Answer:
To reflect a triangle across the y-axis, you need to negate the x-coordinate of each vertex.
The original triangle with vertices (1, 3), (2, 5), and (4, 3) will be reflected across the y-axis to become a new triangle with the following vertices: (-1, 3), (-2, 5), and (-4, 3).
Keep in mind that a reflection across the y-axis means that the object is flipped along the y-axis. Therefore, the x-coordinate of each vertex is multiplied by -1, which flips the object horizontally.
The perimeter
of a kitchen is
528 inches. If the
Width of the kitcher
is 120 inches, what
is the length of the
kitchen?
Answer: 144 took the quiz
Step-by-step explanation:
Answer: 408 length
Step-by-step explanation:
528 inches of the kitchen subtract the width which is 120inches and you get 108 so add the width an length and you get 528
please help
here need it today
The answers to the compound fractions are given as follows;
a) 3 2/3
b) 1 1/2
c) 1 5/8
d) 1 1/3
e) −6 1/2
f) 2 5/12
What are the steps for the above calculations?a) Given 1 1/5 + 3 1/3 - 13/15
convert mixed numbers into improper fractions
That is:
6/5 + 10/3 - 13/15
68/15 - 13/15
11/3
= 3 2/3
b) 2 1/3 - 5/6
= 7/3 - 5/6
= 3/2
= 1 1/2
c) 3 1/2 - 1 7/8
= 7/2 - 1 7/8
= 7/2 - 15/ 8
=13/8
= 1 5/8
d) 7 - 5 2/3
= 7 - 17/3
= 4/3
= 1 1/3
e ) 6 - 12 1/2
= 6 - 25/2
= -13/2
= - 6 1/2
f) 2 1/4 - 1 1/3 + 1 1/2
= 9/4 - 4/3 + 3/2
= 11/12 + 3/2
= 29/12
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What is the volume of this sphere? Use pie = 3.14 and round to the nearest hundredth. Radius is 4
Answer:
Volume of a sphere is 268.08yd³
Step-by-step explanation:
To Find the volume of a sphere we apply the given formula,
[tex]Volume = \frac{4}{3} \pi r^{3}[/tex]
In the given information the radius is 4
Hence the volume of the sphere is,
[tex]Volume=\frac{4}{3} X3.14X4^{3}[/tex]
[tex]Volume = 268.08yd^{3}[/tex]
What is the example of parallel lines and perpendicular lines?
The example of parallel lines :
y = 3x + 4 and y = 3x - 10
and the example of perpendicular lines:
y = 3x + 4 and x + 3y = 6
Consider a slope-intercept form of equation of line.
y = mx + c
where m is the slope of the line
and c is the y-intercept of the line.
Consider a line y = 3x + 4
here the slope of the line is 3 and the y-intercept of the line is 4
We know that the slopes of parallel lines are equal.
so, any line having slope 3 would be parallel to 3.
So, y = 3x - 10 is a line parallel to line y = 3x + 4
also, as we know the productof slopes of perpendicular lines is -1.
this means, any line with slope -1/3 must be perpendicular to line y = 3x + 4
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The tables show some input and output values:
Table A
Input Output
1 7
2 7
2 9
3 9
Table B
Input Output
6 1
7 3
7 2
8 5
Which tables represent functions?
1. Neither A nor B
2. Only B
3. Both A and B
4. Only A
Neither table A nor B represents the functions. The correct option is 1.
What is a function?The expression that established the relationship between the dependent variable and independent variable is referred to as a function. In the function as the value of the independent variable varies the value of the dependent variable also varies.
The given tables are:-
Table A
Input Output
1 7
2 7
2 9
3 9
Table B
Input Output
6 1
7 3
7 2
8 5
For the same input values, there can not be two different output values. In both the tables the same input is giving different outputs.
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When solving a system of equations by substitution which of the following is the first step?
The first step in solving a system of equations is to solve one of the equations with a variable.
A collection of one or more linear equations containing the same variables is known as a system of equations. When the graphs do not meet, there is no solution to a system of linear equations. When the graphs of the equations overlap at all locations, there can be an endless number of solutions or just one when they do not.
Solving one of the equations for one of the variables in terms of the other variable is the first step in solving a system of equations by substitution. In order to eliminate one of the variables and generate a more straightforward equation that can be solved for the remaining variable, this expression can then be added to the other equations.
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Find two consecutive even integers such that the sum of the larger and 3 times smaller is 234
The number of the largest series and 3 times the smallest is 234 would be = 58 and 60.
What is an integer?An integer is a whole number, regardless of sign, that goes from 0 to infinity or to minus infinity.
Let's suppose the first integer is x then the second will be x + 2
Sum of the larger and 3 times the smaller is 234
(x + 2) + 3x = 234
4x + 2 = 234
4x = 232
x = 58 so x + 2 = 60
Therefore, both consecutive even integers such that the sum of the larger and 3 times the smaller is 234 is 58 and 60.
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What is defined as the incorporating paraphrasing restating or generating in a new form information that is already classified?
The incorporating paraphrasing restating or the rephrasing or restating information that has already been classified is commonly known as paraphrasing.
It process mainly will involve the taking of the original information and expressing it in a new way while maintaining the same meaning. This can be done by changing the wording, and sentence structure, or by using synonyms. The goal of paraphrasing is to make the information more understandable or to make it suitable for a different audience or purpose. It is often used in academic writing to avoid plagiarism by not using the same words or phrases as the original source.
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when three positive integers a, b, and c are multiplied together, their product is 100. suppose a < b < c. in how many ways can the numbers be chosen?
In 4 different ways can the number be chosen .
The positive divisors of 100 are
[1,2,4,5,10,20,25,50,100]
We can do casework on a:
If a=1, then there are 3 cases:
b=2,c=50
b=4,c=25
b=5,c=20
If a=2, then there is only 1 case:
b=5, c=10
In total, there are 3+1= 4 ways to choose distinct positive integer values of a, b, c.
Zero, a positive natural number, or a negative integer denoted by a minus sign are all examples of integers. The inverse additives of the equivalent positive numbers are the negative numbers. The boldface Z is a common way to represent the set of integers in mathematical terms.
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Which of the following are the roots of `3x^(2)+2x-1=0`?
(i) `-1" "(ii)" "(1)/(3)" "(iii)" "-(1)/(2)`
The roots of the quadratic equation 3x^(2)+2x-1=0 are -1/3 and -1.
A quadratic equation is a type of polynomial equation of the form ax^2 + bx + c = 0, where a, b, and c are constants and x is the variable. The variable x is raised to the power of 2 (squared) in this equation, which gives the equation its name "quadratic", which comes from the Latin word "quadratum" meaning square.
Quadratic equations can have two solutions, known as roots or zeros, which can be found by using the quadratic formula: x = (-b ± √(b^2-4ac))/2a.
The solutions of a quadratic equation can also be found by factoring the equation or by completing the square method.
Quadratic equations are used in many areas of mathematics
The roots of the equation 3x^(2)+2x-1=0 are the values of x that make the equation true. To find the roots, we can use the quadratic formula: x = (-b ± √(b^2-4ac))/2a.
In this case, a = 3, b = 2, and c = -1, so we have:
x = (-2 ± √(2^2-43(-1)))/2*3
Simplifying the above expression we get:
x = (-2 ± √(4+12))/6
x = (-2 ± √(16))/6
x = (-2 ± 4)/6
This gives two possible solutions:
x = (-2+4)/6 or x = (-2-4)/6
x = 2/6 or x = -6/6
x = 1/3 or x = -1
So the roots of the equation 3x^(2)+2x-1=0 are: x = 1/3 or x = -1
Therefore, The roots of the quadratic equation 3x^(2)+2x-1=0 are -1/3 and -1.
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Brody's new home had a purchase price of $187,500. He got a 30-year fixed mortgage for 95% of the purchase price. The interest rate on the loan is 3. 875%
a. The monthly payment would be $1,061.76.
b. Total amount paid would be $382,636.16.
c. The cost of the loan would be $195,136.16.
A mortgage is a type of loan used to purchase a property or real estate. The borrower (in this case, Brody) uses the property as collateral for the loan, and makes monthly payments to the lender (usually a bank or mortgage company) to repay the principal (the amount borrowed) plus interest. Mortgages typically have a fixed interest rate, meaning the interest rate stays the same over the life of the loan, and a fixed term, typically 15 or 30 years.
a. To calculate the monthly payment for Brody's loan, you would use the formula for a fixed-rate mortgage, which is:
M = P [ i(1 + i)ⁿ ] / [ (1 + i)ⁿ ⁻ ¹]
Where M is the monthly payment, P is the principal (the amount borrowed), i is the interest rate (expressed as a decimal), and n is the number of payments (in this case, 30 years x 12 months/year = 360 payments).
Plugging in the numbers, the monthly payment would be:
M = $187,500 x [0.03875(1 + 0.03875)^360] / [(1 + 0.03875)³⁶⁰ ⁻ ¹]
M = $1,061.76
b. To calculate the total amount paid, you would multiply the monthly payment by the number of payments:
Total amount paid = $1,061.76 x 360 = $382,636.16
c. The cost of the loan is the total amount paid minus the amount borrowed:
Cost of the loan = $382,636.16 - $187,500 = $195,136.16
The complete question is shown below.
Brody's new home had a purchase price of $187,500. He got a 30-year fixed mortgage for 95% of the purchase price. The interest rate on the loan is 3.875%.
a. What is his monthly payment for the loan?
b. What is the total amount paid?
c. What is the cost of the loan?
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Lola scored 21 out of 27 points on a mid-unit quiz in math . Later she scored 66 points out of 80 on the unit test . Did she increase or decrease the percent she scored from the quiz to the test
She increased the percent she scored from the quiz to the test.
What is percentage?Percentage is defined as the representation of a part of a value per 100 which is represented with the symbol of %.
The test score of Lola in the mid-unit quiz in math = 21
The percentage of 21 point from the over all points;
= 21/27 ×100
= 2100/27
= 77.8%
The test score of Lola on the unit test = 66 points out of 80
The percentage of 66 points from the over all point ;
= 66/80×100
= 6600/80
= 82.5%
Therefore, it can be concluded that Lola increased the percent she scored from the quiz to the test.
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Consider the following expression: (1+x)^2.
A) Use the Binomial Theorem to find the first four terms of this polynomial.
B) Why is 1 + nx a good approximation of this expression when x is less than 1?
Answer:
Step-by-step explanation:
A) The Binomial Theorem states that for any positive integer n and any real numbers a and b, the expression (a + b)^n can be expanded as a sum of the form:
(a + b)^n = C(n,0)a^n b^0 + C(n,1)a^(n-1)b^1 + C(n,2)a^(n-2)b^2 + ... + C(n,n)a^0b^n
where C(n,k) = n!/(k!(n-k)!) is the binomial coefficient.
Applying this to the expression (1 + x)^2, we have:
(1 + x)^2 = C(2,0)1^2 x^0 + C(2,1)1^1 x^1 + C(2,2)1^0 x^2
= 11^21 + 21x + 1*x^2
The first four terms of the polynomial are: 1, 2x, x^2
B) The binomial theorem states that the first term is a constant term and the second term is linear. When x is less than 1, the linear term 2x is much smaller than the constant term 1, so the linear term can be ignored as a good approximation. Therefore, 1 + nx will be a good approximation of the expression (1+x)^2 when x is less than 1.
Help please! Write the function x^3 - 6x^2 - x + 30 in factored form knowing that one of the roots is 5
Group of answer choices
(x - 5)(x -2)(x + 3)
(x + 5)(x - 2)(x + 3)
(x + 5)(x + 2)(x - 3)
(x - 5)(x + 2)(x - 3)
The required factors of the given expression x³ - 6x² - x + 30 is (x - 5)(x + 2)(x -3).
What are the factors?A number or algebraic expression that evenly divides another number or expression—i.e., leaves no remainder—is referred to as a factor.
Here,
Gien expression,
= x³ - 6x² - x + 30
= (x - 5)(x + 2)(x -3)
Thus, the required factors of the given expression x³ - 6x² - x + 30 is (x - 5)(x + 2)(x -3).
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PLSPLSPLS HELP WITH THIS QUESTION I NEED TO SUBMIT THE ASSIGNMENT RLLY SOON
For the given equation, values to get equal the value of w equals [tex]\frac{7}{16}[/tex].
Algebraically speaking, an equation is a statement that shows the equality of two mathematical expressions.
The three primary forms of linear equations are point-slope, standard, and slope-intercept.
A simple equation is a mathematical formula that expresses the relationship between two expressions on both sides of the "equal to" sign.
These equations contain a variable, which is frequently written as x or y. It is frequently necessary to rearrange simple equations in order to solve them.
Given, the equation is
[tex]2 \frac{2}{3} w = 1 \frac{1}{6}[/tex]
Simplifying the equation,
[tex]\frac{8}{3}w = \frac{7}{6}[/tex]
[tex]w = \frac{7}{6} \times \frac{3}{8}[/tex]
[tex]w = \frac{7}{16}[/tex]
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i’m timed, this is stressing me out. please someone help
Answer:
Step-by-step explanation:
(f+g)(x) = -12x^3-10-6x+2
= -12x^3-6x-8
Since the problem asks for (f+g)(x), plug in the value 12 to get your answer.
(f+g)(12)=-20736-72-8 = -20816
Next, (f-g)(x).
(f-g)(x)=-12x^3-10+6x-2
=-12x^3+6x-12
=6144-48-12
=6084
if molly can mow a lawn in 3 hours and her little brother can do it in 6 hours, how long will it take working together?
It would take them 2/W hours, or approximately 1 hour and 36 minutes, to mow the lawn working together.'
What is rate ?
The rate is a measure of how much of a quantity is completed or changed per unit of time. It is often represented as a ratio of the amount of work done to the amount of time it takes to complete the work. For example, in the context of mowing a lawn, the rate could be expressed as the amount of lawn mowed per hour.
Let's call the amount of work required to mow a lawn "W".
Molly can do it in 3 hours, so her rate of work is W/3.
Her little brother can do it in 6 hours, so his rate of work is W/6.
When they work together, their combined rate of work is (W/3) + (W/6) = W/2.
So, working together, they can mow the lawn in W/2 hours, or 2/W hours.
Therefore, it would take them 2/W hours, or approximately 1 hour and 36 minutes, to mow the lawn working together.
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It would take them 2/W hours, or approximately 1 hour and 36 minutes, to mow the lawn working together.'
The rate is a measure of how much of a quantity is completed or changed per unit of time. It is often represented as a ratio of the amount of work done to the amount of time it takes to complete the work. For example, in the context of mowing a lawn, the rate could be expressed as the amount of lawn mowed per hour.
Let's call the amount of work required to mow a lawn "W".
Molly can do it in 3 hours, so her rate of work is W/3.
Her little brother can do it in 6 hours, so his rate of work is W/6.
When they work together, their combined rate of work is (W/3) + (W/6) = W/2.
So, working together, they can mow the lawn in W/2 hours, or 2/W hours.
Therefore, it would take them 2/W hours, or approximately 1 hour and 36 minutes, to mow the lawn working together.
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heyyy guys sometimes some of the answers are wrong
Answer:
6.1 x 10⁴
that is the answer for you sir
14+(−812)+14 I need help with this
Answer:
Step-by-step explanation:
14+(-812)+14= 14-812+14
= -798+14
= -784
If 7x 3 = 24, what is the value of 5 - 4x? a. -23 b. -7 c. 1 d. 17 show steps pls
The value of 5 - 4x is 7/3, which is equivalent to option (d) d. 17
If 7x³ = 24, we can solve for x by taking the cube root of both sides:
[tex](7x^3)^{1/3} = (24)^{1/3} \\x = (24)^{1/3} \div7^{1/3}[/tex]
To find the value of 5 - 4x, we can substitute the expression for x into the second equation:
5 - 4x = [tex]5 - 4(24)^{1/3} \div 7^{1/3[/tex]
Simplifying, we get
5 - 4x = 5 - 4(2/3)
5 - 4x = 5 - (8/3)
5 - 4x = (15/3) - (8/3)
5 - 4x = 7/3
So the value of 5 - 4x is 7/3, which is equivalent to option (d) d. 17
The cube root of a number is a value that when multiplied by itself twice, produces the original number.
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Kaylee cut a 20-cm by 20-cm piece of paper along a diagonal to form two
congruent triangles. What is the length of the hypotenuse of one of the triangles?
Express your answer in simplest radical form.
The length of the hypotenuse of one of the triangles would be = 28 cm
What is a triangle?A triangle is defined as the polygon that has three sides with the total angle of 180°.
The paper that was cut by Kaylee has a side of 20 cm by 20 cm. Using the Pythagorean formula the hypotenuse can be calculated as follows:
c² = a² + b²
where c = hypotenuse = X
a = 20
b = 20
C² = 20² + 20² = 400+400 = 800
c = √800
c = 28cm (approximately)
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What does it mean when you substitute a value into an equation and the result is a true statement?
A variable's value that, when substituted into the equation, results in a true assertion is known as the solution. The process of finding the solution to an equation is called solving the equation.
What in mathematics is a linear equation?
A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.
Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.
To insert a value into an equation, what does that mean?
By solving for one variable, you can then enter that expression into the other equation using the substitution approach.
Making sure you are always substituting equivalent values is crucial in this situation. For instance: Sean is five years older than his daughter, who is his son's age.
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Can a log be linear?
Logarithms can be used to convert non-linear functions into linear functions. The outcome has a linear relationship with the variables' logarithm.
Similar to a linear function, a logarithmic function takes a number as input and produces another number as an output. The relationship between that input and output, however, is not linear; rather, it is logarithmic.
Economic models benefit from linear functions since a solution is simple to find. However, using logarithms, non-linear functions can be made into linear functions.
The given function is:
y = [tex]ax^b[/tex]
This function can be recast as the following by taking the logarithms of both sides:
log y = log a + b log x
The outcome has a linear relationship with the variables' logarithm.
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Similarity Sample Work
Answer: Scroll Down
Step-by-step explanation:
I already answered all your questions except for the last two.
The second to last is angle F
The last answer is QP
The colours of cars at a garage are in the
ratios:
white red= 7:3
red: blue = 5:2
Sam thinks the ratio of white : blue is 7 : 2
Explain the mistake that Sam has made and
give the correct ratio.
Answer:
Step-by-step explanation:
The mistake that Sam made is that he tried to find the ratio of white to blue cars by combining the ratios of white to red cars and red to blue cars. However, this method does not work because the ratios are not independent of each other.
To find the correct ratio of white to blue cars, we need to use the fact that the ratio of red to blue cars is 5:2 and the ratio of white to red cars is 7:3. We can use these ratios to find the fraction of cars that are white and blue in the garage.
Firstly, we can find the fraction of red cars by taking the ratio of red to blue cars which is 5:2 and simplifying it to 5/7.
Now we can find the fraction of white cars by taking the ratio of white to red cars which is 7:3 and simplifying it to 7/10.
Now, to find the ratio of white to blue cars, we can subtract the fraction of red cars from the fraction of white cars.
So,
(7/10) - (5/7) = (7/10) - (5/7) * (3/3) = (7/10) - (15/21) = (721 - 1510) / (210) = (147 - 150) / 210 = -3/210
The correct ratio of white to blue cars is -3/210 which can be understood as NO white cars in the garage. Sam has made an error in his calculation.
the owner of a car dealership planned to develop strategies to increase sales. he hoped to learn the reasons why many people who visit his car lot do not eventually buy a car from him. for one month he asked his sales staff to keep a list of the names and addresses of everyone who came in to test drive a car. at the end of the month he sent surveys to the people who did not buy the car, asking them why. about one third of them returned the survey, with 44% of those indicating that they found a lower price elsewhere. which is true? i. the population of interest is all potential car buyers. ii. the survey design suffered from non-response bias iii. because it comes from a sample, 44% is a parameter, not a statistic
Statement I and II are true, i.e.,
l. Population of interest is all potential car buyers.
II. The survey design suffered from non-response bias.
We have, a car owner who develop a plan strategies to increase sales. The purpose of study to know reason that why many people who visit his car lot do not eventually buy a car from him. The study is based on survey, his staff members collects a data of people's who visit his car lot but not buy a car. After one month, the owner sent survey to persons who not buy a car and ask them why they did it . Then, one third are responded the survay and 44% of those indicating that they found a lower price elsewhere. Now, we check each statements one by one,
I) All car buyers potential act as population in this problem. So, it is true statement.
II) This survay is based on response of people's who visit his car lot but not buy a car but only but not all non car buyers response there, so the survey design suffered from non-response bias. Therefore, it is true.
III)This survey is based on a sample of non car buyers response regarding reason for not buying a car. So, 44% is a part of sample i.e., it is statistic but not parameter. Thus, it is not true.
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What is the value of k if one of the zeroes of the quadratic polynomial k 1 x2 kx 1 is 3?
The value of k if one of the zeroes of the quadratic polynomial kx2 kx 1 is 3 is -2 or 2.
What is quadratic polynomial?A quadratic polynomial is a polynomial of degree 2, meaning it has the form ax^2 + bx + c, where a, b, and c are constants and a is not equal to zero. It is also known as a second-degree polynomial. This type of polynomial is commonly used for modelling physical phenomena, such as the trajectory of a projectile or the vibration of a spring. A quadratic polynomial can also be used to solve equations that involve x2, such as the quadratic formula.
The quadratic equation kx2 kx 1 0 has two solutions, or zeroes, which are given by the quadratic formula: x = (k ± √(k2 - 4))/2. If one of the solutions is 3, then we can substitute 3 in for x and solve for k.
3 = (k ± √(k2 - 4))/2
6 = (k ± √(k2 - 4))
6 - (k ± √(k2 - 4)) = 0
k2 - 4 ± k - 6 = 0
k2 ± k - 2 = 0
k ± 2 = 0
k = -2 or k = 2.
Therefore, the value of k if one of the zeroes of the quadratic polynomial kx2 kx 1 is 3 is -2 or 2.
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What are the roots of the inequality X² 3x 2 0?
The roots of the inequality X² 3x 2 0 are x = 0 and x = 2.
X² - 3x + 2 = 0
X² - 3x - 2x +2 = 0
(X-2)(X+1) = 0
X-2 = 0 or X+1 = 0
X = 0 or X = 2
The roots of the inequality X² 3x 2 0 are the values of x that make the inequality true. To solve for the roots, we need to set the equation equal to zero and factor it. The equation is
X² - 3x + 2 = 0.
When we factor it, we get
(X-2)(X+1) = 0.
This means that
X-2 = 0 or X+1 = 0.
We solve each equation separately. When X-2 = 0, we get X = 2. When X+1 = 0, we get X = 0. Thus, the roots of the inequality
X² 3x 2 0 are x = 0 and x = 2.
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consider an unfair coin tossed at random independently where probability of getting head is 2 3 . (a) (geometric) suppose that y is the number of tails until you get the first head. find the moment generating function (m.g.f.) of y , and compute the mean of the number of tails until the first head. (b) generalize the result in (a) by considering a coin with probability of getting head p. what is the m.g.f and mean?
The moment generating function (m.g.f.) of y is (2/3)*(1/(1 - p)) where p = (1/3)*e^t. By considering a coin with probability of getting head p. the m.g.f and mean is (p)/(1 - p) and p + p^2/(1 - p) respectively.
(a) Let Y denote the number of tails until the first head is observed in a sequence of tosses of an unfair coin, where the probability of getting a head is 2/3.
The moment generating function (m.g.f.) of Y is given by
M(t) = E[e^(tY)]
= (2/3)e^(t*0) + (1/3)*e^(t*1) + (2/3)(1/3)e^(t*2) + (1/3)^2*e^(t*3) + (2/3)(1/3)^2*e^(t*4) + …
= (2/3)*(1 + (1/3)*e^t + (1/3)^2*e^(2t) + (1/3)^3*e^(3t) + …)
= (2/3)*(1/(1 - (1/3)*e^t))
= (2/3)*(1/(1 - p))
where p = (1/3)*e^t.
The mean of Y is given by
E[Y] = (2/3)*(1/(1 - p)) + (1/3)*p/(1 - p)
= 2/3 + (1/3)*p
= 2/3 + (1/3)*((1/3)*e^t)
= 2/3 + (1/9)*e^t.
(b) The m.g.f. of Y for a coin with probability of getting head p is given by
M(t) = (p)*(1 + p*e^t + p^2*e^(2t) + p^3*e^(3t) + …)
= (p)*(1/(1 - p*e^t))
= (p)/(1 - p).
The mean of Y is given by
E[Y] = (p)/(1 - p) + p*p/(1 - p)
= p + p^2/(1 - p).
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The diagram shows the graph of y = f(x), with a tangent to the curve drawn at
point A.
Use the tangent to work out an estimate for the gradient of the curve at point A to 1
d.p.
The gradient of the curve at point A to 1 is 0.4. The slope of tangent is equivalent to the slope of the curve.
What is a tangent of a curve?The tangent line to a curve at a point in geometry is the straight line that best approximates (or "clings to") the curve at that point. As the second point approaches the first, it may be considered the limiting position of straight lines passing through the given point and a nearby point of the curve.
The tangent cuts the curve at A.
The coordinate of A is (8,3). The tangent passes through the point (1,0.2).
The slope of the points (x₁, y₁) and (x₂, y₂) is [(y₂ - y₁)/(x₂ - x₁)
The slope of the tangent is (0.2-3)/(1-8) = 0.4.
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