Find the values of a and b that complete the mapping diagram

Hi! I'm happy to help! (sorry for the wait, my computer crashed)

A linear function is where one variable is independent (x), and another is dependent. This means that we use x to solve for y, y depends on x to be found.

To solve this, we use an equation call slope intercept form, which states that y=mx+b.

There is only 1 solution line. (to solve for how to find y, you only have to have two verifications)

For our first table, we have x as 1, 2, 3,and 4. y is 3, 6, 12, and 24.

For our first set, with x is one and y is 3, there are infinite solutions, so we have to test and see if it matches the second set of x is 2 and y is 6.

How I like to check for what m will be, I check the first two y values. The first two are 3 and 6. They have an increase of 3, so m will be 3. (this only works when x increases by 1)

With m being 3, we can solve for b, to complete the equation:

3=(3(1))+b

3=3+b

With this, b must equal 0

3=3+0

Now, we just have to check if this equation matches all of the other x values:

6=(3(2))+0

6=6+0

__________________________________

12=(3(3))+0

12=9+0

12≠9

This equation doesn't seem to work, so this is not a linear function.

For our next table, our first two y values are 2 and 5, which have a increase of 3, so our m will be 3 again.

Now, let's solve for b:

2=(3(1))+b

2=3+b

In this case, b will be -1 because 2=3-1

Now, let's check if this matches up with our other values:

5=((3)2)-1

5=6-1

_______________________________

9=((3(3)-1

9=9-1

9≠8

This equation doesn't work, so it is not a linear function.

For our next table, we have our first two y values as -3, and -5. This has a decrease of 2, so our m will be -2.

Now, let's solve for b:

-3=((-2)1)+b

-3=-2+b

In this equation, b will be -1 because -3=-2-1.

Now, let's check our other values:

-5=(-2(2))-1

-5=-4-1

___________________________________________

-7=(-2(3))-1

-7=-6-1

______________________________________________

-9=(-2(4)-1

-9=-8-1

All of these values match, so this is a linear function.

If you wanted to (you don't have to, but if you needed verification) you could check the fourth problem.

Has a decrease of 2, so m would be -2. Plug it in:

-2=(-2(1))+b

-2=-2+b

b would be 0.

Check it on the second problem:

-4=(-2(2))+0

-4=-4+0

Check the third:

-2=(-2(3))+0

-2=-6+0

-2≠-6

The fourth table doesn't match either, so it is not a linear function.

You should choose option 3 because it is a linear function.

I hope this was helpful, keep learning! :D

Answer:

first one is rough endoplasmic reticulum and the second is cell membrane

Answer:

4)Y axis :X=0

5)A:2units B:4 units C:7units D:7units

A':2units B':4units C':7units D':7units

6)They are correspondingly the same

7)A(2;1) B(4;4) C(7;4) D(7;1)

A'(-2;1) B'(-4;4) C'(-7;4) D(-7;1)

Answer:

72

Step-by-step explanation:

The smallest number that is divisible by two given numbers is called the Least Common Multiple (LCM) of those numbers.

What's the smallest number that is a multiple of 8 and also a multiple of 18?

One way to find out is to start making lists of multiples:

Multiples of 8:  8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96, and so on,

Multiples of 18:  18, 36, 54, 72, 90, 108, and so on.

This method can be a bit tedious, but in this case, it's clear that 72 is the LCM of 8 and 18.

Another method is to use the prime factorization of the two numbers.

Write 8 and 18 as the product of prime numbers; each number has a unique prime factorization.

8 = 2 x 2 x 2 = 2^3

18 = 2 x 3 x 3 = 2^1 x 3^2

To form the LCM, build a product of primes using the highest exponent in either of the two numbers.

LCM = 2^3 x 3^2 = 8 x 9 = 72.

Answer:

7×148= 1036

Step-by-step explanation:

This is the easiest way to solve ...

But you are asking a model to be used for solving...

No idea about it

Answer:

10

Step-by-step explanation:

1:5

10:50

Answer:

10

Step-by-step explanation:

5 minutes = 1 area

→ Divide the 50 by the 5

50 ÷ 5 = 10

→ Multiply this by the area

10 × 1 = 10

Step-by-step explanation:

The distance between two point (x_1, y_1) and (x_2, y_2) is

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Therefore, the distance between (-1,4) and (1,-1) is

[tex]d=\sqrt{(1-(-1))^2+(-1-4)^2}=\sqrt{4+25}=\sqrt{29}=5.4[/tex]

Answer:

60°

Step-by-step explanation:

2x and x are linear pair,

=> 2x + x = 180

=> 3x  = 180

=> x = 180/3

=> x = 60°

=>2x =120°

Answer:

x = 60

Step-by-step explanation:

x + 2x =  180   {linear pair}

Combine like terms

3x  = 180

Divide both sides by 3

x = 180/3

x = 60

Answer: Therefore, 14% of cats and dogs got shelter during the day.

Step-by-step explanation:

cats = 5/50 * 100%

    = 5*2% = 10%

dogs = 2/50* 100%

       = 2*2% = 4%

so

= 10% + 4% = 14%

Answer:

Option A

SEE IMAGE FOR SOLUTION

Hope it helps

Have a great day

Answer:

4/25

Step-by-step explanation:

Answer:

16% as a fraction is 4/25

Step-by-step explanation:

Every percentage is over a 100. This means that 16% is the same as 16/100 and simplifying this it will be 4/25 ( dividing both by 4)

Answer:

Surface area of sphere = 4 π r²

154 = 4 × 22/7 × r²

154 = 88/7 × r²

154 × 7/88 = r²

12.25 = r²

3.5 = r

Now

Volume of sphere = 4/3 × π r³

Volume = 4/3 × 22/7 × (3.5)³

Volume = 88/21 × 42.875

Volume = 154 cm³

Volume of sphere = Volume of cube

Volume of cube = 154 cm³

Answer:

hundredth:0.3800

thousand:0.4000

tenth:0.3780

Answer:

$125 is the interest that you might earn

[tex]\\ \sf\longmapsto I=\dfrac{PRT}{100}[/tex]

[tex]\\ \sf\longmapsto I=\dfrac{5000(2.5)(1)}{100}[/tex]

[tex]\\ \sf\longmapsto I=\dfrac{12500}{100}[/tex]

[tex]\\ \sf\longmapsto I=\$ 100[/tex]

Answer:

120°

Step-by-step explanation:

The protractor shows that ∠AOE is 120°. If A started from the left, then it would be 60°.

Answer:

120

Step-by-step explanation:

Answer:

A área de um quadrado cujo perímetro é de 320 m é 6400 m2

Step-by-step explanation:

Answer:

Answer:

Midpoint= (0, 4)

Step-by-step explanation:

[tex]\boxed{midpoint = ( \frac{x1 + x2}{2} , \frac{y1 + y2}{2}) }[/tex]

Using the formula above,

midpoint

[tex] = ( \frac{2 - 2}{2} , \frac{8 + 0}{2}) [/tex]

[tex] = (0, \frac{8}{2} )[/tex]

[tex] = (0,4)[/tex]

Answer:

B =57

Step-by-step explanation:

The sum of the angles of a triangle is 180

A+B+C = 180

58+B+65 = 180

123+B = 180

B = 180-123

B =57

The angle sum property of a triangle:

∠A + ∠B + ∠C = 180°

⇛58° + 65° + x = 180°

⇛123° + x = 180°

⇛x = 180° - 123°

⇛x = 57°

Option B is the correct answer

Answer:

solution:

here,

or, (2x+30)°=(3x+20)°

or,2x+30°=3x+20°

or, 2x+3x=30°+20°

or, 5x=50°

or, x=50°÷5

so that: x=10° ans

Hi ;-)

[tex]-28=2x+8-5x\\\\2x+8-5x=-28\\\\2x-5x=-28-8\\\\-3x=-36 \ \ /:(-3)\\\\\huge\boxed{x=12}[/tex]

Answer:

x=12

Step-by-step explanation:

-28=2x+8-5x

-28=-3x+8

Add 3x on both sides:

3x-28=-3x+8+3x

3x-28=8

Add 28 on both sides:

3x-28+28=8+28

3x=36

Divide 3 on both sides:

3x/3=36/3

x=12

Step-by-step explanation:

28y-42-5y=-21

28y-42=-21+5y

-42=-21+5y-28y

-42=-21-23y

42=21+23y

23y=42-21

23y=21

y=21/23

Answer:

y = 15

Step-by-step explanation:

[tex] \frac{4y - 6 - 5y}{7} = - 3[/tex]

➡️ [tex] \frac{ - y - 6}{7} = - 3[/tex]

➡️ [tex] - y = 6 = - 21[/tex]

➡️ [tex] - y = - 21 + 6[/tex]

➡️ [tex] - y = - 15[/tex]

➡️ [tex]y = 15[/tex]

Answer: 36/a^2b

Step-by-step explanation:

Starting with the question 4a^3b^-2*9a^-5b

Since we have multiplication we multiply our numbers and add exponents

So

4*9=36

and exponents

3+-5=-2

-2+1=-1

So 36a^-2b^-1

BUTTT because we absolutely CANNOT have negative exponents we put them in the denominator to make them positive so our final answer is

[tex]\frac{36}{a^2b}[/tex]

Answer:

x=-10

Step-by-step explanation:

15x+8=-2+14x

15x-14x=-2-8

x=-10

Answer:

1/5

Step-by-step explanation:

the prob that you will pick a blue marble would be 12/16, easy.

then the prob of picking a yellow marble after that would be 4/15 since one marble is already missing. multiply the numerator and denominator of each fraction. so 12 x 4 and 16 x 15 to get 48/240. then divide each by 48 to get 1/5.

the answer is 1/5

hope that solve your problem for whoever gets this question

Answer:

Answer:

4 ≥ x÷2.1

Step-by-step explanation:

Answer:

$76-$14-$24=$38

Step-by-step explanation:

She owed her mother $76, and has paid back $38, leaving $38 left to be paid. If this helped, please mark as Brainliest :)

Answer:

76-14-24 or another expression is 14+24-76

Step-by-step explanation:

the answer for the expression is 38

Answer: $ 48.46

Step-by-step explanation:

If the price of 50 Kg of coffee was 2422.99, what is the cost of 1 Kg of coffee?

50/1 = 2422.90/x (cross multiplication)

48.46