Determine whether the relation is a function {(8, 0), (5, 4), (9, 3), (3, 8)}

Answers

Answer 1

It is a function. A function is a set of data points that do not repeat the an x value. We can clearly see that it does not repeat any numbers in the x value space.
8,5,9,3 are all different numbers, so the relation is a function.
Hope this helps!
Answer 2

Answer: It is a function.

Step-by-step explanation:

By definition,  a function is a relation in which the input value (the x value) has one and only one output value (value of y).

The first number of each ordered pair is the input value and the second number of each ordered pair is the output value.

As you can see, the inputs value of the relation given in the problem have one and only one output value. Therefore, you can conclude that the relation is  a function.


Related Questions

find the mean median and interquatile for the data set below . 17 23 8 5 9 16 22 11 13 15 17 18

Answers

Answer: Interquartile: 8.25

Mean: 14.5

Median: 15.5

Step-by-step explanation:

Lara is a skier. She completed a ski race in 1 minute 54 seconds. The race was 475 m in length. Lara assumes that her average speed is the same for each race.

a) Using the assumption, work out how long Lara should take to complete a 700m race. Give your answer in minutes and seconds.

b) Lara's average speed actually increases the further she goes. How does this affect your answer to part a?

Answers

Answer:

a) 2 minutes 48 seconds

b) The time would decrease as it takes less time for Lara to finish the race.

Step-by-step explanation:

Speed = Distance / Time

Speed = 475 / 114

Speed = 4.16m/s

Distance = 700m

Time = Distance/Speed

Time = 700/4.16

= 168 seconds

= 2 minutes and 48 seconds

what is the measure of qrp

Answers

Check the picture below.

notice chord QR is a diameter, thus the vertex at P has a right-angle by Thales theorem.

The first group collected 238 cans. The second group collected 345 cans. How many cans did the two groups collect?​

Answers

Answer:

The two groups collected 573.

Step-by-step explanation:

238

+345

=

573

Solve |x| + 7 < 4.

1. {x | x < -11 or x > -3}
2. {x | -3 < x < 3}
3. Ø

Answers

Answer:

3. Ø

Step-by-step explanation:

[tex]|a|=a\ \text{for}\ a\geq0\\\\|a|=-a\ \text{for}\ a<0[tex]|x|+7<4\qquad\text{subtract 7 from both sides}\\\\|x|+7-7<4-7\\\\|x|<-3\to x\in\O\ \text{because}\ |x|\geq0\ \text{for any value of }\ x.[/tex]===================[/tex]

Dave is 8 years younger than 4 times Julia‘s age. If Dave is 16, how old is Julia?
A. 6 years
B. 24 years
C. 32 years
D. 56 years

Answers

Answer: d

Step-by-step explanation:

so 16+16=32

and to make things easier 32+32=64

64-8=56

The age of Julia is,

⇒ 6 years

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

Dave is 8 years younger than 4 times Julia‘s age.

Let Julia age = x

Hence, Age of Dave is,

⇒ 4x - 8

Here, Age of Dave is, 16

Hence,

⇒ 4x - 8 = 16

⇒ 4x = 16 + 8

⇒ 4x = 24

⇒ x = 6

Thus, The age of Julia is,

⇒ 6 years

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Which function is a quadratic function?

Answers

Answer:

The function which is quadratic is:

           [tex]y-3x^2=3(x^2+5)+1[/tex]

Step-by-step explanation:

We know that the general equation of a quadratic function is given by:

[tex]y=ax^2+bx+c[/tex]

where a , b and c are real numbers.

1)

[tex]y-3x^2=3(x^2+5)+1[/tex]

On solving we get:

[tex]y-3x^2=3x^2+15+1\\\\\\y=3x^2+3x^2+1+15\\\\\\y=6x^2+16[/tex]

Hence, the function is quadratic.

2)

[tex]y^2-7x=2(x^2+6)+7[/tex]

It is not a quadratic equation since we have a term as : [tex]y^2[/tex]

and hence the equation will not match the general equation of the quadratic function.

3)

[tex]y-2x^2=6(x^3+5)-4[/tex]

as it has a term of [tex]x^3[/tex]

Hence, it is a equation of a cubic function.

4)

[tex]y-5x=4(x+5)+9[/tex]

On solving we get:

[tex]y=9x+29[/tex]

It does not has any term of [tex]x^2[/tex]

Hence, the equation is not a quadratic function it represent a linear function.

The functions that are quadratic functions are [tex]y - 3x^2 = 3(x^2+5)+1\\[/tex] and [tex]y^2-7x= 2(x^2+6) +7[/tex].

The highest power of the polynomial is called the degree of the polynomial. The polynomial of degree two is called a quadratic polynomial.

According to the question,

1)

[tex]y - 3x^2 = 3(x^2+5)+1\\ y = 3x^2+ 15 + 3x^2 +1\\ y = 6x^2 +16[/tex]

Since the polynomial is of degree 1, It is a quadratic function.

2)

[tex]y^2-7x= 2(x^2+6) +7\\y^2= 2x^2 +7x+19[/tex]

The function is a quadratic function.

3)

[tex]y - 3x^2= 6(x^3+5)-4[/tex]

The degree of x is 3, so it is a cubic function.

4)

[tex]y - 5x = 4(x+5)+9 y \\= 4x + 5x+ 29y\\ = 9x+29[/tex]

The function is a linear function.

The functions which are quadratic equations are [tex]y - 3x^2 = 3(x^2+5)+1\\[/tex]and  [tex]y^2-7x= 2(x^2+6) +7[/tex] .

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Im a randomly generated list of numbers from 0 to 6, what is the chance that each number will occur?

Answers

Answer:

1/7

Step-by-step explanation:

The list of numbers generated is; 0, 1, 2, 3, 4, 5, 6,

There are 7 possible outcomes and each outcome is equally likely. The probability or chance that each number will occur is given by;

number of times the number occurs / 7

In our case, each number occurs only once, so the chance will be;

1/7

Answer:

of it say 0 out of 3 its on the one with 3 numbers

Suppose you want to determine the number of miles you can drive in your car. Your car gets 20 miles per gallon. The number of miles traveled varies directly with the number of gallons of gas the tank holds. Write a direct variation equation that represents the situation. Let y be the dependent variable and let x be the independent variable

Answers

Answer:

y = 20x

Step-by-step explanation:

We know that the car gets 20 miles per gallon and the number of miles traveled varies directly with the number of gallons of gas the tank holds.

We are to write a direct variation equation which represents this situation.

Direct variation is expressed in the form [tex]y=kx[/tex], where [tex]k[/tex] is the constant of variation.

So for this situation, the direct variation equation will be:

[tex]y=20x[/tex]

Answer: [tex]y=20x[/tex]

Step-by-step explanation:

By  definition, a direct variation equation has the form shown below:

[tex]y=kx[/tex]

Where k is a constant, y is the dependent variable and x is the independent variable.

According to the problem, you know that your car gets 20 miles per gallon. The number of miles traveled varies directly with the number of gallons of gas the tank holds.

Then, you can write the following direct variation equation that represents the situation:

y: The number of miles traveled

x:  the number of gallons of gas the tank holds.

k: 20 (Because your car gets 20 miles/gallon)

Then:

[tex]y=20x[/tex]

the simple interest I ( in dollars) for a savings account is jointly proportional to the product of the time t (in years) and the principal P (in dollars). After five months, the interest on a principal of $3892 is $92. a) find the constant of variation.
b) what will the interest be after 3 years​

Answers

Answer:

Part a) The constant of variation is [tex]r=0.0567[/tex] or [tex]r=5.67\%[/tex]

Part b) [tex]I=\$662.03[/tex]

Step-by-step explanation:

Part a) Find the constant of variation.

we know that

The simple interest formula is equal to

[tex]I=P(rt)[/tex]

In this linear direct variation the constant r represent the constant of proportionality

where

I is the Interest Value

P is the Principal amount of money to be invested

r is the rate of interest  

t is Number of Time Periods

in this problem we have

[tex]t=5/12\ years\\ P=\$3,892\\ I=\$92\\r=?[/tex]

substitute the values and solve for r

[tex]92=3,892(r(5/12))[/tex]

[tex]r=(92*12)/(3,892*5)[/tex]

[tex]r=0.0567[/tex]

Part b) what will the interest be after 3 years

in this part we have

[tex]t=3\ years\\ P=\$3,892\\ I=?\\r=0.0567[/tex]

substitute the values

[tex]I=3,892(0.0567*3)=\$662.03[/tex]

Which graph represents the piecewise function?

Answers

Answer: I can barly see that sry i cant awnser

Step-by-step explanation:

Answer:

3rd graph

Step-by-step explanation:

just that easy

Rhett made a simple drawing of his house.It is a three-dimensional figure with four faces that are rectangular and two that are square. What kind of figure is it.

Answers

Answer:

it is a rectangular prism

Step-by-step explanation:

it is 3D and when something has four faces that are rectangular and two that are sqaure it makes it a rectangular prism. imagine the rectangles on the sides and sqares at the end, it looks like a rectangle =).

Find the solution to the system of equations. You can use the interactive graph below to find the solution. { y = x − 4 y = 4 x + 2 ⎩ ⎪ ⎨ ⎪ ⎧ ​ y=x−4 y=4x+2 ​ x = x=x, equals

Answers

Final answer:

The solution to the system of equations y = x - 4 and y = 4x + 2 is found by setting the two equations equal to one another and solving for x and y. The solution is (-1.5, -5.5).

Explanation:

The solution to the system of equations can be found by setting the two equations equal to each other, as they are both equal to y.

Equation 1: y = x - 4

Equation 2: y = 4x + 2

To find the point of intersection, set the two equations equal to each other: x - 4 = 4x + 2. Solve this for x to get that x = -1.5. Then, substitute x = -1.5 into one of the original equations to solve for y. If we use Equation 1, we get that y = -1.5 - 4 = -5.5. Therefore, the solution to the system of equations is (-1.5, -5.5).

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The solution to the system of equations is [tex]\(x = -2, y = -6\)[/tex]. The point of intersection is [tex]\((-2, -6)\)[/tex].

The solution to a system of equations is the point where the graphs of the two equations intersect.

1. Set the Equations Equal to Each Other:

[tex]\[ x - 4 = 4x + 2 \][/tex]

2. Solve for x:

[tex]\[ -3x = 6 \][/tex]

[tex]\[ x = -2 \][/tex]

3. Substitute x back into one of the original equations to find y

[tex]\[ y = -2 - 4 = -6 \][/tex]

So, the  solution to the system of equations is [tex]\(x = -2, y = -6\)[/tex]. The point of intersection is [tex]\((-2, -6)\)[/tex].

QUICKLY !!!
What is the image of (-5,8) after a reflection over the y-axis?

Answers

Answer:

red is the reflection ,black is (-5,8)

Step-by-step explanation:

Answer:

the image of (-5,8) after a reflection over the y-axis is (5,8)

Step-by-step explanation:

the image of (-5,8) after a reflection over the y-axis

When a point is reflected over y axis, then the value of x changes to -x.

the value of y remains the same.

If (x,y) is reflected over y axis , then it becomes (-x,y)

The point (-5,8) after reflection over y axis it becomes (-(-5),8) that is (5,8)

the image of (-5,8) after a reflection over the y-axis is (5,8)

Mary bought 7 dozen candles. How many candles did she buy?

Answers

Answer:

the answer is 84

Step-by-step explanation:

a dozen is 12 so you take 12 times 7 and get 84

Heyaaa

The answer is 84 Candles .

There are 12 in a dozen , and there are 7 dozen.

12 x 7 = 84

Good luck :)

how do you represent 12 fourths in 3 ​

Answers

Answer:

See below for explanation

Step-by-step explanation:

Another way to think about this is to think "How many fourths are in 3".  There are 4 fourths in 1, and there are 3 1's in 3, so we have

3(4) = 12 fourths in 3

Algebraically you can write it as.

1(4)x = 3         this means "one fourth time some value is 3"  which is a rewording of what I explained above.  Solve for x by multiplying both sides by 4...we get x = 12, so

one fourth, 12 times gives us 3

Final answer:

The fraction 12/4 simplifies to 3 because the numerator and denominator can both be divided by their greatest common divisor, which is 4.

Explanation:

The question is related to the conversion of a fraction to a simpler form. The fraction 12/4 can be converted into a simpler form by dividing both the numerator and the denominator by their greatest common divisor. The greatest common divisor of 12 and 4 is 4. So, we can divide the numerator 12 and the denominator 4 by 4.

Here's how to do it:

12 ÷ 4 = 3 4 ÷ 4 = 1

As a result, the fraction 12/4 reduces to the whole number 3. Thus, 12 fourths is represented as 3 in its simplest form.

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Over the summer, Alexis read 15 books in 12 weeks. The diagram below can be used to track her progress. If Alexis read at the same rate each week, how many books had she read in 4 weeks? in 8 weeks? complete the diagram

Answers

12weeks-15 books

4 weeks-5 books

8 weeks-10 books

Answer:

4 to 5

8 to 10

Step-by-step explanation:

3,350 to the nearest ten.

Answers

Your answer will be 3350
3350 is the answer and is to nearest ten

find the product of
(x2 + 3x + 1)(x2 + x + 2)

Answers

Answer: [tex]x^4+4x^3+6x^2+7x+2[/tex]

Step-by-step explanation:

To solve the exercise you must apply the following proccedure:

- Apply the distributive property.

- Keep on mind that when you multiply two powers with equal base, you must add the exponents.

- Add like terms.

Therefore, you obtain the following product:

[tex]=x^{(2+2)}+x^{(2+1)}+2x^2+3x^{(1+2)}+3x^{(1+1)}}+6x+x^{2}+x+2\\=x^4+x^3+2x^2+3x^3+3x^2+6x+x^2+x+2\\=x^4+4x^3+6x^2+7x+2[/tex]

Hello!

The answer is: [tex]x^{4}+4x^{3}+6x^{2}+7x+2[/tex]

Why?

To find the product of the given expression, we need to apply the distributive property and then, group each like term.

The distributive property states that:

(a+b+c)(d+e+f)=a*d+a*e+a*f+b*d+b*e+b*f+c*d+c*e+c*f

Then, we have to group each like term. Like terms are the terms that have the same variable and exponent , for example:

[tex]x+x+x^{2}=2x+x^{2}[/tex]

For this case, the variable "x" has two Like terms, since both have the same exponent (1), then, we add each other in order to group term.

Also, we must remember the following power property:

Product of powers property,

[tex]a^{n}*a^{m}=a^{n+m}[/tex]

So, solving the product we have:

[tex](x^{2}+3x+1)(x^{2}+x+2)=x^{2}*x^{2}+x*x^{2}+2x^{2}+3x*x^{2}+3x*x+6x+x^{2}+x+2\\(x^{2}+3x+1)(x^{2}+x+2)=x^{2+2}+x^{1+2}+2x^{2}+3x^{2+1}+3x^{1+1}+6x+x^{2}+x+2\\(x^{2}+3x+1)(x^{2}+x+2)=x^{4}+4x^{3}+6x^{2}+7x+2[/tex]

Have a nice day!

Debits are entered on the _____ side of a T-account. FETL Unscramble

Answers

The LEFT side is the correct answer

Debits are entered on the left side of a T-account.

Debits and credits are fundamental concepts in accounting used to record financial transactions. In a T-account format, which visually splits an account into two sides, debits are always entered on the left side of the T-account. Conversely, credits are recorded on the right side.

For example, when a company purchases office supplies for cash, the office supplies account will have a debit entry (left side), while the cash account will have a credit entry (right side). This ensures that the accounting equation balances.

A florist arranges 10 flowers in each vase how many vases does the florist need to arrange 49 flowers

Answers

Answer:

Five Vases

Step-by-step explanation:

In this type of questions, you can't have a reminder. You would have to round up instead.

49 flowers / 10 per case = 4 remainder 9

Because you have a remainder you need to round 4 up to 5.

You need 5 vases.

I need help on 13 and 14

Answers

13) (3, 2)
14) (-2, 0)

The answer to this wuestion

Answers

Answer:

A   942

Step-by-step explanation:

3/5ths is .6

125.6 / 2 = 62.8

62.8 * 15 = 942

Answer: Its A 942 hope this helped

What is the measure of the vertex angle of an isosceles triangle if one of its base angles 54

Answers

In an isosceles triangle, the two angles at the base are the same. So, the base angles are both 54°, for a total of 108.

Since the interior angles of a triangle sum up to 180°, the remaining angle must be

[tex]180-54-54=180-108=72[/tex]

y varies inversely with x. k, the constant of inverse variation, is 9.62. When y is 2.6, what is x? Round your answer to the nearest tenth, if necessary.

Answers

Answer:

3.7

Step-by-step explanation:

2.6  = 9.62/x

2.6x = 9.62     Multiplied each side by x

     x = 3.7       Divided each side by 2.6.

Find the value of x if A, B, and C are collinear points and B is between A and C
AB=5, BC=3x+7, AC=5x-2

Answers

Answer:

x = 7

Step-by-step explanation:

5 + 3x + 7 = 5x - 2

Solve for x and you get 7

Answer:

x = 7

Step-by-step explanation:

We are given that A, B and C are collinear points and B is in between A and C.

The length from A to B is [tex] 5[/tex], length from B to C is [tex] 3x + 7 [/tex] and AC is [tex] 5 x - 2 [/tex].

We are to find the value of x.

[tex] A B + B C = A C [/tex]

[tex] 5 + 3 x + 7 = 5 x - 2 [/tex]

[tex] 5 x - 3 x = 5 + 7 + 2 [/tex]

[tex] 2 x = 1 4  [/tex]

[tex] x = \frac { 1 4 } { 2 } [/tex]

x = 7

I'm really confused, can someone please help me with this problem?

Answers

Answer: x = 6.25

5 ÷ 0.8

= 6.25

Find the slope and y- intercepts of the line given by 3x+5y=45

Answers

[tex]\huge\text{Slope: $\boxed{-\frac{3}{5}}$}\\\huge\text{$y$-intercept: $\boxed{9}$}[/tex]

We need to convert this line to slope-intercept form, or [tex]y=mx+b[/tex], where [tex]m[/tex] is the slope and [tex]b[/tex] is the y-intercept.

[tex]\begin{aligned}3x+5y&=45&&\smash{\Big|}&&\text{Start with the original equation.}\\5y&=-3x+45&&\smash{\Big|}&&\text{Subtract $3x$ from both sides.}\\y&=\boxed{-\frac{3}{5}}x+\boxed{9}&&\smash{\Big|}&&\text{Divide everything by $5$.}\end{aligned}[/tex]

QUICK
What is the image point of (1,4) after a translation left 5 units and down 3 units ?

Answers

Answer:

(-4,1)

Step-by-step explanation:

First, subtract 1-5. (When you move left or down you subtract. When you move right or up you add.) Left and right affect the x-axis

Second, subtract 4-3. Up and down Affect the y-axis

It would look like this:

(1,4)

=(1-5,4-3)

=(-4,1)

Answer:

here you go(image included)

Step-by-step explanation:

Please help me on number 5

Answers

15 slices, when you divide 3/72=24 then 360 divided by 24 is 15

The answer is 5 slices because a pie is 360 degrees and 360/72=5 making each slice 72 degrees and 5 slices in all.

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