There are two methods of indirect proof:
Proof of the contrapositive and proof by contradiction.
Now, According to the question:
Let's know:
An indirect proof, also called a proof by contradiction, is a roundabout way of proving that a theory is true. When we use the indirect proof method, we assume the opposite of our theory to be true. In other words, we assume our theory is false.
Hence, There are two methods of indirect proof:
Proof of the contrapositive and proof by contradiction.
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A company sells shirts for $10 each. Its revenue function is r(x) = 10x.
Its costs are $3 per shirt plus $9,000 of fixed costs. Its cost function is
c(x) = 3x + 9000. Use this information for Problems 13-15. The first
one is done for you.
13. Find the company's revenue and costs if it sells 2000 shirts.
Revenue = $20,000; costs = $15,000
14. Profit equals the difference between revenue and cost. Write the
function, p(x), for this company.
15. In 2012, the company sold 5000 shirts. Find its profit.
1
Original content Copyright by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsi
135
a) To find the company's revenue and costs if it sells 2000 shirts, we can substitute 2000 for x in the given revenue and cost functions:
What does a math equation mean?The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.
Revenue: r(x) = 10x, so r(2000) = 10(2000) = $20,000
Costs: c(x) = 3x + 9000, so c(2000) = 3(2000) + 9000 = $15,000
b) The profit function, p(x), is the difference between the revenue function and the cost function. So, the profit function for this company is:
p(x) = r(x) - c(x) = 10x - (3x + 9000) = 7x - 9000
c) To find the company's profit in 2012, when it sold 5000 shirts, we substitute 5000 for x in the profit function:
p(5000) = 7(5000) - 9000 = $20,000
So, the company had a profit of $20,000 in 2012 when it sold 5000 shirts.
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Write the explicit function defines the sequence -8, -6, -4, ...?
Answer:
I think it's -2
Step-by-step explanation:
because it keeps going down by 2 and 4-2=2 so its -2
The drawing shows three point charges fixed in place. The charge at the coordinate origin has a value of q1 = +8.00 µC; the other two have identical magnitudes, but opposite signs: q2 = -5.00 µC and q3 = +5.00 µC.
(a) Determine the net force (magnitude and direction(measured counter clockwise from the x-axis)) exerted on q1 by the other two charges
(b) If q1 had a mass of 1.50 g and it were free to move, what would be its acceleration?
(a) The net force equation on q1 is 10.6N towards q2. (b) The acceleration of q1 would be 6.8x10^7m/s^2.
a) The Coulomb's law equation for the force between two charges q1 and q2 is given by:
F = k(q1q2)/r2
Where k is the Coulomb's constant and r is the distance between the two charges.
Using this equation, the force on q1 due to q2 can be calculated as:
F12 = (8.99x109 N m2/C2)(8.00x10-6C)(-5.00x10-6C)/(1.00m)2
F12 = -44.8x10-6 N
Similarly, the force on q1 due to q3 can be calculated as:
F13 = (8.99x109 N m2/C2)(8.00x10-6C)(5.00x10-6C)/(2.00m)2
F13 = 55.2x10-6 N
The net force on q1 can be calculated as the vector sum of F12 and F13:
F1 = F12 + F13
F1 = 10.6N towards q2
b) The acceleration of q1 can be calculated using Newton's second law of motion:
F = ma
a = F/m
Where m is the mass of q1.
Therefore, the acceleration of q1 can be calculated as:
a = (10.6N)/(1.50g)
a = 6.8x107m/s2
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Do the points 3 2 2 3 and 2 3 form a triangle?.
Yes, the given points (3 ,2) , ( -2 ,- 3 ), and ( 2, 3 ) forms a triangle.
As given in the question,
Given points to form a triangle is given be :
(3 ,2) , ( -2 ,- 3 ), and ( 2, 3 )
Let the triangle name be ABC.
Coordinates of vertex A(x₁ ,y₁ ) = ( 3, 2 )
Coordinates of vertex B(x₂ ,y₂ ) = ( -2, -3 )
Coordinates of vertex C(x₃, y₃) = ( 2, 3 )
General distance formula is :
= √ ( x₂ - x₁ )² + ( y₂ - y₁ )²
Distance between :
AB = √( -3-2)² + (-2 -3)²
= 5√2
BC = √(3+ 3)² + (2 + 2)²
= 2√13
CA = √( 3-2)² + (2 -3)²
= √2
Using Pythagoras theorem we have:
( Hypotenuse )² = ( Side1 )² + ( Side 2)²
Right hand side
= (5√2)² + (√2 )²
= 50 + 2
= 52
= ( 2√13)²
= Left hand side
This implies the triangle formed by the points is right angled triangle.
Therefore, yes the given points forms a right angled triangle.
The above question is incomplete , the complete question is:
Do the points (3 ,2) , ( -2 , -3 ), and ( 2, 3 ) form a triangle?.
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The prices paid for a model of a new car are approximately normally distributed with a mean of $17,000 and a standard deviation of $500. The price that is 3 standard deviations above the mean is $ . The price that is 2 standard deviations below the mean is $ . The percentage of buyers who paid between $16,500 and $17,500 is % The percentage of buyers who paid between $17,000 and $18,000 is %. The percentage of buyers who paid less than $16,000 is %.
The price that is 3 standard deviations above the mean is $18,500. The price that is 2 standard deviations below the mean is $15,500.
The percentage of buyers who paid between $16,500 and $17,500 is approximately 13.6%.
The percentage of buyers who paid between $17,000 and $18,000 is approximately 34.1%.
The percentage of buyers who paid less than $16,000 is approximately 2.3%.
It's important to note that these values are approximate and based on the assumption that the prices paid for the car are approximately normally distributed with a mean of $17,000 and a standard deviation of $500. It's also worth mentioning that these percentages are based on the standard normal distribution table which assumes a normal distribution with a mean of 0 and a standard deviation of 1.
I hope this helps :)
An assorted snack tray has three popcorn bags, four granola bars, and six apples. What is the probability that the next two customers both select popcorn
The probability that the next two customers would both select popcorn is 1/78.
What is the probability?Probability is the odds that a random event would happen. The odds that the random event happens has a probability value that lies between 0 and 1. The more likely it is that the event would occur, the closer the probability value would be to one.
The probability that the next two customers would both select popcorn = number of popcorns / total number of snacks x [(number of popcorns / total number of snacks) - 1]
Total number of snacks = 3 + 4 + 6 = 13
2/13 x 1/12 = 1/78
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What is sin 45 simplified?.
Under Trigonometric ratios, the values of sin, cos, and tan are defined by the ratio of sides of a right-angled triangle.
One of the three fundamental functions in trigonometry, along with cosine and tan functions, is the sine function.
The ratio of the opposite side of a right triangle to its hypotenuse is known as the sine x or sine theta.
To determine a right triangle's unknown angle or sides, utilize the sine function. The sine function for any right triangle with an angle, let's say ABC, will be:
Opposite/hypotenuse = Sin
According to the trigonometric table, the value of Sin 45=[tex]\sqrt[/tex]2/2 which can be simplified as [tex]\sqrt{2} /2[/tex]×[tex]\sqrt{2} /\sqrt{2} =2/\sqrt[]{2}[/tex][tex]=1/\sqrt{2}[/tex]
Simplified value of Sin 45=1/[tex]\sqrt{2}[/tex]
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Help i want answerrrrrrrr pls
The length of TW is given as follows:
TW = 17.4 units.
How to obtain the length of TW?The length TW is the hypotenuse of a right triangle of sides WU and UT.
The Pythagorean Theorem states that for a right triangle, the length of the hypotenuse squared is equals to the sum of the squared lengths of the sides of the triangle.
The side lengths are given as follows:
TU = 12.6, as it is tangent just like TV.WU = 12.Hence the length TW is obtained as follows:
(TW)² = 12.6² + 12²
[tex]TW = \sqrt{12.6^2 + 12^2}[/tex]
TW = 17.4 units.
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What is the quadratic polynomial whose sum and the product of zeroes is 2 â…“ respectively?.
Zero of the quadratic polynomial whose X²+3X+2 are -2 and -1.
Sum of zeros ( alpha + beta) = -3
Product of zeros ( alpha × beta) = 2.
Quadratic polynomial = X²-(alpha + beta)X+ Alpha× beta = X²-(-3)X+2.
= X²+3X+2 is the required quadratic polynomial.
A = 1 , b = 3 , C = 2
X²+ 3X +2
X² + 2X+ X + 2
X(X+2) +1 ( X+2)
(X+2). ( X+1)
X+2 = 0. X+1 = 0
X = -2. X= -1
Zero of the quadratic polynomial whose X²+3X+2 are -2 and -1.
A polynomial is described as an expression that consists of variables, constants, and exponents, which might be mixed with the use of mathematical operations along with addition, subtraction, multiplication, and department (No division operation by a variable).
In arithmetic, a polynomial is an expression that includes indeterminates and coefficients, that entail best the operations of addition, subtraction, multiplication, and fine-integer powers of variables. An instance of a polynomial of an unmarried indeterminate x is x² − 4x + 7.
Polynomials are sums of phrases of the form k⋅xⁿ, in which okay is any wide variety and n is a positive integer. for example, 3x+2x-5 is a polynomial. advent to polynomials.
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Complete Question:
Find a quadratic polynomial, the sum, and the product of whose zeroes are -3 and 2 respectively. hence find the zero
Please help me with this
Answer:
1 d.p to c 7m
Step-by-step explanation:
you should use phythagoras theorem to caculate the leght of BF ang that is my answer
find the size of QRS.
8 cm
12 cm
4 cm
Q
R
P
The size of QRS in the given figure 15 cm.
How to find the size of QRS?A fundamental Euclidean geometry relationship between the three sides of a right triangle is the Pythagorean theorem, also referred to as Pythagoras' theorem. According to this definition, the area of the square whose side is the hypotenuse is equal to the sum of the areas of the squares on the other two sides.
step1
We know
PS=8cm
PQ=12cm
QR=4cm
because we know that both of these parts have to do with right triangles, we know that we can use the Pythagorean theorem.
a² + b² = 4² (add in values)
8² + 12² +4²
64 + 144 +16=224
find the square root of 224= 15
Size of QRZ =15 cm
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What number is one more than 79?.
The number one more than 79 is 80.
Number:
Numbers are mathematical objects used for counting, measuring, and labeling. The original example is the natural numbers 1, 2, 3, 4, etc. [1] Numbers can be linguistically represented by numerals. More generally, individual numbers can be represented by symbols called digits. For example, "5" is the number representing the number five. Since only a relatively small number of symbols can be remembered, basic numbers are usually organized into number systems, which are systematic ways of representing each number. The most common number system is the Hindu-Arabic number system, which can represent any number using combinations of 10 basic numeral symbols called digits. In common parlance, a number is indistinguishable from the number it represents.
Greater than Number:
It is a mathematical term used to compare two quantities and to establish a relationship between two quantities in which one term is greater than the other. The terms greater than, less than, and equal are used to compare two numbers, amounts, or amounts. Each term has a separate letter. B. "greater than" is represented by ">", "equal to" is represented by "=", and "less than" is represented by "<".
According to the Question:
To better understand this question,
It can be expressed as 1 more than 79, 1 more than 79, 1 more than 79, 79 plus 1.
Thus,
1 more than 79 is the same as 79 plus 1. So the answer for 1 greater than 79 is calculated as:
Therefore,
1 + 79 = 80.
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Can anyone answer this math question for me?
The correct answer is option A (4, 3), 35 units squared.
How to find the vertices?The coordinates of the three vertices of a rectangle are :
A(-3,3) , b(-3,-2) and c(4,-2)
The easy way to find the fourth vertex by the graphing the given points
See the attached figure
the given points are in blue color
and by using the symmetry of the rectangle
So, the coordinates of the fourth point D is (4,3) which are in red color
The base of the rectangle is the distance BC
From the graph ⇒⇒ BC = 7
The height of the rectangle is the distance AB
From the graph ⇒⇒ AB = 5
The area of the rectangle = base * height = 7 * 5 = 35
So, the correct answer is option A(4, 3), 35 units squared.
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Pleas help me I need the answers asap. The reason why I have 3 copy's of the same question is to show the multiple choices.
The solution for the equations is at x = -1 and y = -3.
2: the system of equations has the same slope and the same y-intercept so the system of equations has infinitely many solutions.
What are linear equations?When an algebraic equation is graphed, it always results in a straight line since each term in a linear equation has an exponent of 1. For this reason, it is referred to as a "linear equation."
There are both one-variable and two-variable linear equations.
Given the equations,
-2x + 4y = -10
2x + 2y = -8
adding both the equations so -2x and +2x will be eliminated
-2x + 4y + 2x + 2y = -10 - 8
6y = -18
y = -18/6
y = -3
substitute the value of y in equation 2x + 2y = -8
2x + 2(-3) = -8
2x = -8 + 6
x = -1
2: Given equations y = -x + 5 .........(1)
y + x = 5 .........(2)
equation 2 can be written as,
y = -x + 5
so both the equations have the same slope and the same value of y-intercept,
so the line overlaps each other and has infinitely many solutions.
Hence the solution s at x = -1 and y = -3.
2: Equations have infinitely many solutions.
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Attachments:
2 Photographs 1.4 MB each
Video 1.8 MB each
4 Spreadsheets 1.2 MB each
Answer:
there's nothing there?
The length of my living room is 24 feet.the width of my living room is 1/2 the length.what is the area of my living room
Answer: 24 x 1/2(24) = 288
Step-by-step explanation:
Half of 24 is 12.
Multiply 24 by 12 = 288
Create a number pattern that follows the rule
x
+
7
. Include 3 terms using the pattern.
Answer: 8, 9, 10
Step-by-step explanation:
Set [tex]x=1, 2, 3 \implies x+7=8, 9, 10[/tex].
simplify:cos^2(90°+ß) sin(90°-ß)/cos(360°+ß) sin(360°-ß) sin(180°-ß)
By trigonometric formulas and algebra properties, the trigonometric equation [cos² (90° + β) · sin(90° - β)] / [cos (360° + β) · sin (360° - β) · cos (180° - β)] is equivalent to - 2.
How to simplify a trigonometric equation
In this question we find a trigonometric equation, that is, an equation involving trigonometric functions, that must be simplified by trigonometric formulas and algebra properties. First, write the entire trigonometric formulas:
[cos² (90° + β) · sin(90° - β)] / [cos (360° + β) · sin (360° - β) · cos (180° - β)]
Second, eliminate the cosine squared of the equation by trigonometric formula:
[[1 + cos (180° + 2 · β)] · sin(90° - β)] / [cos (360° + β) · sin (360° - β) · sin (180° - β)]
[sin (90° - β) + cos (180° + 2 · β) · sin(90° - β)] / [cos (360° + β) · sin (360° - β) · sin (180° - β)]
Third, simplify the trigonometric functions for angle additions and subtractions:
[sin (90° - β) + cos (180° + 2 · β) · sin(90° - β)] / [cos (360° + β) · sin (360° - β) · cos (180° - β)]
[cos β - cos 2β · cos β] / [cos β · sin (- β) · sin β]
- (cos β - cos 2β · cos β) / (cos β · sin β · sin β)
Fourth, simplify the expression by algebra properties:
- (1 - cos 2β) / sin² β
(cos 2β - 1) / sin² β
Fifth, eliminate the double angle by trigonometric formulas:
(cos² β - sin² β - sin² β - cos² β) / sin² β
Sixth, simplify the expression by algebra properties:
- 2 · sin² β / sin ² β
- 2 · 1
- 2
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7
If f(x)=√x-5 and g(x) = -x², what is the value of g(f(9))?
A 4
C 16
B -14
D 2
Option (a) represents the correct answer i.e. The value of g(f(9)) is -4.
What is a function?
A relation known as a function connects members of one set in a specific way to those of another set.
Given, f(x)=√x-5 and g(x) = -x²
here, g(f(x)) = g(√x-5 )
= - (√x-5)²
So, g(f(9)) = - (√9 - 5)²
= - (3-5)²
= -4
Hence, Option (a) is correct.
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Option (a) represents the correct answer i.e. The value of g(f(9)) is -4.
What is a function?a mathematical phrase, rule, or law that establishes the link between an independent variable and an outcome variable (the dependent variable). An input and also an output are linked by a function. It functions similarly to a machine with an input or an output. Additionally, the input and output are somehow connected. The traditional format for writing a function is f(x) "f(x) =... "
Given, f(x)=√x-5 and g(x) = -x²
here, g(f(x)) = g(√x-5 )
= - (√x-5)²
So, g(f(9)) = - (√9 - 5)²
= - (3-5)²
= -4
Hence, Option (a) is correct.
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Graph and please explain answer with steps!
f(x)=-x+3,x<=-3
f(x)=-x^(2)+6,x>-3
The graph of the function f(x)=-x+3,x<=-3 and f(x)=-x^(2)+6,x>-3 is given attachment.
What is function?A function is a procedure or a relation that links each element of a non-empty set A, at least, to one element of a different non-empty set B. In mathematics, a relation f between two sets, A and B, is referred to as the function's domain and co-domain, respectively. f = {(a,b)| for all a ∈ A, b ∈ B}
If each element of set A has exactly one image in set B, then the relation is said to be a function.
A function is a relation from a non-empty set B such that its domain is A and no two different ordered pairs in f share the same first element.
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Please answer this question with decent explanation. Thank you.
Answer: Transversal
Step-by-step explanation:
Altitude is in the triangle as it has vertexes shown by the line, Hypotenuse is the longside of the triangle which is shown, and the legs, every single triangle has legs, which leaves us with transversal which means a straight line that cuts a parrel line. Which isn't shown so that's the answer. Have a good day ;)
Is A ={ x x² 4 and 3x 9 an empty set justify your answer?.
x²= 4 and 3x=9 is not an empty set because there is no element we can say that is an empty set but there is an element, so it is not an empty set.
In arithmetic, the empty set is a completely unique set having no elements; its size or cardinality (depending on elements in a fixed) is 0. some axiomatic set theories make certain that the empty set exists by including an axiom of the empty set, whilst in different theories, its lifestyles may be deduced. Many feasible properties of sets are vacuously genuine for the empty set.
Any set aside from the empty set is known as non-empty. In a few textbooks and popularizations, the empty set is known as the "null set". but, a null set is a distinct belief inside the context of the measure concept, wherein it describes a hard and fast degree 0 (which is not always empty). The empty set may also be referred to as the void set.
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Complete Question:
Is A={x:x²=4 and 3x=9} an empty set justify your answer?
Please help! Its worth 15 point things
It will cost Caden $5445 to paint the outside walls and roof of the warehouse.
What is the superficial area of the warehouse?The superficial area can be calculated using the following formula:
2 (lh +wh + lw )
2 (38 x 45 + 30 x 45 +38 x 30)
2 (1710 + 1350 + 1140)
2 x 4200
8400 square foot
Now, let's subtract the area of the floor that will not be painted.
30 x 38 = 1140
8400 - 1140 = 7260 feet to be painted
How much will it cost to paint this area?7260 x 0.75 = $5445
Based on this, the total cost to paint the area desired is $5445.
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the circumference of a circle is 74.48
Answer:
question is not mentioned properly
Step-by-step explanation:
i can answer but first what's the question
If You Are Measuring The Electrical Potential Difference From A Rectangular \( 9 \Mathrm{~V} \) Battery, Which Setting Should You
A battery is a nice illustration. Atoms have had their electrons chemically removed in batteries. Because the positive ions and electrons are stored at the opposing ends of the battery, there is a potential difference between the two ends.
What is Rectangular?A rectangle in Euclidean plane geometry is a quadrilateral with four right angles. It can alternatively be explained in terms of an equiangular quadrilateral a term that refers to a quadrilateral whose angles are all equal or a parallelogram with a right angle. A square is an irregular shape with four equal sides. A rectangle is a sort of quadrilateral with parallel sides that are equal to one another and four vertices that are all 90 degrees apart. Because of this, it is also known as an equiangular quadrilateral. Because the opposite sides of a rectangle are equal and parallel, it can also be referred to as a parallelogram.To learn more about Rectangular, refer to:
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Amy flicks the spinner 200 times and it comes up gray 157 times. Do you think Amy's spinner is fair? Explain.
The percentage of getting grey is 78.5%. Amy's spinner is fair.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that Amy flicks the spinner 200 times and it comes up grey 157 times.
The percentage of the grey comes up 157 times will be calculated as:-
P = 157 / 200
P = 0.785 x 100
P = 78.5%
Amy's spinner is fair.
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What is it called when you substitute a number for each variable and simplify?.
When you substitute a number for each variable and simplify it is called a Substitution method.
I will demonstrate how the substitution method works. Suppose we have the following systems of linear equations with two variables:
Equation 1: 3x + 2y = 11
Equation 2: -x + y = 3
By solving these two equations we get x=1 and y=4.
The substitution method is a quick and easy way to algebraically solve a set of linear equations and determine the variables' solutions. According to what the name implies, this method entails determining the value of the x-variable in terms of the y-variable from the first equation and then substituting or replacing the value of the x-variable in the second equation. We can solve and determine the value of the y-variable in this method. Finally, we may use any of the above equations to obtain x by substituting the value of y. This procedure can also be switched around so that we first solve for x before solving for y.
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you go to a store to buy clothes. shirt cost 10.25$ each and pants cost $17 each. let x equal the number of shirts and y equal the number of pants you buy. you can only spend up tp $50 at the store.
Answer:
10.25x+17y ≥ 50
Step-by-step explanation:
10.25x is how much shirts you can buy
17y is how much pants you can buy
50 is the total money you can spend
HOPE THIS HELPED!
The inequality that represents the situation is 10.25x + 17y ≤ 50.
What is an inequality?In mathematics, "inequality" refers to a relationship between two expressions or values that are not equal to each other. To solve the inequality, you may multiply or divide each side by the same positive number, add the same amount to each side, take the same amount away from each side, and more. You must flip the inequality sign if you multiply or divide either side by a negative number.
Given:
You go to a store to buy clothes.
The shirt cost 10.25$ each and the pants cost $17 each.
Let x equal the number of shirts and y equal the number of pants you buy. you can only spend up to $50 at the store.
That means,
10.25x + 17y ≤ 50
Therefore, the inequality is 10.25x + 17y ≤ 50.
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At which points are the functions y = f(x) and y = g(x) equal? What are the x-values of the solution?
The correct option regarding the solution to the system of equations is given as follows:
It is a solution to f(x) = g(x) because it is the x-coordinate where the two graphs intersect.
Hence the x-value of the solution is given as follows:
x = 3.
How to obtain the solution to the system of equations?We want to obtain the graphic solution for the system of equations, hence we obtain the point of intersection of the two equations.
The point of intersection in this problem has a x-coordinate of 3, hence the third option is the correct option.
Missing InformationThe complete problem is given as follows:
If x=3 is a solution to f(x)=x²-x and g(x)=2x, why is it also a solution to f(x) = g(x)
(1 point)
O It is a solution to f(x) = g(x) because it is the x-intercept of the two graphs
O it is a solution to f(x) = g(x) because it is the y-intercept of the two graphs.
O It is a solution to f(x) = g(x) because it is the x-coordinate where the two graphs intersect
O it is a solution to f(x) = g(x) because both graphs are positive at x = 3.
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R is the midpoint of QS and P is the midpoint of QT
If ST=u+60 and PR = 4u+2, what is PR
By using the fact that the triangles are similar, we can see that u = 8, then the length of side PR is:
PR = 68
How to find the length PR?
We know that R is the midpoint of QS and P is the midpoint of QT, this means that tiangles QRP and QST are similar triangles, and that the scale factor between them is 2.
Then we know that:
ST = 2*RP
We know that:
RP = 4u + 2
ST = u + 60
Then we can write the linear equation:
u + 60 = 2*(4u + 2)
u + 60 = 8u + 4
60 - 4 = 8u - u
56 = 7u
56/7 = u
8 = u
Now we can find the length of side PR.
PR = u + 60
PR = 8 + 60
PR = 68
Learn more about similar triangles at:
https://brainly.com/question/14285697
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