And irrational number is a number than cannot be written as a simple fraction.
Two good examples of irrational numbers are PI and the square root of 2. These numbers have never-ending decimals, and their decimals never repeat.
Answer:
An irrational number cannot be expressed as a ratio between two numbers and it cannot be written as a simple fraction because there is not a finite number of numbers when written as a decimal. Instead, the numbers in the decimal would go on forever, without repeating.
Step-by-step explanation:
Find f^1(x) for f(x)= -3x+2 and state whether or not it is a function.
a : f^1(x)= -1/3x +2/3 ; function
b : f^1(x)= 1/3x -2/3 ; not a function
c : f^1(x)= 1/3x +2/3 ; function
d : f^1(x)= -1/3x -2/3 ; function
Answer:
A
Step-by-step explanation:
f^-1(x) is a common notation for the inverse of the function. An inverse of a function is a reflection over the line y=x. This results in the points (x,y) of the function becoming (y,x) for the inverse. Algebraically you find the inverse by switching the location of y and x in the equation of the function and solving.
y = -3x + 2
x = -3y + 2
x - 2 = -3y
-(x-2)/3 = y
-1/3x + 2/3 = y
The inverse of the function is a linear function because it follows the form y = mx+b for its equation. All lines are functions. The inverse is a function.
Answer: a : f^1(x)= -1/3x +2/3 ; function
Step-by-step explanation:
Solve for x. 1/2x = -9
Answer:-18
Step-by-step explanation:x in (-oo:+oo)
(1/2)*x = -9 // + 9
(1/2)*x+9 = 0
1/2*x+9 = 0 // - 9
1/2*x = -9 // : 1/2
x = -9/1/2
x = -18
x = -18
brainliest please
Kelie randomly chooses a number 1 to 10 what is the probability she chooses a number less than 3
Answer:
1/5
Step-by-step explanation:
She has 2 outcomes that satisfy a number less than 3. She can choose either 1, or 2.
There are 10 possible choices, so the probability is
2/10 = 1/5
Answer: [tex]=\dfrac{1}{5}[/tex]
Step-by-step explanation:
Given : The total numbers from which Kelie randomly chooses a number = 10
The numbers less than 3 = 1,2
Now, the probability she chooses a number less than 3 will be :-
[tex]=\dfrac{\text{Numbers less than 3}}{\text{Total numbers}}\\\\=\dfrac{2}{10}\\\\=\dfrac{1}{5}[/tex]
Hence, the probability she chooses a number less than 3 [tex]=\dfrac{1}{5}[/tex]
Manjeet made a pizza for his family using their four favorite toppings - pepperoni, mushrooms, onions and olives. He put twice as many onions as pepperoni and half as many mushrooms as olives. If there are 39 individual toppings on the pizza how many of each topping did he use? How many different combinations can you come up with?
Answer:
Let
x = the number of pepperoni added to the pizza.
y = the number of mushrooms added to the pizza.
z = the number of onions added to the pizza.
u = the number of olives added to the pizza.
Twice as many onions as pepperoni
z = 2*x
Half as many mushrooms as olives
y = u/2
There are 39 individual toppings on the pizza
x + y + z + u = 39
We are dealing with a system of equation with 4 unknowns and only three equations.
2*x - z = 0
y - u/2 = 0
x + y + z + u = 39
This means that there are an infinite number of solutions for your problem
For example, here is one solution
x = 1
z = 2
1 + y + 2 + (2y) = 39
3y = 36
y = 12
u = 24
Tommy has a pet monkey every day his monkey eats 4 apples in the morning. The monkey also eats two bananas for every banana that Tommy eats. Write an equation to describe this situation where X is the number bananas Tommy eats and y is the total number of fruits the monkey eats
Answer:X*2+4=y
Step-by-step explanation:Ok, so, we can pull four different points from this equation.
The monkey eats 4 apples each morning
The monkey eats 2 bananas for each 1 Tommy has
The number of bananas Tommy eats is marked as X
The number of fruits the monkey eats is marked as y
Let's start with Tommy.
X
Tommy eats X amount of bananas. Next the monkey.
X=y
The monkey eats y amount of bananas, but if you notice, he eats double to amount Tommy eats. So let's double Tommy's bananas.
X*2=y
You'll also notice, the monkey eats four apples everyday. Now, we're looking for the monkey's FRUIT intake, where as we're only looking at Tommy's BANANA intake. So, let's add that to the equation.
X*2+4=y
And there's the equation right there.
Ella and her brother are driving between 2 cities that are 330 miles apart at a rate of 55 mph.How long will it take them to make the trip
Answer:
6 hours
Step-by-step explanation:
1. Divide the total miles (330) by the speed (55)
330/55 = 6
sin(Sin^-1 x)=x for -1<=x<=1. True or false?
Answer:
True
Step-by-step explanation:
In general, when you compose a function [tex]f(x)[/tex] with its inverse [tex]f^{-1}(x)[/tex], you always get the identity function:
[tex]f(f^{-1}(x))=x[/tex]
The limitation [tex]-1\leq x \leq 1[/tex] is necessary because the arcsin function wouldn't be defined otherwise.
The statement 'sin(sin^-1 x) = x' is true for all real numbers x.
The statement 'sin(Sin^-1 x)=x for -1<=x<=1' is true. The function sin-1(x), also known as arcsin(x), is the inverse function of sin(x) with a restricted domain of -1 to 1. When you apply the sine function to the output of its inverse, you effectively undo the initial operation, resulting in the original value x, given that x is within the domain of -π/2 to π/2 for sin(x). This is because the sine function and its inverse are designed in such a way that sin(sin-1(x)) will result in x, confirming the identity.
Which represents the number of lines of symmetry that are possessed by a regular n-gon?
A. n/2
B. n
C. 180/n
D. 360/n
Answer:
Option B. n
Step-by-step explanation:
we know that
A regular polygon is a convex polygon whose angles are all congruent.The number of lines of symmetry in a regular polygon is equal to the number of sides a regular polygon has.
therefore
the answer is option B. n
Academy Sports buys baseball bats for $40. If they increase the price 75%, how much will the bats cost?
Answer:
$70
Step-by-step explanation:
$40x.75=30
30+40=$70
This is very important!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
Step-by-step explanation:
Ronnie brought a 25pound bag of food kills dog 810 2/5 lb of food in the first month and 10 or 5 pound of food and the second one how much dog food and pound was remaining in the bag at the end of two months
In an underground parking lot, the charge for parking is $1 for the first hour and $0.50 for each additional hour (or part of an hour). A customer's parking stub shows that their car was parked for 3 hours and 49 minutes.
How much does this customer have to pay the parking attendant?
Answer:
$2.50
Step-by-step explanation:
just do 1 for the first hour then .5 for the next 2 then .5 for the remaining 49 minutes
Answer: $2.50
Step-by-step explanation: The formula to solve the cost of parking is $1 for the first hour + (3 x .5) for the additional three hours.
1 + (3 x .50) = 1 + 1.50 = $2.50 is the cost to park.
Identify the domain of the function shown in the graph.
all positive real numbers
Answer:
C. All real numbers
Step-by-step explanation:
The domain refers to all values of x that makes the function define.
The given given graph represents a linear function.
A linear function is a polynomial function.
Polynomial functions are defined for all real numbers.
The correct choice is C.
PLz help me
Derek and Susan each open interest-bearing accounts in a bank and put the same amount of money into their accounts. Derek's account earns simple interest. The balance, in dollars, in Derek's account after t years is represented by the function D.
D(t)=500(1+2.5t)
Susan's account earns interest at a lesser rate than Derek's account, but the interest is compounded annually. The balance, in dollars, in Susan's account after t years is represented by the function
S. S(t)=500(1+1.8)^t
Which statement is true?
A. At first Derek's account balance will be greater, but eventually Susan's account balance will be greater.
B. Derek's account balance will always be greater than Susan's account balance.
C. Susan's account balance will always be greater than Derek's account balance.
D. At first Susan's account balance will be greater, but eventually Derek's account balance will be greater.
Answer:
Option A.
Step-by-step explanation:
we have
Derek's account
[tex]D(t)=500(1+2.5t)[/tex]
Susan's account
[tex]S(t)=500(1+1.8)^t[/tex]
Using a graphing tool
see the attached figure
At first Derek's account balance will be greater, but eventually Susan's account balance will be greater
At school baje sale a total of 40 cupcake and muffins were sold. The total number of cupcake sold was four more than twice the number of muffins. How many cupcake and muffins were sold at the bake sale
Answer:
28 cupcakes and 12 muffins were sold.
Step-by-step explanation:
First identify what variable to use for cupcakes and muffins.
X→ Cupcakes
Y→ Muffins
Then you need to write two equations.
X+Y= 40
X= 4+2Y
Since you have the value of X you need to substitute.
(4+2Y)+Y= 40
Combine like terms.
4+3Y= 40
Now use Subtraction Property of Equality.
4+3Y= 40
-4 -4
Now you have 3Y= 36
You have to use Division Property of Equality now.
[tex]\frac{3Y}{3}[/tex]= [tex]\frac{36}{3}[/tex]
If done correctly you should get Y= 12
Afterwards you must get 12 and subtract it from 40.
40-12= 28
28 is the amount of cupcakes sold.
To check you can see that 28 is equal to 12×2+4.
Hope this helped!
The bake sale sold 28 cupcakes and 12 muffins. This was determined by setting up a system of two equations based on the problem details and solving for the number of cupcakes and muffins sold.
Explanation:This is a problem of algebraic equations related to the real-world scenario of a bake sale. Here, we have two types of food items: cupcakes and muffins. According to the problem, the total number of cupcakes and muffins sold was 40. The information provided also states that the number of cupcakes sold was four more than twice the number of muffins sold.
To solve this problem, we need to set up a system of two equations. First, we know that the combined number of cupcakes (C) and muffins (M) is 40, so we can write this equation: C + M = 40. Secondly, we know that the number of cupcakes is four more than twice the number of muffins, giving us the second equation: C = 2M + 4.
Now, we can substitute the second equation into the first one, resulting in: 2M + 4 + M = 40. Simplifying this gives 3M + 4 = 40. Subtracting 4 from both sides gives 3M = 36. Dividing both sides by 3 then gives M = 12. Substituting M = 12 back into the first equation (C + M = 40), we find that C = 40 - 12 = 28.
So, the bake sale sold 28 cupcakes and 12 muffins.
Learn more about Algebraic Equations here:https://brainly.com/question/953809
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Given 1+tan x/ 1+ cot x= 2 , find a numerical value of one trigonometric function of x
[tex]b. \tan(x) = 2[/tex]
A right triangle has an area of 33mm squared and a height of 11mm how long is the base of the triangle
To find the answer for this, it's a bit hard, but here is the formula
[tex](area \times 2) \div h[/tex]
We plug our numbers into the formula...
[tex](33 \times 2) \div 11[/tex]
66÷11=6
So the answer is 6mm
The number of fish in the lake decreased by 25% between last year and this year last year they were 60 fish in the lake what is the population this year
Answer:
45 fish this year
Step-by-step explanation:
60 x .25 = 15
60 - 15 = 45
The solution of two linear equations is (-2,2). One equations has a slope of 3. The slope of the other equation is the negative reciprocal of the slope of the first.
The system described above is represented by the following equations.
Answer:
Its true ⇒ answer (a)
Step-by-step explanation:
* The solution of two linear equation means that this solution
is a solution for each equation
* To check if the point is a solution of an equation
- Substitute its coordinates in the equation, if the left hand side
is equal the right hand side, then the point is a solution
of this equation
* Lets study our problem
- (-2 2) is the solution of two linear equations
- The slope of one equation is 3
- The slope of the second equation is the negative reciprocal
of the slope of the first, means = -1/3
* Check the this conditions in the given equations
- In the equation y = 3x + 8 ⇒ the slope = 3
- In the equation y = -1/3 x + 4/3 ⇒ the slope = -1/3
* Now lets substitute the solution (-2 , 2) in the both equations
- First equation
∵ y = 2 ⇒ L.H.S
∵ 3(-2) + 8 = 2 ⇒ R.H.S
∵ L.H.S = R.H.S
∴ (-2 , 2) is a solution of the equation y = 3x + 8
- Second equation
∵ y = 2 ⇒ L.H.S
∵ (-1/3)(-2) + 4/3 = 2/3 + 4/3 = 6/3 = 2 ⇒ R.H.S
∵ L.H.S = R.H.S
∴ (-2 , 2) is a solution of the equation y = -1/3 x + 4/3
∴ (-2 , 2) is the solution of the two equations
* Its true
State the domain and range for the function.
f(x)= 2 csc (x/2) )
Answer:
Option b
Step-by-step explanation:
Since we are dealing with a question that deals with domain and range, it is best if we solve the problem graphically with the help of a calculator or any plotting tool.
Please, see attached image
We graph the equations and find the behavior of the graph
Domain
All reals except multiples of 2π
Range:
f(x) ∈ (-∞,-2] ∪ [2,∞)
Final answer:
The domain of f(x) = 2 csc(x/2) is all real numbers except for x = 2nπ where n is an integer, and the range is y ≤ -2 or y ≥ 2, since cosecant is undefined for sine values of zero and has range outside of [-1, 1] multiplied by 2.
Explanation:
To state the domain and range of the function f(x) = 2 csc(x/2), we first need to understand the behavior of the cosecant function, which is the reciprocal of the sine function. The sine function has a domain of all real numbers and a range of [-1, 1]. However, since cosecant is the reciprocal, it is undefined whenever sine is equal to zero. Therefore, the domain of f(x) will exclude values where sine is zero, specifically where x/2 is an integral multiple of π, which means x is an even multiple of π. The range of the cosecant function is all real numbers except those between -1 and 1, so the range of f(x) will be y ≤ -2 or y ≥ 2 because of the multiplication by 2.
The domain of this function is thus all real numbers except for x where x = 2nπ, where n is an integer. The range is all real numbers y such that y ≤ -2 or y ≥ 2.
the area of a parallelogram that has a base of 30 feet and a height of 20 feet.
area of parallelogram=base x height
= 30 x 20
= 600feet
12 less than 7 times a number is the same as 32 less than the product of -3 and a number
The question involves setting up and solving an algebraic equation to find a number such that 12 less than 7 times this number equals 32 less than the product of -3 and the number. The solution to the equation 7x - 12 = -3x - 32 is x = -2.
The phrase '12 less than 7 times a number' can be represented as 7x - 12, where 'x' is the number in question. The phrase '32 less than the product of -3 and a number' translates to -3x - 32. Setting these two expressions equal to each other gives us the equation 7x - 12 = -3x - 32.
To solve for 'x', we can first add 3x to both sides of the equation, which will give us 10x - 12 = -32. Next, we add 12 to both sides to isolate the term with 'x', resulting in 10x = -20. Finally, we divide both sides by 10 to find the value of 'x', which yields x = -2.
Therefore, the number that satisfies the condition is -2.
Given tanx=8/15 when pi < x < 3pi/2, find tan x/2.
Answer:
[tex]tan(x/2)=-4[/tex]
Step-by-step explanation:
we know that
The angle x belong to the III quadrant -----> given problem
step 1
Find the angle x
[tex]x=arctan(8/15)=28.07\°[/tex]
Remember that the angle x belong to the III Quadrant
so
[tex]x=28.07\°+180\°=208.07\°[/tex]
step 2
Find angle x/2
[tex]x/2=208.07\°/2=104.035\°[/tex]
step 3
Find tan(x/2)
[tex]tan(104.035\°)=-4[/tex]
Give the coordinates of Point P without using any new variables.
(Please show your work.)
Answer:
(a-b, c)
Step-by-step explanation:
The midpoints of the two diagonals are the same, so we have ...
(P + (-a, 0))/2 = (O +(-b, c))/2
Multiplying by 2 and subtracting (-a, 0), we get ...
P = (0, 0) +(-b, c) -(-a, 0)
P = (a-b, c)
At lunch,8 friends share 5 cookies equally. What fraction of a cookie does each friend get.
It is 5/8 because it is 5 per 8. You cut up the cookies and not the people. It does not reduce.
Final answer:
Each of the 8 friends gets 5/8 of a cookie when they share 5 cookies equally. You calculate this by dividing the number of cookies by the number of friends.
Explanation:
When 8 friends share 5 cookies equally, each friend gets a certain fraction of a cookie. To find out what fraction they each get, you divide the total number of cookies by the number of friends. In this case, you divide 5 cookies by 8 friends.
The calculation is 5 cookies ÷ 8 friends = 5/8 of a cookie for each friend.
Therefore, this means each friend gets 5/8 of a cookie. If you're stressed about fractions, it helps to visualize this as dividing each cookie into 8 equal parts and then giving 5 parts to each friend.
PLEASE HELP ASAP!!!
let f(x) = 2x^2 + x - 3 and g(x) = x - 1
find (g/f)(x) and state its domain.
ANSWER
[tex]( \frac{g}{f} )(x) = \frac{1}{ 2x+3} [/tex]
The domain is:
[tex]x \ne1 \: or \: x \ne - \frac{3}{2}[/tex]
EXPLANATION
The given functions are:
[tex]f(x) = 2 {x}^{2} + x - 3[/tex]
and
[tex]g(x) = x - 1[/tex]
[tex]( \frac{g}{f} )(x) = \frac{g(x)}{f(x)} [/tex]
[tex]( \frac{g}{f} )(x) = \frac{x - 1}{2 {x}^{2} + x - 3 } [/tex]
Factor the quadratic trinomial in the denominator.
[tex]( \frac{g}{f} )(x) = \frac{x - 1}{2 {x}^{2} +3 x - 2x- 3 } [/tex]
[tex]( \frac{g}{f} )(x) = \frac{x - 1}{ x(2x+3) -1 (2x + 3 )} [/tex]
[tex]( \frac{g}{f} )(x) = \frac{x - 1}{ (2x+3) (x-1)} [/tex]
Cancel the common factors,
[tex]( \frac{g}{f} )(x) = \frac{1}{ 2x+3} \: where \: x \ne1 \: or \: x \ne- \frac{3}{2} [/tex]
In their stamp collections, Marlee has 62 stamps, Xavier has 56 stamps, Nicki has 48 stamps, and Cameron has 89 stamps. Estimate how many stamps they would have if they combined their collections by rounding to the nearest ten first and then adding the rounded numbers
Answer:
260 total stamps
Step-by-step explanation:
Marlee - 60
Xavier - 60
Nicki - 50
Cameron - 90
60+60+50+90= 260
In how many ways can a judge award first, second, and third places in a contest with 10 entries?
1,000
720
30
The number of ways a judge can award first, second, and third places in a contest with 10 entries is:
720
Step-by-step explanation:We know that the choosing and arranging of r entries out of a total of n entries is given by the method of permutation and the formula is given by:
[tex]n_P_r=\dfrac{n!}{(n-r)!}[/tex]
Here we have to chose and arrange 3 people according to their ranks out of a total of 10 entries.
i.e. r=3 and n=10
Hence, the formula is given by:
[tex]{10}_P_3=\dfrac{10!}{(10-3)!}\\\\\\{10}_P_3=\dfrac{10!}{7!}\\\\\\{10}_P_3=\dfrac{10\times 9\times 8\times 7!}{7!}\\\\\\{10}_P_3=10\times 9\times 8\\\\\\{10}_P_3=720[/tex]
Hence, the answer is:
720 ways
I will mark brainliest
ANSWER
Q(5,-2),S(-3,4)
The given points have coordinates,
P(5,2) and R(-3,-4).
The mapping for a reflection across the x-axis is
[tex](x,y)\to (x,-y)[/tex]
This implies that,
[tex]P(5,2)\to Q( 5,-2)[/tex]
and
[tex]R(-3,-4) \to S(-3,4)[/tex]
The correct choice is A.
Answer:
The correct option is A.
Step-by-step explanation:
Current research indicates that the distribution of the life expectancies of a certain protozoan is normal with a mean of 48 days and a standard deviation of 10.2 days. find the probability that a simple random sample of 49 protozoa will have a mean life expectancy of 49 or more days.
[tex]X[/tex] is the random variable for lifespan of a protozoan and [tex]X\sim\mathcal N(48,10.2^2)[/tex]. Let [tex]\bar X[/tex] be the mean of a sample from this distribution, so that [tex]\bar X\sim\mathcal N\left(48,\left(\dfrac{10.2}{\sqrt{49}}\right)^2\right)[/tex].
For the sake of clarity, I'm denoting a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] by [tex]\mathcal N(\mu,\sigma^2)[/tex].
We have
[tex]P(\bar X\ge49)=P\left(\dfrac{\bar X-48}{\frac{10.2}{\sqrt{49}}\ge\dfrac{49-48}{\frac{10.2}{\sqrt{49}}\right)\approx P(Z\ge0.6863)\approx0.2463[/tex]
(where [tex]Z[/tex] follows the standard normal distribution)