A rectangular box has dimensions 4 by 5 by 2 . Increasing each dimension of the box by the same amount yields a new box with volume six times the old. Use the ALEKS graphing calculator to find how much each dimension of the original box was increased to create the new box. Round your answer to two decimal places.

Answers

Answer 1
Answer:

Answer:

2.68 units

Step-by-step explanation:

We are given that a rectangular box has dimensions 4 by 5 by 2.

We have to find that how much each dimension of the original box was increased to create the new box

Let x be the  increased value  in each dimension

We know that volume of rectangular box=lbh

Volume of original box=4* 5* 2=40 cubic units

Volume of new box =6* 40=240 cubic units

Dimension of new box=(x+4)(5+x)(2+x)

Volume of new box=240

(x+5)(x+4)(x+2)=240

x^3+11x^2+38x+40-240=0

x^3+11x^2+38x-200=0

By graph we get

x=2.679

Round to two decimal places then we get

x=2.68

Hence, each dimension was increased by 2.68 units


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A certain species of tree grows an average of 3.8 cm per week. Write an equation for the sequence that represents the weekly height of this tree in centimeters if the measurements begin when the tree is 5 meters tall.

Answers

The answer is f(x) = 500 + 3.8x

The number of weeks is x. So, weekly, the tree grows 3.8x. 
If the measurements of the growth begin when the tree started to grow, the equation would be: f(x) = 3.8x.
But, the measurements begin when the tree is 5 m tall. Since 1 m is 100 cm, this means that 5 m is 500 cm. Thus, the equation for the sequence that represents the weekly height of this tree in centimeters if the measurements begin when the tree is 5 meters tall is:
f(x) = 500 + 3.8x

Answer:

n=500+8(n-1)

DO NOT FORGET that the tree is already 5 meters tall on the FIRST WEEK, not the 0th week. So, f(x)=500+3.8x is incorrect.

(For example, on the second week the tree should be 503.8 meters tall. But if you plug 2 in f(x)=500+3.8x, you would get 507.6, which is the height of the tree on the third week.)

Find all real number x such that 
6x-21≥3 or 14x+11≤-7

Answers

6x-21 \geq 3\n \n 6x \geq 3+21\n \n 6x \geq 24\n \n x \geq (24)/(6)\n \n \boxed{x \geq 4}

14x+11 \leq -7\n \n 14x \leq -7-11\n \n 14x \leq -18\n \n x \leq (19)/(14)\n \n x \leq (9)/(7)

I need help please ASAP!!!

Answers

Answer:

The answer to your question is:  x = 1/4

Step-by-step explanation:

                (9^(4) )^(x)  = 9^(1)

               

x = (1)/(4)

It is 1/4 because 4 times equals 1

Please answer 1-6 worth 22 points

Answers

1. 10 times six is 60 dollars
2. 4 times 3 is 12
3.3 times 1.50 is 4.50 dollers for a 3 pack
4. 4 times 35 is 140 dollars
5. 40 times 5 is 200
6. 37.75
1. 60 dollars
2. 12
3. 4.50 dollars for a 3 pack
4. 140 dollars
5. 200
6. 37.75

Please help with these.

Answers

the answer to the question

June plans to buy a new pair of jeans. they are on sale for 25% off. if the original price is $35.00, how much will she save on her jeans?

Answers

To find the discount, multiply the decimal version of the percent by the original price.
25% = 0.25
0.25 • 35.00 = 8.75
This means there is a $8.75 discount, or $8.75 off in other words.
All that's left to do is subtract the discount amount from the original price.
35.00 - 8.75 = 26.25
So the price of the jeans with the sale is $26.25.
25% off of $35.00 is...

*multiply 35 × .25 (move decimal over to the left twice so that it is not a "percentage")

*35 × .25 = 8.75 (now since 25% is 1/4th of 100% you can multiply 8.75 by 4 to make sure you get the full 100% price of $35.00)

*now you know 8.75 is 25% of $35.00

*subtract 8.75 (25%) from 35 (100%)

*35 - 8.75 = 26.25

*june will pay $26.25 with the 25% sale off of the $35.00 original price of the jeans.