The value of the function ƒ(g(3)) is 239, when ƒ(x) = x³ + 5x² − 2x − 1 and g(x) = x² – 4.
What is function?A function is an equation with just one solution for every value of y in the equation. A function pairs each input of a particular type with exactly one output.
Instead of y, it is typical to name functions f(x) or g(x). f(2) instructs us to calculate the value of our function when x is equal to 2.
We have given to find ƒ(g(3))
when ƒ(x) = x³ + 5x² − 2x − 1
and g(x) = x² – 4
When g(3) = (3)² – 4
= 9 - 4
= 5
For
ƒ(g(3)) = (5)³ + 5(5)² − 2(5) − 1
= 125 + 125 - 10 - 1
= 239
Thus, the value of the function ƒ(g(3)) is 239, when ƒ(x) = x³ + 5x² − 2x − 1 and g(x) = x² – 4.
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The organizer of a potluck dinner sends 6 people a list of 10 different recipes and asks each person to bring one of the items on the list. If all 6 people randomly choose a recipe from the list, what is the probability that at least 2 will bring the same thing?
The probability of at least two people bringing the same item is 0.19.
What is probability?Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true.
Given that, The organizer of a potluck dinner sends 6 people a list of 10 different recipes and asks each person to bring one of the items on the list.
The probability of two people bringing the same item can be calculated using the formula P(A∩B) = P(A) × P(B).
In this case, P(A) and P(B) are both 1/10, because each person has the same chance of choosing any one of the 10 items on the list.
Therefore, the probability of two people bringing the same item is 1/100. To calculate the probability of at least two people bringing the same item, we can use the formula P(A∪B) = P(A) + P(B) - P(A∩B).
In this case, P(A∪B) = 1/10 + 1/10 - 1/100 = 0.19.
Hence, the probability of at least two people bringing the same item is 0.19.
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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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How do you find a 60 degree triangle?.
60° triangle can be calculated in radians as π/3 radians.
60 degree angle is an acute angle in geometry and is expressed as π/3 in radians. Each angle in an equilateral triangle is equal to 60 degrees.
A 60-degree angle is an acute angle since angles less than 90 degrees are considered acute. In the case of a geometric angle, the arc is confined by the sides and is centered at the vertex. When rotated, the arc is centered in the center of rotation and is limited to any other point and its image.
Thus, 60° triangle can be calculated in radians as π/3 radians.
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HELP MEEEEEEE PLEASEEEEEEEE
Answer:
A to B: Scale of 3, and (10,6)
B to A: Scale of (1/3) and (10,6)
Step-by-step explanation:
See attached worksheet.
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
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
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?
/
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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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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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
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Ai Mi has a loyalty card good for a 13% discount at her local hardware store. What would her total in dollars and cents be, after the discount and before tax, if the total cost of all the items she wants to buy is $39? Round to the nearest cent.
In linear equation, $33.93 would her total in dollars and cents be, after the discount and before tax, if the total cost of all the items she wants to buy is $39.
What in mathematics is a linear equation?
A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept. Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables. Equations with variables of power 1 are referred to be linear equations. One example with only one variable is where ax+b = 0, where a and b are real values and x is the variable.
Item she wants to buy is priced at $39
After the discount, and before tax, the price is $33.93.
39.00 x .13 = 5.07
39.00 - 5.07 = $33.93
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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
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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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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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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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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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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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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Use trigonometric identities to simplify each expression
c) sec^2(pi/2-x) (sin^2(x)-sin^4(x))
Using trigonometric identities to simplify the expression, we have sec²(π/2 - x) (sin²(x)-sin⁴(x)) = cos²x
What are trigonometric identities?Trigonometric identities are equations that contain the trigonometric ratios.
How to use trigonometric identities to simplify the expression?Since we have the trigonometric expression sec²(π/2 - x) (sin²(x)-sin⁴(x))
We desire to simplify it as follows.
sec²(π/2 - x) (sin²(x)-sin⁴(x))
Using the trigonometric identity sec²(π/2 - x) = 1/cos²(π/2 - x), we have that
sec²(π/2 - x) (sin²(x)-sin⁴(x)) = 1/cos²(π/2 - x) × (sin²(x)-sin⁴(x))
Also, using the fact that cos²(π/2 - x) = sinx, we have that
1/cos²(π/2 - x) × (sin²(x)-sin⁴(x)) = (sin²(x) - sin⁴(x))/sin²x
Factorizing out sin²x, we have that
(sin²(x) - sin⁴(x))/sin²x = (sin²(x)(1 - sin²(x))/sin²x
= 1 - sin²x
= cos²x
So, sec²(π/2 - x) (sin²(x)-sin⁴(x)) = cos²x
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what is the exact value of cos 5pi/12
The value of cos 5pi/12 is found to be 0.2588.
Define the term trigonometric ratios?Trigonometric ratios are derived from the value of a ratio of sides of a right-angled triangle and contain the values of all trigonometric functions. These trigonometric ratios of a given acute angle are the ratios of the sides of either a right-angled triangle having respect to that angle.The given trigonometric ratio is-
= cos (5π/12)
The value of π in degrees is 180, substitute it.
= cos (5*180/12)
= cos (900/12)
= cos (75)
Using calculator
≈ 0.2588
Thus, the value of cos 5pi/12 is found to be 0.2588.
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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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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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Tom i 5 year older than jerry. In 2 year, jerry will be three fourth a old a tom. Find their age now
Their age now are 13 years old for Jerry and 18 years old for Tom.
How to find their age?As per data given, Tom age now = 5 + Jerry age now. After time = 2 year, Tom age : Jerry age = 4 : 3. We can determine their age now by substitute methods as follow:
After 2 years = Tom age : Jerry age = 4 : 3
Tom age now + 2 : Jerry age + 2 = 4 : 3
Substitute Tom age now to jerry age now from first formula, so:
Tom age now + 2 : Jerry age now + 2 = 4 : 3
5 + Jerry age now + 2 : Jerry age now + 2 = 4 : 3
3 ( 5 + Jerry age now + 2) = 4 (Jerry age now + 2)
21 + 3 Jerry age now = 4 Jerry age now + 8
Jerry age now = 21 - 8
Jerry age now = 13 years old
Find the tom age from first formula
Tom age now = 5 + Jerry age now
Tom age now = 5 + 13
Tom age now = 18 years old
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Why is the square root of x undefined?.
The square root of negative x undefined is undefined for the set of Real numbers.
We know that the square root of a number is nothing but the factor/value that we can multiply by itself to get that number.
Finding a square root of number is an inverse method of squaring a number.
A radical symbol '√' used to represent the square root of number.
If m is the square root of n, then it is represented as m = [tex]\sqrt{n}[/tex],
We can write above relation as, m² = n
We know that square of any real number is positive.
For example, 3² = (3 × 3) = 9
(-3)² = (-3) × (-3) = 9
i.e., the square root of 9 is 3 and -3
Thus the square root of number is not defined for negative real number.
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The complete question is:
Why is the square root of negative x undefined?.
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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Arthur sits in the park reading a newspaper, then starts walking home at a constant pace. He stops for bagels, then walks the rest of the way home.
Use the graph to answer questions about this scenario.
1. What does the x-axis represent in this situation?
2. What does the y-axis represent?
3. During which parts of the graph does Arthur's distance from home decrease?
4. When is Arthur waiting for bagels? Explain how you know.
5. If Arthur's pace had not been constant after leaving the bagel shop, which part of the graph would change? Explain how that part of the graph would change.
6. If Arthur had spent less time reading his newspaper, which part of the graph would change? How would that part change?
The answers to each part is below..
What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given is a graph as shown in the image.
The {x} - axis represents the time.The {y} - axis represents the distance from the home.During the 2nd and 4th part.During the 2nd part, he is waiting for bagels.The 2nd part of the graph would change.The first part would have changed.Therefore, the answers to each part is given above.
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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].
Kurt is starting a business selling handmade necklaces. He has decided to invest an initial amount of $20 for advertising, and materials cost $7 for each necklace he makes. Kurt can sell his creations for $9 per necklace. Once he makes and sells a certain number of necklaces, he will break even, with identical expenses and sales. How many necklaces would that take? What would the total expenses and sales be then?
PLEASE ANSWER FAST WILL MARK BRAINLIEST!!!
The number of necklaces at the break-even point will be 10.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
Kurt is beginning a business selling high-quality neckbands. He has chosen to contribute an underlying measure of $20 for publicizing, and materials cost $7 for every accessory he makes. Kurt can sell his manifestations for $9 per piece of jewelry.
Let 'x' be the number of necklaces. Then the equations are given as,
Cost = 7x + 20
Sell = 9x
The number of necklaces at the break-even point is calculated as,
Sell = Cost
9x = 7x + 20
2x = 20
x = 10
The number of necklaces at the break-even point will be 10.
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Use the distributive property to write an expression that is equivalent to 8(a + 4)
Using the distributive property we will find the equivalent expression:
8*(a + 4) = 8a + 32
How to use the distributive property?Remember that the distributive property for the multiplication says that:
A*(B + C) = A*B + A*C
So we distributed the product along the addition.
Here we want to rewrite the expression:
8*(a + 4)
Using the distrubitive property, we can rewrite this as:
8*(a + 4) = 8*a + 8*4
= 8a + 32
That is the equivalent expression.
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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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