Part a) Identify the coordinates of the image of triangle ABC after a dilation about the origin by a factor of 2Part b) Identify the coordinates of the image of triangle ABC after a rreflection over the y-axis
Answers
Part A
Coordinates before dilation
A = (-2, 4)
B = (-2, 3)
C = (-4, 3)
Coordinates after dilation with a scale factor of 2
A' = (-4, 8)
B' = (-4, 6)
C' = (-8, 6)
Part B
Coordinates after a reflection over the y-axis
Coordinates of triangle ABC after a reflection over the y-axis by negating the x-axis.
A' = (2, -4)
B' = (2, -3)
C' = (4, -3)
Related Questions
Identify a2 in the sequence below , 12 , 7 , 2 , -3
Answers
Answer:
a₂ = 7
Step-by-step explanation:
The subscript 2 on a₂ represents the second term in the sequence.
The second term is 7 , so
a₂ = 7
what is the value of y?
Answers
Answer:21
Step-by-step explanation:
Answer:
y = 3
Step-by-step explanation:
9 - y = 2y
Step 1: Add y to both sides
9 - y + y = 2y + y
9 = 3y
Step 2: Divide both sides by 3
9 / 3 = 3y / 3
3 = y
Answer: y = 3
John took a 5 1/2 mile walk to his friend's house. He left at 11 a.M. And arrived at his friend's house at 12:45 p.M. Therefore it took him 1 3/4 hours to get to his friends house. If the return trip took 2 1/4 hours, what is the average speed on the return trip?
Answers
Answer:
The average speed on the return trip is 2.44 miles/h.
Step-by-step explanation:
To find the average speed we need to use the following equation:
\( \overline{v} = \frac{d}{t} \)
Where:
d: is the distance
t: is the time
Since the question is to find the average speed on the return trip, we will take the data of the time and speed of only the return trip.
\(\overline{v} = \frac{d}{t} = \frac{5 + 1/2}{2 + 1/4} = 2.44 miles/h\)
Therefore, the average speed on the return trip is 2.44 miles/h.
I hope it helps you!
Similarly, converting between units can be very important, and it can be done by canceling units. For example, suppose that I want to convert 66 feet/second into miles per hour. If I know that there are 5280 feet in a mile, 60 seconds in a minute, and 60 minutes in an hour, then I can convert the quantity by multiplying it by those conversion factors in such a way that they cancel: ( 1 s
66ft )( 1 min60 s )( 1hr 60 min )( 5280ft1 mile )=45mile/hr I can do this because each conversion factor is equal to one, and multiplying by one does not change anything. Notice that if you cancel all the units that you can, you are left with the desired units. The numbers are evaluated with normal arithmetic. Cglints = 1 filn 4 ZCOS=1 strord Now you try, except I'm going to make up some fictional units for you to work with: There are 12 grees in a zool. There are 2 grees in 10 twibbs. There are 5 grees in a blob. There are 6 glints in a filn. There are 4 zools in a strord. 12 grees =1 ZOO 2 grees =10 twibs 5 grees =1 bic (a) Convert the quantity 7 glint/twibb (i.e., 7 glints-per-twibb) into filn/strord (i.e., filns-per-strord). As always, show your work. (b) Often we use prefixes for scientific units. For example, there are one-hundred centimeters in a meter. Similarly, the prefix kilo- means a factor of 10
3. For example, a kilometer is 10 3 meters or 1000 meters. If you need to review these prefixes, there is a handy chart on Wikipedia: ht tpa://en.wikipedia.org/wiki/Metric_prefix. Convert your answer from part (a) into megafiln/strord (i.e., megafilns-per-strord). (Hint: Check your answer for plausibility. Should the number of megafilns-per-strord be bigger or smaller than the number of filns-per-strord? If someone is going 1 foot-per-hour, are they going a larger number of feet-per-hour or a larger number of miles-per-hour?)
Answers
The number of megafilns-per-strord should be smaller than the number of filns-per-strord since a mega is a conversion factor of 10³ and is greater than 1, hence 1 megafiln is greater than 1 filn.
(a) The given units can be converted as follows: 6 glints = 1 filn...
(1)12 grees = 1 zool...
(2)2 grees = 10 twibbs...
(3)5 grees = 1 bic...
(4)Note that the grees are in both the numerator and denominator of the second unit conversion factor (3). Hence we can cancel out the grees by using it twice in the numerator and denominator. Now using the given conversion factors in equation (1), we get:
7 glint/twibb=7 glint/ (10 grees/2 grees)=14 glint/10 grees=14 glint/ (5 grees/12 grees)=16.8 filn/strord
(b) We need to convert the result of part (a) from filn/strord to megafiln/strord.
1 mega = 106
Thus 1 megafiln = 106 filn
16.8 filn/strord = (16.8 filn/strord) x (1 megafiln/106 filn) = 1.68 x 10-5 megafiln/strord
The number of megafilns-per-strord should be smaller than the number of filns-per-strord since a mega is a factor of 10³ and is greater than 1, hence 1 megafiln is greater than 1 filn. Similarly, going 1 foot-per-hour would mean going a smaller number of feet-per-hour than going 1 mile-per-hour since there are 5280 feet in a mile.
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a family has 4 children. let x represent the number of sons. is the probability distribution of x normally distributed?
Also, what is the probability distribution of x?
Answers
For each value of x (0, 1, 2, 3, 4), you can substitute the respective k value into the probability formula to calculate the probability distribution of x.
The number of sons in a family with 4 children can be represented by the random variable x. The possible values for x are 0, 1, 2, 3, or 4.
The probability distribution of x follows a binomial distribution, not a normal distribution. In a binomial distribution, each child is considered an independent Bernoulli trial with a fixed probability of success (in this case, having a son) and failure (having a daughter).
The probability of having a son (success) is denoted by p, and the probability of having a daughter (failure) is denoted by q = 1 - p.
The probability distribution of x can be calculated using the binomial probability formula:
P(x = k) = C(n, k) * p^k * q^(n-k)
Where C(n, k) represents the binomial coefficient, n is the number of trials (4 children in this case), k is the number of successes (number of sons), and p and q are the probabilities of success and failure, respectively.
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the region bounded by in quadrant i is rotated around . given that the volume of the solid generated by this revolution is , find the value of .
Answers
The volume of the solid generated by revolving the region in the first quadrant enclosed on the left by the y-axis and on the right by the curve x = 6 ( y² − y³ ) , rotated about the x-axis is π/5 cubic units.
The region is enclosed on the left by the y-axis and on the right by the curve x = 6(y² - y³).
The curve x = 6(y² - y³) intersects the y-axis at y = 0 and the curve x = 0 at y = 1. So, we can integrate from y = 0 to y = 1 to get the total volume of the solid.
The radius of each cylindrical shell is the distance between the x-axis and the curve x = 6(y² - y³). This can be expressed as 6y² - 6y³.
Putting it all together, the volume of each cylindrical shell is given by:
V = 2π(6y² - 6y³)dy
To get the total volume of the solid, we integrate this expression from y = 0 to y = 1:
V = ∫(0 to 1) 2π(6y² - 6y³)dy
Evaluating the integral gives:
V = π/5
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Complete Question:
Find the volume of the solid generated by revolving the described region about the given axis: The region in the first quadrant enclosed on the left by the y-axis and on the right by the curve x = 6 (y² − y³) , rotated about the x-axis.
What is the volume of a triangular pyramid?
Answers
Answer:
1/2 Bh
Step-by-step explanation:
find the area of the base (B) by multiplying.5 xlengthxwidth. The take this answer, multiply by .5 and the height of the pyramid.
The volume of a triangular pyramid is 1/2 × area of the base× height.
What is a triangular pyramid?
A pyramid with a triangular base is referred to as a triangular pyramid. Vertices are essentially corners in geometry. Both regular and irregular triangular-based pyramids have four vertices. Pyramids with triangular bases have six edges, three of which run along the base and three of which rise above the base.
The volume of an object has defined as the space that is occupied by the object.
The volume of a triangular pyramid is 1/2 × B × h.
B = area of the base of the triangular pyramid.
h = Height of triangular pyramid
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Find the percent of each number a. 50% of 46 b. 70% of 110
Answers
how many ways can patricia choose 4 pizza toppings from a menu of 19 toppings if each topping can only be chosen once?
Answers
There are 3876 ways in which Patricia can choose 4 pizza toppings from a menu of 19 toppings if each topping can only be chosen once. In permutation, the order is very important, and it is denoted by "P." which means that each item can only appear once in the lineup, and there are no duplicates. The formula for permutation is given as: P(n, r) = n!/(n-r)!
What is combination?In a combination, the order is not essential, and it is denoted by "C." It means that things can be jumbled up, and there are no duplicates. The formula for a combination is given as: C(n, r) = n! / (r! * (n-r)!)How to calculate the number of ways to choose 4 pizza toppings from a menu of 19 toppings?
To calculate the number of ways to choose 4 pizza toppings from a menu of 19 toppings, we need to use the combination formula, which is: C(n, r) = n! / (r! * (n-r)!)Here, n = 19 and r = 4, so the formula becomes: C(19,4) = 19!/(4!(19-4)!) = 19!/(4!15!) = (19*18*17*16)/(4*3*2*1) = 38,76. Therefore, there are 3876 ways in which Patricia can choose 4 pizza toppings from a menu of 19 toppings if each topping can only be chosen once.
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Skylar bought 30 movie ticket for a total of $200. Adult ticket cot 58 each, child ticket cot $3. 50 cach, and enior ticket cot $6 each. He bought twice the number of adult ticket than the number of child and enior ticket combined. How many of each type of ticket did Skylar buy?
Answers
He spent $200 on 0 tickets for children, 10 tickets for adults, and 20 tickets for seniors.
What is equation?The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.
Here,
Total number of tickets brought=30
Total amount paid=$200
Cost of kid ticket=$3.5
Cost of adult ticket=$8
Cost of senior ticket=$6
Let x, y, z be the number of tickets brought for kid, adult, senior.
x+y+z=30
3.5x+8y+6z=200
2y=x+z
x+y+z=30
3y=30
y=10
x+z=20
z=20-x
3.5x+80+6(20-x)=200
3.5x+80+120-6x=200
2.5x=0
x=0
z=20
He bought 0 tickets for kid, 10 tickets for adult and 20 tickets for senior with an amount of $200.
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Please, let me get the answers in 15 mins. Explain what a
strategy canvas is and how it is used
Answers
A strategy canvas is a visual framework used to analyze and compare the strategic positioning of different companies or products within an industry.
It is a tool developed by W. Chan Kim and Renée Mauborgne, the creators of the Blue Ocean Strategy, to help organizations identify and create new market spaces by differentiating their offerings.
The strategy canvas consists of two axes: the horizontal axis represents the key factors that the industry competes on, and the vertical axis represents the offering level or degree of offering provided for each factor. By plotting the current state of competing products or companies on the canvas, organizations can gain insights into the competitive landscape and identify areas of opportunity for innovation and differentiation.
The strategy canvas helps visualize the competitive factors that are driving the industry and highlights areas of convergence or similarity among existing offerings. It allows organizations to identify untapped market spaces where they can create unique value propositions and redefine the competitive boundaries.
To use a strategy canvas effectively, organizations need to analyze the key factors that customers value in the industry and assess the relative performance of their offerings compared to competitors. By identifying the factors where they are underperforming and overperforming, organizations can focus on enhancing their value proposition by reallocating resources, investing in areas of differentiation, and eliminating or reducing elements that do not create significant customer value.
A strategy canvas is a powerful tool for strategic analysis and innovation. It helps organizations visualize the competitive landscape, identify areas for differentiation, and create new market spaces by providing a clear understanding of customer preferences and the competitive factors that drive industry success.
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1. P = \(\begin{pmatrix}-\sin \left(x\right)&\cos \left(x\right)\\ \cos \left(x\right)&\sin \left(x\right)\end{pmatrix}\)
Q = \(\begin{pmatrix}\sin \left(x\right)&\cos \left(x\right)\\ \cos \left(x\right)&-\sin \left(x\right)\end{pmatrix}\)
and I is a 2×2 identity matrix. Find PQ +2I
2. P = \(\begin{pmatrix}\cos \left(x\right)&-\sin \left(x\right)\\ \sin \left(x\right)&\cos \left(x\right)\end{pmatrix}\)
Q =\(\begin{pmatrix}\cos \left(x\right)&\sin \left(x\right)\\ -\sin \left(x\right)&\cos \left(x\right)\end{pmatrix}\)
and I is a 2×2 identity matrix. Find PQ +2I
Answers
Answer:
We know that:
\(\left[\begin{array}{cc}a&b\\c&d\end{array}\right] = ad - bc\)The 2x2 identity matrix has a = d = 1 and b = c = 0sin²x + cos²x = 1#1The values:
\(P = \left[\begin{array}{cc}-sinx&cosx\\cosx&sinx\\\end{array}\right] = -sin^2x-cos^2x= -1\)\(Q = \left[\begin{array}{cc}sinx&cosx\\cosx&-sinx\\\end{array}\right] = sin^2x-(-cos^2x)= sin^2x+cos^2x=1\)\(I = \left[\begin{array}{cc}1&0\\0&1\\\end{array}\right] = 1-0=1\)The sum:
PQ + 2I = (-1)*1 + 2*1 = -1 + 2 = 1#2The values:
\(P = \left[\begin{array}{cc}cosx&-sinx\\sinx&cosx\\\end{array}\right] = cos^2x-(-sin^2x)= 1\)\(Q = \left[\begin{array}{cc}cosx&sinx\\-sinx&cosx\\\end{array}\right] = cos^2x-(-sin^2x)= 1\)\(I = \left[\begin{array}{cc}1&0\\0&1\\\end{array}\right] = 1-0=1\)The sum:
PQ + 2I = 1*1 + 2*1 = 1 + 2 = 3Can someone pls answer this
How do these numbers compare?
Drag the correct comparison symbol to the box.
10.09 10.9
< = >
Answers
Addressing issue at hand, we can state that the correct linear equation comparison symbol to the box. 10.09 10.9 f < = > is => 10.09 < 10.9
What is a linear equation?The algebraic equation y=mx+b is known as a linear equation. M serves as the y-intercept, and B serves as the slope. The previous clause has two variables, y and x, and is sometimes referred to as a "linear equation with two variables". Bivariate linear equations are those with two independent variables. The following are a few examples of linear equations: 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3. When an equation takes the form y=mx+b, with m denoting the slope and b denoting the y-intercept, it is referred to as being linear. The term "linear" refers to an equation having the form y=mx+b, where m stands for the slope and b for the y-intercept.
the correct comparison symbol to the box.
10.09 10.9
< = >
10.09 < 10.9
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2 diagonals of a regular nonagon (a 9-sided polygon) are chosen. What is the probability that their intersection lies inside the nonagon
Answers
The probability of the intersection of the two diagonals chosen lying inside the nonagon is 2/3.
What is the probability?
Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, with 0 representing an impossible event and 1 representing a certain event.
In this problem, the event of interest is the intersection of the two diagonals lying inside the nonagon. A nonagon is a 9-sided polygon, so there are 9 total corners, each of which can be one end of a diagonal. Therefore, there are 9 choose 2 = 36 total ways to choose two diagonals.
To find the number of favorable outcomes, we need to find the number of ways to choose two diagonals such that their intersection is inside the nonagon. To do this, we can notice that the diagonals that have an intersection inside the nonagon are the diagonals that connect non-adjacent corners of the nonagon. There are 8 non-adjacent corners, so there are 8 choose 2 = 28 ways to choose two non-adjacent corners.
So the probability of the intersection of the two diagonals lying inside the nonagon is:
P(intersection inside nonagon) = favorable outcomes / total outcomes = 28/36 = 2/3
Hence, the probability of the intersection of the two diagonals chosen lying inside the nonagon is 2/3.
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The probability of the intersection of the two diagonals chosen lying inside the nonagon is 2/3.
What is the probability?
Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, with 0 representing an impossible event and 1 representing a certain event.
In this problem, the event of interest is the intersection of the two diagonals lying inside the nonagon. A nonagon is a 9-sided polygon, so there are 9 total corners, each of which can be one end of a diagonal. Therefore, there are 9 choose 2 = 36 total ways to choose two diagonals.
To find the number of favorable outcomes, we need to find the number of ways to choose two diagonals such that their intersection is inside the nonagon. To do this, we can notice that the diagonals that have an intersection inside the nonagon are the diagonals that connect non-adjacent corners of the nonagon. There are 8 non-adjacent corners, so there are 8 choose 2 = 28 ways to choose two non-adjacent corners.
So the probability of the intersection of the two diagonals lying inside the nonagon is:
P(intersection inside nonagon) = favorable outcomes / total outcomes = 28/36 = 2/3
Hence, the probability of the intersection of the two diagonals chosen lying inside the nonagon is 2/3.
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a Rewrite the equation (4^x-1)²-6(4^x-1) + 8 = 0 in the form y² + by + c = 0, where y = 4^x-1 and b and c are constants to be found.
(1 mark)
b Factorise your equation from part a and hence, or otherwise, solve for x. You must show each step of your working.
(3 marks)
Answers
The values of constants are b = -6 and c = 8
The values of x are log base 4 of 3 or log base 4 of 5
Given equation,
(4^x-1) ²- 6(4^x-1) + 8 = 0
Let this equation be f(x) i.e., f(x) = (4^x-1) ²- 6(4^x-1) + 8 (equation 1)
In question it's mentioned that y = 4^x-1
Now substitute this 'y' value in equation 1. We get,
f(y) = y ²- 6y + 8 (Here, f(x) changed to f(y) because the equation now is in terms of y)
It's in form of y² + by + c = 0 where b = -6 and c = 8
Factorizing f(y),
y ²- 6y + 8 = 0
y ²- 4y -2y + 8 = 0 (Since, -6 = -4 -2)
y(y - 4) -2(y - 4) = 0
(y - 2)(y - 4) = 0
So, y = 2 or 4
i.e., 4^x-1 = 2 or 4
if 4^x-1 = 2 then
4^x-1 = 2
4^x = 3
x = log base 4 of 3
else (i.e., 4^x-1 = 4)
4^x-1 = 4
4^x = 5
x = log base 4 of 5
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How Many Solutions does this have?
Y= 12x + 9y = -36
Y= 4x + 3y= -12
Answers
Answer:
it has two solutions,,
Step-by-step explanation:
step 1,,, you have to find the difference between the first y and the second y,,,,,y=12x+9y=-36_y=4x+3y=-12 the solution is y= 8x+6y=24,,where again you have to find the value of x by substitution method,,,
trapezoid W'X'Y'Z' Is the image of a trapezoid WXYZ under a dilation through point C. What scale factor was using the dilation
Answers
Answer:
It is 7/3 i took the test
Step-by-step explanation:
Answer:
I need help on geometry its kinda like this one please respond if u can help :)
Step-by-step explanation:
Somebody already answered this question, so pls comment yes and ill say the question ty!
Calculate the volume of oil exiting the pipe every hour: Calculate the volume of oil exiting the pipe every day: Convert cu in/day to cubic feet per day: cu. in/hour cu in/day cu ft/day
Answers
The volume of oil exiting the pipe is approximately 100 cu in/hr, 2,400 cu in/day, and 1.39 cu ft/day when converting cu in/day to cubic feet per day.
To calculate the volume of oil exiting the pipe every hour, you would need to know the flow rate of the oil in cubic inches per hour. Let's assume the flow rate is 100 cubic inches per hour.To find the volume of oil exiting the pipe every day, you would multiply the flow rate by the number of hours in a day. There are 24 hours in a day, so the volume of oil exiting the pipe every day would be 100 cubic inches per hour multiplied by 24 hours, which equals 2,400 cubic inches per day.
To convert the volume from cubic inches per day to cubic feet per day, you would need to divide the volume in cubic inches by the number of cubic inches in a cubic foot. There are 1,728 cubic inches in a cubic foot. So, dividing 2,400 cubic inches per day by 1,728 cubic inches per cubic foot, we get approximately 1.39 cubic feet per day.
Therefore, the volume of oil exiting the pipe is approximately 100 cubic inches per hour, 2,400 cubic inches per day, and 1.39 cubic feet per day.
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A certain college graduate borrows $6600 to buy a car. The lender charges interest at an annual rate of 10%. Assuming that interest is compounded continuously and that the borrower makes payments continuously at a constant annual rate k dollars per year, determine the payment rate k that is required to pay off the loan in 5 years. (Round your answer to two decimal places.) k = $ per yr
Answers
The borrower would need to make payments of approximately $943.57 per year to pay off the loan in 5 years.
To determine the payment rate required to pay off the loan in 5 years, we can use the continuous compound interest formula:
A = P * \(e^{(rt)\),
where A is the final amount, P is the initial principal, e is the base of the natural logarithm (approximately 2.71828), r is the annual interest rate, and t is the time in years.
In this case, the initial principal is $6600, the annual interest rate is 10%, and the time is 5 years. We want to find the payment rate, so let's set A equal to zero, indicating that the loan is fully paid off:
0 = 6600 * \(e^{(0.10 * 5)\)- k * 5,
Simplifying the equation, we have:
\(e^{(0.5)\) = k / 6600.
Now, we can solve for k by multiplying both sides of the equation by 6600:
k = 6600 * \(e^{(0.5)\),
Using a calculator or software, we find that k is approximately $943.57 per year.
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multiply this please
Answers
Answer: C is the answer hope this helps!
Step-by-step explanation: Merry Christmas!
Answer:
A. 12x^4 + 10x^3 - 22x^2 - 15x
Step-by-step explanation:
(6x^2 - 4x - 5)(2x^2 + 3x)
2x^2 (6x^2 - 4x - 5) + 3x(6x^2 - 4x - 5)
12x^4 - 8x^3 - 10x^2 + 18x^3 - 12x^2 -15x
12x^4 + 10x^3 - 22x^2 - 15x
One of the most common types of volcanoes is called a cylinder cone volcano. These types of volcanoes are the smallest type of volcano, ranging between 300 feet and 1200 feet tall, and are in the shape of a cone.
Find the volume of a cinder cone volcano with a height of 350 feet and a diameter of 1100 feet. Use 3.14 for and round your answer to the nearest cubic foot.
Answers
The volume of a cinder cone volcano will be 110872040 cubic feet.
What is the volume of a cone?The volume of a cone is defined as the amount of space occupied by a cone in a three-dimensional plane.
The volume of the cone (V) = 1/3 πhr²
Given,
Radius of cone (r) = 1100/2 = 550 feet
Height of cone (h) = 350 feet
The volume of a cinder cone volcano = 1/3 πhr²
Substitute the values of h and r,
The volume of a cinder cone volcano = 1/3 × 3.14× (550)² × (350)
The volume of a cinder cone volcano = 110872040 cubic feet.
Thus, the volume of a cinder cone volcano will be 110872040 cubic feet.
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Choose all of the following angles that cannot
be an interior angle in a regular polygon.
40° 45° 108° 132° 179°
Answers
Answer:
40 45 because the minimum internal angle is 60
Determine the values of m and if the straight line y = mx + c passes through the point (3, 5) and has a gradient -4 .
Answers
Answer:
y = -4x + 17
Step-by-step explanation:
y = -4x + b
5 = -4(3) + b
5 = -12 + b
17 = b
What is the fully factored form of 16x^3+5x?
Answers
Answer:
Step-by-step explanation:
Answer: CLICK TO VIEW
16x^3+5x?
A local charity held a crafts fair selling donated, handmade items. Total proceeds from the sale were $1,950. A total of 150 items were sold, some at $5 each and the rest at $25 each.
How many items were sold at $25 ?
Answers
By using the unitary method, we found that 60 items were sold at $25 each, while 90 items were sold at $5 each at the charity's craft fair.
In this problem, we know the total number of items sold and the total revenue earned. Let's assume that the number of items sold at $5 each is x, and the number of items sold at $25 each is y. Therefore, we can write two equations based on this information:
x + y = 150 (Equation 1)
5x + 25y = 1950 (Equation 2)
Equation 1 represents the total number of items sold, while Equation 2 represents the total revenue earned from the sale. Now, we can use the unitary method to find the value of y, which represents the number of items sold at $25 each.
Let's rearrange Equation 2 to solve for y:
5x + 25y = 1950
25y = 1950 - 5x
y = (1950 - 5x)/25
Now, we can substitute this expression for y into Equation 1:
x + (1950 - 5x)/25 = 150
Simplifying this equation, we get:
25x + 1950 - 5x = 3750
20x = 1800
x = 90
Therefore, we know that 90 items were sold at $5 each. Now, we can use Equation 1 to find the number of items sold at $25 each:
y = 150 - x
y = 150 - 90
y = 60
Hence, 60 items were sold at $25 each.
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A triangle has two sides of length 19 and 3. What is the smallest possible whole-number length for the third side?
Answers
Answer:
17
Step-by-step explanation:
You have length 19 and 3:
19-3 = 16 AND 19+3=22
You have a range of 16 and 22 and the smallest number between this specific interval is 17, you do not include 16 or 22 in the interval.
How to do this question????
Answers
The values of A-B and B-A are 27 and 36.
We are given that;
WA=(x/x=3".n≤6,nEN)
B= (x/x=9",n≤ 4,n € N)
Now,
First, let’s write the sets A and B using roster notation, which means listing all the elements inside curly braces.
A = {x | x = 3n, n ≤ 6, n ∈ N} = {3, 6, 9, 12, 15, 18}
B = {x | x = 9n, n ≤ 4, n ∈ N} = {9, 18, 27, 36}
Now, let’s find A - B by removing the elements that are common to both sets from A.
A - B = {3, 6, 9, 12, 15, 18} - {9, 18, 27, 36} = {3, 6, 12, 15}
Similarly, let’s find B - A by removing the elements that are common to both sets from B.
B - A = {9, 18, 27, 36} - {3, 6, 9, 12, 15, 18} = {27, 36}
Therefore, by the equation the answer will be 27 and 36.
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Can you help me find the area and
centroid of the following function? ∫-1/6π 2/3π 5 sin^2 (θ+π/4) dθ
Answers
To find the area of the given function, we need to integrate it over the given limits:
Area = ∫-1/6π to 2/3π 5 sin^2 (θ+π/4) dθ
Using the identity sin^2 θ = (1/2)(1 - cos 2θ), we can write:
Area = ∫-1/6π to 2/3π 5/2 [1 - cos(2θ + π/2)] dθ
= ∫-1/6π to 2/3π 5/2 [1 + sin(2θ)] dθ
= [5/2 θ - (5/4) cos(2θ)]-1/6π to 2/3π
= [5/2 (2/3π + 1/6π) - (5/4) cos(4/3π) + (5/4) cos(1/3π)]
= [5/2 (3/6π) - (5/4) (-1/2) + (5/4) (√3/2)]
= [15/4π + 5/8 + (5/4) (√3/2)]
≈ 6.016
To find the centroid of the function, we need to find the coordinates (r, θ) of the center of mass, where:
r = (1/Area) ∫∫r^2 dA
θ = (1/(2Area)) ∫∫θr^2 dA
Since the function is only defined for r = 5, we can simplify the above equations as follows:
r = (1/Area) ∫-1/6π to 2/3π ∫0 to 5 r^3 sin^2 (θ+π/4) dr dθ
= (5/Area) ∫-1/6π to 2/3π sin^2 (θ+π/4) dθ
θ = (1/(2Area)) ∫-1/6π to 2/3π ∫0 to 5 θr^3 sin^2 (θ+π/4) dr dθ
= (5/(2Area)) ∫-1/6π to 2/3π θ sin^2 (θ+π/4) dθ
We can use the same integrals we found for the area to evaluate these equations:
r = (5/6π + 5/16 + (5/8) (√3/2)) / (6.016)
≈ 1.686
θ = (5/(2(6.016))) [(2/3π)(1/2) - (1/6π)(-1/2) + (√3/2)(1/4π) - (-√3/2)(2/3π)]
≈ 0.193 radians
Therefore, the centroid of the given function is approximately (1.686, 0.193).
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Help I’m to lazy to do it
Answers
The following table shows the number of candy bars bought at a local grocery store and the
total cost of the candy bars:
Candy Bars: 3, 5, 8, 12, 15, 20, 25
Total Cost: $6.65, $10.45, $16.15, $23.75, $29.45, $38.95, $48.45
If B represents the number of candy bars purchased and C represents the total cost of the candy bars, write the linear model that models the cost of any number of candy bars.
Answers
The linear model that represents the cost of any number of candy bars can be written as: C = $1.90B + $0.95
To write the linear model that models the cost of any number of candy bars, we need to find the equation of a line that best fits the given data points. We'll use the variables B for the number of candy bars purchased and C for the total cost of the candy bars.
Looking at the given data, we can see that there is a linear relationship between the number of candy bars and the total cost. As the number of candy bars increases, the total cost also increases.
To find the equation of the line, we need to determine the slope and the y-intercept. We can use the formula for the equation of a line: y = mx + b, where m is the slope and b is the y-intercept.
First, let's find the slope (m) using two points from the given data, for example, (3, $6.65) and (25, $48.45):
m = (C2 - C1) / (B2 - B1)
= ($48.45 - $6.65) / (25 - 3)
= $41.80 / 22
≈ $1.90
Now, let's find the y-intercept (b) using one of the data points, for example, (3, $6.65):
b = C - mB
= $6.65 - ($1.90 * 3)
= $6.65 - $5.70
≈ $0.95
Therefore, the linear model that represents the cost of any number of candy bars can be written as:
C = $1.90B + $0.95
This equation represents a linear relationship between the number of candy bars (B) and the total cost (C). For any given value of B, you can substitute it into the equation to find the corresponding estimated total cost of the candy bars.
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