Based on the calculations using the given points, the slope in this situation is equal to 5.
What is a slope?A slope is also referred to as gradient and it's typically used to describe both the ratio, direction and steepness of the function of a straight line.
How to calculate the slope of a line?Mathematically, the slope of any straight line can be calculated by using this formula;
[tex]Slope = \frac{Change\;in\;y\;axis}{Change\;in\;x\;axis}\\\\Slope = \frac{y_2\;-\;y_1}{x_2\;-\;x_1}[/tex]
Substituting the given points into the formula, we have;
Slope = (30 - 10)/6 - 2)
Slope = 20/4
Slope = 5.
In conclusion, the slope of the line that passes through the given points is equal to 5.
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3. Disney on Ice is traveling to Chicago to perform. The revenue from their ticketsales is a function of the ticket price, x, and can be modeled with (x - 8)(450 – 3x).What are the ticket prices at which Disney on Ice would make no money at all?Type Here: They would earn no money when the function is equal oExplain or show your reasoning.Type Here: (x-3)(450-3x) = 0
the price of the ticket which Disney on ice would make no money at all is:
[tex](x-8)(450-3x)=0[/tex]and here, are two posible solutions:
[tex]\begin{gathered} 1)x-8=0 \\ 2)450-3x=0 \end{gathered}[/tex]for the first one 1)
[tex]x=8[/tex]for the second one 2)
[tex]\begin{gathered} 450=3x \\ \frac{450}{3}=x \\ 150=x \end{gathered}[/tex]and in this problem the realistic answer is the first one, so the solution is $8 dollars
IS this a function or no (ALGEBRA
We can see that the same input is mapped into two different outputs, so this is not a function.
Is this a function?A relation maps elements called inputs into another elements called outputs.
Such that a relation is a function if each input is mapped into only one output.
The notation used is (input, output).
So, here we can see the points:
(4, 12) and (4, 15).
The input 4 is being mapped into two different outputs, thus, this is not a function.
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Evaluate the integral.
[tex]\pi\int\limits^{\frac{3\pi}{4}}_{\frac{\pi}{6}} {sin^4x+4sin^2x} \, dx[/tex]
By using trigonometric formulas and integration rules, we conclude that the integral is approximately equal to - 7.764 units.
How to determine the value of a definite integral
In this problem we must determine the solution to a definite integral of trigonometric equations, which requires the use of trigonometric formula and integration rules to be found. The integral can be simplified by using the following formulas:
sin⁴ x = (1 / 8) · (3 - 4 · cos 2x + cos 4x)
sin² x = (1 /2) · (1 - cos 2x)
Then, the integral is simplified into this form:
[tex]I = \pi \int \limits_{\frac {\pi}{6}}^{\frac{3\pi}{4}} \sin^{4} x \,dx + 4\pi \int \limits_{\frac {\pi}{6}}^{\frac{3\pi}{4}} \sin^{2} x \,dx[/tex]
[tex]I = \frac{\pi}{8} \int \limits_{\frac {\pi}{6}}^{\frac{3\pi}{4}} (3 - 4\cdot \cos 2x + \cos 4x) \,dx + 4\pi \int \limits_{\frac {\pi}{6}}^{\frac{3\pi}{4}} (1 - \cos 2x) \,dx[/tex]
[tex]I = \frac{3\pi}{8}\cdot x - \frac{\pi}{4} \cdot \sin 2x + \frac {\pi}{32}\cdot \sin 4x - 4\pi \cdot x - 2\pi\cdot \sin 2x[/tex], for x ∈ [π / 6, 3π / 4]
And the definite integral is:
I = 2.159 + 1.466 - 0.085 - 23.028 + 11.724
I = - 7.764
The definite integral of f(x) = sin⁴ x + 4 · sin² x for x ∈ [π / 6, 3π / 4] is approximately equal to - 7.764.
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1b. Below is a graph of the equation x + y = 500. Change it so that itrepresents solutions to the inequality representing this situation. Statewhat line you will use (dashed or solid line) and which side you will shade(A or B). **
Given:
The equation of the graph is x + y = 500.
The objective is to change the equation as inequality and to choose the correct region for shading.
Explanation:
As the equation is given as x + y = 500, the sum of the values of x and y lies within the 500. As its total sum is also equal to 500, the graph must lie with in the maximum range of 500 that is at A along with solid line. (If sum is not equal to 500, the graph will contain dotted line).
Representation of inequality:
The given equation can be represented in the form of inequality as,
[tex]x+y\le500[/tex]Graph:
Then, the graph of the inequality will be,
Hence, the inequality is x + y ≤ 500 and the graph contains solid line with shaded region in A.
help me!!! Write an equation of the line passing through the point (2, 8) that is perpendicular to the line 2x - 3y = 7
Answer:
y = -3/2x +11
Step-by-step explanation:
First you have to change the equation from standard form to slope form.
y = mx + b
2x-3y=7 --> subtract 2x from both sides
-3y = -2x + 7 --> now divide both sides by -3 to get y by itself
y = 2/3x - 7/3 --> the reason 2/3x is positive is because when there are two negatives it turns to a positive.
now you have to use point slope form y - y1 = m (x - x1)
x1 and y1 would be your point. 2 is x1 and 8 is y1
y - 8 = -3/2 (x - 2) --> the reason that m is -3/2 is because a perpendicular equation is the opposite reciprocal of the original slope
next distribute the -3/2
y-8 = -3/2x + 3 --> and now add 8 to 3 to get why by it self
now you have y = -3/2x + 11
14) Solve. Which number will be an ordered pair for the solution of y = 6x + 1; (2,__) a) 13 b) 11 c) 8 d) 3
14) y = 6x + 1
( 2, y)
if x = 2 as stated in the coordinate, then y = 6(2) + 1 = 12 + 1 = 13
y =13
The ordered
What is the sum of all the numbers less than 496 that divide evenly into 496?
Based on the numbers that are all less than 496 and yet divide evenly into 496, the sum is 496
How to find the sum?The numbers that are less than 496 and yet are able to divide evenly into it are known as the factors of 496. These numbers will not leave a reminder when they divide 496.
The factors of 496 include:
1, 2, 4, 8, 16, 31, 62, 124, 248, 496.
The sum of these numbers that are less than 496 is:
= 1 + 2 + 4 + 8 + 16 + 31 + 62 + 124 + 248
= 496
In conclusion, the sum of all the numbers less than 496 that are able to divide it evenly is 496.
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There are 12 F/A-18 aircraft, where: 3 are F/A-18A's 4 are F/A-18E's 5 are F/A-18F's If three of these twelve aircraft are selected at random, so that every possible selection is equally likely, what is the probability that all three of them will be F/A-18E's, rounded to two decimal places?
When three of these twelve aircraft are selected at random, the probability that all three of them will be F/A-18E's is 0.018.
How to calculate the probability?Based on the information given, there are are 12 F/A-18 aircraft, where: 3 are F/A-18A's 4 are F/A-18E's 5 are F/A-18F's. The total number of aircraft will be 12.
When three of these twelve aircraft are selected at random, so that every possible selection is equally likely, the probability that all three of them will be F/A-18E's will be:
= 4/12 × 3/11 × 2/10
It should be noted that this is without replacement that's why we have 10, 11 and 12 as the denominator.
= 4/12 × 3/11 × 2/10
= 1/3 × 3/11 × 1/5
= 3 /165
= 0.018
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An airport in a country that has an elevated occurance of terrorism profiles airline passengers and semi-randomly selects who will undergo additional screening. If one person is stoped, everyone they are traveling with is also stopped. Over the course of several months, the airport security stops 15% of passengers for this extra screening. On a certain day, 519 passengers go through security at this airport. Let the variable be the number of those people who are chosen for additional screening.
Is the number of passengers who are chosen for additional screening a binomial random variable? Select all that apply.
Yes. All four conditions are met.
No. There is not a fixed number of trials.
No. The trials cannot reasonably be assumed to be independent.
No. The outcomes cannot be described as only "success" and "failure."
No. The probability of success is not the same for each trial.
No. there is not a fixed number of trials. The correct option is B.
What is a binomial random variable?A variable with only two outcomes is said to be binary. Examples of binary categorical variables are sex (male/female) and having a tattoo (yes/no).
Each trial must be independent, meaning that it must have a defined number of trials and a constant success rate. Its probability needs to range from 0 to 1.
There are only two conceivable outcomes for each individual. They are either filtered or they are not. We are not interested in learning how many people were screened, though.
It is an inverse binomial, we want to know how many persons will be screened before 10, which is a binomial. Therefore, since there are an arbitrary number of trials, this is not a binomial equation, and option B provides the solution.
Therefore, there is not a fixed number of trials. The correct option is B.
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Simplify the expression.
Answer:
Step-by-step explanation:
[tex]m^{a}[/tex] × [tex]m^{b}[/tex] = [tex]m^{a+b}[/tex]
[tex](m^{a}) ^{b}[/tex] = [tex]m^{ab}[/tex]
write an equation of the line that passes the through point (0, 9) and has slope m=2/3
An equation of the line that passes the through point (0, 9) and has slope m = [tex]\frac{2}{3}[/tex] is 3y-2x-27=0
What is point-slop equation of a line?
The point-slope equation of a line is
y - [tex]y_{1}[/tex] = m ( x -[tex]x_{1}[/tex] )
The equation is useful when we know:
one point on the line: ( [tex]x_{1}[/tex],[tex]y_{1}[/tex]) andthe slope of the line: m,and want to find other points on the line.
Given that,
slope , m = [tex]\frac{2}{3}[/tex] and passing through the point is (0,9)
An equation of a line given the slope and a point is
y - [tex]y_{1}[/tex] = m ( x -[tex]x_{1}[/tex] )
or y - 9 = [tex]\frac{2}{3}[/tex] (x - 0)
or y - 9 = [tex]\frac{2}{3}[/tex] x
or y = [tex]\frac{2}{3}[/tex] x + 9
or y = [tex]\frac{2x + 27}{3}[/tex]
or 3y = 2x + 27
or 3y - 2x - 27 = 0
Hence, an equation of the line that passes the through point (0, 9) and has slope m = [tex]\frac{2}{3}[/tex] is 3y-2x-27=0
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f(x)=4x^4−19x^3−10x^2+35x−50 and g(x)=x−5, find (f/g)(x) and (f/g)(1)
Answer:
(f/g)(x) = 4x^3 +x^2 -5x +10(f/g)(1) = 10Step-by-step explanation:
You want to find the rational function (f/g)(x) and its value for x=1 when f(x) = 4x^4−19x^3−10x^2+35x−50 and g(x) = x-5.
Polynomial divisionThe ratio function is the ratio of the given functions, found by dividing f(x) by g(x). Since g(x) is a binomial with a leading coefficient of 1, synthetic division is recommended. The attachment shows the result.
[tex](f/g)(x)=\dfrac{f(x)}{g(x)}=\dfrac{4x^4-19x^3-10x^2+35x-50}{x-5}\\\\\boxed{(f/g)(x)=4x^3+x^2-5x+10}[/tex]
The value of this function when x=1 is ...
(f/g)(1) = 4·1³ +1² -5·1 +10 = 4 +1 -5 +10
(f/g)(1) = 10
Write the equation of the line in point-slope form that passes through the given point with the given slope. (,)open 1 comma 5 close; =−m equals negative 3
The equation of the line in point slope form that passes through (1,5) and slope = -3 , is y = -3x+6 .
The equation of line in point slope form passing through the points (x₁,y₁) and slope =m is given by the formula
(y-y₁)=m(x-x₁)
In the question ,
it is given that
the line passes through the point (1,5) and has a slope m = -3.
so the values become x₁=1 and y₁=5 and m = -3
Substituting the values in the formula for equation of line , we get
(y-5)=(-3)(x-1)
y-5= -3x + 1
y = -3x + 1 + 5
y = -3x+6
Therefore , the equation of the line in point slope form that passes through (1,5) and slope = -3 , is y = -3x+6 .
The given question is incomplete , the complete question is
Write the equation of the line in point-slope form that passes through the point (1,5) with slope = -3.
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Evaluate the following function for the given value.
f(x)=-x-2; find f(-7).
Answer: f(-7)=-9
Step-by-step explanation:
Please help I’ll mark you as brainliest if correct !!
47 had a finished basement with 0 three-car garage .
What is reasoning ?Thinking and cognition are related to reasoning, which requires using one's intellect. The study of logic focuses on how people can construct logically sound arguments using formal reasoning. Deductive, inductive, and abductive reasoning are three examples of logical reasoning that can be used to further break down reasoning. Aristotle distinguished between logical discursive reasoning (reason proper) and intuitive reasoning, noting that the former may lean toward the subjective and the personal, despite being correct. While logical and intuitive styles of reasoning might clash in certain social and political circumstances, in others they are considered as complimentary rather than competitive.
Calculationall the values are given that how many houses had a finished basement with no 3-car garage.
the no. of houses are = 47 .
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The revenue for selling x units of a product is R = 113.95 x. The cost of producing x units is C = 93 x + 750. In order to obtain a profit, the revenue must be greater than the cost. For what values of x will this product produce a profit? (Enter a number. Round your answer up to the nearest whole unit.)
For profit with the revenue of R=113.95x and cost of C=93x + 750 the value of x is 36units.
As given in the question,
Revenue for selling x units of a product is R = 113.95 x
Cost of producing x units is C = 93 x + 750
For profit, the revenue must be greater than the cost.
R > C
113.95x > 93x +750
Subtract 93x from both the sides
113.95x -93x >93x-93x +750
⇒20.95x > 750
Divide by 20.95
⇒x > 750/20.95
⇒x>35.7995
Nearest whole number is 36.
Value of x to produce a profit is 36units
Therefore, to make a profit with the revenue of R=113.95x and cost of
C =93x + 750 the value of x is 36units.
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what is the percent value of 5/8
Answer: The correct answer is 62.5% and not 67.5 %
Step-by-step explanation: Yes you do 5 divided by 8 and then you move the decimal point two places to the right.
Hope this helped!!!!
Match the vocab word with the definition:
Question 1 options:
Order of Operations
Operator
Equation
Constant
Numerical Expression
Exponent (Power)
Evaluate
Variable Expression
Variable
Open Sentence
Term
Coefficient
Grouping Symbol
Inequality
1.
Devices, such as parentheses, brackets, and fraction bars, used to set apart an expression that should be simplified before other operations are performed
2.
An expression that consists of numbers, operations, and sometimes grouping symbol.
3.
The order in which operations must be computed when more than one operation is involve.
4.
A number representing how many times the base number should be multiplied by itself.
5.
A Symbol that represents a value that can change.
6.
A single number or variable, or numbers and variables multiplied together.
7.
The numerical factor in a term. A number being multiplied by a variable.
8.
A number on its own, it has a fixed value.
9.
A combination of variables, numbers, and operations.
10.
You replace, or substitute, all the variables with numbers and then simplify.
11.
A statement that the values of two math expressions are equal (indicated by the sign =).
12.
The relation between two expressions that are not equal, employing a sign such as ≠ “not equal to,” > “greater than,” or < “less than.”.
13.
The symbol of a math operation.
plus, minus, times, divided by, equals
14.
An equation or inequality containing one or more variable.
Answer:
1 : Grouping Symbol
2 : Operator
3 : Order of Operations
4 : Exponent
5 : Variable
6 : Term
7 : Coefficient
8 : Constant
9 : Numerical Expression
10 : Variable Expression
11 : Equation
12 : Inequality
13 : Evaluate
14 : Open Sentence
Write an equation of the line passing through (4,-3) and perpendicular to x+3y=-15
The equation of line passing through(4,-3) and perpendicular to x+3y=-15 is y = 3x - 15.
How do you determine a line's equation?Using the slope formula, determine the slope.
To find the y-intercept, use the slope and one of the points (b).
You can obtain the equation for a line by entering the values of m and b into the slope-intercept form of the line (y = mx + b).
Given,
coordinates = (4,-3)
equation of line = x+3y=-15
equation of line in standard form
⇒ y = -1/3x -5
Slope of line = -1/3
The slope of the line passing through (4,-3) and perpendicular to line x+3y=-15 is 3.
The equation of line becomes
(y + 3) = 3 (x - 4)
y + 3 = 3x - 12
y = 3x - 15
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There are ten options, but I cannot send all ten at once. Please draw out the correct graph!
To answer this question we need to remember that:
[tex]\sec \theta=\frac{1}{\cos \theta}[/tex]then:
[tex]\begin{gathered} \sec \theta=-\frac{13}{5} \\ \frac{1}{\cos \theta}=-\frac{13}{5} \\ \cos \theta=-\frac{5}{13} \\ \theta=\cos ^{-1}(-\frac{5}{13}) \\ \theta=112.62 \end{gathered}[/tex]There's only one angle that gives this result that it is real. Therefore the answer is 112.62
Help PLEASE thats the question if you have the answer type below
The equation that represent the data in the table shown is y = -2x + 3.
How to know if the system is linear?Linear systems are sets of equations associated with each other and that have two or more variables. In linear systems, only linear equations are entered, that is, expressions where the greatest exponent of the unknowns is equal to 1.
A linear equation is in the form:
y = mx + b
Where:
m is the slope b is the y interceptFrom the table, using the point (0, 3) and (1, 1):
y - 3 = [(1 - 3)/(1 - 0)](x - 0)
y - 3 = -2xy = -2x + 3
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help me
look at the picture
The zeros of the quadratic are (1 and 3), the vertex is (2, -1). Draw the parabola with a "solid" line. Shade the "interior" of the parabola.
What is defined as the inequality?Inequalities are mathematical representations in which neither side is equal. Unlike equations, we consider the two values in inequality.When inequalities are connected together, it is possible to jump so over middle inequality.If, p < q and q < d, then p < dIf, p > q and q > d, then p > dFor the given question;
The inequality of the function is given as;
= x² - 4x + 3
Find the factors;
(x - 3)(x - 1) = 0
x = 1 and x = 3 are the zeros of the equation.
Now, to graph the equation find the point;
Put x = 0; y = 3
Put x = 1; y = 0
Put x = 2, y = -1
Plot the points on the graph and join the points with solid line.
The vertex of the parabola is found at (2, -1).
Thus, the graph of the parabola is plotted.
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what is the geometric mean of 14 and 6 (just need answer)
9.16
1) Considering 14, and 6 the data. Let's calculate the Geometric Mean of it
[tex]X_G=\sqrt[]{14\cdot6}\Rightarrow X_G\approx9.16[/tex]2) To do that we just need to multiply those numbers, and since there are two of them take the square root of that product, between those 2 numbers
3) So the Geometric mean is 9.16 (approximately).
A large pepperoni pizza from Papa Johns costs $14.75. After tax, the pizza is $15.93. What is the sales tax rate?
Answer:
8%
Step-by-step explanation:
divide the after tax price by the before tax price
15.93/14.75=1.08
then subtract 1 from 1.08 (the 1 is the base price of the pizza) and convert the difference to percent to get the answer of 8% tax rate
The distance between 4 7/10 and -8 9/10
Answer: 68/5
Hope this helps! :)
_______ angles are used to relate the values returned by inverse trigonometric functions to angles larger than 90°.
A. Obtuse
B. Acute
C. Right
D. Complementary
Answer:
Acute
Step-by-step explanation:
Obtuse angles are angles that are larger than 90 but less than 180
Acute angles are angles that are less than 90 degrees
Right angles are angles that is exactly 90 degrees
Complementary angles are two angles whose sum is 90 degrees
Using this info, it seems the answer to this question is B. Acute because it says "the values returned by inverse to angles larger than 90" and since acute is the opposite of obtuse imma say B but im not too sure
In which quadrant of the coordinate graph does point F
ie?
• Quadrant I
o Quadrant II
• Quadrant III
O Quadrant IV
Answer:
Quadrant IV .
Step-by-step explanation:
I hope it will be helpful for you.
what is 40 divided by 50
Answer:
See below
Step-by-step explanation:
40 ÷ 50 = 40/50 = 4/5 = .8
3^x-3^y=234,find the value of x and y
Value of x =5 and value of y =2
The exponent of a number indicates how many times a number has been multiplied by itself. For instance, 3^4 indicates that we have multiplied 3 four times. Its full form is 3 3 3 3. Exponent is another name for a number's power. It could be an integer, a fraction, a negative integer, or a decimal. Exponents are necessary since, without them, it is highly challenging to express the product when a number is repeated several times by itself. For instance, it is much simpler to write 5^7 than it is to write 5 5 5 5 5 5.
[tex]3^{x}-3^{y}=234\\ 3^{x-y}.3^{y}-3^{y}=234\\ 3^{y}(3^{x-y}-1)=234\\ 3^{y}(3^{x-y}-1)=3^{2}.26\\[/tex]
Now, by comparison, we get:
[tex]3^{y}=3^{2}\\ y=2\\ Also, \\3^{x-y} -1=26\\ 3^{x-y}=27\\ 3^{x-y}=3^{3}\\ x-y=3\\ x-2=3\\x=5[/tex]
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Find a formula for the nth term in this
arithmetic sequence:
a1 = 7, a2 = 4, a3 = 1, a4 = -2, ...
an
Answer:
an = 7 -3(n -1)
Step-by-step explanation:
You want the formula for the n-th term of the arithmetic sequence 7, 4, 1, -2, ....
Arithmetic sequenceAn arithmetic sequence has a first term (a1) and a common difference (d) found by subtracting the previous term from the current term.
In the given sequence, the first term is a1=7, and the common difference is d=(a2 -a1) = 4 -7 = -3.
The n-th term of the given arithmetic sequence is ...
[tex]a_n=a_1+d(n-1)\\\\\boxed{a_n=7-3(n-1)}[/tex]
__
Additional comment
The formula can be simplified to ...
an = 10 -3n