Final answer:
The statement is true; a tangent line meets a circle at the point of tangency, which is the unique point where the tangent touches the circle without intersecting it.
Explanation:
True, the point at which a tangent line meets a circle is indeed called the point of tangency. This is a fundamental concept in geometry, where a tangent line is defined as a line that touches a curve at exactly one point, without crossing through it. This distinct point is known as the point of tangency.
For example, if we have a circle and a line that touches the circle at just one point and does not intersect it at that point, that line is a tangent to the circle, and the point of contact is the point of tangency. The tangent line is always perpendicular to the radius of the circle at the point of tangency, as can also be seen from the properties of the director circle, which is the locus of points of intersection of perpendicular tangents to the curves like ellipses and hyperbolas.
In the context of a director circle, perpendicular tangents to an ellipse would intersect on this special circle. Although for this particular question, we are focusing on the tangent line to a single circle and its point of tangency. It's interesting to note that according to the properties of circles, every point on a circle allows for exactly one tangent line. Whenever such a line is drawn, it illustrates the concept of tangency.
Identify each function as a constant, direct variation, absolute value, or greatest integer function.
g (x)=x+3
end behavior of F(x)=-x^(3-)2x^(2)+7x-10
A. The graph of the function starts high and ends high
B. The graph of the function starts low and ends low
C. The graph of the function starts high and ends low
D. The graph of the function starts low and ends high
rewrite 7/11 as a division problem
A car travels around a circular track. The inside wheels follow along the line of the inner circle, and the outer wheels follow along the line of the larger circle. The radius of the larger circle is 25 ft, and the radius of the smaller circle is 21 ft. Determine how much farther the outer wheels would travel than the inner wheels after one revolution.
Answer:
CStep-by-step explanation:
What is the ratio of the area of sector ABC to the area of sector DBE?
I am not quite sure how to do this. So far, since there are variables instead of numbers, I have got (pi)(r)^2:(pi)(3r)^2, but I know that is definitely wrong.
Answer:
4/3
Step-by-step explanation:
Find the coordinates of point l that lies along the directed line segment from N(14,4) to M(2,8) and partitions the segment in the ratio of 1:3
Ian has 120 folders to file. So far, he has filed 36 of the folders. What percent of the folders does he have left to file?
The 70 percent of the folders, he have left to file.
What is a fraction?A fraction represents a part of a number or any number of equal parts.
We are given that Ian has 120 folders to file. So far, he has filed 36 of the folders.
The fraction of the amount of folders Ian did not file out of 120 ;
84/120
= 21/30
In order to convert this into a percent, we have to divide both the numerator and the denominator by 1.2.
we will get 70/100.
This new fraction as a percent is 70%.
Therefore, he has 70% of folders left to file.
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The value of a treadmill bought new for $1000 decreases 5% each year. Use a graph to predict the value of the treadmill in 5 years.
A) ≈ $773.78
B) ≈ $857.38
C) ≈ $902.50
D) ≈ $814.50
The predicted value of the treadmill after 5 years, with an annual depreciation rate of 5%, is approximately $773.78. This calculation uses the exponential decay formula and corresponds to option A).
To predict the value of a treadmill in 5 years that was bought new for $1000 and decreases 5% each year, we can use the formula for exponential decay:
V = [tex]P(1 - r)^t[/tex]
Where:
V is the future value of the treadmill,
P is the original value ($1000),
r is the rate of decay (5% or 0.05), and
t is the time in years (5 years).
By substituting the values we have:
V = $1000(1 - 0.05)⁵
V = $1000(0.95)⁵
V = $1000(0.77378) = $773.78
Therefore, the predicted value of the treadmill after 5 years is approximately $773.78, which corresponds to option A).
WILL SOMEONE HELP ME ANSWER THIS PLEASE!!!!
Luca and William are playing a video game and they have scored a total of 20,000 points. Luca scored 4,000 more points than William. If you let l= the number of points that Luca scored, and w= the number of points that William scored, then the problem can be represented by the system:
l+w=20,000 and l=w+4,000
Graph the system. How many points did each boy score?
My possible answers are:
a. William = 8,000 and Luca = 12,000
b. William = 12,000 and Luca = 8,000
d. William = 4,000 and Luca = 16,000
l+w=20000
l=w+4000
w+4000+w=20000
2w+4000=20000
2w=16000
w=8000
l = 8000 +4000 = 12000
William scored 8000, Luca scored 12000
Can someone tell me a disaster that happened in America in the ocean (besides Deepwater Horizon). Thanks!!
Lou’s Shoes is having its annual Flag Day Sale and is offering a 25% discount on all regularly priced shoes. Kayla spends $13.50 buying sandals and sneakers. Determine which equation represents how much Kayla will spend on sandals after the discount.
The equation represents how much Kayla will spend on sandals after the discount is $13.50 = 0.75x.
What is an expression?Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
Given that Lou’s Shoes is having its annual Flag Day Sale and is offering a 25% discount on all regularly priced shoes. Kayla spends $13.50 buying sandals and sneakers.
The equation can be written as:-
$13.50 = 0.75x.
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simplify 6√1,000m^3n^12
The simplified expression is 60mn⁶.
What is factorization?Factorization is a process to simplify the expression by finding the factors of that expression.
And to find the same expression from factors, you have to reverse the process.
Given that the expression is 6√1,000m³n¹².
We can simplify this expression by breaking down 1,000 into its prime factorization:
1,000 = 2³ x 5³
Then we can rewrite the expression as:
6√(2³ x 5³ x m³ x n¹²)
Using the properties of radicals, we can separate the factors inside the radical:
6√2³ x √5³ x √m³ x √n¹²
Simplifying each square root term:
6 x 2 x 5 x m x n⁶
= 60mn⁶
Therefore, the simplified expression is 60mn⁶.
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Suatu jenis roti memerlukan 150 gram tepung dan 50 gram mentega. Roti jenis lain memerlukan 75 gram tepung dan 75 gram mentega, produksi roti membuat sebanyak roti dan dua jenis roti itu. Bahan yang tersedia 2.250 gram tepung dan 1.250 gram mentega, berapakah banyak roti masing masing yang dibuat?
The amount of Bread Type 1 is 10 pieces
The amount of Bread Type 2 is 10 pieces
Further explanationSimultaneous Linear Equations can be solved using one of the following methods :
Elimination MethodSubstitution MethodGraph MethodLet's try to solve the problem now.
Let :
Amount of Bread Type 1 = A
Amount of Bread Type 2 = B
1 piece of bread type 1 requires flour as much as 150 grams and 1 piece of bread type 2 requires flour as much as 75 grams, while the total amount of flour is as much as 2250 grams, then:
[tex]150A + 75B = 2250[/tex]
[tex]2A + B = 30[/tex]
[tex]\boxed{B = 30 - 2A}[/tex] → Equation 1
1 piece of bread type 1 requires butter as much as 50 grams and 1 piece of bread type 2 requires butter as much as 75 grams, while the total amount of butter is as much as 1250 grams, then:
[tex]50A + 75B = 1250[/tex]
[tex]2A + 3B = 50[/tex]
[tex]2A + 3(30 - 2A) = 50[/tex] ← Equation 1
[tex]2A + 90 - 6A = 50[/tex]
[tex]2A - 6A = 50 - 90[/tex]
[tex]-4A = -40[/tex]
[tex]A = -40 \div -4[/tex]
[tex]\large {\boxed{A = 10}}[/tex]
[tex]B = 30 - 2A[/tex]
[tex]B = 30 - 2(10)[/tex]
[tex]B = 30 - 20[/tex]
[tex]\large {\boxed{B = 10}}[/tex]
Conclusion :The amount of Bread Type 1 is 10 pieces
The amount of Bread Type 2 is 10 pieces
Learn morePerimeter of Rectangle : https://brainly.com/question/12826246Elimination Method : https://brainly.com/question/11233927Sum of The Ages : https://brainly.com/question/11240586?Answer detailsGrade: High School
Subject: Mathematics
Chapter: Simultaneous Linear Equations
Keywords: Elimination , Substitution , Graph , Method , Linear , Equation , Simultaneous
Which expression is equivalent to am ÷ an?
am − n
am + n
am ⋅ n
am ÷ n
The equivalent expression is a^m − n
What are properties of exponents?The properties of exponents are mentioned below.
Law of Product: a^m × a^n = a^m+nLaw of Quotient: a^m/a^n = a^m-nLaw of Zero Exponent: a^0 = 1Law of Negative Exponent: a^-m = 1/a^mLaw of Power of a Power: (a^m)^n = a^mnLaw of Power of a Product: (ab)^m = a^m*b^mLaw of Power of a Quotient: (a/b)^m = a^m/b^mGiven expression:
am ÷ an
Now, using the law of exponents we have
a^m ÷ a^n
=a^(m-n)
Hence, the equivalent expression is a^m − n
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In early spring, you are wanting to purchase 6 potted rose plants. The plants to choose from come in 8-inch pots that sell for $12 and 10-inch pots that sell fro $15. If you spend $78, which of the following are the equations for this scenario? Let x= number of 8 inch pots and let y = number of 10 - inch pots.
A. y+15y=6
12x+x=78
B. x+y=6
12x+15y=78
C. x+y=78
12x +15y=6(78
D. x+y=6
15x+12y=78
E. No solution
A scientist measures the angle x and the distance y between the Earth and the moon. Using complete sentences, explain how the scientist can use only these two measurements to calculate the distance between the Earth and the Sun.
tan =opposite/adjacent
In this case: tan =X , opposite=Y and adjacent= D
tan(x)=Y(opposite) /D(adjacent)
All terms in the equation are known except for 'D the distance'.
So the distance between the earth and the sun indicate by the symbol 'D' is equal to: y/tan(x)
Ajay analyzed two companies and has formulated tables to model each company’s growth, where x represents the age of the companies in years and y represents growth in terms of number of employees. Company 1 Company 2
Table 1 Table 2
x l y x l y
0 l 0 0 l 1
1 l 6 1 l 6
2 l 12 2 l 36
3 l 18 2 l 216
4 l 24 4 l 1,296
If the number of employees is an indicator of a successful business, in which company should Ajay invest? company 1 because it is adding six employees each year while company 2 is multiplying its number of employees by six each year company 1 because it is multiplying its number of employees by six each year while company 2 is adding six employees each year company 2 because it is adding six employees each year while c
Answer:
Company 2 because it is gaining six times the number of employees, while Company 1 is only adding 6 employees every year.
Step-by-step explanation:
Looking at the table, the number of employees in Company 1 goes up by 6 employees per year.
The number of employees in Company 2 is multiplied by 6 every year; this means they gain more employees after the first year than Company 2 does (they go from 6 to 36, which is a gain of 30, while Company 1 goes from 6 to 12, a gain of 6).
If we are looking strictly at the number of employees, Company 2 is the better choice.
Answer:
company 2 is multiplying
Step-by-step explanation:
A local newspaper compiles data on the number of days, X, people in a neighborhood receive the newspaper. The probability distribution for the data is shown in the table below. What is the probability that a randomly chosen person receives the newspaper at least one day per week?
Answer: D 83% is the answer
(06.01)What type of association does the graph show between x and y?
Linear positive association
Nonlinear positive association
Linear negative association
Nonlinear negative association
When two balanced dice are rolled, there are 36 possible outcomes. what is the probability that the sum of the numbers on the dice is 6 or 10?
The probability of having a sum of either 6 or 10 is [tex]\frac{2}{9}[/tex]
The sample space has the size [tex]|S|=36[/tex]
Let
[tex]A=\text{the event of having a sum of 6}\\B=\text{the event of having a sum of 10}[/tex]
then
[tex]A=\{(1,5),(2,4),(3,3),(4,2),(5,1)\}\\|A|=5[/tex]
and
[tex]B=\{(4,6),(5,5),(6,4)\}\\|B|=3[/tex]
then, the probability of having a sum of either 6 or 10 will be
[tex]P(A\cup B)=P(A)+P(B)[/tex]
since [tex]A[/tex] and [tex]B[/tex] are mutually exclusive events. Substituting
[tex]P(A\cup B)=P(A)+P(B)\\=\frac{|A|}{|S|}+\frac{|B|}{|S|}\\=\frac{2}{9}[/tex]
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When two balanced dice are rolled, there are 36 possible outcomes. To find the probability that the sum of the numbers on the dice is 6 or 10, count the favorable outcomes and divide it by the total outcomes.
Explanation:When two balanced dice are rolled, there are 36 possible outcomes. To find the probability that the sum of the numbers on the dice is 6 or 10, we need to count the favorable outcomes and divide it by the total outcomes.
For the sum of 6, there are 5 possible outcomes: (1,5), (2,4), (3,3), (4,2), (5,1). For the sum of 10, there are 3 possible outcomes: (4,6), (5,5), (6,4). Therefore, there are 8 favorable outcomes out of 36 total outcomes.
The probability is calculated as:
Probability = Favorable outcomes / Total outcomes = 8 / 36 = 2 / 9
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Which sequence of transformations will result in an image that maps onto itself?
The correct transformation to get result in an image that maps onto itself will be;
''Reflect over the y axis and then reflect again over the y axis''.
What is Translation?
A transformation that occurs when a figure is moved from one location to another location without changing its size or shape is called translation.
Given that;
The statement is,
'' A sequence of transformations will result in an image that maps onto itself''.
Now,
Since, We know that after two reflections over the same axis we get the original image.
Thus, we get;
The correct transformation to get result in an image that maps onto itself will be;
''Reflect over the y axis and then reflect again over the y axis''.
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Which options show the correct steps for finding the x-coordinate of the vertex in the equation y=x^2+6x+8?
simplify 4x+5/6x^2-x-12 subtract 5x/6x^2-x-12
Suppose you add two linear equations that form a system, and you get the result y = −2. how many solutions does the system have?
Sandy has earned $290. That is 20% of the cost of the new computer she wants to buy. What is the total amount of money she needs to buy the computer?
Answer:
1450
Step-by-step explanation:
simply just multiply 290 by 5 and u get 1450 hope this helps you
find the area and circumference of a circle with radius 4 in.
Answer is provided in the image attached.
(03.01)
A newly made car will have a model number, a parts number, and a serial number. A model number is assigned by the manufacturer to identify each type of car. A parts number identifies one part of the smaller parts that make up the car. A serial number is unique to each car produced and identifies it.
Which relation is a function?
(parts number, serial number)
(model number, parts number)
(serial number, model number)
(serial number, part number)
Answer:
Hi!
The corrects answers are:
•(serial number, model number)
Step-by-step explanation:
First, you have to understand the meaning of a function, that is an a relation but have the condition:
The input must be relationed with only one output.
The question says:
"A serial number is unique to each car produced and identifies it." so this will be you input, and will be related with only one model number.
The ratio of girls to boys is 5 to 6. If there are 72 boys, how many girls are there?
A photo that is 4 in wide and 6 in high is enlarged to a poster that is 3ft wide and 4 1/2 ft high what is the ratio of the width of the photo to the width of the poster
Answer:
Required ratio in the simplest form = 1 : 9
Step-by-step explanation:
Width of photo = 4 inches
Height of the photo = 6 inches
Width of the poster = 3 feet
Now, 1 feet = 12 inches
So, Width of the poster = 3 × 12 = 36 inches
Height of the poster = 4.5 feet
= 54 inches
We need to find the ratio of the width of the photo to the width of the poster
⇒ Required Ratio = 4 : 36
⇒ Required ratio in the simplest form = 1 : 9
A pearl is formed in one of every 10,000 oysters what percent of oysters make pearls