The x-intercept represents:
"The number of hours the taxi was driven before running out of fuel"
What does the x-intercept represent?In standard notation, the variable x is the independent variable in the horizontal axis, here we can see that in the horizontal axis we are measuring the time (in hours) that the taxi was driving.
Then the x-intercept (the time when y = 0) is the number of hours until the fuel is down to zero, then the correct option is B i guess, but it should be worded as:
"The number of hours the taxi was driven before running out of fuel"
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If f(x)= e³x, then d/dx(e³x)=? A. 3e³x B. e³x C.ex D. 9e³x
Answer:
the answer is D. 9e³x.
Step-by-step explanation:
If f(x) = e³x, then we can find its derivative using the chain rule of differentiation as follows:
d/dx(e³x) = 3e³x * d/dx(3x) = 3e³x * 3 = 9e³x
= D. 9e³x.
Answer:
A
Step-by-step explanation:
HELP! LOTS OF POINTS!
Answer:
D(last option)
Step-by-step explanation:
This question might be a bit confusing since a lot of questions like this one require actually visualizing the question. The man in the lighthouse isn't trying to throw the rope directly in front of him to the birds, but rather to the boat.
The angle of depression here is the angle formed from the rope and the man's line of sight. Therefore, the angle of depression is congruent to the angle's alternate interior counterpart, which is the angle of elevation formed from the boat to the water.
From there, we solve like an angle of elevation question. We have the rope length, which is the hypothenuse, but we need to find the length of the side adjacent to the angle of elevation. So, we use cosine.
We just need to plug in the values here. The measure of the angle goes right next to the trig function we are using, and in cosine, the measure of the adjacent angle goes over the measure of the hypothenuse.
Therefore, the answer is D, or the last option.
Answer:
[tex]\textsf{D)} \quad \cos \left(24^{\circ}\right)=\dfrac{x}{45}[/tex]
Step-by-step explanation:
The angle of depression is the angle between the horizontal line of sight of the man in the lighthouse, and the direct line of sight to the boat below him.
To find how far from land the boat is, we can model the scenario as a right triangle.
The angle of depression (24°) is the angle formed by the hypotenuse and the horizontal leg of the right triangle.
If the distance to throw a rope from the top of the lighthouse to the boat is 45 feet, then the hypotenuse of the triangle is 45 feet.
The distance between the boat and the land is the side adjacent to the angle, so we can find this by using the cosine trigonometric ratio.
[tex]\boxed{\begin{minipage}{9 cm}\underline{Cosine trigonometric ratio} \\\\$\sf \cos(\theta)=\dfrac{A}{H}$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle. \\\phantom{ww}$\bullet$ $\sf H$ is the hypotenuse (the side opposite the right angle). \\\end{minipage}}[/tex]
Given:
θ = 24°A = xH = 45Substitute these values into the ratio to create the required equation:
[tex]\large\boxed{\cos \left(24^{\circ}\right)=\dfrac{x}{45}}[/tex]
PLEASE HELP! An ethanol railroad tariff is a fee charged for shipments of ethanol on public railroads. An agricultural association publishes tariff rates for railroad-car shipments of ethanol. Assuming that the standard deviation of such tariff rates is $1200, determine the probability that the mean tariff rate of 400 randomly selected railroad-car shipments of ethanol will be within $80 of the mean tariff rate of all railroad-car shipments of ethanol. Interpret your answer in terms of sampling error. The probability is what?
(Round to three decimal places as needed.) Thanks!
If an ethanol railroad tariff is a fee charged for shipments of ethanol on public railroads. The probability is: 84.6%.
How to find the probability?In this case, we have:
Population standard deviation (σ): $1200
Sample size (n): 400
Margin of error (E): $80
The standard deviation of the sample mean can be calculated as:
σM = σ / √n = 1200 / √400 = 60
To find the probability that the sample mean is within $80 of the population mean, we need to find the z-scores for the upper and lower limits of the interval:
Lower limit: z = (mean - E - population mean) / σM = (-80) / 60 = -1.3333
Upper limit: z = (mean + E - population mean) / σM = 80 / 60 = 1.3333
Using a standard normal distribution table or calculator, we can find the area under the curve between these two z-scores:
P(-1.3333 < Z < 1.3333) = 0.8461
Therefore, the probability that the mean tariff rate of 400 randomly selected railroad-car shipments of ethanol will be within $80 of the mean tariff rate of all railroad-car shipments of ethanol is approximately 0.846 or 84.6%.
Interpretation: This means that if we take many samples of 400 railroad-car shipments of ethanol and calculate their mean tariff rates, about 84.6% of these means will be within $80 of the true mean tariff rate of all ethanol shipments. This also means that there is a sampling error of $80, which is the maximum amount by which the sample mean may differ from the population mean due to random sampling variability.
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Carole surveyed the class for a math project. Below are the results of her survey. What type of graph is best for Carole to display her data? A. bar graph B. line graph C. histogram D. circle graph
Answer:
A
Step-by-step explanation:
it is a bar graph because it involves class interval
A. Using the given variables, translate the following to mathematical
expressions.
1. the sum of n and 8
2. M reduced by x
3. 12 subtracted from z
4. cincreased by d
5. 20 more than twice f
6. the square of the sum of x and y
7. twice the product of m and n
8. six less than twice b
9. the sum of the squares of u and v
10.the product of x and y divided by 2
Answer:
n + 8
M - x
z - 12
c + d
2f + 20 or 20 + 2f
(x + y)^2 or (x + y) × (x + y)
2mn or 2 × m × n
2b - 6 or 6 - 2b
u^2 + v^2 or v^2 + u^2
(xy)/2 or xy/2
Select the correct answer.
These lines are perpendicular. Is this statement true or false?
y = - 2/5x + 4
y =5/2x-3
A.true
B. false
The statement "These lines are perpendicular" is true.
These lines are perpendicular. Is this statement true or false?To determine if the two lines are perpendicular, we need to check if the product of their slopes is -1. That is, if:
m1 × m2 = -1
where m1 is the slope of the first line and m2 is the slope of the second line.
The slopes of the two lines are:
m1 = -2/5
m2 = 5/2
So, m1 × m2 = (-2/5) × (5/2) = -1
Since the product of the slopes is -1, the two lines are perpendicular. Therefore, the statement "These lines are perpendicular" is true.
The correct answer is A. true.
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Module Test Form B (RM C3 M8) Second Version) mo
13) Determine whether the following statement is true or false.
The capital letter N produces the same capital letter after being rotated 180°.
O True
O False
The statement "The capital letter N produces the same capital letter after being rotated 180°" is true.
If you rotate the capital letter N 180°, it will produce the same capital letter, as it has rotational symmetry.
The letter N has a vertical line of symmetry in the center, which means that if you rotate it 180°, it will overlap perfectly with its original position, producing the same letter.
So, the statement "The capital letter N produces the same capital letter after being rotated 180°" is true.
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The quadrilateral
�
�
�
�
GRAY is shown below. Find the image of quadrilateral
�
�
�
�
GRAY if it has a translation of 4 units left and 2 units down and then is dilated by a scale factor of
1
2
2
1
The coordinates of the figure after translation & dilation are A''(1,3) ,R''(-1/2,1) , G''(-1,-3/2), Y''(5/2,5/2).
What is quadrilateral?A quadrilateral is a polygon with four sides and four vertices. Some examples of quadrilaterals include squares, rectangles, parallelograms, trapezoids, and rhombuses.
What is meant by scale factor?Scale factor refers to the ratio of the length or size of an object in one dimension to the length or size of a corresponding object in another dimension. It is commonly used in mathematics and geometry to describe the relationship between two similar figures. For example, if one square has a side length of 4 cm and another square is similar to it with a side length of 8 cm, the scale factor between the two squares is 2:1.
A(2,8) R(3,4) G(2,-1) Y(9,7)
Translate it to 4 units left gives the result:
A'(-2,6) ,R'(-1,2) ,G'(-2,-3), Y'(5,5)
Now dilate it:
A''=(-1,3), R''(-1/2,1), G''(-1,-3/2), Y''(5/2,5/2)
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Mary can mow Mrs. Greenway’s lawn in 45 minutes. Mary’s little brother takes twice as long to do the same lawn. How long will it take them if they each have a mower and they work together?
Answer:
30 minutes
Step-by-step explanation:
1/45 m + 1/90 m = 1
2/9 m + 1/90 m = 1
3/90 m = 1 Multiply both sides by 90/3
90/3 x 3/90 m = 1 x 90/3
m = 90/3
m = 30
Helping in the name of Jesus.
Kevin answered 62 questions correctly on his multiple choice history final and earned a grade of 31%. How many total questions were on the final exam?
Answer:
200
Step-by-step explanation:
Turn the 31% back to a decimal = 0.31
62/ x = 0.31
multiply each side of the equation by x to cancel it out from under the fraction
62 = 0.31x
divide each side by 0.31 to have to x alone
200 = x
Check work:
62/200 = 0.31 x 100 = 31%
In July 1964, an elderly woman was mugged in Costa Mesa, California. In the vicinity of the crime a tall, bearded man sat waiting in a yellow car. Shortly after the crime was committed, a young, tall woman, wearing her blond hair in a ponytail, was seen running from the scene of the crime and getting into the car, which sped off. The police broadcast a description of the suspected muggers. Soon afterward, a couple fitting the description was arrested and convicted of the crime. Although the evidence in the case was largely circumstantial, the two people arrested were nonetheless convicted of the crime. The prosecutor based his entire case on basic probability theory, showing the unlikeness of another couple being in that area while having all the same characteristics that the elderly woman described. The following probabilities were used. Characteristic Assumed probability Drives yellow car 1 out of 12 Man over 6 feet tall 1 out of 10 Man wearing tennis shoes 1 out of 4 Man with beard 1 out of 11 Woman with blond hair 1 out of 3 Woman with hair in a ponytail 1 out of 13 Woman over 6 feet tall 1 out of 100 Compute the probability of another couple being in that area with the same characteristics. Would you use the addition or multiplication rule? Why? Are the characteristics independent or dependent? How are the computations affected by the assumption of independence or dependence? Should any court case be based solely on probabilities? Would you convict the couple who was arrested even if there were no eyewitnesses? Comment on why in today’s justice system no person can be convicted solely on the results of probabilities. In actuality, aren’t most court cases based on uncalculated probabilities?
No, any court case should not be based solely on probabilities as probability does not imply certainty.
How to solveCompute the probability of another couple being in that area with the same characteristics
CHARACTERISTIC ASSUMED PROBABILITY
Drives a yellow car 1 out of 12
Man over 6 feet tall 1 /10
Man wearing tennis shoes 1/4
Man with beard 1/11
Woman with blond hair 1/3
Woman with hair in a ponytail 1 /13
Women over 6 feet tall 1/100
We will use the multiplication rule as all the characteristics should be present in the couple.
The probability of another couple being in that area with the same characteristics is given as
P(Drives a yellow car) x P(Man with beard) x P(Woman with blond hair) x P(Woman with hair in a ponytail) x P(Woman over 6 feet tall) = 1/12 x 1/11 x 1/3 x 1/13 x 1/100 = 1/514800
The characteristics dependent on the sum of the probabilities is not equal to 1.
The assumption of independence would lead to use of the addition rule instead of the multiplication rule, and hence the probability would change (the probability would increase).
No, any court case should not be based solely on probabilities as probability does not imply certainty.
No, the couple who was arrested should not be convicted if there were no eyewitnesses as probability does not imply certainty.
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Please see the attached.
Answer:
min: 56
lower quartile: 70
median: 74
upper quartile: 80
max: 86
Matt's parents pay him $5.50 for each half hour he babysits his sister, plus a two dollar tip. If Matt made $18.50, fo how long did he babysit
The number of hours Matt babysits his sister is 1 and half hours.
Given that, Matt's parents pay him $5.50 for each half hour he babysits his sister, plus a two dollar tip.
Let the number of half an hours Matt babysits his sister be x.
Matt made $18.50
So, equation is 5.50x+2 =18.50
5.50x=16.50
x=16.50/5.50
x= 3
Which means 1 and half hours he babysits his sister.
Therefore, the number of hours Matt babysits his sister is 1 and half hours.
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t1
Question 6 (2 points)
When cooking rice, the grain is 1/2 of the part to water. Write the ratio that
represents this.
Rice:Water = 2:1
Water:Ratio = 1:2
Rice:Water = 1:2
Question 7 (2 points) ✓ Saved
Answer:
1:2
Step-by-step explanation:
which statement correctly identifies the line of reflection?
the triangles are reflected across the x-axis
the triangles are reflected across the y-axis
the triangles are reflected across the line y=x
the triangles are reflected across the line y=-x
Answer:
the triangle arereflected across the line y=x
please i need help i literally have an hour and 45 minutes to finish this
Answer:
0.506
0.516
0.609
0.615
Step-by-step explanation:
Select all of the following that are potential roots of
p(x)=x²-9x²
- 4x + 12?
00
00
+2
NI ###
+4
+9
O +3
+6
+12
The potential roots of the function p(x) = x² - 9x² - 4x + 12 are x = 1, -1.5, and 12.
What is the degree of a polynomial?Degree of a polynomial is the highest power of the variable in that polynomial. For example, in a cubic polynomial, the variable [[tex]\bold{x}[/tex]] has the highest power of 3.
Given is the following function with degree of 2 as -
We will plot the graph and find the roots of this function. The number of x - intercepts [coordinates where the graph cuts the x axis] will give us the roots or zeroes of the polynomials. Refer to the graph attached, it shows that the graph intercepts the x - axis at three different coordinates which are → x = 1, x = -1.5, and x = 12. Hence, these three values of [x] are the potential roots of the function p(x) = x² - 9x² - 4x + 12.
Therefore, the potential roots of the function p(x) = x² - 9x² - 4x + 12 are x = 1, -1.5, and 12.
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The potential roots of the given polynomial equation are +4 and -3. These roots are found by factoring the equation, setting each factor equal to zero and solving for x.
Explanation:To find the potential roots of the polynomial equation p(x) = x² - 9x - 12, we can set the equation to zero and solve for x: 0 = x² - 9x - 12.
Next, we look for the factors of 12 which when multiplied would give you -12 and when subtracted would give you 9. There we have -4 and +3. Therefore the factors of the equation are (x - 4)(x + 3) = 0.
So, Final answer:
The potential roots of the given polynomial equation are +4 and -3. These roots are found by factoring the equation, setting each factor equal to zero and solving for x.
Explanation:To find the potential roots of the polynomial equation p(x) = x² - 9x - 12, we can set the equation to zero and solve for x:
0 = x² - 9x - 12.
Next, we look for the factors of 12 which when multiplied would give you -12 and when subtracted would give you 9. There we have -4 and +3. Therefore the factors of the equation are (x - 4)(x + 3) = 0.
So, potential roots of the equation are x = 4 and x = -3 if we set each factor equal to zero and solve for x. This means that from the given options, the potential roots to the equation would be +4 and -3 (though -3 is not mentioned). of the equation are x = 4 and x = -3 if we set each factor equal to zero and solve for x. This means that from the given options, the potential roots to the equation would be +4 and -3 (though -3 is not mentioned).
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the amount of money an hourly employee makes, m for working h hours can be represented by the equation m = 12.80h . what is the constant of propportionality of the equation?
The constant of proportionality of the equation would be = 12.80.
What is constant of proportionality of an equation?The constant of proportionality of an equation is the figure that represents the ratio that exists between two different variables that has direct proportional relationship.
The amount of money made by an employee is directly proportional to the number of hours they worked.
That is m directly proportional to h
The equation = m = k h. where k = 12.80 = constant of proportionality.
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Is the following parallelogram actually a rectangle?
15 m
37 m
V 114
The given parallelogram is not a rectangle.
How to find a rectangle ?One of the tests for a rectangle is if a right angled triangle can be created by diagonally dividing the rectangle .
The test for a right - angled triangle is the Pythagorean Theorem which is :
Side ² + Side ² = Hypotenuse ²
Using, the dimensions, check to see if there is a right triangle :
7. 2 ² + 9. 1 ² = 12 ²
134. 65 ≠ 144
There is no right angled triangle so this is a parallelogram that is not a rectangle .
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I need help!
What is the volume of the prism? Be sure to state your answer with the units included
Answer: 105m
Step-by-step explanation:
Hope this helps! :)
HELP MEEEEE PLEAAASSEE!!
Whoever answers right gets marked brainliest!
Answer:
[tex]m = \frac{4 - ( \sqrt[3]{ - 6} + 4)}{0 - ( - 6))} = \frac{ \sqrt[3]{6} }{6} = .303[/tex]
So the average rate of change of g(x) over -6 < x < 0 is about .303.
Divide. Write your answer as a fraction or mixed number in simplest form 9÷4⅔
Use the definition of Ax
to write the vector equation as a matrix equation.
The matrix equation is enter your response here
If the vector is drawn from (0,0) to (5, -1), the outcome or the required vector is drawn.
Describe vector?A mathematical concept known as a vector has both a magnitude and a direction. Physical quantities like force, velocity, and acceleration are represented by it. In the physical sciences, engineering, and computer graphics, vectors are frequently employed. They can also be used to represent abstract concepts like magnitude, directions, and other things.
Here in the question,
(0, 0) is the beginning position. There should be an arrow above each vector name listed below.
Ink a line beginning at (3, -1). A vector has an origin of (0,0) and a destination of (3, -1).
Put a line through points (2,2). The vector B has a start point of (0, 0) and an end point of (2, 2).
These two vectors add up to: a + b = (3-1) + (2,2) = (5,1) when combined.
Whatever order they are in, b + a = (2,2) + (3, -1) = (5,1) regardless.
Either way, the same conclusion is reached.
The terminal point of A + B is at (5, 1).
If the vector is drawn from (0,0) to (5, -1), the outcome vector is drawn.
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9. A counting number is totally odd if all its digits are odd and their sum is odd. How many totally odd counting numbers less than 1000 are there?
We need to first determine how many totally odd counting numbers there are between 1 and 9. The answer is 250.
What is odd counting number?It is an integer that is not divisible by two and therefore has a remainder of 1 when divided by two. It is also referred to as an odd number, an odd integer, or an uneven number.
For this, let us consider all the digits from 1 to 9, and their respective sums.
Digit: 1 Sum: 1 (odd)
Digit: 3 Sum: 3 (odd)
Digit: 5 Sum: 5 (odd)
Digit: 7 Sum: 7 (odd)
Digit: 9 Sum: 9 (odd)
Since all the digits between 1 and 9 and their respective sums are all odd, it means that any counting number less than 10 that is composed of only these digits would be totally odd. This means that there are 5 totally odd counting numbers less than 10, i.e., 1, 3, 5, 7 and 9.
Now, since any counting number less than 1000 can be composed of any combination of these 5 digits, the total number of totally odd counting numbers less than 1000 can be calculated by multiplying the number of digits (5) by the number of combinations of those digits (999). The result of this calculation is 250, which is the answer to the question.
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Sophia has the following data:
131213141313h
If the range is 3, which number could h be?
A. 10
B. 11
Answer:
To determine the possible values of h, we need to first understand what is meant by the range.
The range is the difference between the highest value and the lowest value in a set of numbers. In this case, we don't know what the full set of numbers is, but we know that the range is 3.
The highest number in the set is 4 (since there are no higher numbers in the set than 4), and the lowest number in the set is either 1 or 2. This is because the range is 3, and there are only two possible sequences of three consecutive integers that include the number 4: 2, 3, 4 and 1, 2, 3.
So to find the possible values of h, we need to add 3 to each of the possible lowest numbers in the sequence.
If the lowest number is 1, then the possible highest numbers are 4 and 5 (4 + 3 = 7 but the sequence only goes up to 4 so the highest should be 5). Therefore, the possible values of h are either 10 or 11.
Therefore, the correct answer is B. 11.
The monthly rents (in dollars) paid by 10 people are given below. (Note that these are already ordered from least to greatest) 905, 940, 955, 965, 1020, 1040, 1045, 1085, 1090, 1105 Send data to calculator Suppose that one of the people moves. His rent changes from $905 to $ 1055 Answer the following (a) What happens to the mean ? decreases by It increases by s Box It stays the same . (b) What happens to the median ? It decreases by s It increases by It stays the same .
Therefore , the solution of the given problem of mean comes out to be $1055 is more expensive than $1020 it increases by.
What is mean?The total of all values variable divided by all of the values constitutes the outcome of a collection, sometimes referred to as the arithmetic mean. It's one of the key trend indicators that's utilised the most and is typically referred as the "mean." To obtain the answer, multiply the collection's overall number of numbers by each value. Either the raw data or information that has been combined into frequency charts can be used for calculations.
Here,
The average rent is determined by adding up all the rents and dividing by the total number of rents.
This is known as the mean.
Given that the person's rent increased by
=>$150, $1055 - $905 = $150.
The entire sum of all rentals would therefore rise, but the overall number of rents would stay the same at 10.
The mean would therefore rise by
=> $150/10
=> $15.
(b) The median rent at the moment is $1020 because the rents are already arranged from lowest to highest.
The new median would be the middle value of the revised list, which would include the new price of $1055,
if one person's rent increased from $905 to $1055.
The median would rise given that $1055 is more expensive than $1020.
Thus , it increases by.
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Mr. Hernandez has a high-speed printer that can produce 32 pages per minute.
Write an equation that shows the relationship between the print time in minutes, x, and the number of pages printed, y.
y =
An equation that shows the relationship between the print time in minutes, x, and the number of pages printed, y is y = 32x
The equation that shows the relationship between the print time in minutes, x, and the number of pages printed, y, can be obtained using the following formula:
y = r * x
where r represents the rate of printing in pages per minute, which in this case is 32 pages per minute.
Therefore, the equation becomes:
y = 32x
This equation states that the number of pages printed, y, is directly proportional to the print time in minutes, x, at a rate of 32 pages per minute.
For example, if Mr. Hernandez wants to print 128 pages, we can use the equation to find out how long it will take him:
128 = 32x
x = 128/32
x = 4
Therefore, it will take Mr. Hernandez 4 minutes to print 128 pages on his high-speed printer.
In summary, the equation y = 32x represents the relationship between the print time in minutes, x, and the number of pages printed, y, when using a high-speed printer that can produce 32 pages per minute.
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What is the lateral surface area
Answer:
A- 304.8 cm²
Step-by-step explanation:
Find the area for the 4 sides (excluding both the top and base).
(2(12×7.5))+(2(12×5.2)) = 302.8
Answer:
A. 304.8 cm²
Step-by-step explanation:
The rectangular prism has a total of 6 rectangular sides
~ two at the bottom and top both of equal dimensions 5.2 x 7.5
~ two at the front and back both of equal dimensions 12 x 7.5
~ two one on the left side and the other on the right side both of equal dimensions 12 x 5.2
The question is asking only for the lateral surface area. This means we ignore the top and bottom surfaces
For each of the other two pairs of rectangles, the surface area is nothing but the product of the dimensions for each rectangle
Therefore area of all the 4 rectangles is
2(5.2 x 7.5 + 12 x 5.2)
We multiply by 2 since there are 2 of each rectangular surface
2(5.2 x 7.5 + 12 x 5.2) = 304.8 cm² ANSWER
50 Points! Multiple choice algebra question. Find the inverse of f(x)=3+5x. Photo attached. Thank you!
the inverse of the function f(x) = 3 + 5x is f^(-1)(x) = (x - 3) / 5.To find the inverse of the function f(x) = 3 + 5x, we need to solve for x in terms of y, then replace y with the inverse notation f⁻¹(x).
what is inverse of the function ?
The inverse of a function is a new function that "undoes" the effect of the original function, meaning that if we apply the inverse function to the output of the original function, we get back the input.
In the given question,
To find the inverse of the function f(x) = 3 + 5x, we need to solve for x in terms of y, then replace y with the inverse notation f⁻¹(x). The steps to find the inverse are as follows:
Step 1: Replace f(x) with y.
y = 3 + 5x
Step 2: Solve for x in terms of y.
y - 3 = 5x
x = (y - 3) / 5
Step 3: Replace x with f⁻¹(x) to get the inverse function.
f⁻¹(x) = (x - 3) / 5
Therefore, the inverse of the function f(x) = 3 + 5x is f⁻¹(x) = (x - 3) / 5.
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An area of land measures 735 metres by 756 metres. It is to be divided up into
square plots of equal size.
(a) What is the area of the largest squares that will fit on it?
(b) How many squares will fit on it?
a) The largest squares that will fit on the land will have sides of length 3 meters. The area of each square is 3 * 3 = 9 square meters.
b) The number of squares that will fit on the land is 61773.
Explain square
A square is a geometric shape with four sides of equal length and four right angles. It is a type of rectangle, but all of its sides are the same length. Squares are used in mathematics to represent and calculate areas and volumes, and they also have applications in architecture and art.
According to the given information
(a) To find the area of the largest squares that will fit on the land, we need to find the greatest common divisor (GCD) of the dimensions 735 and 756, and then square it.
To find the GCD, we can use the Euclidean algorithm:
GCD(735, 756) = GCD(735, 756 - 735) = GCD(735, 21) = GCD(21, 735 - 21 * 35) = GCD(21, 210) = GCD(21, 210 - 21 * 10) = GCD(21, 90) = GCD(21, 90 - 21 * 4) = GCD(21, 6) = GCD(6, 21 - 6 * 3) = GCD(6, 3) = 3
Therefore, the GCD of 735 and 756 is 3. The largest squares that will fit on the land will have sides of length 3 meters. The area of each square is 3 * 3 = 9 square meters.
(b) To find how many squares will fit on the land, we need to divide the total area of the land by the area of each square. The total area of the land is:
735 * 756 = 555960 square meters
The area of each square is 9 square meters, as we found in part (a). Therefore, the number of squares that will fit on the land is:
555960 / 9 = 61773.333...
Since we can't have a fractional number of squares, we need to round down to the nearest integer. Therefore, the number of squares that will fit on the land is 61773.
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