The main difference between tangent and chord is that the tangent touches the curve at only one point whereas the chord touches the curve at two points.
Chord:
A chord is the line segment joining two points on a curve. The term is often used to describe a line segment whose ends lie on a circle.Tangent:
The tangent line (or simply tangent) to a plane curve at a given point is the straight line that "just touches" the curve.The tangent makes an angle of 90 degree with the radius of circle at the point of contact.From above definitions of Chord and Tangent , we say that chord touches the curve at two points where as Tangent touches the curve at only one point .
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A tangent is a line that touches a circle at only one point and is perpendicular to the radius at the point of contact, while a chord is a line segment with both endpoints on the circle.
A tangent and a chord are lines that relate to the curve of a circle, but they have distinct differences. A tangent is a line that touches a circle at exactly one point, and at this point of contact, it is perpendicular to the radius of the circle, which is called the axis in this context. In sharp contrast, a chord is a line segment whose endpoints both lie on the circle. When constructing the perpendicular from the midpoint of a chord, you are drawing an axis. For tangents, the perpendicular erected from the point of contact with the circle is also an axis.
This shows that the tangent is unique in that it has a "no-cut" property; it is the only line that will touch the circle at that single point without cutting through it. When looking at the slope of curves, the slope of the tangent line at the point of contact represents the exact slope of the curve at that point. The differentiation process in mathematics is used to find this slope of the tangent, which is important for understanding the rate of change at a specific point on a curve.
Rewrite each expression below using the distributive property then evaluate each expression for X equals two and Y equals five. a.8x-4= b.6y2+24y c. 7X(y -2) d. 3(9+y)
Which table represents a linear function?
1, 2, 3, or 4?
The price of pears at a farm is $1.41 per pound. Which equation can be used to determine c, the total price of n pounds of pears? c equals 1.41 over n c = 1.41 + n c = 1.41 − n c = 1.41n
For f(x)=3x+1 and g(x)=x^2-6, find (f/g)(x)
A. 3x+1/x^2-6, x≠±√6
B. x^2-6/3x+1
C. x^2-6/3x+1, x≠-1/3
D. 3x+1/x^2-6
Answer:
Answer is A
Step-by-step explanation:
7 to the second power minus 24 divided by 3
Think of the number seven. Now add eight to it. Now add four more. Now subtract nine. Now add three. Your answer is _____.
Answer:
7+8+4-9+3=13
Step-by-step explanation:
We have given the statements and we have to figure out the answer.
Think of the number seven i.e. 7
Now add eight to it i.e. 7+8
Now add four more i.e. 7+8+4
Now subtract nine i.e. 7+8+4-9
Now add three i.e. 7+8+4-9+3
Simplification of expression 7+8+4-9+3
Add the terms,
7+8+4-9+3=22-9
Subtract the terms,
7+8+4-9+3=13
Therefore, The answer is 13.
Parallelogram FGHI on the coordinate plane below represents the drawing of a horse trail through a local park: (Via Image)
In order to build a scale model of the trail, the drawing is enlarged on the coordinate plane. If two corners of the trail are at point A(0, 4) and point D(−6, −5), what is another point that could represent a corner of the trail?
1) (4, 4)
2) (11, 4)
3) (6, −5)
4) (−17, −5)
Answer:
Correct choice is 3)
Step-by-step explanation:
Enlargment is a dilation. A dilation is a transformation that preserves parallel lines and each side length of the pre-image parallelogram is multiplied by the same coefficient.
Note that
[tex]\overrightarrow{IF}=(-7-(-9),5-2)=(2,3);\\ \\\overrightarrow{DA}=(0-(-6),4-(-5))=(6,9)=3\cdot (2,3)=3\overrightarrow{IF}.[/tex]
From this statement you can conclude that the factor of dilation is 3.
Since
[tex]\overrightarrow{FG}=(-3-(-7),5-5)=(4,0),[/tex]
then
[tex]\overrightarrow{AB}=3\overrightarrow{FG}=3(4,0)=(12,0)\ \text{or}\ \overrightarrow{BA}=(12,0)[/tex]
and
[tex]\overrightarrow{DC}=(12,0)\ \text{or}\ \overrightarrow{CD}=(12,0)[/tex]
Yhis gives you that B(12,4) (or B(-12,4)) and C(6,-5) (or C(-18,-5)).
A room contains 5 cats and 2 dogs. If the ratio is 5 to 2 the rate can be expressed as 5 cats __ 2 dogs
Answer:
Per is the answer (Apex)
Step-by-step explanation:
Anybody know? Also, what pattern?
suppose an investment of $8200 doubles in value every 7 years. how much is the investment worth after 28 years
Answer:
After 28 years, it will be $131,200
Step-by-step explanation:
It is given that the investment doubles in value every 7 years.
So, after 7 years, it will be 8200 × 2 = 16,400
After 14 years, it will be 16,400 × 2 = 32,800
After 21 years, it will be 32,800 × 2 = 65,600
After 28 years, it will be 65,600 × 2 = 131,200
Hence, the investment is $131,200 worth after 28 years.
Find the excluded value of the rational expression 2x + 6/4x - 8
Answer:
for connections
1.a
2.c
3.d
4.c
Step-by-step explanation:
All 500 seats to the Friday Night Seniors' Play were sold, and a total of $3312.50 was collected. If adult ticket cost 7.50 each and Senior tickets cost $4 each, how many bills of each type were sold?
The number of senior tickets is 375 and the adult tickets is 375 if All 500 seats to the Friday Night Seniors' Play were sold, and a total of $3312.50 was collected.
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
It is given that:
All 500 seats to the Friday Night Seniors' Play were sold, and a total of $3312.50 was collected.
From the question:
A + S = 500
7.5A + 4S = 3312.50
-3.5S = - 437.50
S = -437.50/-3.5
S = 125
A = 500 - S
A = 375
Thus, the number of senior tickets is 375 and the adult tickets is 375 if All 500 seats to the Friday Night Seniors' Play were sold, and a total of $3312.50 was collected.
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Matt and Brian were solving a system of equations. They both noticed that the two lines had the same slope. Brian said that because each line in the system had the same slope, the two lines had to be parallel, which meant the solution to the system was "no solutions." Matt disagreed, and said they should also look at the y-intercepts before determining how many solutions there were. Who is correct?
Answer: A. Matt is correct. Though two lines with equal slopes are often parallel, if they have the same y intercept, they are the same line and have infinitely many solutions.
Step-by-step explanation: Apex Answer
Needing this for tomorrow thanks help me please is hurry
39) 6 *15 = 90 in deposits
40) 5 + 10 + 15 = 30 withdrew
41) 35 +90 = 125 - 30 = 95 in the account
You are considering a 5/1 ARM. What does the 5 represent?
What is the domain of the function f(w) = 0.5(35 – 2w)? Explain your answer.
A piggy bank containing only quarters had a mass of 850 grams when empty and 7822 grams when filled. If a quarter weighs 5.6 grams , estimate the amount of money inside the piggy bank
An ellipse has a vertex at (14, –1). The focus of the ellipse nearest that vertex is located at (8, –1). If the center of the ellipse is located at (–1, –1), what is the equation of the directrix on that side of the ellipse?
x =
Answer:
24
Step-by-step explanation:
edge 2022
Joyce has as much money as George; then they bet 5 cents each and George lost. If, after the bet, George has x cents, how much does Joyce have ?
Joyce would have x + 5 cents after the bet.
Explanation:To determine how much money Joyce has after the bet, we need to consider the information given in the question. It states that Joyce has as much money as George, and after they bet 5 cents each, George lost and ended up with x cents. Since they both bet the same amount and George lost, it means Joyce must have won the bet and still has the original amount of money they each had, plus the 5 cents George lost.
Therefore, Joyce has x + 5 cents after the bet.
If the graph of f(x) has the point (2,7) then what is one point that will be on the graph of f-1(x)
The graph of f^-1 (x) is called the inverse function of f (x). The relationship between the two is that the point (x,y) is on the graph of f (x) if and only if the point (y,x) is on the graph of f^-1 (x).
This means that if the point (2, 7) is on f (x), therefore the point (7, 2) is on f^-1 (x).
Answer: (7, 2)
Answer: The required point is (7, 2).
Step-by-step explanation: Given that the graph of f(x) has the point (2, 7).
We are to find one point that will be on the graph of [tex]f^{-1}(x).[/tex]
We know that
if a point (a, b) lies on the graph of a function g(x), then the point (b, a) will always lie on the the graph of the inverse function [tex]g^{-1}(x).[/tex]
Therefore, the one point that will lie on the graph of [tex]f^{-1}(x)[/tex] is (7, 2).
Thus, the required point is (7, 2).
Esmerelda rents a car from a company that rents cars by the hour. She has to pay an initial fee of $50, and then they charge her $9 per hour. She has $200 available to spend on car rental. What is the greatest number of hours for which she can rent the car? (The car cannot be rented for part of an hour.)
The correct answer is 16 hours
Phil and Lorena are playing golf. Phils score after the first round is -1 Lorena score is -4 the player with the lower score is the winner Who wins?
Lorena with the score of -4 is the winner.
To determine the winner of the match, we need to look at the following given details:
In golf, the player with the lower score wins. Let's compare Phil and Lorena's scores:Phil's score: -1Lorena's score: -4We know that in negative numbers, the higher count number is lower in value than lower count.For example: -50 is lower than -20.
Hence, we know that -4 is less than -1, Lorena has the lower score and thus wins the game.
A student runs 100 meters in 11 second s . What is the speed of the student
The total mass of Abdul and his baby brother is 15.25kg . The mass of Abdul and his father is 72.25kg . The mass of Abdul's father is 13 times as heavy as Abdul's baby brother. What is Abdul's mass?
Define a simulation to represent correct answers on a true-or-false quiz. Use the simulation to find the probability of getting exactly 4 correct answers on a ten-question quiz.
A steel cylinder with a moveable piston on top is filled with helium (He) gas. The force that the piston exerts on the gas is constant, but the volume inside the cylinder doubles, pushing the piston up.
Which of the following answers correctly states the cause for the change described in the scenario?
The temperature increased.The density of the helium atoms decreased.The pressure decreased.The helium atoms increased in size.Final answer:
To determine the probability of passing a 10-question true-false quiz with at least a 70% score when guessing, we calculate the probabilities of getting 7, 8, 9, and 10 answers correct and sum them, using the binomial probability formula.
Explanation:
A student takes a 10-question true-or-false quiz and guesses randomly without studying. To find the probability of getting exactly 4 correct answers out of 10 questions, we can use a binomial probability formula which is P(X=k) = (n choose k) * p^k * (1-p)^(n-k), where 'P(X=k)' is the probability of 'k' successes in 'n' trials, 'p' is the probability of success on a single trial, and '(1-p)' is the probability of failure on a single trial.
In this case, guessing true or false correctly is a 50% chance or 'p' equals 0.5, since there are only two possible outcomes, and 'n' is 10. To calculate the probability of passing the quiz with at least a 70 percent score, we need at least 7 correct answers out of 10. We will calculate the probabilities of getting exactly 7, 8, 9, and 10 correct answers and then sum these probabilities.
The calculation for P(X=7) would be (10 choose 7) * 0.5^7 * 0.5^(10-7). Similarly, we would calculate P(X=8), P(X=9), and P(X=10) using the same formula with different values for 'k'. Once we have these probabilities, we can add them up to find the total probability of scoring at least 70 percent on the quiz.
Remember to round answers to relative frequency and probability problems to four decimal places for accurate results.
Rita's mother is 4 times as old as she is. Her grandmother is twice as old as her mother. If the sum of their age is 194, how old are Rita, her mother, and her grandmother?
Through setting up and solving an algebraic equation, we find that Rita is 15 years old, her mother is 60 years old, and her grandmother is 120 years old. These ages satisfy the conditions that the sum of their ages is 194, Rita's mother is 4 times her age, and her grandmother is twice the age of her mother.
Explanation:Let's use algebra to solve the problem of finding the ages of Rita, her mother, and her grandmother. We will start by defining the variable x to represent Rita's age. According to the information provided, Rita's mother's age is 4 times as old as Rita, so we can express that as 4x. The grandmother is twice as old as the mother, which can be written as 2(4x) or 8x.
Next, we need to use the fact that the sum of their ages is 194. We can set up the following equation based on all the information we have:
x (Rita's age) + 4x (Mother's age) + 8x (Grandmother's age) = 194
Combining like terms, we get:
13x = 194
Now, we solve for x by dividing both sides of the equation by 13:
x = 194 / 13
x = 14.923 (As ages are typically expressed as whole numbers, we would round this to the nearest whole number if necessary, but in this case, 194 is evenly divisible by 13, so x = 15).
Now that we know Rita's age, we can find out her mother's and grandmother's ages:
These are the ages of Rita, her mother, and her grandmother.
Please help what is the additive inverse of this expression: -2.5 - 1.5 plz help
The additive inverse of the expression -2.5 - 1.5 is 4. This is determined by first resolving the expression to -4 and then flipping the sign of this result to its opposite, yielding 4.
Explanation:In mathematics, the additive inverse of a number is the number that when added to the original number results in zero. To find the additive inverse of the expression -2.5 - 1.5, follow these steps:
First, resolve the expression by subtracting 1.5 from -2.5 which gives -4.Second, to find the additive inverse of -4, you simply flip the sign of the term to positive, so the additive inverse of -4 is 4.This is applicable similarily like in vector subtraction we add the first vector to the negative of the vector that needs to be subtracted. This is analogous to the subtraction of scalars.
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write an equation with an even product
product is multiplication:
2 * 2 = 4
Solve the inequality for b 10 < -2/3(9+12b)
Final answer:
To solve the inequality 10 < -2/3(9+12b), distribute -2/3 inside the parentheses, simplify, and divide by -8, which reverses the inequality. The solution is b < -2.
Explanation:
To solve the inequality 10 < -2/3(9+12b), we must first distribute the -2/3 across the parentheses:
Multiply -2/3 by 9 to get -6.
Multiply -2/3 by 12b to get -8b.
The inequality now looks like this: 10 < -6 - 8b. Next, we simplify by moving the constant term -6 to the left side:
Add 6 to both sides: 10 + 6 < -8b.
Combine like terms: 16 < -8b.
Finally, we divide both sides by -8, remembering that this reverses the inequality symbol:
Divide by -8: -2 > b or b < -2.
Therefore, the solution to the inequality is b < -2.
The volume of
100
drops of a liquid is
0.1
fluid ounce.
What is the volume of
10,000
drops?
Final answer:
The volume of 10,000 drops of liquid, given that 100 drops equal 0.1 fluid ounce, is calculated to be 10 fluid ounces.
Explanation:
The question is asking to calculate the volume of 10,000 drops of a liquid, given that the volume of 100 drops is 0.1 fluid ounce. First, we determine the volume of a single drop. Then, we multiply that volume by 10,000 to find the total volume.
To start, we have the following relationship:
100 drops = 0.1 fluid ounce.
Next, we calculate the volume of one drop:
1 drop = 0.1 fluid ounce / 100 drops.
Then, we multiply the volume of one drop by 10,000 to find the volume of 10,000 drops:
10,000 drops * (0.1 fluid ounce / 100 drops) = 10 fluid ounces.
Therefore, the volume of 10,000 drops of the liquid is 10 fluid ounces.