Circle 1 is centered at (−5, 4) and has a radius of 15 units. Circle 2 is centered at (−5, −3) and has a radius of 9 units. What transformations can be applied to Circle 1 to prove that the circles are similar? Enter your answers in the boxes. The circles are similar because you can translate Circle 1 using the transformation rule ( , ) and then dilate it using a scale factor of .
Answers
The circles are similar because you can translate Circle 1 using the transformation rule (0, -7) and then dilate it using a scale factor of 3/5.
Translation involves moving an object in a straight line without changing its size or shape. In this case, we can translate Circle 1 7 units down to match the y-coordinate of Circle 2. The transformation rule for this translation is (0, -7), since we are not changing the x-coordinate.
Dilation involves uniformly scaling an object, either making it larger or smaller. We can dilate Circle 1 by a scale factor of 3/5 to make it have the same radius as Circle 2. The scale factor is determined by taking the ratio of the radii:
scale factor = radius of Circle 2 / radius of Circle 1
scale factor = 9 / 15
scale factor = 3/5
The center of dilation is the center of Circle 1, since we want to preserve its position.
Therefore, we can transform Circle 1 into Circle 2 by translating it 7 units down and dilating it by a scale factor of 3/5. The transformation rule is:
(0, -7) followed by dilation with a scale factor of 3/5
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Related Questions
According to a weather report, there is a 44% chance it will rain tomorrow. What is the probability that it will not rain tomorrow?
a. Design a geometric model for this probability.
b. What is the probability of the event that it will not rain tomorrow? Explain your answer.
a. Design a geometric model for this probability. Select all that apply.
A. A square spinner divided into parts of equal area by a diagonal. Choose a part by a random spin.
B. A circular spinner divided into parts of equal area by 44 radii. Choose a part by a random spin.
C. A rectangular grid with 44 out of 100 cells shaded. Choose a cell at random.
D. A circular grid with 1 out of 44 sectors shaded. Choose a sector at random.
E. A circular grid with 44 out of 100 sectors shaded. Choose a sector at random.
F. A rectangular grid with 1 out of 44 cells shaded. Choose a cell at random.
because
cell(s) or sector(s) are shaded, so out of cell(s) or sector(s) are not shaded.
b. The probability that it will not rain tomorrow is
(Type integers or decimals.)
Answers
The probability that it will not rain tomorrow is 56%, and the geometric models that represent the probability that it will rain tomorrow are:
C. A rectangular grid with 44 out of 100 cells shaded. Choose a cell at random. E. A circular grid with 44 out of 100 sectors shaded. Choose a sector at random. What are probabilities?Probabilities are used to determine the chances of events
The given probability is:
\(p= 44\%\) -- the probability that it will rain tomorrow
The probability that it will not rain tomorrow is calculated using the following complement rule
\(q= 1 -p\)
This gives
\(q= 1 -44\%\)
\(q= 56\%\)
This means that:
The probability that it will not rain tomorrow is 56%
Also, options (c) and (e) represent the geometric models that it will rain tomorrow
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A scientist needs 72 milliters of distilled water for each of 15 experiments
Answers
Answer: 4.8
Step-by-step explanation:
72÷15=4.8
The athletic departments at 10 randomly selected U.S. universities were asked by the Equal Employment Opportunity Commission to state what percentage of their nursing scholarships were presently held by women. The responses were 5, 4, 2, 1, 1, 2, 10, 2, 3, 5. what is the midrange
Answers
Answer:
5.5
Step-by-step explanation:
Given the set of data
5, 4, 2, 1, 1, 2, 10, 2, 3, 5.
The average of the least and the greatest value is known as the midrange
The formula for calculating the midrange is expressed as shown:
Midrange = (Greatest value + Least value)/2
Given
Greatest value = 10
Least value = 1
Midrange = 10+1/2
Midrange = 11/2
Midrange = 5.5
Hence the midrange of the data is 5.5
Adam is baking 4 pizzas. Each pizza is a rectangle. It takes Adam 35 minutes to bake the pizzas. He divides each pizza into the equal-size square slices shown.
Adam multiplies to find the total number of square Slices for each pizza.
For each pizza tell the factors Adam multiplies .
Answers
For Pizza 1, Adam multiplies 6 by 6 slices
For Pizza 2, he multiplies 6 by 7 slices
For Pizza 3, he multiplies 4 by 7 slices, while
for Pizza 4, he multiplies 4 by 8 slices.
What is multiplication?A product is the outcome of multiplication or an expression that indicates factors to be multiplied in mathematics.
To put it another way, we may deduce that in math, multiplying implies adding equal groups.
The number of items in the group grows as we multiply. A multiplication issue includes the two elements and the product. The factors in the multiplication problem, 4 7 = 28, are the numbers 4 and 7, while the result (product) is the number 28.
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Assume that when human resource managers are randomly selected, 44% say job applicants should follow up within two weeks. If 5 human resource managers are randomly selected, find the probability that exactly 2 of them say job applicants should follow up within two weeks.
The probability is ....
Answers
Answer: 3.4%
Step-by-step explanation:
There's a 44% chance that if you pick a random human resource manager, then he will say job applicants should follow up.
So let's look at these 5 people individually then.
The question asks you to find the probability that exactly 2 will say yes.
So the probability of 1 person saying yes is 0.44, probability of another person saying yes is 0.44, the probability of a person saying no is 0.56, and so on.
With this reasoning, we will come up with 0.44 * 0.44 * 0.56*0.56 * 0.56
or 0.44^2 * 0.56^3 or 0.033999 = 3.4%
What îs judy’s motto about zootopia to Find out skip count by 5s then crack the code
Answers
Just from a quick search, the motto of Zootopia is "anyone can be anything"
Question 7(Multiple Choice Worth 5 points)
(04.02 MC)
The two-way frequency table contains data about students' preferred exercise.
Likes running 28
Does not like running 46
Column totals 74
What is the joint relative frequency of students who do not like to run and enjoy swimming?
O23%
37%
Enjoys swimming Enjoys cycling Row totals
62
90
64
110
126
200
46%
072%
Answers
The joint relative Frequency of students who do not like to run and enjoy swimming, based on the given two-way frequency table, is approximately 62.16%.
The joint relative frequency of students who do not like to run and enjoy swimming, we need to find the intersection of the row and column corresponding to those categories in the two-way frequency table.
Given the following information from the table:
Likes running: 28
Does not like running: 46
Column totals: 74
Enjoys swimming: 62
Enjoys cycling: 90
Row totals: 110
The joint relative frequency, we divide the number of students who do not like running and enjoy swimming by the total number of students:
Joint relative frequency = (Number of students who do not like running and enjoy swimming) / (Total number of students)
From the table, the number of students who do not like running and enjoy swimming is given as 46.
Total number of students is given as 74.
Joint relative frequency = 46 / 74
Calculating this value, we find that the joint relative frequency is approximately 0.6216, which is equivalent to 62.16%.
Therefore, the joint relative frequency of students who do not like to run and enjoy swimming is approximately 62.16%.
In conclusion, the joint relative frequency of students who do not like to run and enjoy swimming, based on the given two-way frequency table, is approximately 62.16%.
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whats the equation of a line that passes through point (-1,3) with slope of 1
Answers
The equation of the line that passes through the point (-1, 3) with a slope of 1 is y = x + 4.
To find the equation of a line that passes through the point (-1, 3) with a slope of 1, we can use the point-slope form of a linear equation.
The point-slope form of a linear equation is given by:
y - y1 = m(x - x1)
where (x1, y1) represents the coordinates of a point on the line, and m represents the slope of the line.
Using the given point (-1, 3) and slope 1, we substitute these values into the point-slope form equation:
y - 3 = 1(x - (-1))
Simplifying:
y - 3 = x + 1
Now, we can rewrite the equation in the standard form:
y = x + 4
Therefore, the equation of the line that passes through the point (-1, 3) with a slope of 1 is y = x + 4.
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Sabas Company has 40,000 shares of $100 par, 1% preferred stock and 100,000 shares of $50 par common stock issued and outstanding. The following amounts were distributed as dividends: Year 1: $50,000 Year 2: 90,000 Year 3: 130,000 Determine the dividends per share for preferred and common stock for each year. If an answer is zero, enter '0'. Round all answers to two decimal places.
Answers
The dividends per share for preferred stock for each year are: Year 1 - $1.25, Year 2 - $2.25, Year 3 - $3.25. The dividends per share for common stock for each year are all $0.
To determine the dividends per share for preferred and common stock for each year, we need to divide the total dividends by the number of shares for each type of stock.
Preferred Stock:
Dividends per share of preferred stock = Total dividends for preferred stock / Number of preferred shares
Year 1:
Dividends per share of preferred stock for Year 1 = $50,000 / 40,000 shares = $1.25
Year 2:
Dividends per share of preferred stock for Year 2 = $90,000 / 40,000 shares = $2.25
Year 3:
Dividends per share of preferred stock for Year 3 = $130,000 / 40,000 shares = $3.25
Common Stock:
Dividends per share of common stock = Total dividends for common stock / Number of common shares
Year 1:
Dividends per share of common stock for Year 1 = ($50,000 - Total dividends for preferred stock) / 100,000 shares = ($50,000 - $50,000) / 100,000 shares = $0
Year 2:
Dividends per share of common stock for Year 2 = ($90,000 - Total dividends for preferred stock) / 100,000 shares = ($90,000 - $90,000) / 100,000 shares = $0
Year 3:
Dividends per share of common stock for Year 3 = ($130,000 - Total dividends for preferred stock) / 100,000 shares = ($130,000 - $130,000) / 100,000 shares = $0
The dividends per share for preferred stock for each year are: Year 1 - $1.25, Year 2 - $2.25, Year 3 - $3.25. The dividends per share for common stock for each year are all $0.
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Solve the following using synthetic division: (9a^3+64a-67a-16)+(a+8)
Answers
So the quotient of the division is 9a² - 72a + 573, and the remainder is -1856.
What is polynomial?A polynomial is a mathematical expression consisting of variables and coefficients, combined using arithmetic operations such as addition, subtraction, multiplication, and exponentiation. The variables in a polynomial can only have non-negative integer exponents, and the coefficients can be any real number. Polynomials can have one or more variables and can be of different degrees, which is determined by the highest exponent of the variable in the expression.
Here,
First, let's simplify the expression by combining like terms:
(9a³ + 64a - 67a - 16) + (a + 8) = 9a³ - 3a + 8
Now we can use synthetic division to divide 9a³ - 3a + 8 by (a + 8).
The coefficients of the terms in 9a³ - 3a + 8, written in descending order of degree, are 9, 0, -3, and 8. To use synthetic division, we will need to include a placeholder coefficient of 0 for the missing term of degree 1:
-8 | 9 0 -3 8
|___ -72 576 -1864
| 9 -72 573 -1856
The last number in the bottom row, -1856, is the remainder. Therefore, we have:
9a³ - 3a + 8 = (a + 8)(9a²2 - 72a + 573) - 1856
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Complete question:
Solve the following using synthetic division: (9a³ - 3a + 8)/(a + 8)
Find the angle on the unit circle
Answers
The angle on the unit circle is solved to be
56.01 degrees (to the nearest tenth)
How to find the angleTo find the angle of the terminal side through the given point on the unit circle, we can use the inverse trigonometric functions.
given that P = ((√5)/4, (√11)/4)
θ = arctan ((√11)/4 / (√5)/4)
θ = arctan((√11)/(√5))
θ ≈ 56.01 degrees
hence to the nearest tenth of a degree, the angle of the terminal side through the point P = ((√5)/4, (√11)/4) on the unit circle is approximately 56.01 degrees.
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Hey! I’m doing a test and I’m really stuck on this problem
3 (y + 6) + 10 = -8
What is y?
Answers
Answer:
y= -12
Step-by-step explanation:
3y+18+10=-8
Basically just used the distributive property
Combine like terms:
3y+28=-8
-28. -28
3y=-36
y=-12
Answer:
y = -11
Step-by-step explanation:
3(y+6) + 10 = -8
3y + 18 + 10 = -8
3y = -8 - 18 - 10
/3 /3
y = -12
find all polar coordinates of point p where p= (4, pi/3)
Answers
Answer:
With polar coordinates this isn’t true. In polar coordinates there is literally an infinite number of coordinates for a given point. For instance, the following four points are all coordinates for the same point. Here is a sketch of the angles used in these four sets of coordinates.
Step-by-step explanation:
The value of Maggie's car decreased by 30% since last year, when she bought it. If the car is now worth $22,000.00, how much was the car worth when
she bought it?
A.
$29.333.33
ОВ.
$33,846.15
Oc.
$31,428.57
OD.
$28,600.00
Answers
Answer:
$18,200
Step-by-step explanation:
To solve this, you would need to add 30% back to $14,000. To do that, simply multiply $14,000 by 30%. Remember that we will need to also change 30% into its decimal form (30% -> 0.3). $14,000 x 0.3 = $4,200 To find out how much the car was worth when Maggie first bought it, we simply add $4,200 to $14,000. $14,000 + $4,200 = $18,200
Hope it helps!
What is the Pythagorean theorem
Answers
Answer:
The Pythagoras theorem states that if a triangle is right-angled (90 degrees), then the square of the hypotenuse is equal to the sum of the squares of the other two sides. Observe the following triangle ABC, in which we have BC2 = AB2 + AC2. Here, AB is the base, AC is the altitude (height), and BC is the hypotenuse. It is to be noted that the hypotenuse is the longest side of a right-angled triangle.
Pythagoras Theorem Equation
The Pythagoras theorem equation is expressed as, c2 = a2 + b2, where 'c' = hypotenuse of the right triangle and 'a' and 'b' are the other two legs. Hence, any triangle with one angle equal to 90 degrees produces a Pythagoras triangle and the Pythagoras equation can be applied in the triangle.
Answer:
The Pythagoras theorem states that:The sum of the squares on the edges of a right triangle angle is equal to the squareon the hypotenuse.Mathematically stated as: a² +b² = c²Hope this helps.Good luck ✅.In a recent year, companies spent a total of $87.5 billion on newspaper, television, and radio ads. The total amount spent on television and
radio ads was only $2.9 billion more than the amount spent on newspaper ads alone. The amount spent on newspaper ads was $5.4 billion
more than what was spent on television ads. How much was spent on each form of advertising? (Hint: Let the variables represent numbers of
billions of dollars.)
How much was spent on newspaper ads? $
How much was spent on television ads? $
How much was spent on radio ads? $ billion
billion
billion
Answers
Answer:
newspaper ads: $42.3 billiontelevision ads: $36.9 billionradio ads: $8.3 billionStep-by-step explanation:
You want the amount spent on ads in each medium given the total and relations between amounts spent for newspaper, television, and radio ads.
SetupLet n, t, r represent the amounts spent on ads in newspapers, television, and radio, respectively. The given relations tell you ....
n +t +r = 87.5
-n +t +r = 2.9
n -t = 5.4
SolutionThe augmented coefficient matrix can be reduced to row-echelon form using a suitable calculator or spreadsheet. This tells you the amounts spent in each medium. The attachment shows this.
newspaper ads: $42.3 billiontelevision ads: $36.9 billionradio ads: $8.3 billion__
Additional comment
The value of n can be found by subtracting the second equation from the first. That can be used in the third equation to find t, and both of those values can be used in either of the first two equations to find r.
the mass of sugar is 19kg.What is the total mass of 4 such jar of a sugar?
Answers
Answer: 76kg
Step-by-step explanation:
If the mass of sugar in one jar is 19kg, then the mass of 4 such jars of sugar can be found by multiplying the mass of one jar by 4:
Total mass of 4 jars of sugar = 4 × 19kg Total mass of 4 jars of sugar = 76kgTherefore, the total mass of 4 jars of sugar is 76kg.
__________________________________________________________
The mass of sugar is 19 kg. What is the total mass of 4 such jar of a sugar?
Answer:The total mass of four jars of sugar is 76 kg.
Solution and Explanation:The total mass of four jars of sugar can be found by multiplying the mass of one jar by 4:
\(\large\rm{Total\: mass = 19\: kg \times 4 = \boxed{\rm{\:76\: kg\:}}}\)
\(\therefore\) The total mass of four jars of sugar is 76 kg.
What is mass?- Mass is a measure of the amount of matter an object contains. It is a fundamental property of an object and is typically measured in units such as kilograms or grams. Mass is different from weight, which is the force of gravity acting on an object's mass. Mass is an intrinsic property of an object and remains constant regardless of its location, while weight can vary depending on the gravitational field it is in. Essentially, mass determines an object's resistance to acceleration or change in motion.
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5 + 5 + 5 + 5 + 220+ 30004
Answers
Answer:
30244
Step-by-step explanation:
if you take away 25 from a number you will be left with two and halftimes 30. what is the number?
Answers
If you take away 25 from (100) you get 75.
70 also equals 2.5*30
To be eligible for the swim team, the mean pace a student needs to achieve on 5 laps of the pool is 60 seconds (s). The student swims a lap in 63 s, 62 s, 65 s, and 58 s on her first four laps.
What is the maximum time (in seconds) that she can take on her last lap and still make the team?
Answers
52s is the maximum time that she can take on her last lap and still make the team.
What is Statistics?Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.
Given that he mean pace a student needs to achieve on 5 laps of the pool is 60 seconds (s).
The student swims a lap in 63 s, 62 s, 65 s, and 58 s on her first four laps.
We need to find the maximum time (in seconds) that she can take on her last lap and still make the team
Let x be the maximum time (in seconds) that she can take on her last lap
60=(63+62+65+58+x)/5
300=63+62+65+58+x
300=248+x
Subtract 248 on both sides
300-248=x
x=52s
Hence, 52s is the maximum time that she can take on her last lap and still make the team.
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Match the following. Match the items in the left column to the items in the right column. 1. domain the first element of a relation or function; also known as the input value. 2. output a relation in which every input value has exactly one output value. 3. input the x-value of a function. 4. relation any set of ordered pairs (x, y) that are able to be graphed on a coordinate plane. 5. function the y-value of a function. 6. range the second element of a relation or function; also known as the output value.
Answers
The matching of items and their corresponding descriptions are 1. Domain, 2.Output, 3. Input, 4. Relation, 5. Function, and 6. Range.
What is the appropriate matching of the following items?1. Domain - the first element of a relation or function; also known as the input value.
3. Input - the x-value of a function.
6. Range - the second element of a relation or function; also known as the output value.
4. Relation - any set of ordered pairs (x, y) that are able to be graphed on a coordinate plane.
2. Output - a relation in which every input value has exactly one output value.
5. Function - the y-value of a function.
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melissa has $5000 and adds $20 each week to it. chris has $6820 and spends $50 from it each week. after how many weeks will both melissa and chris have the same amount
Answers
Answer:
It will take approximately 36.4 weeks for Melissa and Chris to have the same amount of money.
Step-by-step explanation:
To determine how many weeks it will take for Melissa and Chris to have the same amount of money, you can set up an equation based on the information given. Let W be the number of weeks it takes for Melissa and Chris to have the same amount of money.
Melissa's total amount of money after W weeks will be 5000 + 20W.
Chris's total amount of money after W weeks will be 6820 - 50W.
Therefore, you can set up the equation 5000 + 20W = 6820 - 50W and solve for W.
First, you can add 50W to both sides of the equation to get 50W + 5000 = 6820.
Next, you can subtract 5000 from both sides of the equation to get 50W = 1820.
Finally, you can divide both sides of the equation by 50 to get W = 36.4.
A spherical gasoline tank has been drained. If the result was 65,450 cubic feet of gasoline, what was the diameter?
Answers
The required diameter of the spherical gasoline tank is given as 50 feet.
What is volume?Volume is defined as the mass of the object per unit density while for geometry it is calculated as profile area multiplied by the length at which that profile is extruded.
Here,
The volume of the cylinder = 4/3πr³
4/3πr³ = 65450
r³ = 15625
r = 25 feet
Diameter = 2 × r
= 2 × 25
= 50 feet
Thus, the required diameter of the spherical gasoline tank is given as 50 feet.
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what is the value of d+3
Answers
Answer:
you need to explain
Step-by-step explanation:
What's the answer to 8.546 rounded to the nearest ones place
Answers
Answer:
8.5
Step-by-step explanation:
because the hundredths place is not above 5
A drum of water is 3/4 full. When 9 litres are drawn from it, it is half full. How much water does the drum hold what is the capacity of the drum
Answers
Answer:
OK, Here is your answer
Step-by-step explanation:
Let's assume the capacity of the drum be C litres.Since the drum is initially 3/4 full, the amount of water in it is 3/4 × C = (3/4)C liters.When 9 liters of water are drawn from the drum, the remaining amount of water is (3/4)C - 9 liters.Since the drum is now half full, the amount of water remaining in it is (1/2)C liters.Therefore, we can write the equation: (3/4)C - 9 = (1/2)CTo solve for C, let's first get rid of the fractions by multiplying both sides by 4.(3/4)C - 9 = (1/2)C → 3C - 36 = 2C → C = 36Therefore, the capacity of the drum is 36 liters.Hence, the drum holds 3/4 × 36 = 27 liters of water initially and after 9 liters of water are drawn, the remaining amount of water in it is 27 - 9 = 18 liters.
Answer:
18 Lieters.
Step-by-step explanation:
found the answer in his answer. ↑↑↑↑
What is 12 divided by 3/5
Answers
Answer:
20
Step-by-step explanation:
12 / 3/5
12 / 0.6
20
Answer:
12 divided by 3/5 = 20
I NEED HELP PLEASE SHOW STEP BY STEP, I NEED THIS ASAP, WILL MARK BRAINLEST TO BEST ANSWER
Answers
Answer:
first, dilate triangle ABC with respect to the origin by scale factor of 2.
then rotate it 90 degrees counterclockwise about the origin
Step-by-step explanation:
Boris started on the treadmill after setting timer for 99 minutes. The display says he have finished 43% of his run. How many minutes have gone by. Round to the nearest tenth
Answers
99 minutes * 0.43 = 42.57 minutes
Rounding to the nearest tenth, we can say that approximately 42.6 minutes have gone by.
-2 x + 4 > -4x + 8. helppp
Answers
Answer:
1/2 but unsure
Step-by-step explanation:
I solved for X and I got 1/2 I want to verify what you are solving for so I could further help you