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3 years ago

If 2^(x+3) - 2x = k(2^x) what is the value of k

Mathematics

1 answer:

svlad2 [7]3 years ago

8 0

Answer:

$\large\boxed{C)\ 7}$

Step-by-step explanation:

Use:

$a^n\cdot a^m=a^{n+m}$

$2^{x+3}-2^x=2^x\cdot2^3-2^x=8\cdot2^x-2^x=(8-1)\cdot2^x=7\cdot2^x\\\\2^{x+3}-2^x=k(2^x)\\\\7\cdot2^x=k(2^x)\Rightarrow k=7$

$8\cdot2^x-2^x=8\cdot2^x-1\cdot2^x=(8-1)(2^x)=7\cdot2^x\\\\\text{distributive property:}\ a(b-c)=ab-ac$

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The fraction

anzhelika [568]

0.17 because its in the hundredths place

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2 years ago

Read 2 more answers

1. What is the theoretical probability that the family has two dogs or two cats?

gogolik [260]

let dogs be heads. Let cats be tails. A coin has two sides, in which you are flipping two of them. Note that there can be the possible outcomes

h-h, h-t, t-h, t-t.

How this affects the possibility of two dogs & two cats. Note that there are 1/2 a chance of getting those two (with the others being one of each), which means that out of 4 chances, 2 are allowed.

2/4 = 1/2

50% is your answer

Heads represents cats and tails represents dogs. There is two coins because we are checking the probability of two pets. You have to do the experiment to get your set of data, once you get your set of data, you will be able to divide it into the probability for cats or dogs. To change the simulation to generate data for 3 pets, simply add a new coin and category for the new pet.

Hope this helps you out!

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3 years ago

They estimate that their current (older) fridge, which they got for free, costs them about $17 a month in electricity charges to

Eddi Din [679]

Step-by-step explanation:

Step one:

given

current (older) fridge

electricity charges= $17 monthly

maintenance costs= $220

let the number of months be x

and the total cost be yo

the expression for the cost for the old fridge is

yo=220+17x---------1

New fridge

electricity charges= $6 monthly

costs= $1,050

let the number of months be x

and the total cost be yn

the expression for the cost for the old fridge is

yn= 1050+6x---------2

Hence the system of equation for the situation is

yo=220+17x---------1

yn= 1050+6x---------2

Step two

for 10 years there are 12*10= 120 months

put x= 120 in both expressions and compare the total

yo=220+17(120)---------1

yo=220+2040

yo=$2,260

yn= 1050+6(120)---------2

yn=1050+720

yn=$1770

Based on the analysis it will be less expensive to get the new fridge, hence buying the new fridge is worth it.

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3 years ago

The area of rectangle is ( 30x²y + 20xy ) cm² and its breadth is 10xy cm .Find its length.

emmasim [6.3K]

Step-by-step explanation:

1) The area of rectangle is ( 30x²y + 20xy ) cm² and its breadth is 10xy cm .Find its length....

= Solution ,

Length ( L ) = ?

breadth ( b ) = 10xy cm

area ( a ) = ( 30x² + 20xy )

Now ,

area ( a ) = l × b

or, ( 30x²y + 20xy ) = L × 10xy cm

$or,\frac{30 {xy + 20xy}^{2} }{10xy} = l \\$

$or, \: l = 3 {x}^{2 - 1} + 2cm$

$\boxed{\sf{l = (3x+2)cm}}$

2) Subtract the quotient when 20x⁴y² is divided by 5x³y from the product of 2x and 3y.

= Solution,

$= \frac{20 {x}^{4} {y}^{2} }{5 {x}^{3} y} \\$

$= 4xy$

The product of 3x and 4y = 6xy

= 6x - 4xy

$= \boxed{\sf {2xy}}$

hope it helped !!!!

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1 year ago

the area of a square garden is 267 ft^2 what is the side length of each side? round your answer to the nearest hundredth place.

aksik [14]

Answer:

Side Length=16.34 ft
No

Step-by-step explanation:

The area of the square garden= $267$ ft^2$

Area of a Square of Side length s $=s^2$

Therefore:

$s^2=267$ ft^2\\$Take the square root of both sides\\s=\sqrt{267} \\$Side Lenght, s=16.34 ft (to the nearest hundredth place)$

Perimeter

Perimeter of a Square of Side length s=4s

Therefore, the perimeter of the garden =4*16.34=65.36 ft

Since 65 ft < 65.36 ft

Therefore, if you had 65 ft of fencing, it will not be enough to go around and cover the garden.

5 0

2 years ago