The linear function can be represented by slope intercept form, point slope form and standard form.
Given,
Linear function;
A straight line on the coordinate plane is represented by a linear function. As an illustration, the equation y = 3x – 2 depicts a linear function because it is a straight line in the coordinate plane. This function can be expressed as f(x) = 3x - 2 since y can be replaced with f(x).
We can represent linear function by;
The slope intercept form, point slope form, and standard form can all be used to express a linear function.
Slope intercept form;
The equation of a straight line in the form y = mx + b where m is the slope of the line and b is its y-intercept.
Point slope form;
The equation of a straight line that passes through a particular point and is inclined at a specific angle to the x-axis can be found using the point slope form.
Standard form;
Ax+By=C is the usual form for two-variable linear equations. A standard form linear equation is, for instance, 2x+3y=5. When an equation is given in this format, finding both intercepts is rather simple (x and y). When attempting to solve systems involving two linear equations, this form is also quite helpful.
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Where is the function decreasing?
The function decreases when x is less than –7.
The function decreases when x is greater than –6.
The function decreases when x is between 0 and 4.
The function decreases when x is between –6 and 0.
The linear function decreases when x is between –6 and 0.
Linear FunctionAn equation can be represented by a linear function. The standard form for the linear equation is: y= mx+b , for example, y=5x+2. Where:
m= the slope.
b= the constant term that represents the y-intercept.
For the given example: m=5 and b=2.
A function can be classified as:
increasing - when the values of y increase with the increasing of x-values decreasing - when the values of y decrease with the increasing of x-valuesFrom the graph is possible to see that the function decreases when x is between –6 and 0 because the values of y decrease with the increasing of x-values.
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How do you find the remainder when a polynomial in x is divided by a binomial of the form XR?
There are two ways to find the remainder when a polynomial in x is divided by a binomial of the form x-r, the use of synthetic division or calculate P(r).
Synthetic division
The Synthetic division is a shortcut way of polynomial division, especially if we need to divide it by a linear factor. It is generally used to find out the zeroes or roots of polynomials and not for the division of factors.
Polynomial
A polynomial is defined as an expression which is composed of variables, constants and exponents, that are combined using mathematical operations such as addition, subtraction, multiplication and division.
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why is an understanding of the central limit theorem essential to the concepts of estimation an hypothesis testing?
Because it permits one to assume that the sampling distribution of the mean would typically be normally distributed, the central limit theorem is helpful when examining big data sets. This makes statistical analysis and inference simpler.
Hypothesis :
In statistics, hypothesis testing is used to identify the variance in the group of data that results from genuine variation. Based on the presumptions, the sample data are taken from the population parameter. The hypothesis can be divided into many categories. A hypothesis is described in statistics as a formal statement that explains the relationship between two or more variables belonging to the specified population. It aids the researcher in converting the stated issue into an understandable justification for the study's findings. It provides examples of various experimental designs and guides the investigation of the research procedure.
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How do you graph a rational function on a graphing calculator?
To graph a rational function on a graphing calculator, enter the equation into the Y= editor, then press the graph button. The calculator will display the graph of the rational function.
1. Enter the equation for the rational function into the Y= editor of your graphing calculator. Be sure to include all terms, coefficients, and operators.
2. Press the graph button. This will tell the calculator to generate the graph of the equation.
3. The calculator will display the graph of the rational function, including any asymptotes, zeroes, and intercepts.
4. Adjust the window settings as desired to get a better view of the graph. This can be done by pressing the WINDOW button, then setting the appropriate Xmin, Xmax, Ymin, and Ymax values.
5. Press the GRAPH button again to view the adjusted graph.
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What two rational expressions sum to 3x−4x2+x−12?
PLEASE HELP URGENTLY!!!!!!
Answer:
Step-by-step explanation:
g
Step-by-step explanation:
16. +. 5
__. ____
7(x+4). 7 (x-3)
in a certain country license plates consist of zero or one digit followed by four or five uppercase letters from the roman alphabet. how many different license plates can the country produce?
118,813,760 different combination license plates can the country produce
Permutations and combinations:
permutations and combinations, the various ways in which objects from a set may be selected, generally without replacement, to form subsets. This selection of subsets is called a permutation when the order of selection is a factor, a combination when order is not a factor. By considering the ratio of the number of desired subsets to the number of all possible subsets for many games of chance in the 17th century, the French mathematicians Blaise Pascal and Pierre de Fermat gave impetus to the development of combinatorics and probability theory.
Given that
In a certain country license plates consist of zero or one digit followed by four or five uppercase letters from the roman alphabet
X = 10 × 26 × 26 × 26 × 26 × 26
= 10 × 11881376
= 118,813,760
118,813,760 different combinations license plates can the country produce
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An electrician need to run a cable from the top of a 68-foot tower to a tranmitter box located 51 feet away from the bae of the tower. Fidn how long he hould cut the cable
By using Pythagoras' theorem the required length of the cable is 85 feets.
What is Pythagoras' theorem?The square of the hypotenuse side in a right-angled triangle is equal to the sum of the squares of the other two sides, according to Pythagoras' theorem. Perpendicular, Base, and Hypotenuse are the names given to the triangle's sides. The hypotenuse is the longest side in this case because it is opposite the angle of 90°.
What is the name of Pythagoras' formula?The Pythagorean theorem states that the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides of a right-angled triangle. Alternatively, the sum of the squares of a right triangle's two legs equals the square of its hypotenuse.
Given:
Height of the tower = 68 feet = perpendicular
distance of box form tower = 51 feet = base
Let's assume lenght of the cable = L = hypotenous
Acoording to the question by using Pythagoras' theorem,
[tex]hyp^{2}= perpendicular^{2} +base^{2} \\(L)^2 = (68)^2 + (51)^2\\L^2 = 4624 + 2601\\L^2 = 7225\\L =\sqrt{7225}\\L = 85 feet[/tex]
Hence by using Pythagoras' theorem the required length of the cable is 85 feets.
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Considerine line y=3/5x+4.
Find the equation of the line that is parallel to this line and passes through the point (-5, -1)
Answer:
y = 3/5x + 2
Step-by-step explanation:
Parallel lines have the same gradient, so
y = 3/5x + c
Put in your point (-5,-1):
(-1) = 3/5(-5) + c
-1 = -3 + c
-1 + 3 = c
2 = c
So
y = 3/5x + 2
a manufacturer wishes to set a standard time required by employees to complete a certain process. times from 21 employees have a mean of 6 hours and a standard deviation of 2 hours. test if the mean processing time exceeds 5.5 hours. what is the -value of the test (round off to second decimal place)? assume normal population.
The -value of the test is 1.90. This indicates that the mean processing time is significantly greater than 5.5 hours, supporting the manufacturer's desire to set a standard time required by employees to complete a certain process
The t-value will be equal to 1.39 for the given statistics.
How to calculate the t-value?To test if the mean processing time exceeds 5.5 hours, we can use a one-sample t-test.
The null hypothesis is that the mean processing time is less than or equal to 5.5 hours:
H0: µ ≤ 5.5
The alternative hypothesis is that the mean processing time is greater than 5.5 hours:
Ha: µ > 5.5
We will use a significance level of 0.05.
The formula for the t-test statistic is:
t = (X - µ) / (s / √n)
Where:
X = sample mean
µ = hypothesized population mean
s = sample standard deviation
n = sample size
Substituting the given values, we get:
t = (6 - 5.5) / (2 / √21) = 1.386
The degree of freedom for the t-test is n-1 = 20.
Using a t-table or calculator, the p-value associated with a t-value of 1.386 and 20 degrees of freedom is 0.093.
Since the p-value (0.093) is greater than the significance level (0.05), we fail to reject the null hypothesis. Therefore, there is not enough evidence to suggest that the mean processing time exceeds 5.5 hours.
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amy spent 60$ on 5 daylilies and 5 bunches of ornamental grass,james spent 78$ on 8 daylilies and 5 bunches of ornamental grass,what is the cost of one daylily and the cost of one bunch of ornamental grass?
Answer:
both cost the same price of 6 dollars for each
Step-by-step explanation:
we can make a system of equation
d- daylilies
o- ornamental glass
5d+5o=60
8d+5o=78
-8d. -8d
5o=78-8d
5d+78-8d=60
-3d+78=60
-78. -78
-3d= -18
/-3. /-3
d=6
5(6)+5o=60
30+5o=60
-30. -30
5o=30
/5. /5
o=6
they both are 6 dollars each
hopes this helps
You purchae 200 hare of a tock at a price of $70 per hare. You purchae 200 call option on the
tock with exercie price of $72 and a call premium of $5. 75 per call option. You alo write (ell) 300
put option on the ame tock with exercie price of $68 and put premium of $2,87 per put option. All the option expire on the ame date. Calculate the profit on your entire trategy (portfolio) at the
expiration of the contract if the Stock price at that time i $81. 50. (Aume you ell all your hare
the date that the option expire. )
On your entire strategy at the expiration of the contract if the stock price at that time is $81.50 then the profit is $2189.
A portfolio is a collection of financial investments like stocks, bonds, commodities, cash and cash equivalents, including closed-end funds and exchange traded funds.
A stock is a security that represents the ownership of a fraction of the issuing corporation. Units of stock are called "shares" which entitles the owner to a proportion of the corporation's assets the owner equal to how much stock they own.
We know that,
Profit on the strategy
= Profit on the shares + Profit from long calls + Profit from short puts
= 200(81.50 - 70) + 200(Max(81.50-72,0)-5.75) + 300(-Max(68 - 81.50,0)+2.87)
= 2300 + 750 - 861
= 2189
Therefore profit on strategy is $2189.
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Rewrite 2x2x2x2 as an exponent.
The required exponent form is obtained as 2 x 2 x 2 x 2 = 2⁴.
What are the rules of exponents?Some of the rules of exponents are as follows,
The product of two exponents having the same power is equal to the power of their base multiplied.
The product of two exponents having the same base is equal to the sum of the powers of different exponents to the same base.
The given expression is 2 x 2 x 2 x 2.
It can be written in exponent form as,
2 x 2 x 2 x 2
The number 2 is multiplied to itself by four times,.
Thus, the exponent form is given as 2⁴.
Hence, the exponent form of the given expression is 2⁴.
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The pheasant population on an island is declining at a rate of 1. 7% per year. The population was 4600 in the year 2009. Which answer is the best prediction of the population in the year 2015? responses 4010 4010 4080 4080 4120 4120 4150.
The best prediction of the population in the year 2015 will be 4150
rate of decrease involves The rate of reduction expressing a decrease as a percentage of the initial value.To compute a percentage drop, first determine the difference (decrease) between the two values being compared. Then, divide the reduction by the original number and multiply the result by 100.
Given that an island's peasant population is falling at a rate of 1.7% per year,
A 1.7% decrease means that 98.3% will remain.
as a result, decrease = 0.983/year
A(t) = A(original) multiplied by (0.983)^t
As a result, after 6 years, A(6) = 4600 x (0.983)6 = 4150
As a result, the population in 2009 will be 4150.
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Write the negation of each quantified tatement. 3. Everyone failed the quiz today
The negation of the given statement " Everyone failed the quiz today " is given by " No one failed the quiz today."
As given in the question,
Given statement is written as:
S : Everyone failed the quiz today.
Negation of the given statement represent the conversion of true statement into false statement or conversion of false statement into true statement.
Here given statement is true statement.
Convert the given statement into false statement.
So Negation of statement S is represented by ~ S.
~S : No one failed the quiz today.
Therefore, the negation of the given statement is equal to " No one failed the quiz today".
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A student concluded that 8x−12=4(12x−6) has infinitely many solutions. Which statement best describes the student’s conclusion? Responses The conclusion is incorrect because the equation has no solution. The conclusion is incorrect because the equation has no solution. The conclusion is incorrect because there is exactly one solution to the equation. The conclusion is incorrect because there is exactly one solution to the equation. The conclusion is correct because there are exactly two solutions to the equation. The conclusion is correct because there are exactly two solutions to the equation. The conclusion is correct because when simplified, both sides of the equation are equivalent. The conclusion is correct because when simplified, both sides of the equation are equivalent.
Answer:
The conclusion is incorrect because there is exactly one solution to the equation.
Step-by-step explanation:
8x - 12 = 4(12x - 6)
4 x 12x = 48x 4 x -6 = -24
8x - 12 = 48x - 24
Move the terms
8x - 12 - 48x = -24
Move the constant to the right-hand side and change its sign
8x - 48x = -24 + 12
-40x = -24 + 12
-40x = -12
Divide both sides by -40
40x = -12
40 = 40
x = [tex]\frac{3}{10}[/tex] or, alternate form, x = 0.3
What is closure under addition Give 2 example?
The closure property of addition states that the sum of two whole numbers will always be a whole number.
A whole number is a set of all positive integers from 0 to infinity. Now we all know that if we add two positive numbers up, the sum will either remain constant (if the number is 0) or be greater than both numbers. This means that the sum of two whole numbers has to be a whole number.
Example 1 If we add 0 and 45
0 + 45
= 45
We already know that 45 is a whole number.
Example 2- If we add 486 and 354
486 + 354
= 840
From the definition, we can say that 840 is a whole number.
This is the closure property.
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Write the algebraic expreion for the number of total hour in y hour and 45 minute
The algebraic expression for the given statement total number of hours present in y hours and 45 minutes is equal to ( y + 0.75 ) hours.
As given in the question,
Given statement is equal to :
The total number of hours present in y hours and 45 minutes .
Here we have to convert whole equation into hours we have :
1 hour = 60 minutes
⇒ 1 minute = ( 1 / 60 ) hours
⇒ 45 minutes = ( 45 / 60 ) hours
⇒ 45 minutes = 0.75 hours
Algebraic expression for the given statement in hours is given by :
y hours and 45 minutes
= y hours + 45 minutes
= y hours + 0.75 hours
= ( y + 0.75 ) hours
Therefore, the algebraic expression for the given statement is given by
( y + 0.75 ) hours.
The complete question is:
Write an algebraic expression for the total number of hours in y hours and 45 minutes.
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Is the sum of any two whole numbers always a whole number answer it with at least 3 example?
Yes, the sum of 2 whole numbers is always a whole number.
Any number that ranges from 0 to infinity with 1 as the denominator in its smallest form is called a whole number.
For example- 0, 3, 78, 9363, etc.
Now if we take up two numbers say 34 and 78.
34 + 78
= 112
According to the definition of the whole number, we can say that this is a whole number.
Another example can be 0 + 237
The sum is 237
which again is a whole number.
The last example can be 2365 + 930
= 3295
This too is a whole number.
Hence the sum of two whole numbers will always be a whole number.
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5. Marianne has a credit card with a line of credit at $15,000. She made the following purchases:
$1,374.90, $266.21, 39.46, and $903.01. What is Marianne's available credit?
Answer:
Available credit = $2,416.42
Step-by-step explanation:
$1,374.90
$266.21
39.46
$903.01
Sum = $2,583.58
$2,583.58 was spent. Subtract this from $5,000 to find Marianne's available credit.
$5,000
- $2,583.58
Available credit = $2,416.42
24. Omar is standing 75 feet away from the base of a building. The angle of elevation from the ground where Omar is standing to the top of the building is 24.
(MGSE9-12.G.SRT.8)
Part A: Draw a diagram to represent this situation. (1 point)
25. Jonat backyard daughter garden, sc rectangul:
(MGSE9-12
Part B. Calculate the height of the building to the nearest tenth of a foot?
Explain your process for arriving at the answer.
a. The diagram that represents this situation is given by the image shown at the end of the answer.
b. The height of the building is of: 33.4 feet.
What are the trigonometric ratios?The three trigonometric ratios are defined as follows:
Sine of angle = length of opposite side divided by the length of the hypotenuse.Cosine of angle = length of adjacent side divided by the length of the hypotenuse.Tangent of angle = length of opposite side divided by the length of the opposite side.As shown by the diagram given at the end of the answer, this situation is represented by a right triangle in which:
There is an angle of 24º.The adjacent side to the angle is of 75 feet.The height of the building is of x feet.Then the height of the building is calculated as follows:
tan(24º) = x/75
x = 75 x tangent of 24 degrees
x = 33.4 feet. -> height of the building.
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7w+6 i need help plese
Answer: 7w + 6
Step-by-step explanation:
Your question was "7w + 6". When we simplify this, we get 7w + 6. So your answer is 7w + 6.
There are 8 squares and 10 triangles. What is the simplest ratio of squares to triangles?.
Answer: 4:5
Step-by-step explanation: The lowest form
Answer:
Step-by-step explanation:
4:5
What is meant by 6% slope?
6% slope means on a run of 100 units, there is just a 6-unit rise. The basic definition of slope is the gradient or incline of the terrain.
A steep slope is an abrupt incline, and a gentle slope is a gradual incline. The river's route flows between the steep, forested hills and their softer counterparts.
This is accomplished by comparing the vertical and horizontal changes, which are frequently stated as rise/run.
Since "percent" or "%" denotes "out of 100" or "per 100," x% can be expressed as
For instance
You can come across a road sign that says "6% Grade" or "Steep Grade" while driving down a highway. The road's grade is essentially its slope, multiplied by 100.
6% thus equals 6/100.
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1 mile = 1.6 kilometers
A car goes 3 miles.
How many kilometers does it go?
Answer:
4.82803
Step-by-step explanation:
3 x 1.6
Find the surface area of that part of the plane 10x+7y+z=4 that lies inside the elliptic cylinder x^2/25+y^2/9=1
The surface area of that part of the plane 10x+7y+z=4 inside the elliptic cylinder x^2/25+y^2/9=1 is equal to πab, where a=5 and b=3. Therefore, the surface area is equal to 45π.
How can you calculate a surface area?Total area on a three-dimensional shape's surface is known as surface area. The surface area of a cuboid with six rectangular faces can be calculated by adding the areas of each face. Alternatively, you can write down the cuboid's length, width, and height and use the formula surface area (SA)=2lw+2lh+2hw.
Why does surface area have a formula?The general formula for a cube's surface area is as follows: The area of the base plus the area of the cube's vertical surfaces will add up to the cube's total surface area. The cube's total surface area is calculated using the formula 6a2, where an is the side length.
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find the value of x.
Answer: 7
Step-by-step explanation:
[(8 x 10-3) x (0.0002)
Answer:
Step-by-step explanation:
0.0154, I think, I apologize if this is wrong.
A publiher need to end many book to a local book retailer and will end the book in a combination of mall and large boxe. Each mall box can hold 20 book and each large box can hold 45 book. There were twice a many large boxe ent a mall boxe, which altogether can hold 440 book. Write a ytem of equation that could be ued to determine the number of mall boxe ent and the number of large boxe ent. Define the variable that you ue to write the ytem
The formula is = 7 and 3. It may be used to calculate the number regular mall boxes as well as the number of big boxes.
Which equation has ever been the hardest?What is the world's most difficult arithmetic problem? A mathematical conundrum that has baffled mathematicians over decades is finally solved earlier this week. Diophantine Equation, sometimes referred to as the "sum of three cubes," is what it is: Find x, y, & z such that, for any k between 1 and 100, x3+y3+z3=k.
Briefing:Let x= Number of small boxes , y = Number of large boxes.
As per given , 30x+55y=375 (i)
x+y=10 (ii)
Multiply (ii) by 30, we get
30x+30y=300 (iii)
Eliminate (iii) from (i), we get
25y=75
⇒ y= 3
Put y=3 in (ii), we get
x+3=10 ⇒ x=7
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531
x 47
Long multiplication :) please help
What is a perpendicular line to Y =- 4x 7?
The original equation is in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept. A perpendicular line to Y = -4x + 7 would be Y = 4x + 7.
To find the equation of a line perpendicular to Y = -4x + 7, we need to switch the x and y variables and then change the sign of the slope.
The original equation is in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept.
Since the original equation has a slope of -4, the perpendicular line will have a slope of 4.
Therefore, the equation for the perpendicular line is y = 4x + b.
We can find the y-intercept by plugging in a point from the original equation.
For example, if we plug in (0,7), we get 7 = -4(0) + b, or b = 7.
Therefore, the equation for the perpendicular line is y = 4x + 7.
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