In mathematics, a relation is a function if each input has a unique output. This one-to-one correspondence distinguishes functions, vital for modeling relationships and solving mathematical problems.
In mathematics, a relation is considered a function if each input (or element from the domain) corresponds to exactly one output (or element in the range).
Every element in the domain is associated with a unique element in the range.
A function is a specific type of relation between two sets, usually called the domain and the range.
In a function, each element in the domain is paired with exactly one element in the range.
Function Notation:
If f is a function, we often use the notation f(x) to represent the output (or value in the range) corresponding to the input x in the domain.
Key Criteria for a Relation to be a Function:
Domain-Range Pairs: Each element in the domain must be paired with an element in the range.
Uniqueness: Each element in the domain must have a unique partner in the range. No two different elements in the domain can have the same output.
Testing for a Function:
Vertical Line Test: If any vertical line intersects the graph of the relation at more than one point, the relation is not a function.
Mapping Diagram: A mapping diagram can visually represent the pairing of elements from the domain to the range.
Example:
Consider the relation where each person is paired with their date of birth. This is a function because each person has a unique date of birth.
Notation for Functions:
A function f is often denoted as f:A→B, where A is the domain and B is the codomain.
Therefore, a relation is a function if each input value maps to only one output value.
Learn more about function here
brainly.com/question/35114770
#SPJ3
The above question is incomplete, the complete question is:
Explain which relations are known as function ?
Write an equation in slope-intercept line form form for the line perpendicular to 2x-3y=12 that passes through the point (8,5)
Answer:
3x+2y=34
Step-by-step explanation:
L1: 2x-3y=12 => the slope m1=-2/(-3)=2/3
L2 perpendicular to L1 => m2= -1/m1= -3/2
the point A(8,5) ∈ L2
=> y–yA=m2(x–xA)
L2: y-5=-3/2 *(x-8)
L2: 2y-10=-3x+24
L2: 3x+2y=34
The company's annual profit (in millions of dollars) as a function of the app's price (in dollars) is modeled by
P(x) = -2(2-3)(x - 11)
What would be the company's profit if the app price is 0 dollars?
Answer:
0 dollars
Step-by-step explanation:
An icicle drips at a rate that can be represented by the function f(x) = −x2 + 9x − 18, where 0 ≤ x ≤ 10 and x is the number of hours after the sun has risen. When f(x) is a negative number, the icicle is not dripping. Determine the values when the icicle starts and stops dripping.
x = −3 and x = 6
x = 3 and x = −6
x = 3 and x = 6
x = −3 and x = −6
Answer: x=3 and x=6
Step-by-step explanation:
Put the first equation in math-way and find the roots/zeros
An icicle drips at a rate that can be represented by the function
[tex]f(x) = -x^2 + 9x - 18[/tex], where 0 ≤ x ≤ 10 and x is the number of hours after the sun has risen. So, The solution are x = 3 and x = 6.
What is a quadratic equation?A quadratic equation is the second-order degree algebraic expression in a variable. the standard form of this expression is ax² + bx + c = 0 where a. b are coefficients and x is the variable and c is a constant.
An icicle drips at a rate that can be represented by the function
[tex]f(x) = -x^2 + 9x - 18[/tex],
where 0 ≤ x ≤ 10 and x is the number of hours after the sun has risen.
First, we have to find its solution since it is a quadratic function;
[tex]f(x) = -x^2 + 9x - 18\\\\f(x) = -x^2 + 3x+ 6x - 18\\\\f(x) = x (3-x) - 6(3-x)\\\\f(x) = (3-x)(x-6)[/tex]
So, The solution are x = 3 and x = 6.
Learn more about quadratic equations;
brainly.com/question/13197897
#SPJ2
Combine the like terms to create an equivalent expression:
-4q-(-8q)+10
A water tank holds 621 gallons but is leaking at a rate of 4 gallons per week. A second water tank holds 828 gallons but is leaking at a rate of 7 gallons per week. After how many weeks will the amount of water in the two tanks be the same?
Answer:
69 weeks
Step-by-step explanation:
Let the number of weeks be x.
The first tank holds 621 gallons is leaking at a rate of 4 gallons per week. This means that after x weeks, the amount of water in the tank is:
621 - 4x
The second tank holds 828 gallons is leaking at a rate of 7 gallons per week. This means that after x weeks, the amount of water in the tank is:
828 - 7x
After a certain amount of weeks, the amount of water in both tanks is the same. That means that:
621 - 4x = 828 - 7x
=> 7x - 4x = 828 - 621
3x = 207
x = 207 / 3 = 69
This means that the amount of water in the tank will be the same after 69 weeks.
What is the measure of ZDBE?
O A. 170°
OB. 85°
O c. 40°
O D. 130
Answer:
Your answer is A!
Step-by-step explanation:
Have a great day!
The measure of ∠ABC is 85 degrees from intersecting chords theorem.
What is Circle?A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre.
We have to find the measure of ∠ABC.
The intersecting chords theorem is a statement in elementary geometry that describes a relation of the four line segments created by two intersecting chords within a circle.
∠ABC = 1/2 (130+40)
∠ABC = 1/2(170)
Divide 170 by 2
∠ABC = 85 degrees.
Hence, the measure of ∠ABC is 85 degrees from intersecting chords theorem.
To learn more on Circles click:
https://brainly.com/question/11833983
#SPJ7
Solve the riddle.
Dividing my dog’s age by 4 and adding 6 is the same as dividing my dog’s age by 8 and adding 8.
StartFraction x Over 4 EndFraction + 6 = StartFraction x Over 8 EndFraction + 8
How old is my dog?
Answer:
16 years old
Step-by-step explanation:
got it right on edge 2020.
Please mark as Brainliest
Please say thank you.
Simplify the expression. −5x + 8y + 2x − 3y
Final answer:
To simplify the expression −5x + 8y + 2x − 3y, combine like terms, resulting in −3x + 5y.
Explanation:
To simplify the expression −5x + 8y + 2x − 3y, you want to combine like terms. The like terms are those with the same variable raised to the same power. In this expression, −5x and 2x are like terms, as are 8y and −3y.
Combine −5x and 2x: (−5 + 2)x = −3x
Combine 8y and −3y: (8 − 3)y = 5y
After combining like terms, the simplified expression is −3x + 5y.
MARK BRAINLIEST!!!!!!!!!!!!!!! pls answer soon, this is due today !!!!!
The yearly profits of a company are $25,000. The profits have been decreasing by 6% per year.
Write an exponential decay function to represent this situation.
a sound wave is traveling at 3,810 m/s and has a wave length of 8 m. what is the frequency of the wave?
Answer:
476.25 hertz
Step-by-step explanation:
Since the speed of a wave is the wave length multiplied by the frequency, the frequency can be written as the speed divided by the wave length. 3810/8=476.25 hZ. Hope this helps!
Adrian can purchase a 10-pound item from several different sellers. Which is the best buy?
PLEASE HELP ME
A) Buy online for $50 plus pay shipping costs of $1 per pound.
B) Buy online for $47 plus pay shipping costs $2 per pound.
C) Buy at a local store for $60 and use a $5-off coupon.
Answer:
the answer is c because i answered it on a test and got it right
Step-by-step explanation:
what is 8/3 times 12/5
Answer: 6.4 In decimal form. 32/5 in fraction form.
Step-by-step explanation:
So first times 8 by 12 which is 96
then, 3 times 5 which is 15
Simplify to 32/5
Answer: 32/5
Step-by-step explanation: When multiplying two fractions together, remember that we can cross-cancel.
In this problem the 12 and 3 reduce to 4 and 1.
So we have 8/1 · 4/5.
Next we simply multiply across the numerators and multiply across the denominators and we have our answer which is 32/5.
WILL MARK BRAINLIEST PLSSS HELP
Choose each angle to complete the linear pairs.
∠AMY and ∠AMX
∠BMY and
∠BMX and
∠AMX and
Answer:
AMY, BMY, BMX
Step-by-step explanation:
its right
Answer:
the second , the second and the first . ( B,B,A)
Step-by-step explanation:
Which answer choice shows the decimals in order from greatest to least?
A. 0.013, 0.0104, 0.0118, 0.0108, 0.00149
B. 0.00149, 0.0104, 0.0108, 0.0118, 0.013
C. 0.013, 0.0118, 0.0108, 0.0104, 0.00149
D. 0.013. 0.0118. 0.0108. 0.00149. 0.0104
Answer:
B.) 0.00149, 0.0104, 0.0108, 0.0118, 0.013
Step-by-step explanation:
The more decimal places, the lower the number.
PLEASE HELP!!! (will give brainliest for best answer)
a) If side a measures 90 feet and side b measures 120 feet, how many feet of flowers will be planted along side c, the hypotenuse of the triangle? Show your work and explain your reasoning.
(image below)
Answer:
90 squared is 8,100, and 120 squared is 14,400. So to figure out what c is you do 90^2 + 120^2 = Square Root of 22,500 which is 150.
So c = 150
Step-by-step explanation:
So C=150
hope this helps :D
By using the Pythagorean theorem, we will see that side C measures 150ft.
How to get the length of side C?
We can see that side C is the hypotenuse of a right triangle. We know both catheti of said triangle, then we can use the Pythagorean theorem.
It says that the sum of the squares of the cathetus is equal to the square of the hypotenuse. Then we have:
A^2 + B^2 = C^2
We know that:
A = 90ft
B = 120ft
Replacing that we get:
√((90ft)^2 + (120ft)^2) = C = 150ft
Then we conclude that side C measures 150ft.
If you want to learn more about right triangles, you can read:
https://brainly.com/question/2217700
PLEASE HELP!!!!whats the first step of factoring 4x^2+10x-24
Answer
2(2x-3)(x+4)
Step-by-step explanation:
Answer:
Exponents
Step-by-step explanation:
First its parentheses but you don't have any and then its exponents and then you multiply and divide and lastly you add or subtract
What angle is included by AC and BC?
A.
B.
C.
Answer:
B is the answer to this question due to the angle being a 90 degree angle
Josh wanted to buy a new shirt for a school dance. At the store, he couldn't decide between a purple plaid shirt and a scarlet striped shirt. Since the shirts were on sale for $19.95 each, Josh decided to buy them both. He saved a total of $9.10. If he saved the same amount on each shirt, what was the original price of each one? $
Answer:
$24.50
Step-by-step explanation:
Answer:
24.50
Step-by-step explanation:
Plz help i will give brainliest
Answer:
$96
Step-by-step explanation:
First, let's find the price for a ticket with the markup.
Normally, you pay for 100% of the ticket price, but now you also have to pay an extra 20% of the ticket price.
100%+20%=120%
So, you are basically paying for 120% of the normal ticket price, $16
Multiply 120% and $16
120%*16
Convert 120% to a decimal by dividing by 100, or moving the decimal place 2 spots to the left
120%/100=1.20
120.0-->12.0-->1.20
1.20*16=19.2
Now, each adult ticket costs $19.20
Next, find how much 5 tickets will cost.
Multiply 5 and $19.20
5*19.20=96
5 adults will pay $96 with the ticket markup
Geno signed up for a text messaging plan. He pays a $5.00 monthly fee and $0.04 per text message.
Which expression can Geno use to find the cost for one month if he used n messages?
A: 0.02
B: 5.041
C: 0.04r + 5.00
D: 5.00n +0.04
Answer:
The correct answer is [C.) 0.04r + 5.00}
Step-by-step explanation:
hope this hlps
Which point lies on the line x-5 =0
Answer:
see explanation
Step-by-step explanation:
Any point with an x- coordinate of 5 will lie on the line, that is
(5 , - 2), (5, 0), (5, 10)
since 5 - 5 = 0 makes the equation true
I need help? With proof for this one.
Answer:
See below.
Step-by-step explanation:
ABC is an isosceles triangle with BA = BC.
That makes angles A and C congruent.
ABD is an isosceles triangle with AB = AD.
That makes angles ABD and ADB congruent.
Since m<ABD = 72 deg, then m<ADB = 72 deg.
Angles ADB and CDB are a linear pair which makes them supplementary.
m<ADB + m<BDC = 180 deg
72 deg + m<BDC = 180 deg
m<CDB = 108 deg
In triangle ABD, the sum of the measures of the angles is 180 deg.
m<A + m<ADB + m<ABD = 180 deg
m<A + 72 deg + 72 deg = 180 deg
m<A = 36 deg
m<C = 36 deg
In triangle BCD, the sum of the measures of the angles is 180 deg.
m<CBD + m<C + m<BDC = 180 deg
m<CBD + 36 deg + 108 deg = 180 deg
m<CBD = 36 deg
In triangle CBD, angles C and CBD measure 36 deg making them congruent.
Opposite sides DB and DC are congruent making triangle BCD isosceles.
Write the coordinates of one point that lies in the
third quadrant of the coordinate plane?
(Sorry at home learning isn't easy in 6th grade)
Answer:
Example Quadrant 3 coordinate value (-2, -2)
Step-by-step explanation:
Coordinates are written (x, y)
Quadrant 1: both x and y are positive values. Example (2, 2)
Quadrant 2: x is negative and y is positive. Example (-2, 2)
Quadrant 3: both x and y are negative values. Example (-2, -2)
Quadrant 4: x is positive and y is negative. Example (2, -2)
GIVING BRAINLIEST ANSWER QUICK!!
Fala is painting the stairs on her deck. she has 6/4 quarts of paint. She needs 4/8 quart of paint for each stair-step.
Fala can paint ______ one whole step.
Fala can paint exactly ______ step(s) with the paint she has.
Answer:
1. Fala can paint more than one whole step
2. She can paint 3 steps
Step-by-step explanation:
1. In the second question we found that she has enough for 3 steps and 3 is more than 1 so she can paint more than one step
2. 6/4=12/8 so she has 12/8 quarts and needs 4/8 for each step
Divide 12 by 4 = 3 So she has enough paint for 3 steps
Answer: more than,3
Step-by-step explanation:
Plz I need answer ASAP
Answer:
a³ - 5a² + 4a + 5
Step-by-step explanation:
To solve this, remove the parentheses. If you were subtracting the two phrases, you would distribute the negative sign to the second phrase, but you are adding so you will not have to do this
4a - a³ - 3 + 2a³ - 5a² + 8
a³ - 5a² + 4a + 5
HELP PLEASE VERY QUICK, I'LL MARK AS BRAINLIEST!
Answer:
Greater ; Greater
Smaller ; Greater
Step-by-step explanation:
Slopes
First row
A: 15/2
B: (25-12.5)/(4-2) = 12.5/2
A has a greater slope than B
-4x + 2y = 8
2y = 4x + 8
y = 2x + 4
A: 2
B: 3/2
A has a greater slope than B
Second Row
A: (2.6-2)/(3-0) = 0.6/3 = 0.1
B: (5-4)/(4-0) = 1/4 = 0.25
A has a smaller slope than B
A: 60
B: (325-50)/5-0) = 275/5 = 55
A has a greater slope than B
Can someone please find the volume of this shape?
A) 1224 m^3
B) 2160 m^3
C) 6480 m^3
D) 2851 m^3
We have been an image of a triangular pyramid. We are asked to find the volume of the given pyramid.
We know that volume of triangular pyramid is [tex]\frac{1}{3}b\cdot h[/tex], where,
b = Base area,
h = Height of pyramid.
We can see that base of pyramid a right triangle.
[tex]\text{Area of triangle}=\frac{1}{2}\times\text{Base}\times\text{Height}[/tex]
Now we will find height of base triangle using Pythagoras theorem.
[tex]h^2=30^2-24^2[/tex]
[tex]h^2=900-576[/tex]
[tex]h^2=324[/tex]
[tex]\sqrt{h^2}=\sqrt{324}[/tex]
[tex]h=18[/tex]
[tex]\text{Area of base triangle}=\frac{1}{2}\times24\times 18[/tex]
[tex]\text{Area of base triangle}=12\times 18[/tex]
[tex]\text{Area of base triangle}=216[/tex]
[tex]\text{Volume of triangular prism}=\frac{1}{3}b\cdot h[/tex]
[tex]\text{Volume of triangular prism}=\frac{1}{3}\cdot 216\cdot 30[/tex]
[tex]\text{Volume of triangular prism}=216\cdot 10[/tex]
[tex]\text{Volume of triangular prism}=2160[/tex]
Therefore, the volume of the given prism is [tex]2160\text{ m}^3[/tex] and option B is the correct choice.
Answer:
its B
Step-by-step explanation:
What is the value of sin 0 in the diagram below
Answer:
Please include the diagram
Step-by-step explanation:
Answer:
The answer is 24/25
Step-by-step explanation:
Sin (angle) = Opposite leg / Adjacent Leg
Sin (angle) = Y / r
Sin (angle) = 24/25 / 1 = 24/25
The answer is 24/25
Hope this helps
What is the circumference of the sun?
Answer:
2.720984 million miles
Step-by-step explanation:
A new laptop computer costs $800. The sales tax on the computer is $48. What is the PERCENT of the sales tax?
Answer:
6% sales tax
Step-by-step explanation:
48 / 800 = x / 100
What did you do to turn 800 into 100? Divide by 8.
Since we divided the denominator by 8, we also divide the numerator by 8.
48 / 8 = 6
6% sales tax
Final answer:
The percent of the sales tax on an $800 laptop computer with a $48 sales tax is 6%. This is found by dividing the sales tax by the cost of the computer and then multiplying by 100.
Explanation:
To calculate the percent of the sales tax for the laptop computer, you need to follow these steps:
Convert the sales tax amount to a decimal by dividing the sales tax by the cost of the item before tax.
For example: $48 (sales tax) ÷ $800 (cost of the laptop) = 0.06.
Then, convert the decimal to a percentage by multiplying it by 100.
Continuing the example: 0.06 × 100 = 6%.
Therefore, the sales tax rate for the laptop computer is 6%.