f(x) and g(x) are closed under subtraction because when subtracted, the result is also a polynomial.
Option B is the correct answer.
What is a polynomial?Polynomial is an equation written as the sum of terms of the form kx^n.
where k and n are positive integers.
We have,
f(x) = a(0) + a(1)x + a(2)x² + ......... + a(n)[tex]x^n[/tex]
g(x) = b(0) + b(1)x + b(2)x² + .......... + b(n)[tex]x^n[/tex]
Now,
f(x) - g(x)
= a(0) + a(1)x + a(2)x² + ......... + a(n)[tex]x^n[/tex] - b(0) - b(1)x - b(2)x² - .......... - b(n)[tex]x^n[/tex]
= (a(0) - b(0)) + (a(1) - b(1))x + (a(2) - b(2))x² + ........... + (a(n) - b(n))[tex]x^n[/tex]
This is also a polynomial.
Thus,
f(x) and g(x) are closed under subtraction.
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what's 5 plus 5 guys I'm so tired
Answer: it think 10
Step-by-step explanation:
and Get some sleep bro
Answer: 10
Step-by-step explanation:
5+5=10
HELP
______________________
Inverse of function f(x) is f⁻¹(x) = x³/125 - 7
What is inverse function?An inverse function or an anti function is defined as a function, which can reverse into another function. In simple words, if any function “f” takes x to y then, the inverse of “f” will take y to x. If the function is denoted by 'f' or 'F', then the inverse function is denoted by f⁻¹ or F⁻¹.
Given function,
f(x) = 5∛(x + 7)
f⁻¹(x) = 5∛(f(x) + 7)
Cubing both sides
x³ = 5³(f(x) + 7)
x³ = 125 (f(x) + 7)
f(x) + 7 = x³/125
f(x) = x³/125 - 7
Hence, f⁻¹(x) = x³/125 - 7 is inverse of function f(x).
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Algebra 1, please help,
Answer:
I don’t even know
Step-by-step explanation:
Ms. Pesko pulled 5 candy bars out of a bag. She pulled the following candies: Twix, Kit-Kat, Milky Way, Twix, Twix. What is the experimental probablity of getting a Twix?
Answer:
Step-by-step explanation:
The experimental probability of getting a Twix is 3/5 or 60%.
calculate the measure of x
The measure of x use Pythagorean Theorem
1. x= 15
x= 26x= 7.6About Pythagorean TheoremTh Pythagorean theorem only applies to right triangles. This is the same as explained in the Pythagorean Theorem Module which states that for each right triangle, the area of the square on the hypotenuse is equal to the sum of the areas of the squares on the other side or the sides of the right angle.
Meanwhile, there is the opposite of the Pythagorean theorem which functions to determine the type of triangle if the lengths of the sides are known. The types of triangles include:
A right triangle is a triangle in which one of the angles is a right angle or equal to 90 degrees. An acute triangle is a triangle in which all three angles are acute or less than 90 degrees. An obtuse triangle is a triangle in which one of the angles is obtuse or measures more than 90 degrees.Learn more about Pythagorean theorem at
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evaluate, correct to four significant figure,(573.06× 184.25)
Answer:
103,847
103,847.0
Step-by-step explanation:
Step 1: Multiply the two numbers: 573.06 x 184.25 = 106,157.45
Step 2: Round the answer to four significant figures: 106,200
Which of the following shows independent events?
Select the correct answer below:
drawing a jack and then drawing a 7 without replacement from a standard deck of cards
drawing a 10 and then drawing a 9 without replacement from a standard deck of cards
rolling two 4's from two rolls of a standard die
rolling a sum less than 3 from two rolls of a standard die and rolling a 1 for the second throw
Answer:
Step-by-step explanation:
Mei Mei signed up for a streaming music service that costs $6 per month. The service allows Mei Mei to listen to unlimited music, but if she wants to download songs for offline listening, the service charges $0.50 per song. How much total money would Mei Mei have to pay in a month in which she downloaded 35 songs? How much would she have to pay if she downloaded
�
s songs?
Answer:
She would have to pay $17.50 for 35 songs.
Step-by-step explanation:
We have the amount it costs per song (0.50), and we have the amount of songs that she wants to buy (35). If we multiply 35 the amount of songs by 0.50 the price per song, we will have a grand total of $17.50.
35 * 0.50 = 17.50
-Hope this helped
After a 75% reduction, you purchase a new dvd player on sale for $150. What was the original price of the dvd player ?
Step-by-step explanation:
The original price was 150 / (1 - 0.75) = $600.
Help me asap and need the answer quick
Answer:20 m/s
Step-by-step explanation:
Answer:
20 m/s
Step-by-step explanation:
700 ÷ 35 = 20 m/s
Which number line represents the solution set of the inequality -2x + 0.25 > 6.25
Answer:
Step-by-step explanation:
-2x+0.25>6.25
-2x>6
Swap the sign when you divide or multiply by a negative in an inequality.
x<-3
Option #1
will give brainliest to correct answer
The sequence that represents the arithmetic sequence will be {-6, 1, 8, 15, 22,...}. Then the correct option is A.
What is an arithmetic sequence?Arithmetic succession or arithmetic sequential is a numerical series in which the difference between subsequent terms is uniform.
Let's check all the options, then we have
A. {-6, 1, 8, 15, 22,...}, then the common difference is given as,
d = 1 - (-6) = 8 - 1 =
d = 7 = 7
B. {64, 32, 16, 8, 4,...}, then the common difference is given as,
d = 32 - 64 = 16 - 32
d = -32 ≠ - 16
C. {1, 2, 4, 8, 16,...}, then the common difference is given as,
d = 1 - 2 = 2 - 4
d = - 1 ≠ - 2
D. {1, 3, 6, 10, 15,...}, then the common difference is given as,
d = 1 - 3 = 3 - 6
d = - 2 ≠ - 3
The sequence that represents the arithmetic sequence will be {-6, 1, 8, 15, 22,...}. Then the correct option is A.
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Which expression is equivalent to
−
2
�
+
�
+
7
�
−2w+w+7w?
Answer:
The expression equivalent to
−
2
√
√
+
7
√
−2w+w+7w is 7√ - 2w.
Please help me thank you so much!
Answer:
It's the second one because -3x3-5 equals -14
4. Consider the inequality 2n+7>13.
(a) For each value of n in the table, find the (b) Solve the inequality 2n+7>13
value of 2n +7. Then, state whether that
value of n is a solution.
the two-step techniques from class.
Value of 2n+7
The value of 'n' satisfies the inequality 2n + 7 > 13 is [4, ∞).
What are inequalities and their types?Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.
The symbol a < b indicates that a is smaller than b.
When a > b is used, it indicates that a is bigger than b.
a is less than or equal to b when a notation like a ≤ b.
a is bigger or equal value of an is indicated by the notation a ≥ b.
The given inequality is 2n + 7 > 13.
Assuming n ∈ I.
Therefore, The values of 'n' that satisfies the giver inequality is,
At, n = 3, 2n + 7 = 13.
So, The values of 'n that satisfies the inequality is [4, ∞).
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Last year at a certain high school, there were 95 boys on the honor roll and 64 girls on the honor roll. This year, the number of boys on the honor roll increased by 20% and the number of girls on the honor roll increased by 25%. By what percentage did the total number of students on the honor roll increase? Round your answer to the nearest tenth (if necessary).
Answer:
1.9 percent
Step-by-step explanation:
95 boys + 64 girls = 159 total honor roll students
To quickly find percentages of numbers, think of the current number as 100%, or 1.00. Then, go from there to find the number to multiply to get the percentage you need.
For example, a 25% decrease in the number of girls means the new number will be 75% of the old number, so we multiply the number of girls by 0.75 to get the new number of girls. 64*0.75 = 48.
Same with the boys, 95 boys is 100%, but this year the number increased by 20%, so we need to find 120% of the number, so we multiply it by 1.20. 95*1.20 = 114
To answer this question, we need to know by what percent the total number of honor students increased by, so we need to know the new total number. 48+114 = 162
To find out what percent 162 is out of 159, we divide them. 162 / 159 = 1.0188, or 101.9 percent if you round to the nearest tenth. So, the number of students increased by 1.9%.
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If your original biconditional statement is true, would the contrapositive be true? Give an example to illustrate your reasoning. ＇
Answer:
Step-by-step explanation:
es, if the original biconditional statement is true, then its contrapositive is also true.
Example: "If it rains, the grass is wet."
The contrapositive of this statement would be "If the grass is not wet, then it didn't rain."
Both the original statement and its contrapositive have the same truth value, as they are logically equivalent.
A car rental agency charges $250 per week plus $0.10 per mile to rent a car.
a. Write an equation that expresses the weekly cost to rent the car, y, in terms of the number of miles driven during the week, x.
b. How many miles did you drive during the week if the weekly cost to rent the car was $260?
Answer:
a. 250+0.10x=y
b. 250+0.10x=260
-250. -250
———————————-
0 + 0.10x = 10
——— ——-
0.10 0.10
—————————————-
X = 100
( you drove 100 miles )
Step-by-step explanation:
In question A, basically you already have a base of 250 and you add 0.10, multiplying it with x, which is the number of miles, equals to the total amount. So the answer for that question is : 250+0.10x = y. For question B, you just had to substitute the y for 260, and solve for x ( subtract 250 from both sides, divide by 0.10 on both sides, and you get x = 100. So the answer for that question is you drove 100 miles.
hope this helped =)
The cost of renting a car can be formulated as y = 250 + 0.10x, with y representing the total cost and x the distance travelled. If the total cost was $260, then 100 miles were driven.
Explanation:The car rental agency's charge can be represented as a linear equation with a fixed cost ($250/week) plus a variable cost ($0.10/mile). This can be represented algebraically as: y = 250 + 0.10x, where y is the total weekly cost and x signifies the number of miles driven.
To find out how many miles (x) were driven for a total cost of $260, substitute y with 260 in the equation and solve for x:
260 = 250 + 0.10xSubtract 250 from both sides: 10 = 0.10xDivide by 0.10 to solve for x: x = 100Therefore, if the weekly cost to rent the car was $260, you drove 100 miles.
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Part A. Write an expression to find the cost of b books at $12 each
Part B. Using the variable h, write an expression to show the total cost you would have to pay a babysitter that charges $10 per hour plus $5 in gas to drive herself to your house.
Part A. The cost of b books at $12 each can be found with the expression: 12 * b
Part B. The total cost to pay a babysitter who charges $10 per hour and $5 in gas can be found with the expression: 10 * h + 5
Consider the graphs of f(x) = 2^x and g(x).
Which transformation can be used to describe g(x)?
Answer:
6 to right
Step-by-step explanation:
The value of y when x equals 0 on f(x) is 1. By looking at the graph of g(x), it looks like it reaches the value of y = 1 when x is 6. It also This means the same point is shifted over 6 to the right (considering it looks like no other modifications are made other than the shift).
A catapult launches a pumpkin from the base of a hill.
The height of the pumpkin is 5.7 m.
What is the height of the pumpkin?
The height of the pumpkin is calculated by applying the following formula.
y = -0.1x² + 4.9x
where;
y = 0.9x
Now, our new equation becomes;
0.9x = -0.1x² + 4.9x
re-arrange the equation, and solve for x
0.1x² = 4.9x - 0.9x
0.1x² = 4
x² = 4 / 0.1
x² = 40
x = √ ( 40 )
x = 6.32
The height of the pumpkin = 0.9x = 0.9 x 6.32 = 5.7 m
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Five times the sum of a number and six is equal to eight times the number, minus six. Find the number.
Answer: x=12
Step-by-step explanation:
[tex]5(x+6)=8x-6[/tex]
On the left side of the equation, open the parentheses:
[tex]5x+30=8x-6\\\\5x+30-5x=8x-6-5x\\\\30=3x-6\\\\30+6=3x-6+6\\\\36=3x[/tex]
Divide both parts of the equation by 3:
[tex]12=x[/tex]
[tex]Thus,\ x=12[/tex]
Peter recorded the snowfall each winter in New York for the last 4 years. He predicts that the snowfall change from year 4 to year 5 will be twice as much as the change was from year 3 to year 4. Plot ONE point on the graph that could represent Peter’s prediction for the snowfall in New York in year 5.
Plot the point on the coordinate grid below. You must graph the specified number of points; any other graphed points will cause all points to be scored as incorrect.
The snowfall change is plotted on the graph attached with the answer below.
What is coordinate geometry?A coordinate plane is a 2D plane that is formed by the intersection of two perpendicular lines known as the x-axis and y-axis. A coordinate system in geometry is a method for determining the positions of the points by using one or more numbers or coordinates.
Given that Peter recorded the snowfall each winter in New York for the last 4 years. He predicts that the snowfall change from year 4 to year 5 will be twice as much as the change was from year 3 to year 4.
Let the snowfall in years 3 to 4 is (2,0) so it will be in year 4 to 5 will be (4,0). Plot the two points on the graph. The graph is attached with the answer below for better understanding.
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A deli is trying out new labels for their cylindrical-shaped wheels of cheese. The label covers the entire wheel except the circular top and bottom.
If the wheel has a radius of 22 centimeters and a height of 16 centimeters, how many square centimeters of the wheel does the label cover? (Approximate using pi equals 22 over 7)
A. 15,488 over 7 square centimeters
B. 36,784 over 7 square centimeters
C. 1,936 over 7 square centimeters
D. 340,736 over 7 square centimeters
Answer: The real answer is 15,488 over 7 square centimeters.
Step-by-step explanation:
For this question, you need to use the formula for surface area of a cylinder: SA = 2πr^2 + 2πrh
Since the label DOES NOT cover the bases, you do not need to do the first part of the formula (2πr^2) because that part is finding the area of the bases. We are only looking for how many square centimeters the label IS covering.
2πrh
So times the radius by 2.
22 * 2 = 44
Now times 44 by the height
44 * 16 = 704
And finally, times 704 by 22/7
22/7 * 704 = 15,488 over 7 square centimeters
So 15,488 over 7 square centimeters is the answer.
You might get it in decimal form (something like this number 2,212.5714285) but if you divide 15,488 by 7 you will get the same decimal.
Also, I did the same test and got 100% so I know the right answer
I have a photo of the question from my test:
Have a good day :)
Ramona and Malika are walking along linear routes in their county. On a map of their county, Ramona’s route passes through the coordinates (2,1)
and (0,−2)
. Malika’s route passes through the coordinates (0,3)
and (−2,0)
. Do the friends pass through a common coordinate, walk along the same route, or never cross routes?
Explain your answer
The path's of the two persons don't cross as their lines don't intersect and thus they never cross routes.
What are linear equations?Linear equations help in representing the relationship between variables such as x, y, and z, and are expressed in exponents of one degree. In these linear equations, we use algebra, starting from the basics such as the addition and subtraction of algebraic expressions.
Given here: Ramon's path passes through the co-ordinates (2,1)
and (0,−2) while Malika's passes through (0,3)
and (−2,0)
Thus using the two point of a line to construct the linear equations we get
Ramona's path is y=1.5x−2
Malika's path is y=1.5x+3
Now solving for the two equations we get
1.5x-2=1.5x+3
-2=3 which is not possible
Hence, The path's of the two persons don't cross as their lines don't intersect and thus they never cross routes.
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Troy has to order 8 pounds of ham, 15 pounds of cheese, and 12 pounds of turkey. What is the total cost of Troy’s order?
A. $93.75
B. $110.25
C. $204.23
D. $293.66
The total cost of Troy’s order is $93.75 for ham, cheese, and turkey.
The price chart below shows the ingredients that Troy needs to buy. A pound of onions costs $0.79, a pound of tomatoes costs $0.93, a pound of cheese costs $1.85, a pound of ham costs $3.15, and a pound of turkey costs $3.40.
The question above asks about Troy, who has to order 12 pounds of turkey, 15 pounds of cheese, and 8 pounds of ham for his sandwich bar.
We need to sum up the total price as:
Ham: 8 pounds x $3.15 equals $25.2
Cheese: 15 pounds x $1.85 equals $27.75
Turkey: 12 pounds x $3.40 equals $40.8
The total of the prices is: $25.2 + $27.75 + $40.8 = $93.75
Thus, the right choice is A.
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0
9
You deposit $200 each month into an account earning 7% interest compounded monthly.
a) How much will you have in the account in 35 years?
https://ohm.lumenlearning.com/assess2/?cid=69660&aid=51 5/#/skip/
b) How much total money will you put into the account?
$
c) How much total interest will you earn?
$
Question Help: Video 1 Video 2
a) On compounding the amount of money in account after 35 years will be $356796.54.
b) $84000 is the total money that will be put into the account.
c) The total interest earned is obtained as $272796.54.
What is Compound Interest?
The interest that is calculated using both the principal and the interest that has accrued during the previous period is called compound interest. It differs from simple interest in that the principal is not taken into account when determining the interest for the subsequent period with simple interest. Compound interest is commonly abbreviated C.I. in mathematics.
a) Figure out the period interest rate, i.
Use the formula: i=r/m, where r is the nominal interest rate and m is the number of compounding periods.
If the bank pays 7% compounded monthly, that means that the nominal annual interest rate is 7.0% and the monthly period interest rate is 7/12 = 0.58%.
The principal amount A = $200
The number of times interest applied per time period n = 35 × 12 = 420
Now, use the uniform series compound-amount factor to find the future value.
The equation is -
F = A [((1 + i)^n) - 1] / i
where F is the future value, A is the annuity amount, i is the period interest rate.
Substitute the values into the equation -
F = 200 [((1 + 0.0058)^420) - 1] / 0.0058
F = 200 [((1.0058)^420) - 1] / 0.0058
F = 200 (11.3471 - 1) / 0.0058
F = 200 (10.3471) / 0.0058
F = 200 × 1783.9827
F = 356796.54
Therefore, the amount will be $356796.54 after 35 years.
b) The total money put in the account will be -
Total amount = The principal amount × The number of times interest applied per time period
Total amount = A × n
Substitute the values into the equation -
Total amount = 200 × 420
Total amount = 84000
Therefore, the total amount is $84000.
c) The total interest earned will be -
Total Interest = The future amount - The total money put in the account
Total Interest = F - The total money put in the account
Substitute the values into the equation -
Total Interest = 356796.54 - 84000
Total Interest = 272796.54
Therefore, the total interest is $272796.54.
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Anyone know how to do math work like this?? I'm
Answer: IT IS EZ IT JS 67 AND 194
Step-by-step explanation
11 Answer:
Consecutive integers are integers that follow each other in order (for
example 5, 6, and 7). The sum of three consecutive integers is 417.
Let n be the first one. Write an equation that will determine
the three integers.
12 Answer:
Solve the equation in question #11 for the value of n.
Step-by-step explanation:
n + (n+1) + (n+2) = 417
3n + 3 = 417
3n = 414
n = 138
so, the 3 integers are
138, 139, 140
Answer:
138
Step-by-step explanation:
n,n+1,n+2
so 3n+3=417
3n=414
n=138
Find the Profit value
if the supply cost of each electric bicycle is £950, and the company decides to set the price less than £1300, then we can repeat the above process to find the optimal price and profit.
It can be seen that the sale volume has changed according to its price in different periods. The values have been reported in the following table. This company is going to launch a new product and the price needs to be decided based on the market analysis. Determine the appropriate price for the newly developed electric bicycle with the aim of maximizing the company’s profit. The demand for new products has a direct relationship with its price.
Table 1- Demands of an electric bicycle based on a price level according to previous experiences
Price (£) Demand
1150 415
1185 405
1210 390
1235 380
1260 345
1285 302
1310 270
1335 255
1360 246
1385 240
1410 230
1435 222
1460 216
1485 214
1510 210
1540 200
The main objective of the company is to maximize profit regarding to the new product. It is assumed that the unit production and supply cost of each electric bicycle is £740, so the profit of each unit will be (the sale price – unit production cost).
Determine the optimal demand
Compute the optimal profit.
Interpret the results.
If the supply cost of each electric Bicycle is £250 and then £950 determine the optimal price and interpret the results appropriately.
Suppose that the supply cost is £950 and the company has decided to set the price less than £1300, then what will be the optimal price? Interpret the results
To find the optimal price, we need to find the price that maximizes the company's profit. Profit is calculated as (sale price - unit production cost), and we have been given the unit production cost as £740. So, the profit function can be written as:
Profit = (sale price - £740) * demand
Using the data in the table, we can plot the demand as a function of price and then calculate the profit for each price level:
Price (£) Demand Profit (£)
1150 415 121,750
1185 405 133,650
1210 390 141,600
1235 380 146,200
1260 345 140,100
1285 302 113,640
1310 270 75,600
1335 255 67,170
1360 246 66,480
1385 240 66,600
1410 230 63,700
1435 222 62,820
1460 216 62,160
1485 214 62,370
1510 210 61,500
1540 200 59,200
From the table, we can see that the maximum profit is obtained at a price of £1210, which gives a profit of £141,600. The optimal demand at this price is 390 units.
Interpretation: The company can maximize its profit by setting the price of the electric bicycle at £1210, and the optimal demand at this price is 390 units. The company can earn a profit of £141,600 if it sells 390 electric bicycles at this price.
If the supply cost of each electric bicycle is £250, then the profit function becomes:
Profit = (sale price - £250 - £740) * demand
Profit = (sale price - £990) * demand
Using the same method as before, we can calculate the profit for each price level:
Price (£) Demand Profit (£)
1150 415 157,450
1185 405 169,950
1210 390 177,300
1235 380 181,300
1260 345 174,150
1285 302 146,890
1310 270 110,250
1335 255 96,525
1360 246 95,040
1385 240 95,400
1410 230 92,400
1435 222 91,512
1460 216 90,720
1485 214 91,422
1510 210 89,100
1540 200 85,600
The maximum profit is obtained at a price of £1210, which gives a profit of £177,300. The optimal demand at this price is 390 units.
Interpretation: If the supply cost of each electric bicycle is reduced to £250, then the optimal price remains the same as before at £1210. However, the maximum profit increases to £177,300, which is an increase of £35,700 compared to the previous scenario.
If the supply cost of each electric bicycle is £950, and the company decides to set the price less than £1300, then we can repeat the above process to find the optimal price and profit.
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