formula:
rate = distance / time
where distance is the distance traveled by the runner and time is the time taken to travel that distance.
Given that the runner travels 2/3 of the marathon distance in 10 minutes, we can find the total distance of the marathon by dividing the distance traveled by 2/3:
total distance = distance traveled / (2/3) = distance traveled * 3/2
Let's denote the total distance of the marathon as D. Then:
D = distance traveled * 3/2
distance traveled = D * 2/3
We know that the time taken to travel 2/3 of the distance is 10 minutes. Let's convert this to hours:
10 minutes = 10/60 hours = 1/6 hours
Now we can calculate the runner's rate:
rate = distance / time = (D * 2/3) / (1/6) = (D * 4/3) / 1 = D * 4/3
So the runner's rate in miles per hour is D * 4/3 miles per hour.
Note that we don't have a specific value for the total distance D of the marathon, so we cannot give a numerical answer. We can only express the runner's rate in terms of D as:
runner's rate = D * 4/3 miles per hour
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plss help. i have until monday to do this assignment and I have 42 units to do on Mathia
Answers
value of given expression = 48
What is order of operations?The order of operations is a rule that specifies the correct steps for evaluating mathematical expressions. We can remember the order with PEMDAS -
Parentheses, exponents, multiplication and division (left to right), addition and subtraction (left to right).
Given expression,
9 - 4 ÷ (2 + 2) + 2³ . 5
By PEMDAS rule
First solving parentheses
= 9 - 4 ÷ 4 + 2³ . 5
then solving exponent
= 9 - 4 ÷ 4 + 8 . 5
Now solving multiplication
= 9 - 4 ÷ 4 + 40
Now solving division
= 9 - 1 + 40
Now solving addition
= 49 - 1
Now solving subtraction
= 48
Hence, 48 is the value of the expression.
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during the early days of analytics, data was often obtained from teh domain experts using manual processes to build mathematical or knowledge-based models (true or false)
Answers
This statement 'During the early days of analytics, data was often obtained from the domain experts using manual processes to build mathematical or knowledge-based models' is true and not false.
During the early days of analytics, data was often obtained from domain experts using manual processes to build mathematical or knowledge-based models. Before the advent of computers and digital data storage, data was typically collected and processed manually. This often involved subject matter experts manually collecting data and performing calculations by hand to develop models and draw insights. Over time, as computing technology and data storage capabilities improved, analytics has evolved to rely increasingly on automated processes and sophisticated algorithms.
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a 6-ounce bottle of medicine contains 36 doses. how many doses are in a 15-ounce bottle of the same medicine?
Answers
Answer:
Step-by-step explanation:
If a 6-ounce bottle of medicine contains 36 doses, we can use a proportion to find how many doses are in a 15-ounce bottle:
6 ounces / 36 doses = 15 ounces / x doses
Cross-multiplying, we get:
6 x = 36 * 15
6 x = 540
Dividing both sides by 6, we get:
x = 90
Therefore, a 15-ounce bottle of the same medicine contains 90 doses.
scatter plot that shows a positive association that is not linear.
Answers
Yes, it is possible to have a scatter plot that shows a positive association that is not linear.
What is the scatter plot?
A scatter plot is a type of plot or mathematical diagram using Cartesian coordinates to display values for typically two variables for a set of data. If the points are coded, one additional variable can be displayed.
In a scatter plot, a positive association means that as the values of one variable increase, the values of the other variable tend to increase as well.
However, the relationship between the variables does not have to be linear.
In other words, the pattern of points on the plot does not have to form a straight line.
For example, the relationship between two variables could be curved, such as a quadratic relationship where the increase in one variable initially leads to larger increases in the other variable, but at higher levels of the first variable, the increase in the second variable begins to level off.
Alternatively, the relationship could be exponential, where the increase in one variable leads to an exponential increase in the other variable.
In both cases, the pattern of points on the scatter plot would show a positive association, but not a linear one.
Therefore, it is true that scatter plot that shows a positive association is not linear.
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y=80(1.3)^x growth or decay
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The +equation represents exponential growth
What is the exponential functions?
An exponential function is a mathematical function that has the form f(x) = a*b^x, where a and b are constants, and x is the independent variable.
The equation y = 80(1.3)^x represents exponential growth.
In this equation, "y" represents the value of the function at a given time or input, "x" represents the time or input, and "1.3" is the growth factor, which is greater than 1.
As "x" increases, the value of the function "y" grows at an increasing rate. This is because the growth factor is greater than 1, which means that each input value results in a larger output value than the previous one.
Hence, this equation represents exponential growth.
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Solve by substitution:
3xーy= 17
2x+y= 8
Answers
what is 1.75 times 1.75?
Answers
Answer: 3.06
Step-by-step explanation:
what is ounces per cup?
Answers
Ounces per cup is a measure of volume used in cooking; a standard measuring cup holds 8 fluid ounces.
Ounces per cup is a proportion of volume utilized in preparing and food planning. It alludes to the quantity of liquid ounces that can be held in a standard cup measure. In the US, a standard estimating cup holds 8 liquid ounces, so when somebody alludes to a specific number of ounces per cup, they are normally alluding to the number of liquid ounces that are expected to fill one cup.
Understanding ounces per cup is significant in cooking and baking, as recipes frequently call for fixings to be estimated in cups or liquid ounces. It is additionally essential to take note of that ounces per cup can change contingent upon the kind of fixing being estimated, as certain fixings have various densities or loads per volume.
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For the following set of problems, perform the necessary calculations. Show your work.
A) Consider the following set of scores and calculate the sum of scores (∑X) and the mean (M): 8 2 5 7 12 9 11 3 6
B) If you are presented with a sample of n = 12 scores that has a mean of M = 8, what would be the value of ΣX (sum of scores)?
C) If you are presented with a sample of n = 6 scores and you know that five of the scores are each above the mean by one point, where would the sixth score have to be located relative to the mean? Why? Hint: Think of the sea saw.
D) If you are presented with a sample with a mean of M = 8 that has ΣX=56, how many scores are in the sample?
E) You are presented with two samples. One sample of n = 10 scores had a mean of M = 8, and the second sample of n = 5 scores has a mean of M = 2. If the data from the two samples are combined, what is the mean for the combined sample? Hint: Find the sum of scores for each sample first in order to compute the mean for the combined sample.
Answers
A) Sum of (Score) ΣX equal to 63 and (Mean)M equal to 7.
B) Sum of Score ΣX equal to 96.
C) On the other side of the seesaw, the sixth score must be one point below the mean.
D)The sample has 7 scores.
E) To get the mean for the combined sample, the scores for each sample added together are 6.
A) Here we have to calculate the sum of scores (ΣX),
Add all of the scores together:
8 + 2 + 5 + 7 + 12 + 9 + 11 + 3 + 6
= 63
We sum up all of the scores and divide by the total number of scores (in this example, 9), which gives us the mean (M):
M = ΣX / n
M = 63 / 9
M = 7
B)The following formula may be used to get the value of X when the sample size (n) is 12 and the mean (M) is 8.
ΣX = M x n
ΣX = 8 x 12 = 96
Therefore, ΣX = 96.
C) The sixth score would need to be one point below the mean to balance the total if we know that the first five scores are all one point above the mean. This is thus because, like a seesaw, the mean represents the point of equilibrium in a group of scores. The seesaw is skewed up on one side if five scores are above the mean; the only way to balance it out is to position the sixth score on the other side, one point below the mean.
D) The following formula may be used to get the total number of scores in a sample with a mean (M) of 8 and a sum (X) of 56 scores:
ΣX = M x n
56 = 8 x n
n = 7
Hence, The sample has 7 scores.
E) The sum of the scores for each sample must first be determined in order to get the mean for the combined sample:
First sample, n = 10, M = 8, and the following:
ΣX1 = M x n
ΣX1 = 8 x 10
ΣX1 = 80
Second sample with n = 5 and M = 2:
ΣX2 = M x n
ΣX2 = 2 x 5
ΣX2 = 10
We just put the two amounts together to obtain the combined sample's overall sum of scores (ΣX):
ΣX = ΣX1 + ΣX2
ΣX = 80 + 10
ΣX = 90
We divide the entire sum of scores by the total number of scores to determine the mean for the combined sample:
M = ΣX / n
M = 90 / (10 + 5)
M = 6
Hence, six is the sample's overall mean.
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what is online calculator system of equation
Answers
Online calculator system of equation is an open-source online calculator that shows the value of the variable for the specified set of equations.
The collection or set of equations is referred to as a system of equations in mathematics. The variables in the equations can have their answers found by solving the corresponding equations. We are aware that variables, constants, coefficients, and exponents make up an algebraic equation. There are three different kinds of systems of equations that can be seen when working with a system of linear equations. As follows:
a dependent system with countless possible outcomesa unique system with a single solutionan unreliable system with no fixLearn more about system of equation:
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Name two measures of the variation of a distribution, and state the conditions under which each measure is preferred for measuring the variability of a single data set. A. The mean is preferred when the data is relatively symmetric B. The standard deviation is preferred when the data is relatively symmetric C. The median is preferred when when the data is relatively symmetric D. The standard deviation is preferred when there are many data points E. The interquartile range is preferred when the data is strongly skewed or has outliers. F The interquartile range is preferred when there are few data points G. The z-score is preferred when there are many data points H. The median is preferred when the data is strongly skewed or has outliers.
Answers
Measures of the variation of distribution are variance, standard deviation, range, interquartile range, and coefficient of variation.
Measures of the variation of a distribution:
Measures of the variation of distribution are used to quantify the spread or dispersion of the data points in the distribution.
Variance:The variance is a measure of the variation of distribution that represents how spread out the data points in a distribution are from the mean.
A higher variance indicates that the data points are more spread out, while a lower variance indicates that they are more tightly clustered around the mean.
The variance is useful when the data is normally distributed and there are no extreme outliers in the dataset.
Standard deviation:Standard deviation is a measure that shows how the spread or dispersion of a set of data points from the mean.
The standard deviation can tell us how tightly or loosely the data points are clustered around the mean. A smaller standard deviation indicates that the data points are tightly clustered, while a larger standard deviation indicates that the data points are more spread out.
The standard deviation is useful when the data is normally distributed and there are no extreme outliers in the dataset.
Some of the measures of the variation of distribution are Range, Interquartile range, Coefficient of variation, etc.
Therefore,
Measures of the variation of distribution are variance, standard deviation, range, interquartile range, and coefficient of variation.
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Solve for x pleaseeee
Answers
Answer: 16
Step-by-step explanation:
48/3=16
Answer: x= 20.3333 degress
Step-by-step explanation:
61 degrees=3x
3x=61 degrees
x=61 degrees/3
x=20.3333 degrees
. HELP DUE TOMORROW !!!!!!!!!!!!!!!
For the circle below, find the area of the shaded sector and the length of the arc that outlines the sector. All units are centimeters. Give your answers in terms of π.
Answers
The length of the arc that outlines the sector is 15π centimeters.
What is the area of sector?
The area of a sector is given by the formula:
[tex]A=\frac{\theta}{360^{\circ}} \times \pi r^2[/tex]
where A is the area of the sector, θ is the central angle of the sector (in degrees), and r is the radius of the circle.
To find the area of the shaded sector, we need to use the formula -
[tex]Area=\frac{central \angle}{360^{\circ}} \times \pi r^2[/tex]
In this case, the central angle is 270° and the radius is 10 cm. Plugging these values into the formula, we get:
Area of sector = [tex]\frac{270^{\circ}}{360^{\circ}} \times \pi (10)^2[/tex]
Area of sector = (3/4) x π x 100
Area of sector = 75π
So the area of the shaded sector is 75π centimeters.
To find the length of the arc that outlines the sector, we need to use the formula:
Length of arc = (central angle / 360°) x 2πr
Plugging in the values of the central angle and radius, we get:
Length of arc = (270/360°) x 2π x 10
Length of arc = (3/4) x 20π
Length of arc = 15π
Hence, the length of the arc that outlines the sector is 15π centimeters.
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algebra 1 i need help 100 points
Answers
An equation for each situation in terms of x include the following:
A = 3x + 65
B = 2x + 100
The number of miles driven that would make the cost of each company the same is $35.
How to write a system of equation to model this situation?Based on the information provided above, Company A charges an initial fee of $65 for the rental plus $3 per mile driven. Therefore, the total cost, A, can be represented by this equation:
A = 3x + 65
Since Company B charges an initial fee of $100 for the rental plus $2 per mile driven. Therefore, the total cost, A, can be represented by this equation:
B = 2x + 100
For the cost of each company to be the same, we have the following:
3x + 65 = 2x + 100
3x - 2x = 100 - 65
x = $35.
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how to convert 1c to 1f?
Answers
The steps to convert Celsius to Fahrenheit has been explained
To convert Celsius to Fahrenheit, use the following formula:
F = (C x 1.8) + 32
Where C represents the temperature in Celsius and F represents the temperature in Fahrenheit.
To use this formula, simply multiply the temperature in Celsius by 1.8 and then add 32 to the result. The final result will be the temperature in Fahrenheit.
It's important to note that Celsius and Fahrenheit are two different temperature scales used in different parts of the world. Celsius is used in most countries, including Europe and Canada, while Fahrenheit is used primarily in the United States.
Therefore, the steps of conversion has been explained
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The given question is incomplete, the complete question is:
How to convert Celsius to Fahrenheit?
How do you find the coordinates of a polar point?
Answers
To discover the coordinates of a polar point, you need to recognize its distance from the origin (the polar axis) and the perspective it makes with the superb x-axis.
The space is commonly denoted via the image r, and the angle is denoted by means of the image θ. To devise a polar point, you start by locating the foundation and drawing a line alongside the polar axis.
Subsequently, you measure the angle θ from the fine x-axis, shifting counterclockwise.
In the end, your degree the distance r from the starting place and plot the factor on the corresponding location.
To find the coordinates of a polar point, you can use the subsequent formulas:
x = r cos(θ)
y = r sin(θ)
Right here, x and y constitute the rectangular coordinates of the factor, while r and θ constitute the polar coordinates.
Those formulas let you convert between polar and rectangular coordinates, which can be useful for graphing and solving problems in diverse branches of mathematics and physics.
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How to convert 9/16 to decimal?
Answers
9/16 as a decimal is 0.5625.
A decimal number is a number that is written in the base-ten numeral system, which is the system we use in everyday life. In the decimal system, there are ten digits, from 0 to 9, and each digit has a place value that is ten times greater than the digit to its right.
To convert the fraction 9/16 to a decimal, you can divide the numerator (the top number) by the denominator (the bottom number) using long division or a calculator. Here's how to do it:
Write down the fraction 9/16.
Divide the numerator (9) by the denominator (16).
The quotient is the decimal equivalent of the fraction. In this case, the quotient is 0.5625.
Write the decimal as 0.5625.
Therefore, 9/16 is 0.5625.
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What is the conversion of 27cm to inches ?
Answers
The conversion of 27cm to inch is 10.63 inches.
A centimeter is a metric unit of measurement equal to one-hundredth of a meter. It is commonly used in many countries for measuring small distances, such as the length of an object or the height of a person. One centimeter is equal to 0.3937 inches.
To convert 27 centimeters to inches, we can use the following formula:
1 inch = 2.54 centimeters
Therefore, to convert 27 centimeters to inches, we can divide 27 by 2.54:
27 cm ÷ 2.54 = 10.63 inches (rounded to two decimal places)
So, 27 centimeters is approximately equal to 10.63 inches.
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What is the surface area of the right rectangular prism?
Enter your answer in the box.
ft²
8 ft
18 ft
7 ft
Answers
Greg is building birdhouses in shop class. The amount of wood he has on hand determines how many birdhouses he can build. w = the amount of wood Greg has on hand b = the number of birdhouses Greg can build Which of the variables is independent and which is dependent?
Answers
Answer:
Step-by-step explanation:
w is the independent
b is the dependent
Think of it this way: the number of birdhouses depends on the amount of wood available.
what is 4.5 kg - 7.5 kg?
Answers
In this case, we subtracted 7.5 kg from 4.5 kg and obtained a result of -3 kg.
Subtraction is a mathematical operation that involves taking one number away from another. It can be represented using the "-" symbol, and the number to the left of the symbol is called the minuend, while the number to the right is called the subtrahend.
In this case, we have 4.5 kg as the minuend and 7.5 kg as the subtrahend, which means that we need to take away 7.5 kg from 4.5 kg.
To perform the subtraction, we start by aligning the digits of both numbers in columns according to their place values (i.e., ones, tens, hundreds, etc.).
Since both numbers have the same unit of measurement (kg), we do not need to perform any conversions.
We then begin subtracting the digits in the subtrahend from the corresponding digits in the minuend, starting from the rightmost column and working our way leftwards.
So, it can be written as,
=> 4.5 - 7.5 = -3 kg.
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what is 107 kg to lbs?
Answers
The value of 107 kg into lbs can be converted by multiplying kilogram by 2.204622 so the answer is 235.895 pounds.
Unit conversion is the process of converting the measurement of a given amount between various units, often by multiplicative conversion factors that alter the value of the measured quantity without altering its effects.
The SI unit of mass is the kilogramme (kg). It has the same mass as the international kilogramme prototype. The International Bureau of Weights and Measures maintains a platinum-iridium international prototype similar to this one. A kilogramme is about equivalent to 2.20462262184878 pounds.
The legal definition of a pound, or the international avoirdupois pound, is 0.45359237 kilogrammes.
Pounds = kilograms × 2.20462262184878
= 107 x 2.20462262184878
= 235.895 pounds or lbs.
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if other factors are held constant, what is the effect of increasing the sample variance? group of answer choices it will increase the estimated standard error and increase the likelihood of rejecting h0. it will increase the estimated standard error and decrease the likelihood of rejecting h0. it will decrease the estimated standard error and increase the likelihood of rejecting h0. it will decrease the estimated standard error and decrease the likelihood of rejecting h0.
Answers
if other factors are held constant, what is the effect of increasing the sample variance: B. it will increase the estimated standard error and decrease the likelihood of rejecting h0.
What is a sample proportion?In Mathematics, a sample proportion can be defined as the proportion of individuals in a sample that have a specified characteristic or trait.
Mathematically, the standard error of a sample proportion can be calculated by using this formula:
Standard error = √(p × (1 - p)/n)
Where:
p represents the sample proportion.n represents the sample size.Generally speaking, the effect of increasing the sample variance is an increase in estimated standard error and a decrease in the likelihood of rejecting H_{0} provided that other factors are held constant.
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One important use of the regression line is to do which of the following?
A. To determine the strength of a linear association between two variables
B. To determine if a distribution is unimodal or multimodal
C. To make predictions about the values of y for a given x-value
D. Both A and B are correct
Answers
Answer:
C. To make predictions about the values of y for a given x-value (I THINK)
The angle of elevation to a nearby tree from a point on the ground is measured to be 32
∘
∘
. How tall is the tree if the point on the ground is 71 feet from the tree? Round your answer to the nearest tenth of a foot if necessary.
Answers
The height of the tree is given as follows:
44.4 feet.
What are the trigonometric ratios?The three trigonometric ratios are defined as follows:
Sine of angle = length of opposite side divided by the length of the hypotenuse.Cosine of angle = length of adjacent side divided by the length of the hypotenuse.Tangent of angle = length of opposite side divided by the length of the adjacent side.For the height, we have that:
The opposite angle is of 32º.The side adjacent to the angle of 32º is of 71 feet.Hence the height is obtained as follows:
tan(32º) = h/71.
h = 71 x tangent of 32 degrees
h = 44.4 feet.
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HELP.
A cone with height h and radius r has volume V = 1/3πr^2h. If a certain cone with a height of 9 inches has volume V = 3πx^2 + 42πx + 147π, what is the cone’s radius r in terms of x?
Answers
The cone’s radius r in terms of x is x + 7
How to determine tthe cone’s radius r in terms of x?From the question, we have the following parameters that can be used in our computation:
Volume, V = 3πx^2 + 42πx + 147π
Height, h = 9
The volume of a cone is
V = 1/3πr^2h
Substitute the known values in the above equation, so, we have the following representation
1/3πr^2 * 9 = 3πx^2 + 42πx + 147π
So, we have
3πr^2 = 3πx^2 + 42πx + 147π
Divide by 3π
r^2 = x^2 + 14x + 49
So, we have
r = √(x² + 14x + 49)
Evaluate
r = x + 7
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Please help me!
Write the equation of each line in slope‐intercept form.
Answers
The equation of each line in slope‐intercept form are y = -4x+2 and y = -x+4
What is a slope‐intercept form?The graph of the linear equation y = mx + c is a line with m as slope, m and c as the y-intercept. This form of the linear equation is called the slope-intercept form, and the values of m and c are real numbers.
GIven are two graphs of lines, we need to find the slope‐intercept form of the lines,
We know that, the slope‐intercept form of the line is given by:
y = mx+c, where m is slope and c is the y-intercept,
m = y₂-y₁ / x₂-x₁
1) The line is passing through two points (0.5, 0) and (0, 2) :-
y-0 = 2-0 / 0-0.5 (x-0.5)
y = -4(x-0.5)
y = -4x+2
2) The line is passing through two points (4, 0) and (0, 4) :-
y-0 = 4-0 / 0-4 (x-4)
y = -1(x-4)
y = -x+4
Hence, the equation of each line in slope‐intercept form are y = -4x+2 and y = -x+4
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square root of 2w + 9 + square root of 4 - 3w = 0
Answers
As a result, the equation ((2w + 9) + ((4 - 3w) = 0) has no answer.
What in mathematics is the square root?The term "radical" is used to represent the square root or nth elements. Expression with a square base is referred to as a radical expression. Radicand: A value or phrase contained within the radical sign. Equation with radical formulas and factors as radicands is referred to as a radical equation.
√(2w + 9) + √(4 - 3w) = 0
We need to isolate the variable w.
First, we can move the second term to the other side of the equation by subtracting it from both sides:
√(2w + 9) = -√(4 - 3w)
Next, we can square both sides of the equation to eliminate the square roots:
(√(2w + 9))^2 = (-√(4 - 3w))^2
2w + 9 = 4 - 3w
Now, we can simplify and solve for w:
5w = -5
w = -1
In this case, when w = -1, both square roots are defined, and we can substitute this value back into the original equation to verify:
√(2(-1) + 9) + √(4 - 3(-1)) = √7 + √7 = 2√7
Since 2√7 is not equal to 0, our solution is not valid.
Therefore, there is no solution to the equation √(2w + 9) + √(4 - 3w) = 0.
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