Output for the givin input for function f(x)=-5x+1, f (3) is -14.
What is function ?
A function is a type of rule that produces one output for a single input. Source of the image: Alex Federspiel. This is illustrated by the equation y=x2. Any input for x results in a single output for y. Considering that x is the input value, we would state that y is a function of x.
The characteristic that every input is associated to exactly one output defines a function as a relationship between a set of inputs and a set of allowable outputs. A mapping from A to B will only be a function if every element in set A has one end and only one image in set B. Let A & B be any two non-empty sets.
f(x)=-5x+1
Then, f(3)=-5*3+1
f(3)= -15+1
f(3)=-14
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∠A and \angle B∠B are complementary angles. If \text{m}\angle A=(2x-13)^{\circ}m∠A=(2x−13)
∘
and \text{m}\angle B=(2x+7)^{\circ}m∠B=(2x+7)
∘
, then find the measure of \angle A∠A.
The measure of ∠A is 29.
What is an angle?
An angle is a figure in plane geometry that is created by two rays or lines that have a shared endpoint. The Latin word "angulus," which meaning "corner," is the source of the English term "angle." The shared terminus of two rays is known as the vertex, and the two rays are referred to as sides of an angle.
Given that,
m∠A = (2x−13)° and m∠B = (2x+ 7)° and ∠A and ∠B are complementary angles.
Therefore
m∠A + m∠B = 90°
(2x−13)° + (2x+ 7)° = 90°
4x + 6 =90
Subtract 6 from both sides:
4x = 84
Divide both sides by 4:
x = 21
Putting x = 21 in m∠A = (2x−13)°:
m∠A = (2 × 21−13)°
m∠A = 29°
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2. How many points of inflection will f(x) = 3x5+2x4 - 5x - 12 have?
5
3
2
4
2 points of inflection will f(x) = 3x5+2x4 - 5x - 12 have.
What is Inflection points definition?
An inflection point is a point on the graph at which the second derivative is equal to zero or undefined and changes sign.
The characteristic that every input is associated to exactly one output defines a function as a relationship between a set of inputs and a set of allowable outputs. A mapping from A to B will only be a function if every element in set A has one end and only one image in set B. Let A & B be any two non-empty sets.
If [tex]$f^{\prime \prime}(x) > 0$[/tex]then f(x) concave upwards.
If [tex]$f^{\prime \prime}(x) < 0$[/tex]then f(x) concave downwards.
[tex]$$f^{\prime \prime}(x)=126 x^5+40 x^3$$[/tex]
Show Steps
Find intervals: Concave Downward: [tex]-\infty < x < 0$, Concave Upward: $0 < x < \infty$[/tex]
Plug x=0 into [tex]$3 x^7+2 x^5-5 x-12: \quad-12$[/tex]
(0,-12)
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Tabatha and Horatio each leave their separate houses and drive to a restaurant to meet for dinner. Tabatha lives 15 miles from the restaurant, and she drives at a rate of 3 miles every 2 minutes. The graph represents Horatio’s distance, in miles, y, from the restaurant after driving for x minutes.
Tabatha drives 1/12 mile more per minute than Horatio drives.
Tabatha drives 1/6 mile more per minute than Horatio drives
Tabatha drives 3 miles more per minute than Horatio drives.
Tabatha drives 9 miles more per minute than Horatio drives.
Answer:
Tabatha drives 1/6 mile more per minute than Horatio drives
Step-by-step explanation:
give a point estimate (mean) for the average height of all people at the place where you work. start by putting the 20 heights you are working with into the blue data column of the spreadsheet. what is your point estimate, and what does this mean?
A point estimate (mean) for the average height of all people at the place where you work is 62.26
Mean is the average of the given numbers and is calculated by dividing the sum of given numbers by the total number of numbers.
In statistics, the mean is one of the measures of central tendency, apart from the mode and median. Mean is nothing but the average of the given set of values. It denotes the equal distribution of values for a given data set.
Given,
Number of observations = 20
Mean = sum of all observation / number of observations
Mean = 66 +65 +66+ 67+ 62+ 70+ 69+ 68+ 71+ 78+ 61+ 62.5+ 64+ 64.2+ 64.3+ 58+ 60+ 63+ 65+ 66.2 / 20
Mean = 1245.2 / 20 = 62.26
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how to simplify this equation
Answer:
25x^2√(2x)
Step-by-step explanation:
2√(50x^5) + 5x√(18x^3) =
2√((2*25) * x^(4+1)) + 5x√((2*9) * x^(2+1)) =
2√(2 * 5^2 * x^4 * x^1) + 5x√(2 * 3^2 * x^2 * x^1) =
5*2√(2 * 1 * x^(2^2) * x) + 3*5x√(2 * 1 * x^2 * x) =
10√(2 * x^(2^2) * x) + 15*x*x√(2 * 1 * x) =
10√(2x * (x^2)^2) + 15*x^2√(2x) =
10x^2√(2x) + 15x^2√(2x) = 25x^2√(2x)
help me pleasee asappp
The median of the data sets 10, 11, 13, 18, 19, 21, 22, 25, 27, 30, 32 is 21.
How to find median?The Median is the "middle" of a sorted list of numbers. In other words, Median, in statistics, is the middle value of the given list of data when arranged in an order.
Therefore, let's find the median of the data sets.
Firstly, we have to sort the data in ascending order before we can find the median in the data set.
10, 11, 13, 18, 19, 21, 22, 25, 27, 30, 32
Hence, the sorted data set is 10, 11, 13, 18, 19, 21, 22, 25, 27, 30, 32.
Therefore,
median = 21
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A sightseeing tour bus can carry 72 people. If 420 people want to go sightseeing on the bus, what is the minimum number of trips the bus will have to make for everyone to go sightseeing?
4
7
6
5
The solution is Option D.
The minimum number of trips of buses to carry 420 people is 5 trips
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is given as
The number of people the tour bus can carry = 72 people
The total number of people who want to go sightseeing = 420 people
So , the equation will be
The number of trips of bus to carry 420 people = total number of people who want to go sightseeing / number of people the tour bus can carry
Substituting the values in the equation , we get
The number of trips of bus to carry 420 people = 420/72
The number of trips of bus to carry 420 people = 5.8
The number of trips of bus to carry 420 people = 5 buses
Therefore , the minimum number of buses is 5 buses
Hence , The minimum number of trips of buses to carry 420 people is 5 trips
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Given f(x) = x² - 1 and g(x) = x + 5, find h(x) = (f. g)(x).
The function h(x) = (f.g)(x) would be x² + 10x + 24.
What are composite functions?
A composite function is generally a function that is written inside another function. The composition of a function is done by substituting one function into another function. For example, f [g (x)] is the composite function of f (x) and g (x). The composite function f [g (x)] is read as “f of g of x”.
To find h(x) = (f.g)(x), we need to find the composition of the functions f(x) and g(x).
The composition of two functions f(x) and g(x) is denoted by (f.g)(x) and is defined as (f.g)(x) = f(g(x)).
In this case, we have:
h(x) = (f.g)(x) = f(g(x)) = f(x + 5)
Substituting x + 5 for g(x) in the equation for f(x), we get:
h(x) = (f.g)(x) = f(x + 5) = (x + 5)² - 1
Simplifying this expression, we get:
h(x) = (f.g)(x) = x² + 10x + 24
Hence, the function h(x) = (f.g)(x) would be x² + 10x + 24.
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HELPPPPP ME NOW PLEASE
Write y=1/8x+7 in standard form unsung integers.
A. 8x-y=56
B. -x+8y=56
C. -x-8y=56
D. -x+8y=56
Answer:
-x + 8y = 56
Step-by-step explanation:
.................
A company has two manufacturing plants with daily production levels of 8x + 15 items and 3x-7 items, respectively. The first plant produces how many more items daily than the second plant?
The first plant produces more items daily than the second plant
(Simplify your answer)
CETTE
What’s the answer
To find the difference in the number of items produced by the two plants, we can subtract the production level of the second plant from that of the first plant. This gives us:
[tex]8x + 15 - (3x - 7) = 5x + 22[/tex]Therefore, the first plant produces [tex]5x + 22[/tex] more items daily than the second plant.
An online furniture store sells chairs for $100 each and tables for $400 each. Every
day, the store can ship no more than 18 pieces of furniture and must sell no less than
$2900 worth of chairs and tables. Also, the store must sell a minimum of 10 tables. If
a represents the number of tables sold and y represents the number of chairs sold,
write and solve a system of inequalities graphically and determine one possible
solution.
PLS INCLUDE THE INEQUALITIES
y ≥ 0 , Zero possible solution.
What is inequality ?
In mathematics, an inequality represents the connection between two values in an imbalanced algebraic statement. A sign of inequality can be used to show that one of the two variables is larger than, greater than or equal to, less than, or equal to another value.
According to question
a represents the number of tables sold and y represents the number of chairs sold
Using a and y as variables, we get
a + y ≤ 18
100y + 400a ≥ 2900
Simplified,
100(y + 4a) ≥ 2900
y + 4a ≤ 29
Given the minimum number of tables that need to be sold, we evaluate using a = 10
y + 4(10) ≥ 29
y ≥ -11
y represents the number of chairs sold
therefore, y ≥ 0
Since we can't purchase -11 chair, we round up our result giving us y ≥ 0
Now
the store must sell a minimum of 10 tables and tables for $400 each
then
10*400 = $4000
which is more than worth of chairs and tables $2900
hence Zero possible solution.
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two thirds of a number b is no more than 12.
two thirds of a number b which is no more than 12, is b ≤ 18
What is inequality ?
In mathematics, an inequality represents the connection between two values in an imbalanced algebraic statement. A sign of inequality can be used to show that one of the two variables is larger than, greater than or equal to, less than, or equal to another value.
According to question
two thirds of a number b = (2/3)b
Given two thirds of number b is no more than 12
⇒ (2/3)b ≤ 12
⇒ 2b ≤ 12*3
⇒ b ≤ (12*3)/2
⇒ b ≤ 36/2
⇒ b ≤ 18
hence the number b whose 2/3 is no more than 12 is, b ≤ 18
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12. What is the maximum value of a periodic
function with amplitude 6.5 and minimum
value 7?
The maximum value of the periodic function with amplitude 6.5 and minimum value 7 is 13.5.
What is a periodic function?
The time interval between two waves is known as a Period whereas a function that repeats its values at regular intervals or periods is known as a Periodic Function.
The maximum value of a periodic function with amplitude 6.5 and minimum value 7 is equal to the sum of the amplitude and the minimum value.
The amplitude of a periodic function is defined as the maximum distance that the function deviates from its centerline. In this case, the amplitude of the function is 6.5.
The minimum value of a function is the lowest value that the function takes on over a given period. In this case, the minimum value of the function is 7.
To find the maximum value of the function, we need to add the amplitude and the minimum value. The maximum value is equal to 6.5 + 7 = 13.5.
Hence, the maximum value of the periodic function with amplitude 6.5 and minimum value 7 is 13.5.
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Given the equation 7m − 11 = 5m + 43 and the possible solution set S: {2, 27, 54, 86}:
Part A: Determine which integer(s) in the solution set makes the equation false. Show all work. (8 points)
Part B: Use a complete sentence to explain how you were able to determine which values make the equation false. (4 points)
A) The integers that make the equation false are {2, 54, 86}
B) We found that by solving the linear equation.
Which integer makes the equation false?
Here we have the following linear equation:
7m - 11 = 5m + 43
And the set of the possible solutions is S: {2, 27, 54, 86}
The simplest way to see which integer makes the equation false, we just need to replace the values of the possible solution sets and see which ones give a false equation.
Another method is to simplify the equation, and i will do that:
7m - 11 = 5m + 43
7m - 5m = 43 + 11
2m = 54
m = 54/2
m = 27
So the equation has a single solution, m = 27.
Then the integers that make the equation false are {2, 54, 86}
B) We determined the only true solution for the linear equation, and thus, all the other possible integers aren't solutions, thus, make the equation false.
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Last winter, a store sold 408 coats in
3 months. This winter, the store plans to sell
coats for 4 months. Based on the average
number of coats sold each month last winter,
how many total coats should the store plan to
sell this winter?
Total coats should the store plan to sell this winter is 952.
Last winter, a store sold 408 coats in 3 months. This winter, the store plans to sell coats for 4 months.
What is sell?
Determine the total cost of all the purchased units. To find the cost price, divide the total cost by the quantity of units purchased. To get the final price, use the formula for selling price (SP), which is: SP = CP + Profit Margin. The cost of the commodity will then be increased by the margin to determine the proper pricing. Retail math describes the mathematical techniques or formulae utilised in the sales industry. It is earning money or receiving change in the most basic sense. Business owners, retailers, managers, and sales representatives all utilise retail math in their daily work.
3month = 408 coats
1 month = 408/3 =136 coats
Then, 4 months = 136*4 = 544 coats
Total coats should the store plan to sell this winter = 544+408 = 952.
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Given the function f(x) = 3(x – 5) + 8, which of the following represents f–1(x)?
Step-by-step explanation:
f(x) = 3(x - 5) + 8
f-1(x) = -1(3(x - 5) + 8)
= -3(x - 5) - 8
= -3x + 15 -8
= -3x + 7
Find the perimeter and total area of the composite shape shown below. All measurements are given in inches. Use = 3.14 in
any formulas used.
The area of the composite shape is 292.96 in² and the perimeter of the composite shape is 65.12 inches
Area of Half circle:The quantity of surface contained within a semicircle's perimeter is known to as its area.
The formula for the Area of a half circle with a Radius (r) is given by
Area of Half circle = πr²/2
The formula for the perimeter of a half circle with a radius (r) is given by
Perimeter of Half circle = πr
Here we have
A picture of a Rectangle with a half circle
Dimensions of Rectangle = 16 in × 12 in
=> Area of rectangle = 16 in × 12 in = 192 in²
=> Perimeter of rectangle shape = 12 + 16 + 12 = 40 inches
[ Here we only take one side of the rectangle since one of the sides is connected with a Half circle ]
The radius of half circle = 8 inch
=> Area of Half circle = π(8)² = (3.14)(64)/2 = 100.96 in²
=> Perimeter of Half circle = πr =(3.14)(8) = 25.12 in
Area of the composite shape
= Ractangle's Area + Half circle's Area
= 192 in² + 100.96 in²
= 292.96 in²
The perimeter of the composite shape
= Ractangle perimeter + Half circle perimeter
= 40 inches + 25.12 inches
= 65.12 inches
Therefore,
The area of the composite shape is 292.96 in² and the perimeter of the composite shape is 65.12 inches
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If A=45° B = 30°, prove that
Sin (A-B) = sinAcos B - Cos Asin B
To prove that Sin (A-B) = sinAcos B - Cos Asin B, we can use the angle subtraction formula for sine:
Sin (A-B) = Sin A Cos B - Cos A Sin B
This formula is derived from the identity:
Sin (A-B) = Sin A Cos B - Cos A Sin B
which can be derived by using the double angle identities for sine and cosine:
Sin (2A) = 2 Sin A Cos A
Cos (2A) = Cos^2 A - Sin^2 A = 2 Cos^2 A - 1 = 1 - 2 Sin^2 A
Substituting these identities into the identity above, we get:
Sin (A-B) = Sin A Cos B - Cos A Sin B
What is an angle subtraction?Angle subtraction formulas is otherwise known as angle subtraction identities. This angle subtraction formulas permit us to find the exact values of less common trigonometric angles by expressing the less common angle as the difference of two common angles. For example, 15 degrees = 45 degrees - 30 degrees.
Therefore, Sin (A-B) = sinAcos B - Cos Asin B.
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lonzo borrowed 15000$ at 1.2% simple interest to buy a car . after 9 months how much will lonzo owe the bank in interest
The simple interest implies that Lonzo owes $1513.5
How to determine the amount Lonzo owes?The given variables can be represented as:
Loan amount P = $1500
Rate of interest, R = 1.2%
Time to pay back the loan, t = 9 months i.e. 0.75 year
The amount from a simple interest can be calculated using:
A = P(1 + RT)
Substitute the known values in the above equation, so, we have the following representation
A = 1500 * (1 + 1.2% * 0.75)
Evaluate
A = 1513.5
Hence, the amount owed is $1513.5
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Seven days a year, Tiger Stadium becomes the fifth largest city in the state of Louisiana. Over 92,000 fans pack the stadium to watch the Tigers play. After the game, if the fans leave at a rate of 10% per minute, how long will it take before the stadium is half empty?
It will take 5 minutes before the stadium is half empty
Given that:
Over 92,000 fans pack the stadium to watch the Tigers play
The fans leave at a rate of 10% per minute
The number of fans that leave per minute will be:
10% of 92,000 = 10/100 × 92, 000 = 9,200
The stadium will be fully empty in:
time = 92,000/9,200 = 10 minutes
The stadium will be half empty in:
time = 10 minutes / 2 = 5 minutes
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The table shows the scores of two teams at the end of the first half of a trivia challenge.
Team Points Scored
Bobcats 2x−7
Huskies 5x−3
How many more points did the Huskies score than the Bobcats?
The point difference between Huskies and Bobcats are 3 x + 4.
What is algebra ?The area of mathematics known as algebra is used to portray situations or problems using mathematical expressions. In algebra, we utilize integers with fixed or definite values, such as 2, 7, 0.068, etc. In algebra, we combine integers with variables like x, y, and z.One-step equations can be solved in four different ways: by adding, subtracting, multiplying, and dividing. In an equation, both sides will stay equal if we add the same amount to either side.The sequence in which you perform operations in arithmetic and algebra is governed by a number of rules. The Commutative, Associative, and Distributive Laws are the three that receive the most attention.Given data :
Difference = Huskies - Bobcats
Hence,
( 5x - 3 ) - ( 2x - 7 )
= 5x - 3 - 2x + 7
= 3x + 4
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find the least commmon multiple (LCM) for each pair of numbers.To solve the riddle the letters to the numberd lines below 2,5 3,15 6,12 2,15 2,3 8,24 4,10 6,9 7,9
The LCM of the given pairs are 10, 15,12,30,6,24,20,18, and 63 respectively.
What is LCM?The least common multiple (LCM) of two numbers is the lowest possible number that can be divisible by both numbers.
There are 9 pairs, so let's name them using the letters A to I.
The LCM of the first pair A (2, 5) is 10.
The LCM of the pair B (3, 15) is 1*3*5 = 15.
The LCM of the pair C (6, 12) is 3*2*1*2 = 12.
The LCM of the pair D (3, 15) is 2*3*1*5 = 30.
The LCM of the pair E (2, 3) is 1*3*2 = 6.
The LCM of the pair F (8, 24) is 2*2*2*1*3 = 24.
The LCM of the pair G (4, 10) is 2*2*5 = 20.
The LCM of the pair H (6, 9) is 3*2*3 = 18.
The LCM of the pair I (7, 9) is 7*9 = 63.
Hence, 10,15,12,30,6,24,20,18,63 are the LCM of the given pairs.
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an item is regularly priced at . it is on sale for off the regular price. how much (in dollars) is discounted from the regular price?
An item is regularly priced at, 1.98$ is discounted from the regular price.
A percentage is a portion of a whole expressed as a number between 0 and 100 rather than as a fraction. All of something is 100 percent, half of it is fifty percent, none of something is zero percent. To determine a percentage, you divide the portion of the whole by the whole itself and multiply by 100.
Given that,
First, change the percentage into decimal:
Let us assume,
Sale of regular price = 1%
1% = 1/100 = 0.01
Assume, item regular price is = 2$
Multiply 2 with 0.01:
2 * 0.01 = 0.02
Note that this number 0.02 (0.01 of 2) is the amount off from the original price (2). Subtract 2 from 0.02
2 - 0.02 = 1.98
Therefore,
An item is regularly priced at, 1.98$ is discounted from the regular price.
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3. Solve the
proportion
x : 15 = 29 : 9.6
The required value of x for the given proportion is 45.31
What is proportion?
Proportion is a mathematical relationship or ratio between two or more values. It is used to compare the size, quantity, or degree of two or more objects or measurements. Proportion can be expressed as a fraction, decimal, or percentage. It is often used in geometry, algebra, and calculus to determine the size of a shape or to solve an equation. Proportion is also used in statistics to compare data sets. In everyday life, proportion is used to make sure that items are in good balance with each other. For instance, proportions are used when baking a cake or making a recipe to ensure that the ingredients are properly combined.
Given, the proportion
x : 15 = 29 : 9.6
or, x = [tex]\frac{29}{9.6}[/tex] × 15
or, x = 45.31
Hence, the required value of x for the given proportion is 45.31
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what is the value of the expression 3^{2}*(2^{3} +4)-22
Answer:
86
Explanation:
3² × (2³ + 4) - 22
9 × (8 + 4) - 22
9 × 12 - 22
108 - 22
86
A new streaming service sent out a survey to 350 households to see who would be interested in its service. The company found that it could charge $55 per month, with a margin of error of ±1.3. If 1,000 people signed up for the service, what is the least amount of monthly revenue the company should expect?
$52,815
$53,700
$54,915
$56,300
Answer:
B) $53700-------------------------------------
The charge of $55 with error margin of ± 1.3 results in the least value of $(55 - 1.3) = $53.7 and greatest value of $(55 + 1.3) = $56.3.
If 1000 people signed up for the service, then the least total amount is:
$53.7*1000 = $53700Correct choice is B.
Write an equation of the line that passes through the points.
4.(-3,0), (-2, 3)
5. (-6, 10), (6, -10)
4.
find slope;
3 - 0/-2 -(-3) = 3/1 = 3
y = 3x + b
0 = (3)(-3) + b
0 = -9 + b
b = 9
y = 3x + 9
3. The vertices for A LML are L(-4,0), M(-2,0) and N(-3,-3). Its image is L'(1,1), M'(3,1) and
N'(2,-2). What is the translation rule that maps the preimage to the image?
The translation rule that maps the preimage to the image is (x, y) ⇒ (x + 5, y + 1)
How to determine the translation rule of the transformationFrom the question, we have the following parameters that can be used in our computation:
Pre-image: L(-4,0), M(-2,0) and N(-3,-3)
Image: L'(1,1), M'(3,1) and N'(2,-2)
The translation rule is calculated as
(x, y) = L' - L
Substitute the known values in the above equation, so, we have the following representation
(x, y) ⇒ (x + 1 + 4, y + 1 - 0)
Evaluate
(x, y) ⇒ (x + 5, y + 1)
Hence, the translation is (x, y) ⇒ (x + 5, y + 1)
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Analise's resting heart rate is 75 beats per minute. When she sleeps, it slows to 60 beats per minute. What percent decrease is this?
Answer:
20% decrease
Step-by-step explanation:
[tex]\frac{75-60}{75}[/tex]
[tex]\frac{15}{75}[/tex] = .2 to make a percent, multiply by 100 = 20%
the sum of the sequence 7+21+63..... to the 9th term
68,887 is the sum of the sequence (7+21+63...) to the 9th term.
That is, the sequence (as far as we are given) has a common ratio r=3, between successive terms. The initial term a= 7 and we are interested in the sum to N = 9 terms.
and the sum of the 9th term is
[a^n = a( 1 - r^N)/1 - r ]
=[7 ( 1 - 3^9 )/ 1 - 3 ]
=7 ( 1 - 19683) / -2
= - 137,774 / -2
= 68,887
9th term = 68,887
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