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3 years ago

Use the domain and range of each of the following relations to determine which is a function.

Mathematics

2 answers:

Dima020 [189]3 years ago

7 0

The answer js A. the first one

Margaret [11]3 years ago

5 0

Answer:

The function is expressed by answer A

Step-by-step explanation:

A function is a mathematical expression in which, for an independent variable , usually called x, we obtain one and only one value after applying the function, usually known as the dependent variable y.

D is not a function as we do not have two corresponding values or coordinate pairs. We only have a list of numbers

In C, B and A we have pairs of coordinate values expressed as (x,y) the independent and dependent variable.

In expression B, we see that the for the value of x=3 in ponts 1 (3.-3) and (3.-9) , the value 3 has two resulting values of y , -3 and -9, so this coordinates do not represent a function.

In option C, occurs something similar in this case with x =9. x=9 has two values in y : y=-6 and y= 2 so these points do not define a function

In A each x value (3.9.0) has a unique avlue of y (-3,-6,-9) so this is a function.

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Find the solution of the given initial value problem. ty' + 6y = t2 − t + 1, y(1) = 1 6 , t > 0

gtnhenbr [62]

Answer:

Step-by-step explanation:

Given is a differential equation as

$ty' + 6y = t^2 - t + 1, y(1) = 1 6 , t > 0$

Divide this by t to get in linear form

$y'+6y/t = t-1+1/t$

This is of the form

y' +p(t) y = Q(t)

where p(t) = 1/t $e^(\int 1/tdt) = t$

So solution would be

$yt = \int t^2-t+1 dt\\= t^3/3-t^2/2+t+C$

siubstitute y(1) = 16

$16 = 16^3/3-128+1+C\\C = -1206$

4 0

3 years ago

Write the numbers 23,643 and 23,987 so they line up by place value. Explain how to line them up

weqwewe [10]

Consider the numbers 23,643 and 23,987.

Since both the given numbers have same digits at ten thousands and thousands place.

So, we can'not compare the numbers on the basis of ten thousands and thousands digit.

So, let us consider the number 23,643

Consider the place value of digit at the hundreds place. Since, the digit at hundreds place = 6.

The place value of 6 = 600

Now, let us consider the number 23,987

Consider the place value of digit at the hundreds place. Since, the digit at hundreds place = 9.

Te place value of 9 = 900

Since, 900 > 600

So, 23,643 > 23,987

Therefore, the number 23,987 is greater than the number 23,643.

4 0

2 years ago

What is lemma? ________________ Thx!

german

A subsidiary or intermediate theorem in an argument or proof.
Source: Wikipedia

5 0

3 years ago

Read 2 more answers

Given the points A(3, 4) and B (6, 10), find the

Dvinal [7]

Answer:

P (5 , 8)

Step-by-step explanation:

P (x,y) partition A (x₁ , y₁) B (x₂ , y₂) into ratio AM:MB = a:b = 2:1 ... a=2 , b=1

x = (bx₁ + ax₂) / (a+b)

= (1 * 3 + 2 * 6) / (2 + 1)

= 15/3

= 5

y = (by₁ + ay₂) / (a+b)

= (1 * 4 + 2 * 10) / (2 + 1)

= 24/3

= 8

P (5 , 8)

8 0

3 years ago

Pls solve the simultaneous equation in the attachment.

siniylev [52]

Answer:

Part a) The solution is the ordered pair (6,10)

Part b) The solutions are the ordered pairs (7,3) and (15,1.4)

Step-by-step explanation:

Part a) we have

$\frac{x}{2}-\frac{y}{5}=1$ ----> equation A

$y-\frac{x}{3}=8$ ----> equation B

Multiply equation A by 10 both sides to remove the fractions

$5x-2y=10$ ----> equation C

isolate the variable y in equation B

$y=\frac{x}{3}+8$ ----> equation D

we have the system of equations

$5x-2y=10$ ----> equation C

$y=\frac{x}{3}+8$ ----> equation D

Solve the system by substitution

substitute equation D in equation C

$5x-2(\frac{x}{3}+8)=10$

solve for x

$5x-\frac{2x}{3}-16=10$

Multiply by 3 both sides

$15x-2x-48=30$

$15x-2x=48+30$

Combine like terms

$13x=78$

$x=6$

Find the value of y

$y=\frac{x}{3}+8$

$y=\frac{6}{3}+8$

$y=10$

The solution is the ordered pair (6,10)

Part b) we have

$xy=21$ ---> equation A

$x+5y=22$ ----> equation B

isolate the variable x in the equation B

$x=22-5y$ ----> equation C

substitute equation C in equation A

$(22-5y)y=21$

solve for y

$22y-5y^2=21$

$5y^2-22y+21=0$

Solve the quadratic equation by graphing

The solutions are y=1.4, y=3

see the attached figure

Find the values of x

For y=1.4

$x=22-5(1.4)=15$

For y=3

$x=22-5(3)=7$

therefore

The solutions are the ordered pairs (7,3) and (15,1.4)

3 0

3 years ago