Olivia finds a combination of two different transformations that moves ABCD onto A" B" C" D". What is one way she might have done this?
Answers
One way Olivia might have achieved this is by performing a translation followed by a rotation.
How could Olivia have combined two different transformations to move ABCD onto A" B" C" D"?One way Olivia might have achieved the transformation of ABCD onto A" B" C" D" is by performing a translation followed by a rotation. Here's a possible approach:
Translation: Olivia could have first translated ABCD by shifting the entire figure in a specific direction (up, down, left, or right) by a certain distance. This would result in a new position for each vertex of ABCD, creating a new figure.Rotation: After the translation, Olivia could have performed a rotation around a point, such as the origin or a specific vertex. The rotation would change the orientation of the translated figure, aligning it with the desired position of A" B" C" D".By combining these two transformations, Olivia could have successfully moved ABCD onto A" B" C" D" and achieved the desired configuration. It's important to note that there could be other valid combinations of transformations as well.
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Related Questions
PLZZZZZZZZZZZZ PLZZZZZZZZZZZZ PLZZZZZZZZZZZZ PLZZZZZZZZZZZZ help
Answers
Answer:
a. option is the correct answer
Show the solution for a two square room have a total floor area of 89m rise to power 2 one room is 3mlonger each way than the other find the dimensions of the two rooms
Answers
Answer:
side length of the smaller room = 5 m
Side length of the larger room = 8 m
Step-by-step explanation:
Total area of two square room = 89 m²
Area of a square = side²
Let
x = side of the smaller square
x + 3 = side of the longer square
Total area = area of room A + Area of room B
89 = x² + (x + 3)²
89 = x² + x² + 6x + 9
89 - 9 = 2x² + 6x
2x² + 6x = 80
2x² + 6x - 80 = 0
Divide through by 2
x² + 3x - 40 = 0
Solve quadratic equation using factorization method
x² + 8x - 5x - 40 = 0
x(x + 8) -5(x + 8) = 0
(x - 5) (x + 8) = 0
(x - 5) = 0 (x + 8) = 0
x = 5 x = -8
The side length of a square room can not be a negative value
Therefore, side length of the smaller room = 5 m
Side length of the larger room = 5 + 3
= 8 m
Consider the following vector function. r(t) = 3t, 1 2 t2, t2 (a) find the unit tangent and unit normal vectors t(t) and n(t).
Answers
The unit tangent vector t(t) is (3, 4t, 2t) / sqrt(9 + 20t^2), and the unit normal vector n(t) is (3, 4, 2t) / sqrt(25 + 4t^2).
The unit tangent vector t(t) of the given vector function r(t) = (3t, 1 + 2t^2, t^2) is obtained by dividing the derivative of r(t) by its magnitude. The derivative of r(t) is (3, 4t, 2t), and the magnitude of this vector is sqrt(9 + 20t^2). Therefore, t(t) = (3, 4t, 2t) / sqrt(9 + 20t^2).
The unit normal vector n(t) can be obtained by dividing the derivative of t(t) by its magnitude. The derivative of t(t) is (3, 4, 2t), and the magnitude of this vector is sqrt(25 + 4t^2). Thus, n(t) = (3, 4, 2t) / sqrt(25 + 4t^2).
These unit vectors t(t) and n(t) represent the direction of motion and the direction of the curve's curvature at each point t, respectively, providing valuable information about the behavior of the vector function r(t).
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4 if the mixing ratio of a sample of air is 2 grams/kilogram, and the temperature of the sample is 25 degrees celsius, yielding a saturation mixing ratio of 20 grams/kilogram, what is the relative humidity of the sample?
Answers
Because the temperature is greater, the relative humidity of the atmosphere is higher.
Relative humidity: What is it?Water vapor is also measured by relative humidity (RH), which is stated as a percentage but RELATIVE to the air's temperature. In plenty of other terms, it is a comparison between the quantity of water vapor that is really present in the air and the maximum amount water vapor that is possible for the air at the current temperature.
How can relative humidity be determined from temperature?By deducting the temperature just on wet-bulb thermometer from of the temperature just on dry-bulb thermometers and utilizing a relative humidity chart, one may determine the relative humidity.
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Apples: $(2x) per pound
Grapes: $(6x – 5) per pound
Oranges: $(x + 2) per pound
A shopper purchases one pound each of
apples, grapes, and oranges and spends
$10.50. How much is spent on each type
of fruit?
Answers
Answer:
Shopper spend $3 on Apples, $4 on Grapes and $3.5 on Oranges
Step-by-step explanation:
Cost of one pound of Apple = $2x
Cost of one pound of Grapes = $(6x-5)
Cost of one pound of Oranges = $(x+2)
A shopper purchases one pound each of apples, grapes, and oranges and spends $10.50.
It can be written as: \(2x+6x-5+x+2=10.50\)
We need to find how much the shopper spend on each fruit.
First we need to find value of x by solving equation
\(2x+6x-5+x+2=10.50\)
Solving:
\(2x+6x+x+2-5=10.50\\9x-3=10.50\\9x=10.50+3\\9x=13.5\\x=\frac{13.5}{9}\\x=1.5\)
The value of x is: x=1.5
Now finding cost of one pound each fruit by putting x=1.5
Cost of one pound of Apple = $2x = 2(1.5) = $3
Cost of one pound of Grapes = $(6x-5) = (6(1.5)-5)= $4
Cost of one pound of Oranges = $(x+2)=(1.5+2)=$3.5
So,
Cost of one pound of Apple = $3
Cost of one pound of Grapes = $4
Cost of one pound of Oranges = $3.5
So, shopper spend $3 on apples, $4 on Grapes and $3.5 on Oranges
∠A and ∠ � ∠B are complementary angles. If m ∠ � = ( 6 � + 2 ) ∘ m∠A=(6x+2) ∘ and m ∠ � = ( 4 � + 18 ) ∘ m∠B=(4x+18) ∘ , then find the measure of ∠ � ∠A.
Answers
The measure of ∠A = 58° and ∠B = 32°.
To find the measure of ∠A and ∠B, we can equate the sum of their measures to 90° since they are complementary angles.
1. Given that m∠� = (6x + 2)° and m∠B = (4x + 18)°.
2. Since ∠A and ∠B are complementary angles, we have the equation: m∠� + m∠A = 90°.
3. Substitute the given values into the equation: (6x + 2)° + (4x + 18)° = 90°.
4. Combine like terms: 6x + 2 + 4x + 18 = 90.
5. Simplify the equation: 10x + 20 = 90.
6. Subtract 20 from both sides: 10x = 70.
7. Divide both sides by 10: x = 7.
8. Substitute x = 7 back into the original equations:
- m∠� = (6x + 2)° = (6(7) + 2)° = 44°.
- m∠A = (6x + 2)° = (6(7) + 2)° = 44°.
- m∠B = (4x + 18)° = (4(7) + 18)° = 46°.
9. Therefore, the measure of ∠A is 44° and the measure of ∠B is 46°.
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use the given domain to find the range of function. help please
Answers
The range for the given domain D = {2, -3, 0} of the function f(x) = 2x² + 7 is; R = {7, 15, 25}
What is the Range of the Function?We are given the function as;
f(x) = 2x² + 7
We are given the domain set as;
D = {2, -3, 0}
Now, the range will simply be gotten by plugging in each domain value into the given function to get the output. Thus;
Range when x = 0 is;
y = 2(0)² + 7
y = 7
Range when x = 2 is;
y = 2(2)² + 7
y = 15
Range when x = -3 is;
y = 2(-3)² + 7
y = 25
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What kind of angle is created by the intersection of two perpendicular liner rays, or line segments?
Answers
Answer:
Right angle
Step-by-step explanation:
Perpendicular is the key word.
PLs, help me with this math question
Answers
Answer
for a area of 10 i would do rays like 2 by 5
Step-by-step explanation:
it would be like 5 over and 2 down
Please help ASAP I don’t understand this and only answer if you know just don’t answer with random letters please!!!!!
Answers
Answer:
x + y + 90 = 180
x = 67
y = 23
Step-by-step explanation:
x + y + 90 = 180
x + 2 = 3y
x + y = 90
x - 3y = -2
x + y = 90
(+) -x + 3y = 2
-----------------------
4y = 92
y = 23
x + y = 90
x + 23 = 90
x = 67
read the existence and uniqueness theorem (theorem 1.61 in the ordinary differential equa- tions project). Then answer the following questions
(a) what is meant by "existence"?
(b) What is meant by "uniqueness"?
(c) Write a sentence interpreting x' = f (t,x)
(d) Interpret x(to) = xo
(e) Graph and interpret R = { (t,x) : 0 ≤ | t - to | ≤ a,0 ≤ | x -xo | ≤ b } under the assumption that a,b E R+. Include (to,xo) on your graph
(f) What is u(t)
(g) Interpret " on some interval |t - to| < h contained in |t - to| < a." Add h to your graph. Whats the relationship between a and h?
(h) How would you summarize the significance of the existence and uniqueness theorem to someone who doesn't study math?
Answers
The existence and uniqueness theorem in the ordinary differential equations are explained below.
(a) "Existence" in the context of the existence and uniqueness theorem for ordinary differential equations (ODEs) refers to the guarantee that a solution to the ODE exists for a certain interval or range of values.
(b) "Uniqueness" means that there is only one solution to the ODE that satisfies certain initial conditions or constraints. It ensures that there are no multiple solutions that meet the given criteria.
(c) The equation x' = f(t, x) represents a first-order ODE, where the derivative of the function x with respect to t is equal to the function f, which depends on both t and x.
(d) The notation x(to) = xo represents the initial condition of the ODE. It specifies the value of the function x at a particular initial time to, which is equal to xo.
(e) The graph of R = {(t, x): 0 ≤ |t - to| ≤ a, 0 ≤ |x - xo| ≤ b} represents a rectangular region in the t-x plane. It includes all points (t, x) that satisfy the conditions: the absolute difference between t and to is less than or equal to a, and the absolute difference between x and xo is less than or equal to b. The point (to, xo) is included in this region.
(f) The symbol u(t) is not mentioned in the given context. Without additional information, it is not possible to provide a specific interpretation or meaning for u(t).
(g) "On some interval |t - to| < h contained in |t - to| < a" implies that there exists a smaller interval, represented by |t - to| < h, which is fully contained within the larger interval |t - to| < a. The value of h represents the size or length of the smaller interval. In the graph, h can be added as a smaller length within the interval defined by a.
The relationship between a and h is that h is a subset of a. This means that h is smaller or equal to a and is fully contained within a. In other words, h represents a sub-interval of the larger interval a.
(h) The significance of the existence and uniqueness theorem in layman's terms is that it provides a mathematical assurance that a specific type of differential equation has a unique solution that satisfies certain conditions. It gives confidence that a solution exists and is unique within a specified range or interval. This is valuable for various scientific and engineering applications, as it allows for the prediction and understanding of systems described by differential equations.
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5. Show 3 different ways on how you can multiply two polynomials to get 30x^3.
Answers
Answer:
\(15x^2\times2x=30x^3\)\(6x^2\times5x=30x^3\)\(10x^2\times3x=30x^3\)Explanation:
The multiplication of the each of following pair of polynomials given the plynomial
\(30x^3\)1.
\(15x^2\times2x=30x^3\)2.
\(6x^2\times5x=30x^3\)3.
\(10x^2\times3x=30x^3\)and so on.
Note:
The combination of any pair of numbers whose products are 30 would surely work, it is important to know the correct degrees of polynomials to use, the ones whose addition of indexes are 3, as required.
they are 8,756 students that attend middle schools in the city of Johnson. Of the students, 3,252 are picked up by car, 2,549 ride the bus home, and 2,955 students walk home. How many students leave school by bus or car?
Answers
The number of students that leave by bus or car is given as follows:
5801 students.
How to obtain the union and intersection set of the two sets?The union and intersection sets of multiple sets are defined as follows:
The union set is composed by the elements that belong to at least one of the sets.The intersection set is composed by the elements that belong to at all the sets.The or operation is equivalent to the union operation, meaning that we add the number of students that leave by bus to the number of students that leave by car.
Hence the number of students that leave by bus or car is given as follows:
3232 + 2549 = 5801 students.
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4/x - 3/y = 1 ............(1)
6/x + 15/y = 8 ........(2)
Answers
Answer:
1. No x-intercept/Zero
2. x = 3/4
Step-by-step explanation:
Which of the following graphs best represents a function that has a minimum value and x-intercepts of 3 and -1?
Answers
Answer:
a
Step-by-step explanation:
please help its due in 5 mind
Answers
Formula:
C = π • d
π (pi) = 3.14
diameter = 2 in
3.14 • 2 = 6.28
You measure 32 textbooks' weights, and find they have a mean weight of 55 ounces. Assume the population standard deviation is 11.4 ounces. Based on this, construct a 99.5% confidence interval for the true population mean textbook weight.
Answers
Sure! Here's the 99.5% confidence interval for the true population mean textbook weight: (49.433, 60.567) ounces.
To construct a confidence interval for the true population mean textbook weight, we can use the formula:
Confidence Interval = (sample mean) ± (critical value) * (standard deviation / √(sample size))
Given the information provided:
- Sample mean = 55 ounces
- Population standard deviation = 11.4 ounces
- Sample size = 32 textbooks
First, we need to find the critical value corresponding to a 99.5% confidence level. Since the sample size is relatively small (32 textbooks), we can use a t-distribution instead of a normal distribution.
The degrees of freedom for a t-distribution are given by (sample size - 1). In this case, the degrees of freedom will be (32 - 1) = 31.
Using a t-table or a statistical calculator, we find the critical value for a 99.5% confidence level and 31 degrees of freedom is approximately 2.750.
Now, we can calculate the confidence interval:
Confidence Interval = 55 ± 2.750 * (11.4 / √32)
Confidence Interval = 55 ± 2.750 * (11.4 / 5.657)
Confidence Interval = 55 ± 5.567
Therefore, the 99.5% confidence interval for the true population mean textbook weight is approximately (49.433, 60.567) ounces.
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Hannah is n years old.
Her aunt Emily is three times older than Hannah.
Emily is 48 years old.
(a) Write down an equation for this information.
(b) Solve your equation to find how old Hannah is.
Answers
Answer:
(this is easy)
n x 3 = 48
48/3 = n
n= 16
Hannah is 16 years old.
Step-by-step explanation:
Melissa is hosting a dinner party. She is making the main course and is assigning the invited guests to bring the following items: appetizer, side dish, salad, beverage, or dessert. Suppose there are nine guests invited to the party. Each is assigned to bring one of the items mentioned, and more than one guest can be assigned to an item so that each guest brings something to the dinner party.
a. Explain why assigning each guest an item to bring to the party is an example of a function.
Answers
Each guest being assigned to bring an item to the party is an example of a function because a unique output (the item to bring) is assigned to each input (the guest).
Why is this a function ?In this case, each guest is the input, and the item they are assigned to bring is the output. Each guest is assigned exactly one item, and there are no two guests assigned to bring the same item. This means that for each guest, there is a unique item that they are assigned to bring, and no two guests are assigned to bring the same item.
Therefore, the assignment of guests to items to bring to the dinner party is an example of a function because it assigns a unique output (the item) to each input (the guest), and it meets the mathematical definition of a function.
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Find the value of x.
Answers
Answer:
x=67º
Step-by-step explanation:
First since the supplementary angle next to 157º is in the triangle, we can find that. 180-157 = 23. Then we can use triangle angle sum theorem to find x. 180-(23+90) = 67º
On a certain hot summer's day, 525 people used the public swimming pool. The daily prices are 1.50 for children and 2.25 for adults. The receipts for admission totaled 969.00 How many children and how many adults swam at the public pool that day?
Answers
Answer: 388
Step-by-step explanation:
120 children and 388 adults bought tickets for the swimming poolExplanation:Create two simultanous equations:Let c stand for the number of children that bought a ticket, and a stand for the number of adults that bought a ticket, you get your first equation, being c+a=508then, you now create a second equation for the prices of the tickets.(price of childrens tickets)(number of children that swam)+(price of adults tickets)(number of adults that swam) = total money collected so:1.75c+2.25a=1083.00now we still know, that a=508−cso we can substitute it into the second formula1.75c+2.25(508−c)=1083now its just simple algebra1.75c+1143−2.25c=108360=0.5c so: c=120now we know, that 120 children went to the swimming pool.and we still have the formula from before:a=508−c so a=388
what is the surface of a cubiod sides 2cm,3cm and 5cm?
Answers
Answer: A cuboid has 6 rectangular faces. To find the surface area of a cuboid, add the areas of all 6 faces. We can also label the length (l), width (w), and height (h) of the prism and use the formula, SA=2lw+2lh+2hw, to find the surface area.
Step-by-step explanation:
Step-by-step explanation:
2×3×2+2×5×2+3×5×2
12+20+30
=62
The ____________particles of an atom which are called electrons.
Answers
Answer:
Atomic Particles
The nucleus (center) of the atom contains the protons (positively charged) and the neutrons (no charge). The outermost regions of the atom are called electron shells and contain the electrons (negatively charged).
Step-by-step explanation:
Write the equation of the line passing through the point (2,-1) with a slope of -3
Answers
Task B. Solve for the probability of the given events. Show your complete solution.
An Hospital, there are 9 nurses and 4 physicians. Five nurses and one physician are males. It
person is selected from the staff, what is the probability that the person is a physician or male?
Answers
There are a total of 13 staff members in the hospital, out of which 5 nurses and 1 physician are males. Therefore, the number of physicians or males in the staff is 4+5=9. The probability of selecting a physician or male from the staff is the ratio of the number of physicians or males to the total number of staff members, which is 9/13.
Therefore, the probability of selecting a physician or male from the staff is 0.69 (rounded to two decimal places) or approximately 69%. To solve for the probability that the person selected from the hospital staff is a physician or male, we will first determine the total number of staff and the number of individuals who meet the criteria. There are 13 staff members (9 nurses and 4 physicians) in total.
Among them, there are 5 male nurses, 1 male physician, and 3 female physicians. To avoid counting the male physician twice, we have a total of 5 male nurses + 1 male physician + 3 female physicians = 9 individuals who are either a physician or male. The probability of selecting a physician or male is then 9/13, or approximately 0.692.
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The graph represents the distance the Pennsylvania Train traveled over 8 hours.
The Baltimore Train traveled 1,020 miles in 12 hours. Both trains traveled at a constant rate. Which sentence is true?
A. The Baltimore Train was faster by 10 miles per hour.
B. The Baltimore Train was faster by 15 miles per hour.
C. The Pennsylvania Train was faster by 10 miles per hour.
D. The Pennsylvania Train was faster by 15 miles per hour.
Answers
Answer:
Baltimore Train: 1,020 mi/12 hr = 85 mph
Pennsylvania Train: 75 mph
So the correct answer is A.
Simplify the expression....
Answers
Answer:
−3x^2+2x /x−2
Step-by-step explanation:
4x−9x^3/ 3x^2−4x−4
= −9x^3+4x /3x^2−4x−4
= x(−3x+2)(3x+2) /(3x+2)(x−2)
= −3x^2+2x /x−2
Today, Andrew borrowed R200 000 from a bank. The bank charges interest at 5.25%p.a, a compounded quarterly. Andrew will make make payments of R6 000 at the end of 3 months. His first repayment will be made 3 months from now, how long in years will it take for Andrew to settle the loan
Answers
In order to calculate the time it will take for Andrew to settle the loan, we can use the formula for compound interest. So, it will take Andrew approximately 5.22 years to settle the loan.
The formula is given as A = P(1 + r/n)^(nt), Where: A = the final amount, P = the principal (initial amount borrowed), R = the annual interest rate, N = the number of times the interest is compounded in a year, T = the time in years.
We know that Andrew borrowed R200 000 from a bank at an annual interest rate of 5.25% compounded quarterly and that he will make repayments of R6 000 at the end of every 3 months.
Since the first repayment will be made 3 months from now, we can consider that the initial loan repayment is made at time t = 0. This means that we need to calculate the value of t when the total amount repaid is equal to the initial amount borrowed.
Using the formula for compound interest: A = P(1 + r/n)^(nt), We can calculate the quarterly interest rate:r = (5.25/100)/4 = 0.013125We also know that the quarterly repayment amount is R6 000, so the amount borrowed minus the first repayment is the present value of the loan: P = R200 000 - R6 000 = R194 000
We can now substitute these values into the formula and solve for t: R194 000(1 + 0.013125/4)^(4t) = R200 000(1 + 0.013125/4)^(4t-1) + R6 000(1 + 0.013125/4)^(4t-2) + R6 000(1 + 0.013125/4)^(4t-3) + R6 000(1 + 0.013125/4)^(4t)
Rearranging the terms gives us: R194 000(1 + 0.013125/4)^(4t) - R6 000(1 + 0.013125/4)^(4t-1) - R6 000(1 + 0.013125/4)^(4t-2) - R6 000(1 + 0.013125/4)^(4t-3) - R200 000(1 + 0.013125/4)^(4t) = 0
Using trial and error, we can solve this equation to find that t = 5.22 years (rounded to 2 decimal places). Therefore, it will take Andrew approximately 5.22 years to settle the loan.
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Rolling a 6 sided die. Find the probability the number rolled is less than 3 given that it’s a factor of 6.
( help please :) )
Answers
Answer:
33.333%
Step-by-step explanation:
a 6 sided die has the number 1,2,3,4,5,6. 2 are less than three so the chances of getting the of getting a number less than 3 is 2/6, simplified 1/3.
a triangular windowpane is 4 feet 8 inches wide and 3 feet 6 inches high. what is the area of the windowpane? if necessary, round to the nearest tenth.
Answers
Rounding to the nearest tenth, the area of the triangular windowpane is approximately 8.2 square feet.
To find the area of a triangular windowpane, we need to use the formula for the area of a triangle, which is:
Area = (1/2) x Base x Height
In this case, the base is 4 feet 8 inches and the height is 3 feet 6 inches. However, we need to convert these measurements to the same units before we can calculate the area. Since there are 12 inches in 1 foot, we can convert the measurements as follows:
Base = 4 feet + 8 inches/12 = 4.67 feet
Height = 3 feet + 6 inches/12 = 3.5 feet
Now we can plug in these values into the formula and calculate the area:
Area = (1/2) x 4.67 feet x 3.5 feet
Area = 8.1675 square feet
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