Use only an associative property to rewrite the following expression. (pk)•r=

#6) Beth saved a total of $30 per month for her first car. Beth saved

babymother [125]

Answer:

Domain = 0≤m≤20 for mEZ+

Range = $100≤A≤$700 for all values of m

Step-by-step explanation:

Initial amount in the account = $100

Amount saved by beth monthly = $30

Amount in the bank after X month = $100+$30X where X is the number of months beth intend to save up to.

The amount in her bank in her first month = $100+$30(1)

= $100+$30

= $130

Amount saved in the second month will be when X = 2

= $100+$30(2)

= $100+$60

= $160

The amount in the bank will keep increasing by $30 monthly until the 20month.

The amount he will have in her bank in the 20th month will be at when X = 20

= $100+30X

= $100+30(20)

= $100+$600

= $700

This means that her money will be $130 in the first month and will keep increasing until it reaches $700 in the 20th month.

The DOMAIN will be the interval of the time she used in saving. Since she saved for 20months, the domain will be expressed as 0≤m≤20 for mEZ+ where m is the number of month she uses to save.

The Range will represent the amount she saved within the specified time and will be expressed as $100≤A≤$700 for all values of m.

Where $100 is the amount in the account initially and $700 is the amount in the account after 20 months.

3 0

3 years ago

Joel made egg sandwiches and tuna sandwiches in the ratio 2:3. He then made 15 more tuna sandwiches and the ratio changed to 1:3

Aleksandr [31]

Answer:

40 sandwiches

Step-by-step explanation:

egg sandwiches : tuna sandwiches

2 : 3

Multiply by x because we do not know how many sandwiches, just the ratio

2x : 3x

Add 15 tuna sandwiches

2x : 3x+15

Now the ratio is 1:3

egg sandwiches : tuna sandwiches

1 : 3

Multiply by y because we do not know how many sandwiches, just the ratio

y : 3y

Set the number of egg sandwiches equal

2x =y

then set the number of tuna sandwiches equal

3x+15 = 3y

We know have a system of 2 equations and 2 unknowns

Substitute y =2x into the second equation

3x+15 = 3(2x)

Distribute

3x+15 = 6x

Subtract 3x from each side

3x-3x+15 = 6x-3x

15 =3x

Divide by 3

15/3 = 3x/3

5 =x

egg sandwiches : tuna sandwiches

2 : 3

Multiply by x because we do not know how many sandwiches, just the ratio

2x : 3x

2*5 3*5

10 15

He originally made 10 egg sandwiches and 15 tuna sandwiches

Then he made 15 more tuna sandwiches

The total number of sandwiches he made is

10+15+15 = 40 sandwiches

5 0

3 years ago

A parabola can be drawn given a focus of (8, 6) and a directrix of x=4. Write the equation of the parabola

Orlov [11]

Answer:

The equation of the Parabola

(y - 6 )² = 8 (x -6)

Step-by-step explanation:

Step(i):-

Given directrix x = 4

we know that x = h - a = 4

h -a = 4 ...(i)

Given Focus = ( 8,6)

we know that the Focus of the Parabola

( h + a , k ) = ( 8,6)

comparing h + a = 8 ...(ii)

k = 6

solving (i) and (ii) and adding

h - a + h+ a = 8 +4

2 h = 12

h =6

Put h = 6 in equation (i)

⇒ h - a =4

⇒ 6 - 4 = a

⇒ a = 2

Step(ii):-

The equation of the Parabola ( h,k) = (6 , 6)

( y - k )² = 4 a ( x - h )

(y - 6 )² = 4 (2) (x -6)

(y - 6 )² = 8 (x -6)

3 0

3 years ago

PLEASE HELP HELP HELP HELP PLEASE PLEASE PLEASE PLEASE PLEASE

oee [108]

Yes they are equal they both have a side that is 25 degrees

5 0

3 years ago

Which could be the first step in simplifying this expression? Check all that apply. (x cubed x Superscript negative 6 Baseline)

PtichkaEL [24]

Answer:

$(x^{-3} )^{2}$

$x^6 x^{-12}$

Step-by-step explanation:

$(x^{3} x^{-6} )^{2}$ is the expression given to be solved.

First of all let us have a look at 3 formulas:

$1.\ p^a \times p^b = p^{(a+b)}\\2.\ (p^a \times q^b)^c = (p^{a})^c \times (q^{b})^c\\3.\ (p^a)^b = p^{a\times b}$

Both the formula can be applied to the expression( $(x^{3} x^{-6} )^{2}$ ) during the first step while solving it.

Applying formula (1):

$(x^{3} x^{-6} )^{2}$

Comparing the terms of $(x^{3} x^{-6} )$ with $p^a \times p^b$

$p=x, a =3, b=-6$

$\Rightarrow x^{3+(-6)}\\\Rightarrow x^{3-6}\\\Rightarrow x^{-3}$

So, $(x^{3} x^{-6} )^{2}$ is reduced to $(x^{-3} )^{2}$

Applying formula (2):

Comparing the terms of $(x^{3} x^{-6} )^{2}$ with $(p^a \times q^b)^c$

$p=q=x, a =3, b=-6, c=2$

$\Rightarrow (x^{3})^2\times (x^{-6})^2\\\text{Applying Formula (3)}\\x^6 x^{-12}$

So, $(x^{3} x^{-6} )^{2}$ is reduced to $x^6 x^{-12}$ .

So, the answers can be:

$(x^{-3} )^{2}$

$x^6 x^{-12}$

8 0

3 years ago