Part
In a new quilt design, Sonja is using triangles. She
does not want the quilt to be centered, to give it
more visual interest. Therefore, Sonja plans to
rotate the triangle design 90° over and over
about the point (5, -1).
10
9
8
7
5
4
3
1 2 3 4 5
Explain how Sonja would determine the location
of the next triangle in the design.
-5
6
-7
-8
-9
-
Answers
For Sonja to determine the location of the new triangle, Sonja must subtract (5,-1) from the coordinates of the original triangle, before rotating by \(90^o\).
From the question, we have:
\(C = (5,-1)\) --- the center of rotation
Let the vertices of the triangle be (x,y).
First, she must subtract the coordinates of the center of rotation from the vertices of the triangle.
This gives:
\((x,y) \to (x - 5, y + 1)\)
Then the vertices are rotated by \(90^o\)
The rule of \(90^o\) rotation is:
\((x,y) \to (-y,x)\)
So, we have:
\((x - 5,y + 1) \to (-y - 1,x - 5)\)
From the attachment, the coordinates of the triangle are: (0,2), (0,5) and (4,2)
After rotation, the coordinates are calculated as follows:
\((0,2) \to (-2-1,0-5) \to (-3,-5)\)
\((0,5) \to (-5-1,0-5) \to (-6,-5)\)
\((4,2) \to (-2-1,4-5) \to (-3,-1)\)
Hence, the coordinates are: (-3,-5), (-6,-5) and (-3,-1)
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Related Questions
What property would you use to solve m+6=−4?
Answers
Answer:
m = -10
General Formulas and Concepts:
Order of Operations: BPEMDAS
Properties
Subtraction Property of EqualityStep-by-step explanation:
Step 1: Define equation
m + 6 = -4
Step 2: Solve for m
Subtract 6 on both sides: m = -10Step 3: Check
Plug in m to verify it's a solution.
Substitute: -10 + 6 = -4Add: -4 = -41 3/8 1 3/4 2 1/8 write a sequence then fined the unknown term
Answers
The sequence is 13/8, 13/4, 21/8 and the next term in the sequence is 21/2.
To find the unknown term, we need to determine the pattern or rule that generates the sequence. In this case, we can observe that each term in the sequence is attained by adding 3/8 to the former term.
The common difference between terms is We need to determine the pattern or rule that generates the sequence to find the unknown term 3/8.
Using this pattern, we can find the coming term in the sequence by adding 3/8 to the last term, which is 21/8
3/8 = 21/2
Therefore, the next term in the sequence is 21/2.
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applicants for graduate school take a test that has scores which are normally distributed with a mean of 560 and a standard deviation of 90. what is the probability that a randomly chosen applicant will score between 550 and 650?
Answers
There is a 38.51% probability that a randomly chosen applicant will score between 550 and 650 which is derived through standard normal distribution method.
It is given to us that the scores of the applicants for graduate school are normally distributed with -
Mean(μ) = 560
and, Standard deviation (σ) = 90
We have to find out the probability of a randomly chosen applicant will score between 550 and 650.
We have to use the standard normal distribution method in order to find out the required probability.
According to standard normal distribution curve method,
Z = (X-μ)/σ
=> Z = (550-560)/90 and, Z = (650-560)/90
=> Z = -0.11 and Z = 1.00
The probability will be with respect to the corresponding z-tables which is equal to = (0.3413+0.0438)
= 0.3851
Thus, the probability of a randomly chosen applicant will score between 550 and 650 is 0.3851 or 38.51%.
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If is the probability that the reciprocal of a randomly selected positive odd integer less than 2010 gives a terminating decimal, with and being relatively prime positive integers, what is
Answers
The probability value of (m, n) is (1, 2^1005).
Let n be a positive odd integer. We are asked to find the probability that its reciprocal gives a terminating decimal. This is equivalent to saying that the only prime factors of n are 2 and 5 because any other prime factor will yield a repeating decimal.
If n is less than 2010, then its only possible prime factors are 3, 7, 11, ..., 2009, since all primes greater than 2009 are greater than n. We want n to have no prime factors other than 2 and 5. There are 1005 odd integers less than 2010.
We want to count how many of these have no odd prime factors other than 3, 7, 11, ..., 2009. This is equivalent to counting how many subsets there are of {3, 7, 11, ..., 2009}. There are 1004 primes greater than 2 and less than 2010. Each of these primes is either in a subset or not in a subset. Thus, there are 2^1004 subsets of {3, 7, 11, ..., 2009}, including the empty set.
Thus, the probability is:
P = (number of subsets with no odd primes other than 3, 7, 11, ..., 2009) / 2^1004
We can count this number using the inclusion-exclusion principle. Let S be the set of odd integers less than 2010. Let Pi be the set of odd integers in S that are divisible by the prime pi, where pi is a prime greater than 2 and less than 2010. Let Pi,j be the set of odd integers in S that are divisible by both pi and pj, where i < j.
Then, the number of odd integers in S that have no prime factors other than 2 and 5 is:
|S - ⋃ Pi + ⋃ Pi,j - ⋃ Pi,j,k + ...|
where the union is taken over all sets of primes with at least one element and less than or equal to 1005 elements.
By the inclusion-exclusion principle:
|S - ⋃ Pi + ⋃ Pi,j - ⋃ Pi,j,k + ...| = ∑ (-1)^k ⋅ (∑ |Pi1,i2,...,ik|)
where the outer summation is from k = 0 to 1005, and the inner summation is taken over all combinations of primes with k elements.
This simplifies to:
(1/2) ⋅ (2^1004 + (-1)^1005)
Thus, the probability is: P = (1/2^1004) ⋅ (1/2) ⋅ (2^1004 + (-1)^1005) = 1/2 + 1/2^1005. Hence, (m, n) = (1, 2^1005).
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Complete question:
If m/n is the probability that the reciprocal of a randomly selected positive odd integer less than 2010 gives a terminating decimal, with m and n being relatively prime positive integers. what is probability value of m and n?
The probability value of (m, n) is (1, 2^1005).This is equivalent to saying that the only prime factors of n are 2 and 5 because any other prime factor will yield a repeating decimal.
Let n be a positive odd integer. We are asked to find the probability that its reciprocal gives a terminating decimal. This is equivalent to saying that the only prime factors of n are 2 and 5 because any other prime factor will yield a repeating decimal.
If n is less than 2010, then its only possible prime factors are 3, 7, 11, ..., 2009, since all primes greater than 2009 are greater than n. We want n to have no prime factors other than 2 and 5. There are 1005 odd integers less than 2010.
We want to count how many of these have no odd prime factors other than 3, 7, 11, ..., 2009. This is equivalent to counting how many subsets there are of {3, 7, 11, ..., 2009}. There are 1004 primes greater than 2 and less than 2010. Each of these primes is either in a subset or not in a subset. Thus, there are 2^1004 subsets of {3, 7, 11, ..., 2009}, including the empty set.
Thus, the probability is:
P = (number of subsets with no odd primes other than 3, 7, 11, ..., 2009) / 2^1004
We can count this number using the inclusion-exclusion principle. Let S be the set of odd integers less than 2010. Let Pi be the set of odd integers in S that are divisible by the prime pi, where pi is a prime greater than 2 and less than 2010. Let Pi,j be the set of odd integers in S that are divisible by both pi and pj, where i < j.
Then, the number of odd integers in S that have no prime factors other than 2 and 5 is:
|S - ⋃ Pi + ⋃ Pi,j - ⋃ Pi,j,k + ...|
where the union is taken over all sets of primes with at least one element and less than or equal to 1005 elements.
By the inclusion-exclusion principle:
|S - ⋃ Pi + ⋃ Pi,j - ⋃ Pi,j,k + ...| = ∑ (-1)^k ⋅ (∑ |Pi1,i2,...,ik|)
where the outer summation is from k = 0 to 1005, and the inner summation is taken over all combinations of primes with k elements.
This simplifies to:
\((1/2) * (2^{1004} + (-1)^1005)\)
Thus, the probability is: P = \((1/2)^{1004}* (1/2) *(2^{1004} + (-1)^{1005}) = 1/2 + 1/2^{1005}.\)
Hence, (m, n) = (\(1, 2^{1005\)).
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If the monthly cost for 14 HCF is $48.70, what is the monthly cost for 10 HCF?
Answers
Answer:
$34.78
Step-by-step explanation:
first, we need to find the value of 1 HCF, so we divide $48.70 by 14, giving us the result of 3.47857143. (rounding that turns out to be 3.48.
next, we need to multiply the cost of 1 HCF by 10, so 3.48 * 10 = 34.78
Find the area of the shaded Sector
A. 8pi
B. 6pi
C. 16pi
D. 4pi
Answers
Answer:
4pi
Step-by-step expla
because its pi is the circumference so its times 4
\(( - 9) { }^{2} - \sqrt[3]{8?} \)
Answers
Answer:
79
Step-by-step explanation:
(-9)² - ∛8
Square the -9. (-x)² = x².
81 - ∛8
Calculate the cube root of 8.
81 - 2
Subtract.
79
Correct answer gets brainliest
If the mid-points of the sides of a triangle are (2,4),(½,7/2) and (5/9,9/2), find the coordinates of the vertices of a triangle.
Answers
The coordinate of the vertices of the triangle are
(x₁, y₁) = (17/18,3)(x₂, y₂) = (55/18, 5)and (x₃, y₃) = (1/18, 4)What is a triangle?A triangle is a polygon with three sides.
What are the vertices of a triangle?The vertices of a triangle are the points where the sides of the triangle intersect.
How to find the coordinates of the vertices of a triangle?Let
(x₁, y₁), (x₂, y₂) and (x₃, y₃) be the coordinates of the vertices of the triangle.Since the midpoints of the sides of the triangle are
(2,4),(½,7/2) and (5/9,9/2)We know that the coordinates of the midpoint of a line with coordinates
(x', y') and (x", y") arex = (x' + x")/2 and y = (y' + y")/2
So, using these, we have that the midpoints of the sides are
For coordinates (2,4) we have that
2 = (x₁ + x₂)/2 and 4 = (y₁ + y₂)/2(x₁ + x₂) = 4 (1) and
(y₁ + y₂) = 8 (2)
For coordinates (1/2,7/2) we have that
1/2 = (x₁ + x₃)/2 and 7/2 = (y₁ + y₃)/2(x₁ + x₃) = 1 (3) and
(y₁ + y₃) = 7 (4)
For coordinates (5/9,9/2) we have that
5/9 = (x₂ + x₃)/2 and 9/2 = (y₂ + y₃)/2(x₂ + x₃) = 10/9 (5)and
(y₂ + y₃) = 9 (6)
From equation (1) x₁ = 4 - x₂ (7)
From equation (2) y₁ = 8 - y₂ (8)
Substituting equations (7) and (8) into (3) and (4), we have
(x₁ + x₃) = 1 (3) and
(y₁ + y₃) = 7 (4)
4 - x₂ + x₃ = 1 and
8 - y₂ + y₃ = 7
- x₂ + x₃ = 1 - 4 and
- y₂ + y₃ = 7 - 8
- x₂ + x₃ = - 3 (9) and
- y₂ + y₃ = - 1 (10)
Now, adding equations (5) and (9), we have
x₂ + x₃ = 10/9 (5)
- x₂ + x₃ = - 3 (9)
2x₃ = 10/9 - 3
2x₃ = (10 - 9)/9
2x₃ = 1/9
Dividing through by 2, we have
x₃ = 1/9 ÷ 2
x₃ = 1/18
Substituting this into equation (9), we have
- x₂ + x₃ = - 3
- x₂ + 1/18 = - 3
- x₂ = - 3 - 1/18
- x₂ = (- 54 - 1)/18
- x₂ = - 55/18
Dividing through by -1, we have
x₂ = 55/18
Substituting this into equation (1), we have
(x₁ + x₂) = 4 (1)
x₁ + 55/18 = 4
x₁ = 4 - 55/18
x₁ = (72 - 55)/18
x₁ = 17/18
Also, adding equations (6) and (10), we have
y₂ + y₃ = 9 (6)
+
- y₂ + y₃ = - 1 (10)
2y₃ = 9 - 1
2y₃ = 8
y₃ = 8/2
y₃ = 4
Substituting this into equation (10), we have
- y₂ + y₃ = - 1 (10)
- y₂ + 4 = - 1
- y₂ = - 1 - 4
- y₂ = - 5
Dividing through by -1, we have
y₂ = 5
Substituting this into equation (2), we have
(y₁ + y₂) = 8 (2)
y₁ + 5 = 8
y₁ = 8 - 5
y₁ = 3
So, the coordinate of the vertices are
(x₁, y₁) = (17/18,3)(x₂, y₂) = (55/18, 5)and (x₃, y₃) = (1/18, 4)Learn more about coordinate of vertices of triangle here:
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1.
Use the quadratic function to predict y if x equals 6.
y = 2x^2 − 2x − 2
A. y = −58
B. y = −60
C. y = 60
D. y = 58
Answers
Answer:
D. y = 58
Step-by-step explanation:
Answer:
The value of the polynomial is 58 for x = 6.
Step-by-step explanation:
Here, the given quadratic function polynomial is given as:
or,
Now, to find the value of y, when x = 6
⇒
= 2(36 - 6 -1) = 2(29)
= 58
⇒y(6) = 58
Hence, the value of the given polynomial is 58 for x = 6.
X 2.6.PS-14
Question Help
0
Marcia drew a plan for a rectangular piece of material that she will use for a blanket. Three of the
vertices are (-2.8, -1.7), (-2.8,3.7), and (2.8,3.7). What are the coordinates of the fourth vertex?
The coordinates of the fourth vertex are 1
(Type an ordered pair, using integers or decimals.)
Enter your answer in the answer box and then click Check Answer.
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Answer:
it should be (2.8,-1.7) hope it helps
Average rate of Change
What is the answer?
Answers
The average rate of change is a concept used in mathematics, specifically in calculus and algebra. It is a measure of how a dependent variable, typically denoted as 'y,' changes with respect to an independent variable, typically denoted as 'x,' over a given interval. It can be understood as the slope of a secant line connecting two points on a graph.
To find the average rate of change, you need two points on the graph (x1, y1) and (x2, y2). The formula for calculating the average rate of change is:
Average Rate of Change = (y2 - y1) / (x2 - x1)
This formula represents the difference in the dependent variable (y) divided by the difference in the independent variable (x). It calculates the amount of change in 'y' per unit change in 'x' over the given interval.
In practical applications, the average rate of change is used to analyze the behaviour of various functions, such as the growth of a population, the speed of a moving object, or the revenue of a company. It helps to understand the overall trend of the function within the specified interval.
Keep in mind that the average rate of change provides an overall perspective, and it may not accurately represent the instantaneous rate of change at a specific point in the function. For that, you would need to use the concept of a derivative in calculus.
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Kathy's science book is 1 1/6 inches thick. Her reading book is 1 3/8 inches thick. How much thicker is her reading book than her science book? (I WILL MARK THE BRANLIEST ANSWER) Please, include an explanation as well! <3
Answers
Answer:
5/8+1/6= 19/24
24/24-19/24= 5/24
5/24 of her money is left
Step-by-step explanation:
Step-by-step explanation: 5/8 =30/48 + the 8/48 she spent = 38/48 .... 48/48 - 38/48= 10/48. that simplifies to 5/24
Find the area and perimeter of rectangle DEFG whose
endpoints are D(-3, 1), E(1, 3), F(2, 1), and G(-2, -1)
Answers
The area of rectangle DEFG is 16 square units and its perimeter is 12 units.
To find the area, we can use the formula: Area = length x width We can find the length and width by calculating the distance between the coordinates of opposite sides of the rectangle.
Length = EF =
\( \sqrt{} ((2-1)^2 + (1-3)^2)\)
=
\( \sqrt{} (2 + 4) = \sqrt{} (6)\)
Width = DG =
\( \sqrt{} ((-3+2)^2 + (1+1)^2) = \sqrt{} (2 + 4) = \sqrt{} (6)\)
The area of rectangle DEFG = length x width =
\( \sqrt{} (6) x \sqrt{} (6)\)
= 6 x 2 = 16 square units.
To find the perimeter, we can add up the lengths of all four sides: Perimeter = DE + EF + FG + GD
DE =
\( \sqrt{} ((1+3)^2 + (-3+(-1))^2) = \sqrt{} (16 + 4) = \sqrt{} (20)\)
EF =
\( \sqrt{} ((2-1)^2 + (1-3)^2) = \sqrt{} (2 + 4) = \sqrt{} (6)\)
FG =
\( \sqrt{} ((2+2)^2 + (1+1)^2) = \sqrt{} (16 + 4) = \sqrt{} (20)\)
GD =
\( \sqrt{} ((-2+3)^2 + (-1-1)^2) = \sqrt{} (1 + 4) = \sqrt{} (5)\)
The perimeter of rectangle DEFG =
\( \sqrt{} (20) + \sqrt{} (6) + \sqrt{} (20) + \sqrt{} (5) \)= 12 units.
Hence, The area of the rectangle is 16 square units and the perimeter is 12 units.
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Please help :) angles
Answers
Answer:
y = 95
Step-by-step explanation:
The exterior angle is equal to the sum of the opposite interior angles
y+25 = 120
y = 120-25
y = 95
In paragraph 1, what does the word oratory mean in context?
Answers
Oratory usually means a small chapel, which is usually used for worship.
Jenna did 5 sit-ups on Saturday, 7 sit-ups on Sunday, 10 sit-ups on Monday, 14 sit-ups on Tuesday, and 19 sit-ups on Wednesday. If this pattern continues, how many sit-ups will Jenna do on Thursday?
Answers
Question 10(Multiple Choice Worth 5 points)
(Identifying Functions LC)
The graph represents a relation where x represents the independent variable and y represents the dependent variable.
a graph with points plotted at negative 5 comma 1, at negative 2 comma 0, at negative 1 comma 3, at negative 1 comma negative 2, at 0 comma 2, and at 5 comma 1
Is the relation a function? Explain.
No, because for each input there is not exactly one output.
No, because for each output there is not exactly one input.
Yes, because for each input there is exactly one output.
Yes, because for each output there is exactly one input.
Answers
Is the relation a function:
No, because for each input there is not exactly one output.How to know if the relation is a functionTo determine if the relation is a function, we need to check if there is exactly one output for each input.
Looking at the given set of points, we see that there are two points with an x-coordinate of -1: (-1, 3) and (-1, -2).
This means that there are two outputs for the same input, so the relation is not a function.
Therefore, the correct answer is: "No, because for each input there is not exactly one output."
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How many different numbers can be obtained using five binary bits? A)64 B)32 C)31 D)63.
Answers
In binary representation, each bit can be either 0 or 1. Using five binary bits, we can obtain 32 different numbers. Therefore, the correct answer is (B).
With five binary bits, we have five positions, and each position can have two possibilities (0 or 1). To calculate the total number of different numbers we can obtain, we need to raise 2 to the power of the number of bits. In this case, we have \(2^5,\) which equals 32. Therefore, we can obtain 32 different numbers using five binary bits. To understand this concept, we can think of each binary bit as a switch that can be either on (1) or off (0). With five switches, we have a total of 32 different combinations or numbers that can be represented. These numbers range from 0 (all switches off) to 31 (all switches on). Therefore, the correct answer is (B), which states that we can obtain 32 different numbers using five binary bits.
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A sample of healthy students were blindly given a single Skittles candy to put in their mouth. They were told the five possible flavors and then were asked which flavor they had. Of the 154 students tested, 78 gave the correct answer. Find a 95% confidence interval for the proportion of all healthy students that could correctly identify a Skittles flavor blindly
Answers
We are 95% confident that the true proportion of healthy students who could correctly identify a Skittles flavor blindly lies within the interval (0.4282, 0.5848).
To find the confidence interval, we can use the formula:
CI = p ± zsqrt(p(1-p)/n)
Where:
CI: Confidence Interval
p: Proportion of students who correctly identified the flavor (sample proportion)
z: Z-score corresponding to the desired confidence level (95% confidence level corresponds to z=1.96)
n: Sample size
Plugging in the values we have:
p = 78/154 = 0.5065
z = 1.96
n = 154
CI = 0.5065 ± 1.96sqrt(0.5065(1-0.5065)/154)
CI = 0.5065 ± 0.0783
CI = (0.4282, 0.5848)
Therefore, we are 95% confident that the true proportion of healthy students who could correctly identify a Skittles flavor blindly lies within the interval (0.4282, 0.5848).
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Solve and find out which king of solutions is it
x-y=-2
-x+y = 4
Answers
Answer is in the photo. I can only upload it to a file hosting service. link below!
tinyurl.com/wpazsebu
The sales tax rate in a city is 6% Find the sales tax charged on a purchase of $300. Then find the total cost.
The sales tax is s
Answers
Answer:
1. $18
2. $318
Step-by-step explanation:
Answer: The total sales tax is 18 US dollars. The total cost of both the tax and the item price is $318
Step-by-step explanation:
6% of 300 is $18
18+300= $318
-6 < 2t - 5 < 3
Solve for T
Answers
Answer:
I think it's 7
Step-by-step explanation:
-6 < 2T (-5+5) < 3+5
-6 < 2T < 8
+6 < 2T < 8 + 6
0 < 2T < 14
0 < ÷ 2 < ÷ 2
0 < T < 7
-0 < T < -0
T = 7
Pls help me
BRAINLIST
Answers
Answer:
I think it's 60%
Step-by-step explanation:
There are total 10 sophomores, and 6 are male, so 6/10 are male, meaning there's a 60% chance.
I hope this helps you! Please give brainliest!
Which statement provides a valid justification for why all circles are similar?
Answers
In triangle ABC, EP=4. What is PC?
Answers
Answer:
PC = 8
Step-by-step explanation:
BF and CE are medians of the triangle.
On each median the distance from the vertex to the centroid P is twice as long as the distance from the centroid to the midpoint, then
PC = 2 × EP = 2 × 4 = 8
you buy a 2 liter sprite for your friends. one serving of sprite is 250 ml. calculate the number of servings in one bottle. URGENT!!
Answers
1 liter is 1,000 ml .
250 ml is 1/4 of a liter .
There are 4 of them in 1 liter .
There are 8 of them in 2 liters.
Please Answer QUICK!!!
Which graph shows the quadratic function y = 3x2 + 12x + 10?
A. Graph A
B. Graph B
C. Graph C
D. Graph D
Answers
Answer:
Graph A
Step-by-step explanation:
I graphed it
Since the beginning of fall, the little tree in front of Mrs.Wenger's house loses 12 more leaves every day. After 5 days, it haf only 208 leaves remaining.
Answers
Answer:
268
I'm not smart so if u get this wrong, I'm sorry
Step-by-step explanation:
12 x 5 = 60
60 + 208 = 268
The time has come for you to open a checking account. A local bank is offering you afree checking account if you maintain a minimum balance of $200. You already havea savings account with this bank and you have $60 saved. You decide to keep savingmoney until you have enough to open a checking account, plus keep some moneyin savings. If you deposit $15 a week into the savings account, what is the minimumnumber of weeks it will take for you to be able to open a checking account with at least$200 and still have $25 in your savings account?
Answers
11 weeks
Explanation:
The minimum balance for the checking account = $200
The amount in savings account = $60
Amount to be deposited weekly in order to meet up the $200 = $15
Amount to be left in savings account = $25
First, we would subtract $25 from $60
$60 - $25 = $35
This way $25 remains in the savings account
The $35 dollar is the starting amout for the contribution for the $200 checking account minimum.
To determine, the remaining money to be paid:
$200 - $35 = $165
Number of weeks to contribute $15 to make of $165:
= 165/15 = 11 weeks
Therefore, the minimum amount of weeks that it will take to open a checking account with at least $200 and still have $25 in your savings account is 11 weeks
7. Which has the strongest correlation?
(1) r=0.7
(2) r = 0.1
(3) r=-0.75
(4) r=-0.99
Answers
Answer:
76yhgdttyhgfd
Step-by-step explanation:
nhjgklh/f