the simplest form of the given expression is 3n+2.
What is polynomials?
Using variables and coefficients, polynomials are algebraic expressions. The term "indeterminates" is sometimes used to describe variables. The terms Poly and Nominal, which together signify "many" and "terms," make up the word polynomial. When exponents, constants, and variables are combined using mathematical operations like addition, subtraction, multiplication, and division, the result is a polynomial (No division operation by a variable). The expression is categorized as a monomial, binomial, or trinomial based on the number of terms it contains.
-n + (-4) - (-4n) + 6
= -n + (-4) + 4n + 6
= 3n -4 +6
= 3n+2
Hence the simplest form of the given expression is 3n+2.
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While taking a hike 80% or 20 of the participants wore hiking boots. How many participants were on the hike?
20 beacuse you need hiking boots to hike
Answer:
25
Step-by-step explanation:
let x = # of participants on the hike
(.80)x = 20
x = 20/0.80 = 25
1
Multiple Choice Question
What type of number is 105?
Choose all that apply
Whole number
Integer
Rational
Irrational
Analyzing the options given in the question, the options that satisfy for the number 105 are: Integer, Rational, Whole number.
What are whole numbers?All natural numbers and 0 are included in the category of whole numbers. They are a subset of real numbers, which exclude negative numbers, decimals, and fractions.
What are rational numbers?A rational number is a number which is in the form of p/q where p and q are both integers and q is not equal to zero.
The number 105 is , Whole number since it falls between all the numbers between 0 to positive infinity. Similarly, the number is an Integer since it does not contain any fractions or decimals. And, the number 105 is rational number since it can be expressed in the form of 105/1.
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If a jacket is marked up 75% to be $350 and a month later is 20% off and then two weeks later is 30% off how much money did the company gain or lose
PLEEEEASE HELP!!!!!
280 AND 245 RS the company GAIN,20% OFF it is 280 rs and 30% off it is 245 rs
How to calculate discount price in rupees?For example, you may want to calculate the sale price of a shirt that regularly costs Rs 1,000. If the shirt is 20% off, you must convert 20% to a decimal (20/100 = 0.2). You have Rs 1,000 * 0.2 = Rs 200. You then subtract the discount from the original price as Rs 1,000 – Rs 200 = Rs 800.Discount is the difference between the marked price (list price) and the selling price of an article. Therefore, the formula used to calculate discount is: Discount = List price - selling price.For example, $100 invested today in a savings scheme that offers a 10% interest rate will grow to $110. In other words, $110, which is the future value (FV), when discounted by the rate of 10% is worth $100 (present value) as of todayTo learn more about discount price refers to:
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10c. What other sequence of transformations would produce the same final image from the original pre image? Check your answer by performing the transformations Then make a conjecture that generalizes your findings.
The pre-image and picture will become congruent to one another by the following transformations: Reflection, Rotation and Translation
what is a sequence?A sequence is a collection of numerals (referred to as "terms"), for example, 2, 5, 8. A specific pattern that some sequences follow may be leveraged to make them infinitely long. To continue the series, add 3 and use the example of 2,5,8. Formulas that show where to look for words inside a sequence can be found there. Informally, a sequence in mathematics is a collection of items that are in some order (or events). It has components, much like a set (also called elements or terms).
Any of the aforementioned modifications result in an exact replica of the pre-image in the picture. The only thing that has changed about the figure is that it has been moved, rotated, or somehow reflected. The figurine is still the same size and form as before. Isometries are the name for these transformations.
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If n is a two-digit number, what is the sum of the digits of 99×n?
Answer: The sum of the digits of 99 × n is 27 - 10 = 17.
Step-by-step explanation:
To find the sum of the digits of 99 × n, we can use the fact that 99 × n = 100 × n - n. The sum of the digits of 100 × n is simply n, since the hundreds digit is zero. Therefore, the sum of the digits of 99 × n is equal to the sum of the digits of n - n, which is simply zero.
For example, if n = 37, then 99 × n = 99 × 37 = 3,699. The sum of the digits of 3,699 is 3 + 6 + 9 + 9 = 27. The sum of the digits of 37 is 3 + 7 = 10. Therefore, the sum of the digits of 99 × n is 27 - 10 = 17.
Prove that limx→2 2^x=4 using the formal definition of limit.
Answer:
Refer to step-by-step
Step-by-step explanation:
Prove that, [tex]\lim_{x \to \22} 2^{x}=4[/tex]
Plug in the value of 2 into the limit.
[tex](2)^{2}=4[/tex]
Thus we proved the limit.
The population of North Carolina was approximately 9.5 million in 2010. The population has increased by about 1.3% per year. If the population continues to grow at this rate, in what year will North Carolina’s population reach 12 million?
The population of North Carolina will reach 12 million in the year 2028.
What is Population Growth?Population growth is defined as the increase in the number of people which is calculated using population growth rate.
Given that,
Population in 2010 = 9.5 million
Population is increasing to 1.3% per year.
Annual growth rate = 1.3% = 1.3/100 = 0.013
We have the population growth formula,
P = P₀ e^(r t)
Here, P₀ = 9.5 million = 9,500,000
and P = 12 million = 12,000,000
r = 0.013
We have to find t.
12,000,000 = 9,500,000 e^(0.013t)
120 / 95 = e^(0.013t)
Taking natural logarithm on both sides and also ㏑(e^m) = m ㏑ e, we get,
㏑(12/9.5) = 0.013t × ㏑e
[㏑(12/9.5) ÷ 0.013] = t [since ln e = 1]
t = 17.97 ≈ 18 years
The year is 2010 + 18 = 2028
Hence in the year 2028, the population will be 12 million.
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Manicure sets at nails by Nina are marked up 47% from the cost of $8.36. What does a manicure set cost in Nina’s store?
Answer:
The cost of a manicure set in Nina's store is $12.30.
Step-by-step explanation:
To find the cost of the manicure set in Nina's store, you can use the following formula:
Selling price = Cost + Cost * Markup percentage
Substituting the given values into this formula, you get:
Selling price = $8.36 + $8.36 * 47%
To find the value of the markup percentage, you can convert 47% to a decimal by dividing it by 100: 47/100 = 0.47
Then you can use this value in the formula to find the selling price:
Selling price = $8.36 + $8.36 * 0.47
Convert the polar equation to rectangular form [tex]r=5cot(\theta)csc(\theta\))[/tex]
Answer:
[tex]\displaystyle x=\frac{1}{5}y^2[/tex]
Step-by-step explanation:
[tex]\displaystyle r=5\cot(\theta)\csc(\theta)\\\\r=5\biggr(\frac{\cos(\theta)}{\sin(\theta)}\biggr)\biggr(\frac{1}{\sin(\theta)}\biggr)\\\\r=\frac{5\cos(\theta)}{\sin^2(\theta)}\\\\r^2=\frac{5r\cos(\theta)}{\sin^2\theta}\\\\r^2\sin^2(\theta)=5r\cos(\theta)\\\\(r\sin(\theta))^2=5x\\\\y^2=5x\\\\x=\frac{1}{5}y^2[/tex]
Melinda, Zachary, and heather went to the mall to shop for school supplies
Heather spend $33.1 on school supplies.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Given that Melinda, Zachary, and heather went to the mall to shop for school supplies
Melinda spent $14.25 on her supplies.
Melinda=$14.25
Zachary spent $2.30 more than Melinda spent
Zachary=$14.25+$2.3
=$16.55
Heather spent 2 times as much money as Zachary spent
Heather=2×$16.55
=$33.1
Hence, Heather spend $33.1 on school supplies.
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Parallel, intersecting, and perpendicular
The conditions of the line to be intersecting, parallel, and coincident are explained below.
What is a linear equation?A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.
The linear equation is given as,
y = mx + c
Where m is the slope of the line and c is the y-intercept of the line.
The types of lines are as follows:
If the slope of the lines is different, then the lines are intersecting lines.If the slope of the lines is the same but the y-intercept of the lines is different, then the lines are parallel lines.If the slope and y-intercept of the lines are the same, then the lines are coincident lines.More about the linear equation link is given below.
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pls help with this question find the slope from 1-6
Answer:
Step-by-step explanation:
1. ( -2, 2), (-1, 5)
(5 - 2)/(-1 + 2)= 3/1= 3
2. (-4, 2), (2, 0)
(0 - 2)/(2 + 4) = -2/6 = -1/3
3. (0, 3), (5, 1)
(1 - 3)/(5 - 0)= -2/5
4. (0, 0), (1, 1)
(1 - 0)/(1 - 0)= 1/1= 1
5. (3, 0), (3, 1)
(1 - 0)/(3 - 3) = 1/0 = undefined
6. (0, -1) (1, -1)
(-1 + 1)/(1 - 0)= 0/1 = 0
Ann 's car can go 132 miles on 4 gallons of gas. During a drive last weekend, Ann used 5 gallons of gas. How far did she drive? Use pencil and paper. Explain how the problem changes if you were given the distance Ann drove last weekend instead of how much gas she used.
Answer:
Ann traveled 165 miles on 5 gallons of gas
Step-by-step explanation:
First we must know how many miles are in a gallon (in this situation). Last weekend Ann drove 132 miles with 4 gallons of gas, we can divide to find out how many miles she drove on 1 gallon. 132/4 = 33. This means Ann drove 33 miles on 1 gallon of gas. To get your answer, simply multiply 5 and 33. 5 times 33 = 165.
Can y’all pls help me solve this!!
Answer:
From left to right picture,
Scale factor = 2/3
x = 24
y = 12
z = 21
Step-by-step explanation:
Look at the two figures and identify the sides where both lengths are known.
That is the top right-hand side.
Scale factor is hence 18/27 = 2/3
Next, find x, y and z:
Bottom left-hand side: 16/x = 2/3
x = 3/2 x 16
x = 24
Bottom right-hand side: y/18 = 2/3
y = 18 x 2/3
y = 12
Top left-hand side: 14/z = 2/3
z = 3/2 x 14
z = 21
What is the meaning of conditionally promoted in school
A biology class examined some flowers in a local meadow. They saw 36 flowers, of which 25% were perennials. How many perennial flowers did the students see?
Answer: nine
Step-by-step explanation: 36 - 25 = 9 or 25% x 1 + 36 = 9
Answer:
9
Step-by-step explanation:
1 first split 36 by 4 because 25% is 1/4
2 once when divided you should get 9 because 9x4 is 36
A store is having a sale on chocolate chips and walnuts. For 4 pounds of chocolate chips and 8 pounds of walnuts, the total cost is $33. For 2 pounds of chocolate chips and 3 pounds of walnuts, the total cost is $13.
Find the cost for each pound of chocolate chips and each pound of walnuts.
Answer:
chocolate chip 7
walnuts 3.5
Step-by-step explanation:
assume x=chocolate chips
y=walnuts.
equation
4x + 8y=33
(2x+3y=13)×2
new eq
4x + 8y=33
4x + 6y=26
------------------
2y=7
y=7/2
4x+ 8y = 33
4x + 8(7/2)= 333
4x= 33-28
x=7.00
I need help with these two questions please help!!
An unknown numerical value in an equation or algebraic expression is represented by a symbol (often a letter) in algebra. The variable is 28 square feet with x = 150 and A = (4)(7).
What is the simple definition of variable?A variable is anything that can take on any one of a number of values, such as a quantity, a sign for a variable, or an element of a scientific experiment that is susceptible to change.
Any traits, figures, or amounts that may be gauged or counted are considered variables. Another name for a variable is a data item. Variables include things like age, sex, business income and expenses, birthplace, capital expenditures, class grades, eye colour, and vehicle type.
A variable is a value that can be altered depending on the mathematical issue. Numerous mathematical expressions and equations use the generic letters x, y, and z.
1)
[tex]$$\begin{aligned}& \frac{6}{100}=\frac{9}{x} \\& \frac{6 x}{6}=\frac{900}{6} \\& x=\frac{300}{2}\end{aligned}$$[/tex]=150.
2)
[tex]$A=(4)(7)$[/tex]
[tex]$A=28$[/tex] thirty feet
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Determine the amount of a semi-annual coupon paid for a 3% bond with a face value of 80,000 which matures after 15years.
The amount (present value) of a semi-annual coupon paid for a 3% bond with a face value of 80,000 which matures after 15 years is $80,000.
What is the price of a bond?The price of a bond is its present value.
The present value can be determined as the discounted cash inflows.
In this situation, we can determine the present value of the bond using an online finance calculator as follows:
N (# of periods) = 30 (15 years x 2)
I/Y (Interest per year) = 3%
PMT (Periodic Payment) = $1,200
FV (Future Value) = $80,000
Results:
Present Value (PV) = $80,000.00
Sum of all periodic payments = $36,000.00
Total Interest = $36,000.00
Thus, the amount of the bond is $80,000.
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42. Let f be a function from the set A to the set B. Let S and T be subsets of A. Show that
a) f(S ∪ T)=f(S) ∪ f(T).
b) f(S ∩ T) ⊆ f(S) ∩ f(T).
Start with any random elements of sets and compute LHS and RHS individually.
a) The proof of f(S ∪ T) = f(S) ∪ f(T) is explained below.
b) The proof of f(S ∩ T) ⊆ f(S) ∩ f(T) is expliane dbelow.
What are sets and subsets?A set is a collection of well-defined objects.
A subset contains all the elements or a few elements of the given set.
The improper subset is when it contains all the elements of the given set and the proper subset is when it doesn't contain all the elements of the given set.
Let, The set A = {1, 2, 3, 4, 5} and B = {2, 4, 5}.
Therefore, S = {1, 2, 3} and T = {1, 4, 5}.
Now, f(S ∪ T) = {1, 2, 3, 4, 5} and f(S) ∪ f(T) = {1, 2, 3} ∪ {1, 4, 5}.
Hence, f(S ∪ T)=f(S) ∪ f(T).
Now, f(S ∩ T) = {1} and f(S) ∩ f(T) = {1, 2, 3} ∩ {1, 4, 5} = {1}.
Therefore, f(S ∩ T) ⊆ f(S) ∩ f(T). (⊆ implies improper subset)
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Round 0.295833333 to the nearest hundredth
Answer:
The answer is 0.30.
I wish you luck in your assignments.
Answer:
0.3
Step-by-step explanation:
Since 5 rounds up, that would cause the 0.09 to become a 0.1, so it would be 0.3
TEXT ANSWER
How can you use the unit price to find the cost of 10
pounds of tomatoes? Please help
To find the cost of 10 pounds of tomatoes, multiply 10 by the unit cost of tomatoes.
What is the unit cost?
The cost a business incurs to create, store, and sell one unit of a specific product is known as the unit cost. All fixed and variable production expenses are included in unit costs. Cost units are a way to measure the quantity of a good or service.
Unitary method: The unitary method is a strategy for problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value.
The unitary method is used to find the unit cost of an object.
To find the cost of a unit object, multiply a by unit cost.
Given that, the unit cost of a unit pound of tomatoes.
The cost of 10 pounds of tomatoes is 10 × unit price of tomatoes.
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what is schur polynomial in numerical analysis.
Schur polynomials, named after Issai Schur, are certain symmetric polynomials in n variables, indexed by partitions, that generalize the elementary symmetric polynomials and the complete homogeneous symmetric polynomials.
What is Schur polynomial?Issai Schur gave the name Schur to a class of symmetric polynomials in n variables that generalize both the complete homogeneous symmetric polynomials and the elementary symmetric polynomials. They are the features of polynomial irreducible representations of the generic linear groups in representation theory. For the space of all symmetric polynomials, the Schur polynomials provide a linear basis. Any Schur polynomial product can be expressed as a linear combination of Schur polynomials with non-negative integral coefficients; these coefficients' values are supplied combinatorially by the Littlewood-Richardson rule. More generally, skew Schur polynomials are connected to pairs of partitions and share Schur polynomials' characteristics.To learn more about Schur polynomial refer to:
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What is the value of x? Show your work in arriving at your answer.
The value of x is 18.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
First, both angles shown are equal to each other.
5x + 5 = 95
Next, the opposite side of the equation to isolate x value (5x).
5x + 5 (-5) = 95 (-5)
5x = 90
Finally, we need to divide both sides of the equation by 5.
5x / 5 = 90 / 5
x = 18
The final answer: x = 18
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Use the graphs of f and g to graph h(x)=(f+g)(x). (Graph segments with closed endpoints).
The required graph of the function of h(x) is shown, where h(x) = |x| + |x + 2|.
What are functions?Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.
Here,
In the graph, functions f and g are absolute functions,
f = |x|
g = |x + 2|
So,
h(x) = f + g
Now substitue the functions,
h(x) = |x| + |x + 2|
Thus, the required graph of the function of h(x) is shown.
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if molly needs to cross a river 16 feet wide how long does she have to walk
Molly has to walk for 16/x minutes where x is the speed of molly.
What is the speed of an object?Speed is the rate at which an object's position changes, measured in meters per second. For example, if an object starts at the origin, and then moves three meters in three seconds, its speed is one meter per second. The equation for speed is simple: distance divided by time
Given here molly needs to cross a river 16 feet then let her speed be x and t be the time taken to cross the river
Then we have x=16/t
t=16/x
Hence, Molly has to walk for 16/x minutes where x is the speed of molly.
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The midpoint of JK is point L at (–1, 8). One endpoint is J(4, –15). Which equations can be solved to determine the coordinates of the other endpoint, K? Select two options. = –1 = 4 –15 + y1 =16 = y1
Using the formula of midpoint of a line, the coordinate of the endpoint k is (-6, 31)
What is Midpoint of a LineThe midpoint of a line is the point that is halfway between the two end points of the line. It can be found by taking the average (mean) of the x-values and the average (mean) of the y-values of the two endpoints.
The formula of midpoint of a line is given as;
M(x, y) = (x₂ + x₁) / 2, (y₂ + y₁) / 2
Since we have the midpoint and one endpoint, we can use the coordinate to find the missing coordinate.
The x - coordinate is calculated as;
-1 = (4 + x₁) / 2
-2 = 4 + x₁
x₁ = -2 - 4
x₁ = -6
The y - coordinates is calculated as;
8 = (-15 + y₁) / 2
16 = -15 + y₁
y₁ = 16 + 15
y₁ = 31
The coordinates of k is (-6, 31)
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What is the solution of the inequality shown
below?
a+5>-7
The required solution for the inequality a + 5 > -7 is (-12, ∞).
What is inequality?Inequality shows relation between two expression which are not equal to each others.
The given inequality is,
a + 5 > -7
To find the solution for the inequality,
Simplify the inequality,
a + 5 > - 7
a > - 7 - 5
a > -12
The value of a is greater than -12, implies that,
The solution for the value of the given inequality is (-12, ∞).
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"-12<-3x-15" less than or equal to 36
Answer:
-17 ≤ x < 1
Step-by-step explanation:
-12 < -3x - 15 ≤ 36
Add 15 to all 3 "sides."
-12 + 15 < -3x - 15 + 15 ≤ 36 + 15
3 < -3x ≤ 51
Divide all 3 "sides" by -3. Remember that when you multiply or divide an inequality by a negative number, you much change the direction of the inequality sign.
3/(-3) > -3x/(-3) ≥ 51/(-3)
-1 > x ≥ -17
Rewrite in standard order.
-17 ≤ x < 1
DIRECTIONS: Use this information to answer Parts A and B. The width of a rectangle is shown. The length is twice the width. Part A 5-1x Write an expression for the perimeter listing each side separately.
Therefore , the solution of the given problem of perimeter comes out to be the perimeter is represented by the expression of Perimeter = 30 -6x.
Define perimeter.In geometry, a shape's perimeter, or overall length, is referred to as its perimeter. The lengths of all a shape's sides and edges are added up to determine its perimeter.
Here,
Given : length = 5 - 1(x) or
=> length = 5-x
Width is twice the length
thus,
=>Width = 2(5-x)
=>Width = 10-2x
So ,To find the perimeter
We use,
=> Perimeter = 2(length + width)
=> Perimeter = 2( 5-x + 10-2x )
=> Perimeter = 2( 15 -3x)
=> Perimeter = 30 -6x
Therefore , the solution of the given problem of perimeter comes out to be the perimeter is represented by the expression of Perimeter = 30 -6x.
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