We can find the instantaneous rate of change at [tex]x=2[/tex] by evaluating the limit
[tex]\displaystyle \lim_{x\to2} \frac{f(x) - f(2)}{x - 2}[/tex]
(i.e. the definition of the derivative)
Since
[tex]f(x) = 2x^3 - 3x \implies f(2) = 10[/tex]
we have
[tex]\displaystyle \lim_{x\to2} \frac{f(x) - f(2)}{x - 2} = \lim_{x\to3} \frac{2x^3 - 3x - 10}{x - 2}[/tex]
Note that [tex]2x^3-3x-10=0[/tex] when [tex]x=2[/tex], which means [tex]x-2[/tex] divides the numerator exactly. By polynomial division, we can show
[tex]\dfrac{2x^3 - 3x - 10}{x - 2} = 2x^2 + 4x + 5[/tex]
Then in the limit, we can write
[tex]\displaystyle \lim_{x\to2} \frac{f(x) - f(2)}{x - 2} = \lim_{x\to2} \frac{(x-2) (2x^2 + 4x + 5)}{x - 2}[/tex]
As [tex]x\neq2[/tex], we can cancel the factors of [tex]x-2[/tex].
[tex]\displaystyle \lim_{x\to2} \frac{f(x) - f(2)}{x - 2} = \lim_{x\to2} (2x^2 + 4x + 5)[/tex]
The function in the remaining limit is continuous at [tex]x=2[/tex], so we can directly substitute [tex]x=2[/tex] to get its value,
[tex]\displaystyle \lim_{x\to2} \frac{f(x) - f(2)}{x - 2} = 2\cdot2^2 + 4\cdot2 + 5 = \boxed{21}[/tex]
(D)
Roster form : {8,12,16}
The Roster form of { 8,12,16 } is {X;X=4k ,k ∈ (2,34)}
Roster form:
A set's roster notation is a straightforward mathematical representation of the set. The elements (or members) of a set are listed in a row inside the curly brackets in the roster form. If the set contains more than one element, each pair of elements is separated by a comma symbol. Because the enumeration is done one by one, the roster form is also known as the enumeration notation.
Given a set in a set builder form i.e.{ 8,12,16 } and asked to convert into Roster form
Roster form of { 8,12,16 } ={X;X=4k, k ∈ (2,34)}
Therefore,The Roster form of { 8,12,16 } is {X;X=4k, k∈ (2,34)}
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Seventh grade > M.8 Find the percent: tax, discount, and more PBM
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A discount store buys a shipment of playground slides at a cost of $290 each. The playground
slides will be sold for $783 apiece. What is the mark-up, as a percentage?
Write your answer using a percent sign (%).
The mark-up for the playground slides is 170%. The mark-up refers to the price added to the cost to find out the selling price of a product.
Mark-up is the difference between the selling price and cost price of a product.It is usually represented as a percentage, the mark-up percentage is calculated over the cost of the product. In other words we can say that mark-up is the profit gained from selling a particular product. Here it is said that the cost of a playground slide is $290 and the selling price of the playground slide is $783. We need to find the mark-up percentage of the playground slide.
Mark-up %=[tex]\frac{selling price-cost}{cost}[/tex]×100=[tex]\frac{783-290}{290}[/tex]x100=[tex]\frac{493}{290}[/tex]x100=170%
Therefore the mark-up percentage of the playground slide is 170%.
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Please answer the question following the instructions
9514 1404 393
Answer:
a. n² +10n +25 = 0
b. 0
c. 1 real solution
Step-by-step explanation:
a. Add 25 to put the equation in standard form.
n² +10n +25 = 0
__
b. The discriminant is d = b²-4ac.
d = 10² -4(1)(25) = 0
The discriminant is 0.
__
c. A discriminant of 0 means there is 1 real solution.
SHOW ALL WORK!
A ticket service is selling tickets to a concert. An order of 4 tickets has a price of $63 and an order
of 6 tickets has a price of $92. Write an equation to find the price of any amount of tickets.
Answer:
y = 14.5x + 5
Step-by-step explanation:
x = Number of tickets for the concert
y = Price of the order of x tickets
y = 14.5x + 5
Step-by-step explanation:
1. Let's review the information given to us to answer the question correctly:
Order of 4 tickets has a price of $63
Order of 6 tickets has a price of $92
2. Write an equation to find the price of any amount of tickets.
Let's find out the price of a ticket to understand if there's a service fee and how much is it, this way:
Price of a ticket = (Order of 6 tickets - Order of 4 tickets)/2
Price of a ticket = (92 - 63)/2
Price of a ticket = 29/2 = 14.50
If a ticket costs $ 14.50, 4 tickets will cost $ 58 and 6 tickets will cost $ 87, therefore there is a service or delivery fee of $ 5.
Order of 4 tickets - Price of 4 tickets = Service or delivery fee
Replacing, we have:
63 - 58 = 5
Order of 6 tickets - Price of 6 tickets = Service or delivery fee
Replacing, we have:
92 - 87 = 5
Now, we can write the equation to find the price of an order of any amount of tickets, this way:
x = Number of tickets for the concert
y = Price of the order of x tickets
y = 14.5x + 5
Divide the fractions:
5/8 divided by 1/24 =
Answer:
The answer to this question is 15.
Step-by-step explanation:
We know that dividing a fraction by another fraction is the same as multiplying a fraction by the other fractions reciprocal, where the numerator and denominator are switched.
5/8 ÷ 1/24 =
5/8 x 24/1 =
120/8
120 ÷ 8 = 15.
Hence, the answer to this question is 15.
Hope this helps! :D
Final Answer:
15
Step-by-step explanation:
5/8 ÷ 1/24
5/8 ÷ 24/1
5/8 × 24/1 = 120/8
120/8 ⇒ 15/1 ⇒ 15
Questlon 10 of 10
In the diagram below, DË is parallel to. What is the value of y?
105
OA. 85
O B. 105
OC. 125
OD. 75
tony earns $100 for walking 5 dogs. how much would he earn for each dog
Answer:
500
Step-by-step explanation:
Answer:
20$
Step-by-step explanation:
because 20*5 =100 which 20 times 5 is the same thing as adding 20+20
+20+20+20 witch is 20$ per dog he walks. hope this helps!
Based on the table of values below, find the slope between points where x = 5 and where x = 10.
Hello!
[tex]\large\boxed{m = 1}[/tex]
Use the slope formula to determine the slope between the points:
m = (y2 - y1) / (x2 - x1)
Plug in the values:
m = (7 - 2) / (10 - 5)
m = 5 / 5
m = 1
Solve for b. d = abc
Given mn, find the value of x.
Please help me
Answer:
126°
Step-by-step explanation:
A line is equal to 180°
to find x you would subtract 180° - 54°
The answer is 126°
My work is in the picture below
I hope it helped!
Have a nice day!
In the figure, the angle x° is an alternate angle with angle 54° so the measure of angle x° is 54°.
We have,
From the figure,
Line m and line n are parallel.
Line t is the transversal line.
Now,
Alternate angles are a pair of angles that are formed when a transversal (a line that crosses two other lines) intersects two parallel lines.
When this happens, the alternate angles are on opposite sides of the transversal and are congruent, which means they have the same measure.
Angle 54° and angle x° are alternate angles.
Alternate angles are equal.
So,
x° = 54°
Thus,
The measure of angle x° in the figure is 54°.
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Could someone help with this math question
Answer:
The last choice {80, 88, 200}
Step-by-step explanation:
If you solve for p, it will be p>64 which means p should be bigger than 64. 80, 88, 200 are the only numbers that all of them could be bigger than 64.
Use these properties to rewrite 7/4 + 1/2 + 5/3 + 1/3 + 1/4 + 1/2 in a way that makes the addition easier. Explain how your changes simplify the addition
The addition of the 7 / 4 + 1 / 2 + 5 / 3 + 1 / 3 + 1 / 4 + 1 / 2 is 5.
What is fraction?A fraction represents a portion of a total. This entire may refer to a place or a group of places. The Latin word "fraction," which means "to break," is the source of the English term "fraction."
The distribution of food and supplies as well as the lack of a metal currency were among the mathematical issues that the Egyptians utilized fractions to solve because they were the first civilization to understand fractions.
Given:
7 / 4 + 1 / 2 + 5 / 3 + 1 / 3 + 1 / 4 + 1 / 2
Rearrange the number as shown below,
7 / 4 + 1 / 4 + 1 / 2 + 1 / 2 + 5 / 3 + 1 / 3
Add the like terms as shown below,
(7 + 1) / 4 + (1 + 1) / 2 + (5 + 1) / 3
8 / 4 + 2 / 2 + 6 / 3
Divide the terms as shown below,
2 + 1 + 2
5
Thus, the addition is 5.
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The graph of y = 2x2 is shifted 8 units down on a coordinate grid. What are the roots of the equation that correspond to the new graph?
Answer:
x=2 or x=-2
Step-by-step explanation:
Answer: correct answer is A! -2 and 2
Step-by-step explanation:
A toy factory makes 15 teddy bears every 10 minutes. The factory makes teddy bears for 8 hours each work day. What is the fewest number of work days the factory will need to make 5,000 teddy bears? Write an explanation to show how you determined your answer.
Answer:
hats
Step-by-step explanation:
What number is represented by point A?
Answer:
Third choice, 3/4
Step-by-step explanation:
There's 3 lines in the middle before it's the number 1, if u count 1 into the lines then there's 4, 1 divided by 4 is 0.25 or 1/4, so each small line is going up or down by 1/4. So it's 0 -> 1/4 -> 2/4 -> 3/4 which is A -> 4/4 which is 1
So A is 3/4
The formula to convert from Celsius to Fahrenheit is
F=95C+32 . Use this formula to complete the statements below. Round your answers to the nearest tenth as needed.
If the temperature is 78 degrees Fahrenheit , that is equivalent to
degrees Celsius.
If the temperature is 41 degrees Celsius, that is equivalent to
degrees Fahrenheit.
The temperature in Celsius will be 25.5556 °C and he temperature in degree Fahrenheit will be 105.8 °F, respectively.
What is a Function?A function assigns the value of each element of one set to the other specific element of another set.
Given the function to convert temperature from Celsius to Fahrenheit is F=(9/5)C+32.
A.) Given that If the temperature is 78 degrees Fahrenheit. Therefore, the temperature in degree Celsius will be,
F = (9/5)C + 32
78 = (9/5)C + 32
78 - 32 = (9/5)C
46 = (9/5)C
C = (46 × 5)/9
C = 25.5556
Hence, the temperature in Celsius will be 25.5556 °C.
B.) Given that the temperature is 41 degrees Celsius. Therefore, the temperature in degree Celsius will be,
F = (9/5)C + 32
F = (9/5)41 + 32
F = 73.8 + 32
F = 105.8
Hence, the temperature in degree Fahrenheit will be 105.8 °F.
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f(x) = 2x³ + 7x² - 4x - 5
g(x) = 3x - 2
Find (f - g)(x).
The value of (f-g)(x) is 2x³ + 7x²-7x-3.
As we know that, the composition of functions is the criteria of combining two or more functions into a single function. A function represents some work. The combination of two or more function always results in a new function.
Given that, f(x) = 2x³ + 7x² - 4x - 5 and g(x) = 3x - 2 and we have to calculate the value of (f - g)(x).
Suppose h(x) = (f - g)(x)
Now, we simply have to solve (f - g)(x), let's proceed to solve
= (f - g)(x)
= f(x)-g(x)
= 2x³ + 7x² - 4x - 5-(3x-2)
= 2x³ + 7x² - 4x - 5-3x+2
= 2x³ + 7x²-7x-3
h(x) = (f - g)(x) = 2x³ + 7x²-7x-3
∴ (f - g)(x) = 2x³ + 7x²-7x-3
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1. how can we get equation B from A
A. 4x+2=6-x
B. 5x+2=6
Answer:
since equation a has -x on one side just add x to both sides to get rid of the -x and since you do it to both sides you maintain balance
Step-by-step explanation:
Answer:
4x+x=6-2
5x=6-2
5x+2=6
Step-by-step explanation:
Justify why the sum of 3a and
2b cannot be represented as 5ab.
Answer:
You cannot add two numbers that have different variables.
Step-by-step explanation:
You can multiply them, but since 3 is multiplied by "a" or a different number than "b" then the answer would be incorrect.
Answer:
because 3a and 3b have different variables. You can't add "unlike terms" to each other because the variables have different values. by writing 3a+2b as 5ab, you're completely changing the meaning of the problem. You would get a totally different answer than you would by just adding the two terms together.
PLZ HELP ME WITH THIS!?!?! I WILL MARK BRAINLIEST!!!
Answer:
a: 1/7 +2/7
b:1/7 +1/7+1/7
Mai earns $7 per hour mowing her neighbor’s lawns. She also earned $14 for hauling away bags of recyclables for some neighbors. Priya babysits her neighbor’s children. She earns $8.40 per hour. Priya and Mai have agreed to go to the movies the weekend after they have earned the same amount of money for the same number of hours. How many hours do they have to work before they can go to the movies? How much will they have earned.
Answer:
5 hours for priya 4 of yard mowing and 1 bag moving and they will both earn 42 dollars
Step-by-step explanation:
Susan is buying juice for a party. She wants to buy as many bottles of juice as possible, but she only has $10.00 to spend. If each bottle of juice costs $1.35, how can Susan calculate the number of bottles that she can buy?
A.Divide $10.00 by $1.35, and round the quotient down to the nearest whole number.
B.Divide $10.00 by $1.35, and round the quotient up to the nearest whole number.
C.Divide $1.35 by $10.00, and round the quotient down to the nearest whole number.
D.Subtract $1.35 from $10.00, and round the difference down to the nearest whole number.
GIVING BRAINLIEST
Answer:
A
Step-by-step explanation:
Answer:
A because $10 needed to be divided by $1.35 and and the rounding is needed to get the answer
(-33/60) (-40/88)
Simplify fraction
The graph below shows the solution to a system of inequalities: Solid line joining ordered pairs 0, 3.75 and 15, 0. Shade the portion of the graph above the line in the first and second quadrant Which of the following inequalities is modeled by the graph? (5 points) Group of answer choices x + 4y ≥ 15; y ≥ 0 x − 4y ≥ 15; y ≥ 0 x + 4y ≤ 15; y ≥ 0 −x − 4y ≥ 15; y ≥ 0
Answer:
x + 4y ≥ 15; y ≥ 0
Step-by-step explanation:
The solid line signifies it is a ≤ or ≥.
The equation of the line joining 0, 3.75 and 15, 0 is gotten using the formula:
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)\\\\Substituting:\\\\y-3.75=\frac{0-3.75}{15-0}(x-0)\\\\ y-3.75=-\frac{1}{4}x\\\\y=-\frac{1}{4}x+3.75\\\\4y=-x+15\\\\4y+x=15[/tex]
Since the first and second quadrant are shaded, this represents y ≥ 0.
Also, above the solid line of 4y + x = 15 is shaded, this represents 4y + x ≥ 15.
Hence the inequality modeled is x + 4y ≥ 15; y ≥ 0
Answer: He right
Step-by-step explanation:
PLEASE HELP FOR ALGEBRA I’M FAILING :(
PLEASE HELPPPPPP. I NEED IT DONEEEEE.
Answer:
1. Couples tickets: $8
Individual tickets: $4
2. Song download cost: $2
Movie download cost: $15
Step-by-step explanation:
You can solve both of these questions by doing system of equations.
Let's start with question 1.
There are 2 variables in this equation:
- Couples tickets price: let's represent these with the letter C
- Individual tickets price: let's represent these with the letter K
Writing the two equations would look this these:
5c + 2k = 48
3c + 2k = 32
Next, isolate a variable. I am going to isolate K in the first equation.
[tex]2k = -5c + 48 \\k = -\frac{5}{2}c + 24[/tex]
Now that we isolated a variable we can plug that back in to the second equation:
[tex]3c + 2(-\frac{5}{2}c + 24) = 32\\3c - \frac{10}{2}c + 48 = 32\\3c -5c + 48 = 32\\-2c + 48 = 32\\-2c = -16\\c = 8[/tex]
We found that c is equal to 8 so we can put that back in to an equation to solve for k.
5(8) + 2k = 48
40 + 2k = 48
2k = 8
k = 4
Therefore, the price for couples tickets is $8 and the price for individual tickets is $4.
Check #1:
5(8) + 2(4) = 48
40 + 8 = 48
48 = 48
3(8) + 2(4) = 32
24 + 8 = 32
32 + 32
Now, let's go on to question 2.
There are 2 variables in this equation:
- Price of songs downloaded: let's represent these with S
- Price of movies downloaded: let's represent these with M
Writing the two equations would look like this:
15s + 11m = 195
15s + 8m = 150
There is a simple way to answer this system, however.
If you change the bottom equations signs to negative you can minus the second equation from the first equation like this:
15s + 11m = 195
-(15s +8m = 150)
Minus them to get this equation:
3m = 45
Solve
m = 15
We have found that each movie download costs $15, now let's plug this back into an equation:
15s + 11(15) = 195
15s + 165 = 195
15s = 30
s = 2
Each song costs $2 to download.
Check #2:
15(2) + 11(15) = 195
30 + 165 = 195
195 = 195
15(2) + 8(15) = 150
30 + 120 = 150
150 = 150
I hope this helps!!
- Kay :)
PLEASE HELP ASAP!!!!
Sue is a waitress in a restaurant. She started the day with $20 in her pocket, and she earns an average of $5 for each table that she waits on. Which of the following graphs represents the money that Sue has in her pocket after waiting on x tables?
the last one
Hope this helps! :3
plz mark as brainliest!
On a coordinate plane, a line is drawn from point J to point K. Point J is at (1, negative 10) and point K is at point (7, 2). What is the y-coordinate of the point that divides the directed line segment from J to K into a ratio of 5:1? y = (StartFraction m Over m + n EndFraction) (y 2 minus y 1) + y 1 –8 –5 0 6
Answer:
5
Step-by-step explanation:
lol
Answer:
the answer is c 0
Step-by-step explanation:
2 Thessalonians 3:16
Now may the Lord of peace himself give you peace at all times and in every way. The Lord be with all of you.
jesus loves you!!!
If $8000 is invested at 5% compounded quarterly , what is the amount after 6 years?
3х — 7y = 21
6x = 14y + 42
Solve each system of equations using elimination (⚠️ I will give you brainliest if you answer correctly!‼️⚠️)