By "limit definition", I assume you mean the derivative. We have
[tex]f'(c) = \displaystyle\lim_{x\to c}\frac{f(x)-f(c)}{x-c}[/tex]
For [tex]f(x)=\frac1{x-1}[/tex] and c = 2, we have
[tex]f'(2)=\displaystyle\lim_{x\to2}\frac{\frac1{x-1}-1}{x-2}[/tex]
[tex]f'(2)=\displaystyle\lim_{x\to2}\frac{\frac{1-(x-1)}{x-1}}{x-2}[/tex]
[tex]f'(2)=\displaystyle\lim_{x\to2}\frac{2-x}{(x-1)(x-2)}[/tex]
[tex]f'(2)=\displaystyle\lim_{x\to2}\frac1{1-x}=-1[/tex]
The tangent line to (2, 1) has slope -1. Using the point-slope formula, it has equation
y - 1 = - (x - 2)
y = - x + 3
Jason delivers newspapers on Saturdays and Sundays only. Each newspaper weighs about 1 pound 5 ounces. If he delivers 15 newspapers each day, how much do the two days' worth of newspapers weigh in pounds and ounces?
Answer:
39pounds 6oz
Step-by-step explanation:
15x2=30
1x30=30pounds
5x30=150oz
30p+150oz=39.37500
37500p=6oz
39pounds and 6 oz
5d+1/2=d-4 section 2.04
Answer: d = -9/8
Steps: 5d + ½ = d - 4
Subtract ½ from both sides: 5d + ½ - ½ = d - 4 - ½
Simplify: 5d = d - 9/2
Subtract d from both sides: 5d - d = d - 9/2 - d
Simplify: 4d = -9/2 ÷ 4
Simplify: d = -9/8
PLz mark brainliest:)
I need to do this assignment but I need help on how to draw it and answer the questions because I am confused on how to do these things. Thank you
1) The domain is [0,300]. The range is [0,250]
2) The slope for the initial climb is 3.57. The equation of the line is
3) The rate of change of the second hill is -1.4
4) The rate of change of the third hill is -2.1
5) The blue hill is steeper
6) It is not a function
Step-by-step explanation:
1)
The domain of a function is the set of values of x (the input) for which the function itself is defined.
Instead, the range of a function is the set of values of y (the output) that the function can take.
To find the domain, we have to look at the x-axis and see for which values of x the function is defined. By looking at the graph, we see that the function is defined between
x = 0 and x = 300
So, the domain is [0,300].
To find the range, we have to look at the y-axis and see for which values of y the function has an output. By looking at the graph, we see that the function has values of y between
y = 0 and x = 250
So, the range is [0,250].
2)
The slope of a function in a certain range is given by
where
is the change in the y-coordinate
is the change in the x-coordinate
For the initial climb (pink line), we have:
Therefore, the slope in this part is
We can now write the equation of the line in the form
y = mx + b
where b is the y-intercept: since it is zero, the line has simply the form
3)
Again, to calculate the slope of the hill, we use:
where
is the change in the y-coordinate
is the change in the x-coordinate
For the green hill, we have:
So the rate of change is
4)
As before, the rate of change of the hill is
For the blue hill, we have:
So the rate of change is
5)
To know which hill is steeper, we need to compare the magnitude of their rate of change.
In fact, both hills have rate of change negative - because we are going down along the slope. Therefore, we have to consider the magnitude of their slope.
For the green hill:
For the blue hill:
We see that the blue hill has a greater slope (in magnitude): therefore, the blue hill is steeper.
6)
A function is defined as a mapping (operation between two sets of variables) in which to one value of x (the input) corresponds one and only one value of y (the output).
This means that a function cannot have multiple values of y for the same x (the input).
By looking at the graph, we see that this function does not respect this criterium: in fact, we see that certain values of x give multiple values of the output, y (for instance, at x=300 the function has two values). So, this is not a function.
How can you use the order of operation to explain why you cannot combine the variable terms before using the distributive property when solving the equation 7(x+5)-x=42
Answer:
Step-by-step explanation:
The Order of Operations is very important when simplifying expressions and equations. The Order of Operations is a standard that defines the order in which you should simplify different operations such as addition, subtraction, multiplication and division.
This standard is critical to simplifying and solving different algebra problems. Without it, two different people may interpret an equation or expression in different ways and come up with different answers. The Order of Operations is shown below.
Parentheses and Brackets -- Simplify the inside of parentheses and brackets before you deal with the exponent (if any) of the set of parentheses or remove the parentheses.
Exponents -- Simplify the exponent of a number or of a set of parentheses before you multiply, divide, add, or subtract it.
Multiplication and Division -- Simplify multiplication and division in the order that they appear from left to right.
Addition and Subtraction -- Simplify addition and subtraction in the order that they appear from left to right.
Before we begin simplifying problems using the Order of Operations, let's examine how failure to use the Order of Operations can result in a wrong answer to a problem.
Without the Order of Operations one might decide to simplify the problem working left to right. He or she would add two and five to get seven, then multiply seven by x to get a final answer of 7x. Another person might decide to make the problem a little easier by multiplying first. He or she would have first multiplied 5 by x to get 5x and then found that you can't add 2 and 5x so his or her final answer would be 2 + 5x. Without a standard like the Order of Operations, a problem can be interpreted many different ways
We cannot combine the variable terms before using the distributive property when solving the equation as it will results in wrong answer.
What is distributive property of multiplication over addition ?
If we multiply a number by the sum of more than two, we use the distributive property of multiplication over addition.
Here the expression given is :
7(x+5)-x=42
The Order of Operations is very important when simplifying expressions and equations. The Order of Operations is a standard that defines the order in which you should simplify different operations such as addition, subtraction, multiplication and division.
Parentheses and Brackets -- Simplify the inside of parentheses and brackets before you deal with the exponent (if any) of the set of parentheses or remove the parentheses.
Exponents -- Simplify the exponent of a number or of a set of parentheses before you multiply, divide, add, or subtract it.
Multiplication and Division -- Simplify multiplication and division in the order that they appear from left to right.
Addition and Subtraction -- Simplify addition and subtraction in the order that they appear from left to right.
Without the Order of Operations one might decide to simplify the problem working left to right. He or she would add two and five to get seven, then multiply seven by x to get a final answer of 7x. Another person might decide to make the problem a little easier by multiplying first. He or she would have first multiplied 5 by x to get 5x and then found that you can't add 2 and 5x so his or her final answer would be 2 + 5x. Without a standard like the Order of Operations, a problem can be interpreted many different ways.
Read more about property of multiplication here :
https://brainly.com/question/14391436
#SPJ2
I need help with Number 7 please!!!
Answer:
8.06 ft or [tex]\sqrt{65}[/tex] ft
Step-by-step explanation:
Since Rebecca bought a square table and squares have equal sides, you can take the square root of the area of the table, which gives you [tex]\sqrt{65}[/tex] ft per side. This can be approximated to 8.06 ft.
A pumpkin grows with a constant of proportionally of 4 cm in diameter per week. If Susan begins growing her pumpkin 10 weeks before Halloween will her pumpkin be larger that 50 cm in diameter?
Is this a function or not a function? (Picture)
Answer:
Not a Function
Step-by-step explanation:
Determine the quotient of 2 over 5 divided by 3 over 4
Answer:
8/15
Step-by-step explanation:
Equivalent Expressions
Warm-Up
Active
Evaluating an Expression
Complete the statements.
Evaluate (15 - 4x) + 5 when x = 3.
Substitute the given value for the
Evaluate within
parentheses.
to simplify.
Use the
inside the
Evaluate exponents.
First, complete the
parentheses.
Next, complete the
parentheses.
Last, complete the addition.
inside the
Multiply and divide
from left to right.
The value is
Add and subtract
from left to right.
Answer:
Complete the statements.
Substitute the given value for the
✔ variable
.
Use the
✔ order of operations
to simplify.
First, complete the
✔ multiplication
inside the parentheses.
Next, complete the
✔ subtraction
inside the parentheses.
Last, complete the addition.
The value is
✔ 8
.
Step-by-step explanation:
Plz give me brainlest
Answer:
Variable, order of operations, multiplication, subtraction, 8.
Step-by-step explanation:
Got it right Edge2021
Which of the following equations has exactly one solution?
O A. 4x - 4 + 2x = 6x - 4
O B. 2(4x + 5) = 8x + 10
C. 4x - 8 = 4(x - 4)
O D. 3x + 5 = 2x - 6
9. What is the likelihood that a randomly selected couple's relationship survived between 90 and 150 days
Answer:
0.5818
Step-by-step explanation:
Suppose the average teenage romantic relationship is normally distributed with a mean number of 100 days with a standard deviation of 30 days.
Answer:
The z score is used to determine how many standard deviations that the raw score is above or below the mean. If the z score is positive then the raw score is above the mean and if it is negative then it is below the mean. It is given by:
[tex]z=\frac{x-\mu}{\sigma}\\ \\where\ \mu=mean,\sigma=standard\ deviation, x=raw\ score[/tex]
Given that:
[tex]\mu=100\ days,\sigma=30\ days\\\\For\ x=90\\\\z=\frac{90-100}{30} =-0.33\\\\For\ x=150\\\\z=\frac{150-100}{30} =1.67[/tex]
Therefore, from the normal distribution table, P(90 < x < 150) = P(-0.33 < z < 1.67) = P(z < 1.67) - P(z < -0.33) = 0.9525 - 0.3707 = 0.5818
What is the slope and y-intercept of the linear equation y = 5x − 4?
m =
b =
Answer:
I got it right on edge 2020/2021
Step-by-step explanation:
m=5
b=-4
ANSWER PLEASE NEED HELP ASAP
Answer: 43 should be divided into 0.37 to find “x”.
Step-by-step explanation:
what is the sale tax on a $14,500 truck if the tax rate is 9%
Answer:
$15, 805.00
Step-by-step explanation:
Tax is based on the state you live in.
C: Determine the measure of the obtuse angle formed at the intersection of AV and HI
Answer:
146°70°104°Step-by-step explanation:
GivenCS║BMTo findA. m∠MIHB. m∠AVMC. Obtuse angle at the intersection of AV and HISolutionA...................................
∠MIH and ∠IHS are same side interior angles and sum up to 180° as per property, therefore
m∠MIH = 180° - 34° = 146°B...................................
∠AVM and ∠VAS are same side interior angles
and ∠VAS and ∠LAH are vertical angles, which are equal as per property of vertical angles, so:
m∠AVM = 180° - m∠VAS = 180° - 110° = 70°C...................................
Obtuse angle at the intersection of AV and HI, if name the intersection point O:
∠AOI = ∠HOV∠AOI = 180° - ∠AOH = 180° - (180° - 34° - 70°) = 104°question 10 I mark as brainliest
Answer:
134 is the answer
Answer: 134
Step-by-step explanation:
54+ (48+72) x 2/3
54+120x2/3=134
4(3x + 1)
What is the answer to 4(3x + 1)
Answer:
Answer is 12x+4. Hope that helped.
For a certain product we obtained a regression line equation Y = 10 - 0.8 X, where X is price (in $) and Y is sales (in $1,000). The slope of the line (- 0.8) represents:___---.
A. If the price were $10, expected sales would be $8,000.B. If the price were zero, expected sales would $800.C. If the price increases by $1, sales will decrease by $800, on average.D. Sales are maximized when the price is $0.8.
E. None of the other answers are correct.
Answer:
C. If the price increases by $1, sales will decrease by $800, on average
Step-by-step explanation:
Slope of regression equation represents the increase/decrease in dependent variable Y due to unit change in independent variable X. Here, independent variable is X is price and dependent variable Y is sales. The slope negative sign represent decrease in dependent variable due to unit increase in independent variable. Sales is given in ($1000) So, (0.8*1000)=800. It means that due to unit dollar increase in price the sales will decrease by $800. Thus, If the price increases by $1, sales will decrease by $800, on average is the correct interpretation.
PLEASEEE HELPPP!!!! Find the slope given the points (-14,-7) and (-11,-16).
Answer:
-3
Step-by-step explanation:
Answer:m= -3
Step-by-step explanation:
what is /4 of 3/4 =
What is 1/4 of 3/4
Answer:
3/16
Step-by-step explanation:
1/4 of 3/4 is just another way of saying (1/4)*(3/4). When multiplying fractions, you must multiply the numerators and denominators to get the product so the numerator of the products is 1*3 and the denominator is 4*4 to get:
3/16
Answer:
3/16
Step-by-step explanation:
1/4 of 3/4
= 1/4 × 3/4
you multipy the numerators together and then multiply both denominators
ie. 1×3 divided by 4×4
= 3/16
Can any one help me?
Point V is on line segment UW. Given VW = 5x - 4, UV = 2x, and
UW = 52, determine the numerical length of VW.
Answer:
VW = 36
Step-by-step explanation:
From the question, we are given:
VW = 5x - 4, UV = 2x,
UW = 52
Hence,
UV + VW= UW
2x + 5x - 4 = 52
7x = 52 + 4
7x = 56
x = 56/7
x = 8
VW = 5x - 4,
VW = 5(8) - 4
VW = 40 - 4
VW = 36
The function h(x)=1/x^2+1 is the result of the composition f(g(x)). If g(x) = x^2+1,what is f(x)? A f(x)=1/square root x B f(x)=1/x C f(x)= 1/x+1 D f(x)=1/x^2+1
Answer:
Option B is correct
Step-by-step explanation:
Given: [tex]h(x)=\frac{1}{x^2+1}[/tex] is the result of the composition [tex]f(g(x))[/tex].
Also, [tex]g(x)=x^2+1[/tex]
To find: [tex]f(x)[/tex]
Solution:
Take [tex]f(x)=\frac{1}{x}[/tex]
Now check whether [tex]h(x)[/tex] is equal to [tex]f(g(x))[/tex] or not.
First find [tex]f(g(x))[/tex]
[tex]f(g(x))=f(x^2+1)=\frac{1}{x^2+1}[/tex]
Also, [tex]h(x)=\frac{1}{x^2+1}[/tex]
Therefore,
[tex]h(x)=f(g(x))[/tex]
So,
Option B is correct
Answer: B. f(x)=1/x
Step-by-step explanation:
Edge
Geometric Sequence♡
5, -2, 4/5
the common ratio was 2/5
find the 10th term
Sub to SZ Lexrn if that does not show search up shiyo on vr and first vid is them please help out , thx bye . If you do it cmt and ill make a post for yall for 100 points, so my friends won't amke fun of me
Answer:
If it counts as a question, lol sure, I'd love to help
A family is purchasing 17 tickets for a downtown walking tour. Adult tickets are $10, child tickets are $7, and senior tickets are $8.50. The total
cost of the tickets is $141.50, and they are purchasing 2 more senior tickets than adult tickets.
Create and solve a system of linear equations to represent this situation. Then select the true statement.
А. The solution to this system is nonviable because it results in a fractional number of tickets.
B. The solution to this system is no viable because it results in a negative number of tickets.
C. The solution to this system is viable.
D. The solution to this system is nonviable because it results in a fractional amount of money.
Answer:
А. The solution to this system is nonviable because it results in a fractional number of tickets.
Step-by-step explanation:
Let x represent the number of adult tickets, y represent the number of child ticket and z represent the number of senior ticket.
Since the number of purchased ticket is 17, hence:
x + y + z = 17 (1)
The total cost of tickets is $141.50, hence:
10x + 7y + 8.5z = 141.5 (2)
they are purchasing 2 more senior tickets than adult tickets, therefore:
x = z + 2 (3)
Solving equation 1 2 and 3 simultaneously gives:
x =17/3, y = 23/3, z = 11/3
Therefore the solution to this system is nonviable because it results in a fractional number of tickets.
Answer:
А.The solution to this system is nonviable because it results in a fractional number of tickets
Step-by-step explanation:
took the test on edmentum and got it correct
Which is true 0.45>0.5
0.45<0.5
4.05=0.45
4.05 <0.45
Answer:
4.05 is greater than 0.45
Kai is making a chessboard using pieces of wood that measure 1 square inch.
When he finishes, the chessboard will have an area of 64 square inches.
How many pieces of wood should he put along each side?
A cube has a volume of 125 cubic inches. What is the length of each edge?
Answer:
The correct option will be: c. 8 pieces of wood.Step-by-step
Use rounding to estimate the product of 5,555 and 4,444 round both numbers to the nearest thousand to find answer
Step-by-step explanation:
Given that the first number is
5,555 and
the second number is 4,444
the product of 5,555 and4,444= 24686420
to the nearest thousand 5,555= 6000
to the nearest thousand 4,444= 5000
Therefore the product of 6000 and 5000 is
=6000x5000
=30000000
Scientists want to estimate the mean weight of mice after they have been fed a
special diet. From previous studies, it is known that the weight is normally
distributed with standard deviation 4 grams. How many mice must be weighed so
that a 95% confidence interval will have margin of error of 0.4 grams?
Write only an integer as your answer.
Answer:
n = 484
Step-by-step explanation:
If Confidence Interval CI = 95 % then α = 5% and α/2 = 2,5 %
α/2 = 0,0125
MOE for normal distribution is:
MOE = z * σ/√n
For α/2 = 0,0125 ⇒ z(score) = -2,2
MOE = |-2,2| * 4/√n
0,4*√n = 8,8
√n = 8,8 / 0,4
√n = 22
n = 484