f(x) = 4. 8x² function can be used to compute the approximate area, in square inches, of a stop sign if it has a side length of x inches.
What do function and example exactly mean?A function, which produces single output from either a single input, is an illustration of a rule. Alex Federspiel was contacted to collect the image. An illustration of this is the equation y=x2. For each input of x, there is simply one output of y. Considering that x is actually the input value, we would claim that y is just a rational number.
Briefing:area = (# of sides * side length^2) / [4 * tan (180/n)]
area = (8 * x^2) / 4 * tan (22.5)
area = 8 x^2 / (4 * 0.41421)
area = 8 x^2 / 1.65684
area = 4.8 x^2
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What are the domain and range of the function f(x)= x^2-3x-28/x+4?
The domain will be D:{x ∈ R| x ≠ 4} and the range will be R:{y ∈ R| y ≠ 11}. Then the correct option is A.
What are domain and range?The domain means all the possible values of x and the range means all the possible values of y.
The function is given below.
f(x) = (x² - 3x - 28) / (x + 4)
Simplify the function, then we have
f(x) = (x² - 7x + 4x - 28) / (x + 4)
f(x) = [x(x - 7) + 4(x - 7)] / (x + 4)
f(x) = [(x + 4)(x - 7)] / (x + 4)
f(x) = x - 7
The Domain of the function is all real numbers except 4. And the range of the function is all real numbers except 11.
The domain will be D:{x ∈ R| x ≠ 4} and the range will be R:{y ∈ R| y ≠ 11}. Then the correct option is A.
The diagram is given below.
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Add the equations.
3x - y = -5
7x + y=15
A. -4x = 10
B. -4x = -20
C. 10x = 10
D. 10x-2y = -20
The addition of the given system of equations is 10x = 10.
What is system of equations?
A set of one or more equations involving numerous variables is referred to as a system of equations. The variable mappings that satisfy all component equations are the solutions to systems of equations, or the points where the components of these equations intersect.
Consider the given system of equations
3x - y = -5 ..(1)
7x + y = 15 ..(2)
We have to find the addition of this equations.
Add equation (1) and equation (2).
3x - y = -5
+ 7x + y = 15
____________
10x + 0 = 10
Hence, the addition of the given system of equations is 10x = 10.
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Please helpp absolute value
-|f| = -16
A) no solution
B) one solution
C) two solution
If a researcher wants to use a control group whose participants receive a placebo pill as well as an experimental group whose participants receive a new treatment medication, which type of statistical test is most appropriate for analyzing the results and why?.
The t-test is appropriate because it can handle small sample sizes and is robust to violations of normality assumptions.
What are Statistical Tests?Mathematical statistical tests are techniques for data analysis and drawing conclusions about a population from a sample. These tests employ mathematical formulae and probability theory to assess if a participant's result is statistically significant, implying that it is unlikely to have happened by chance. Comparing two or more groups, figuring out how variables relate to one another, and assessing the accuracy and validity of data may all be done using statistical tests. They are frequently used to derive inferences from experimental or observational data in disciplines including psychology, economics, and sociology.The outcomes of these tests are used to determine whether to accept or reject a hypothesis and can offer important insights into the underlying patterns and relationships in data.
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x² + 13x + 12 factorise
x²+ 12x + 1x + 12
x(x+12) + 1(x+12)
(X+1) (X+12)
For each equation, determine whether it is linear.
(a) y=4
Equation
(b) y=-4x²+3
(c) y=7x+2
(d) y=-x
Is the equation linear?
Yes
No
Answer:
(a) yes
(b) no
(c) yes
(d) yes
Step-by-step explanation:
You want to know which of these equations is linear.
y = 4y = -4x² +3y = 7x +2y = -xLinear equationFor the purpose here, we will define a linear equation as one that graphs as a straight line. (Other definitions may give different answers.)
In general, a linear equation will have a highest degree of 1. (It may be 0.)
The equation of choice (b) has degree 2, so is not a linear equation.
GraphThe attached graph shows the only equation that is not linear is choice (b).
__
Additional comment
In some branches of mathematics, an equation of the form y = mx+b is not a linear equation. In basic algebra, that is the model of a linear equation, for any values of m and b.
How might you use a perpendicular bisector or an angle bisector in your everyday life?
And why would an orthocenter be the most difficult part of a triangle for someone to identify and use?
You use a perpendicular bisector or an angle bisector in your everyday life and orthocenter be the most difficult part of a triangle.
Everyday life example :
On a clock, the second hand in the middle of the hour hand and minute hand, is working as the angle bisector.
For a perpendicular bisectors, take two ends of a compass needle, with the long end on the North, the short end is pointing South, and the lines of East and West are on the left and right.
Orthocenter :
The orthocenter is the point of intersection of the three altitudes of a triangle. It is the hardest part of the triangle to find because :
It can lie inside a triangle or outside the triangle as it depends on the type of type of the triangle whether it is acute or obtuse. So, in order to identify it we must first know the type of the triangle.
And secondly, the formula for finding orthocenter is quite complicated so it is the hardest part of the triangle to identify and use.
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Suppose a sightseeing tour company charges $7.50 for each hour you rent a motorized scooter, plus a non-refundable fee of $45. Write an equation that represents the total cost, y, of renting the scooter in relation to the number of hours, x.
An equation that plots the total cost, y, of renting the scooter against the duration, x is y=7.50x+45
What is meant by an equation?3x - 5 = 16 is an illustration of an equation. By solving for x, we discover that the variable's value is 7, or x = 7. By deleting parenthesis and merging related terms, you can simplify either side of an equation and obtain the solution. Together with the variables for which the equation must be solved, the values of the variables that must satisfy the equality to compose the answer are referred to as the unknowns. Equations can be categorized as identities or conditional equations. An identity holds true regardless of the value given to the variables. A conditional equation's variables can only have specific values that produce the truth.
Given,
You must pay a non-refundable $45, plus $7.50 per hour, to rent a motorized scooter from a sightseeing tour company.
The equation is y=7.50x+45
Therefore, a formula that plots the total cost, y, of renting the scooter against the duration, x is y=7.50x+45.
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Hello factor the polynomial completely with steps please
The factor form of the cubic equation y = x³ + 3 · x² + x + 3 is y = (x² + 1) · (x + 3).
How to factor a cubic equation
In this problem we find a cubic equation, that is, a polynomial of the form:
y = a · x³ + b · x² + c · x + d
Where a, b, c, d are the real coefficients of the polynomial. Herein we must use algebra properties to find the factor form of the expression:
y = a · Π (x - rₙ) for n = {1, 2, 3, ..., m - 1, m}
Where:
a - Lead coefficient.m - Grade of the polynomial.First, write the entire equation:
y = x³ + 3 · x² + x + 3
Second, use distributive property of real mumbers:
y = x² · (x + 3) + 1 · (x + 3)
Third, use distributive property of real numbers once again:
y = (x² + 1) · (x + 3)
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50th term: –9, 2, 13, 24, 35, ... ______________
Answer: :/ listen to the lesson
Step-by-step explanation:
Answer: the 50th term is 530
Step-by-step explanation:
it increases by 11 each time so 11*49
539 subtract by nine since it starts at -9
530
I am purchasing a smart TV for $648.
I have a coupon for 40% off.
Find the sale price.
Answer:
$1080
Step-by-step explanation:
Since we have 40% off 60 percent of the price is $648 so we can make ratios
60/100=648/x
Cross multiply
60x=100(648)
60x=64800
/60. /60
x=1080
Sales price is $1080
Hopes this helps please mark brainliest
y = 1/4x+1 y =1/4x-1
How many solutions does this system
of equations have?
Answer:
3
Step-by-step explanation:
3 because you have to find x, you have to find x and y and then the overall answer
The given system of equations,
y = 1/4 x + 1
y = 1/4 x - 1
has no solution.
Given a system of equations.
There are two equations in the system.
We have to find the number of solutions for the system if it exists.
Consider the equations,
y = 1/4 x + 1
y = 1/4 x - 1
Since both the equations are in y value, they are equal.
1/4 x + 1 = 1/4 x - 1
1/4 x - 1/4 x = -1 - 1
0 = -2
This is not possible.
This means that the given system has no solution.
Hence the given system of equations has no solution.
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A city is building a fence around a rectangular playground. If the perimeter of the playground is 90 feet and the length of one side of the fence is 26 feet, what is the width of the playground?.
We can conclude that the width of the rectangular ground is 19ft.
What is a rectangle?A quadrilateral with all of its angles equal, or right angles, is a rectangle.
In addition to having all equal angles, a square also has all equal sides. Therefore, a special case of a square is a rectangle.
To put it another way, a rectangle can also be a square.
So, we know that:
The perimeter of the rectangular ground is 90ft.
The length of the rectangular ground is 26ft.
Now, the width will be:
Perimeter of rectangle formula: P = 2(l+w)
Now, put the values and substitute as follows:
P = 2(l+w)
90 = 2(26+w)
90 = 52 + 2w
2w = 90 - 52
2w = 38
w = 38/2
w = 19ft
Therefore, we can conclude that the width of the rectangular ground is 19ft.
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Which one doesn't belong?
1. 5 + 7 = 7 + 5
2. 5 * 7 = 7 * 5
3. 2 = 7 - 5
4. 5 - 7 = 7 - 5
Write a post sharing which equation you think doesn't belong and why.
Answer:
3 does not belong because its not long enough
find a recurrence relation for the number of bit strings of length n that contain three oconsecutive 0
A recurrence relation is an equation in mathematics that states that the nth term of a series of numbers is equal to some combination of the terms that came before it.
What is recurrence relation ?A recurrence relation is an equation in mathematics that states that the nth term of a series of numbers is equal to some combination of the terms that came before it.
For a parameter k that is independent of n, only k preceding terms of the sequence frequently occur in the equation; this number k is known as the order of the relation.
The rest of the series can be determined by continually using the equation if the values of the first integers in the sequence have been provided.
The nth term in linear recurrences is equivalent to a linear function of the k prior terms. The Fibonacci numbers' recurrence is a well-known example.
Hence, A recurrence relation is an equation in mathematics that states that the nth term of a series of numbers is equal to some combination of the terms that came before it.
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help me pleaseeeeeeeeeeeeeeeeeeeeee!!!!!!!!!!!!!!!!
Answer:
5% of $1100 = 55
Year given = 7
So, 55 × 7 = 385
She would get after 7 years all total = (1100 + 385) = $1485
Write the following expression using an exponent. (2y-9) (2y-9) (2y-9) (2y-9) (2y-9)
For the given expression the exponent would be [tex](2y-9)^5$[/tex].
What is an exponent?
An exponent is a number that indicates how many times a base number should be multiplied by itself. For example, in the expression 2³, the base is 2 and the exponent is 3. The exponent indicates that the base should be multiplied by itself 3 times, so the value of the expression is 2 * 2 * 2 = 8.
The given expression is
= (2y-9) (2y-9) (2y-9) (2y-9) (2y-9)
Exponent expression = [tex](2y-9)^5$[/tex]
Hence, for the given expression the exponent would be [tex](2y-9)^5$[/tex].
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For the given expression the exponent would be (2y-9)⁵.
What is an exponent?
An exponent is a number that indicates how many times a base number should be multiplied by itself. For example, in the expression 2³, the base is 2 and the exponent is 3. The exponent indicates that the base should be multiplied by itself 3 times, so the value of the expression is 2 * 2 * 2 = 8.
The given expression is
= (2y-9) (2y-9) (2y-9) (2y-9) (2y-9)
Exponent expression = (2y-9)⁵
Hence, for the given expression the exponent would be (2y-9)⁵.
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one year, the population of a city was 359,000. several years later it was 420,030. find the percent increase.
Answer:
17%
Step-by-step explanation:
seasonality causes comparability problems in ratio analysis. a common solution is to use an average account balance as opposed to an ending account balance. t or f
The given statement is true.
Seasonal inventory or revenue fluctuations that are not based on sales can artificially inflate or deflate the value of the company's assets.
What is Seasonal inventory ?
Products with a seasonal inventory are those that sell more frequently at particular times of the year. Weather, events, and holidays can affect how much demand there is for these products.
Holiday merchandise was probably your first thought when thinking about seasonal inventory. Labor Day weekend, Halloween, and Christmas are a few examples of holiday inventory. Every one of them sells particular goods that people only purchase around the holidays.
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An item on sale costs 45% of the original price. The original price was $39.
Use the ALEKS calculator to find the sale price.
$0
X
S
The sales price of the item is $17.55
How to determine the sales priceFrom the question, we have the following parameters that can be used in our computation:
Sales price = 45% of the original price
The original price = $39
The above parameters mean that
Sales price = 45% * original price
Substitute the known values in the above equation, so, we have the following representation
Sales price = 45% * $39
Evaluate
Sales price = $17.55
Hence, the sales price is $17.55
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In which choice is y a function of x?
A (-2, 3), (0, 2), (-1, 1), (0, 0)
B. (4, 1), (1, 4), (-4, 1), (1, 4)
C. (4, 1), (4, 2), (4,3), (4,4)
D. (0, 2), (1, 1), (3, 0), (0, -2)
Answer:
B. (4, 1), (1, 4), (-4, 1), (1, 4)
Step-by-step explanation:
A mixed number is a number consisting of a whole number and a proper fraction.
It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 1 × 4 = 4. In the following intermediate step, it cannot further simplify the fraction result by canceling. In other words - four minus one quarter is fifteen quarters.
a rhombus has sides of length 51 units each and a shorter diagonal of length 48 units. what is the length, in units, of the longer diagonal?
The length of the longer diagonal of the given rhombus with side length 51units and shorter diagonal 48 units is equal to 90units.
As given in the question,
Side length of the given rhombus 's' = 51 units
Length of the shorter diagonal of given rhombus 'a' = 48 units
Let us consider length of the longer diagonal of the given rhombus be 'b'
As per the property of the rhombus:
Diagonals of the rhombus bisects each other at right angle
Triangle formed by side length bisecting diagonals is right angled triangle.
Using Pythagoras theorem we have,
(Side length)² = (a/2)² + (b/2)²
Substitute the values
⇒ (51)² = (48/2)² + (b/2)²
⇒2601 = 576 + (b/2)²
⇒(b/2)² = 2601 -576
⇒(b/2)² = 2025
⇒b/2 = √2025
⇒ b/2 =45
⇒ b = 90units
Therefore, the length of the longer diagonal of the given rhombus is equal to 90units.
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Mr. Reynolds is a car salesman. He makes a salary of $55,000 a year. He
also earns a commission of of his total sales for the year. This year, Mr.
Reynolds has a sales total of $295,200. Write and evaluate a function to find
Mr. Reynolds's total earnings for the year.
Answer:you speak French pls
Step-by-step explanation:
:::
The Morgan family and the Collins family each used their sprinklers last summer. The Morgan family's sprinkler was used for 35 hours. The Collins family's sprinkler was used for 40 hours. There was a combined total output of 1725 L of water. What was the water output rate for each sprinkler if the sum of the two rates was 45 L per hour?
Answer:
you have to multiply 45^2
2025
What is the rate of change of the function Y= -3/2x + 2 PLEASE HELP I MEED HELP ASAP
Answer:
-3/2
Step-by-step explanation:
rate of change is slope
Order these numbers from least to greatest: 0, 1,
1
2
8
610
9
49
100
11
20
1
13
Answer:
100
Step-by-step explanation:
I did the test
Which relation is not a function?
Answer: C, the table.
Step-by-step explanation:
In a function, there can only be one output (y) per input (x), but you can have multiple inputs (x) per one output (y).
Using this logic, we see that the answer is;
C
Consider the following points on the graphs of y = sin(x) and y = sin(2x), with the added vertical dashed lines:
What are c and d in that order?
From the given graphs the values of c and d are, c = 0.53,
d = 0.95.
What is sinusoidal wave?
A mathematical curve defined in terms of the sine trigonometric function, of which it is the graph, is known as a sine wave, sinusoidal wave, or simply sinusoid. It is a smooth periodic function and a particular kind of continuous wave.
Let the graphs of y = sin(x) and y =sin(2x) are given.
From this graphs we have to find the value of c and d.
First from y = sin(x) to find the value of 'a'.
consider the point [tex](a, -\frac{4}{5})[/tex]
⇒
[tex]sin(a) = -\frac{4}{5} \\a = sin^-^1(-\frac{4}{5})\\ a = -53.13[/tex]
Now to find the value of 'c'.
Plug a = -53.13 in y = sin(2x)
[tex]sin(2a) = c\\sin(2(-53.13)) = 0.52622\\sin2a= 0.53[/tex]
Hence, the value of 'c' is c = 0.53.
Now to find the value of d.
First y = sin(x) to find the value of b.
Consider, the point [tex](b, \frac{5}{13})[/tex]
⇒
[tex]sinb = \frac{5}{13} \\b = sin^-^1(\frac{5}{13})\\ b = 22.62[/tex]
Now to find value of d.
Plug b = 22.62 in y = sin(2x)
[tex]sin(2b) = d\\sin(2(22.62)) = 0.95138\\sin(2b) = 0.95[/tex]
So, the value of 'd' is 'd = 0.95'.
Hence, from the given graphs the values of c and d are, c = 0.53,
d = 0.95.
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w(5)=w(-5) true or false
Answer: False
Step-by-step explanation:
w(5) = 5w
w(-5) = -5w
These aren't the same expressions.
Hope this helps!!! :)
How many gallons of rocket fuel containing 80% liquid oxygen must be mixed with 250 gallons containing 40% liquid oxygen to produce a mixture containing 70% oxygen? PLSSSS EXPLAIN!!!!
750 gallon of fuel at 80% to mix with the 250 gallon at 40% in order to get a mixture at 70% liquid oxygen.
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity
We need to find how many gallons of 80%
8x, since we don't know how many gallons
mixed with 250 gall of 40%: 0.40(250)
and we want a mix at 70%. The mix will include the 0.8x and the 0.4(250) Like this:
8x+0.4(250)=0.7x+0.7*250
Multiply on both sides of the equation
0.8x+100= 0.7x+175 Subtract 100 on both sides
0.8x= 0.7x+75
Subtract 0.7 on both sides
0.1x= 75
Divide both sides by 0.1
x= 750
You need 750 gallon of fuel at 80% to mix with the 250 gallon at 40% in order to get a mixture at 70% liquid oxygen.
Hence, 750 gallon of fuel at 80% to mix with the 250 gallon at 40% in order to get a mixture at 70% liquid oxygen.
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