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jarptica [38.1K]
3 years ago
6

A rectangular piece of metal is 20 in longer than it is wide. Squares with sides 4 in long are cut from the four corners and the

flaps are folded upward to form an open box. If the volume of the box is 1536 incubed​, what were the original dimensions of the piece of​ metal?
Mathematics
1 answer:
Misha Larkins [42]3 years ago
7 0

Answer:

Step-by-step explanation:

This is good!  The length of the metal is 20 inches longer than the width.  But we fold up 4-inch flaps on each side, so the height of the box is 4 inches, and the length and width will each decrease by 8 inches (4 inches on each side).  Since the length and width decrease by the same amount, the length will still be 20 inches longer than the width.  So the equations would be:

l = w + 20

vol = l x w x h = 1716 in3

1716 = (w + 20)(w)(4)

1716 = 4w2 + 80w

4w2 + 80w - 1716 = 0

4(w2 + 20w - 429) = 0

4(w + 33)(w - 13) = 0

w + 33 = 0, so w = -33

w - 13 = 0, so w = 13

Since the width can't be negative, the width of the box is 13 and the length is 33 (13 + 20).

But remember, the length and width of the piece of metal are each 8 inches longer than the box, so it was 41 inches by 21 inches.

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Find the value of x for which 2x ^(1/ 2) = 32.
Mrac [35]

Answer:

The value of x will be 8    

Step-by-step explanation:

We have given that 2\sqrt{x}=32

We have to find the value of x

As 2\sqrt{x}=32

For finding the value of x we have to square both side

On squaring both side

We done squaring both side for easy simplification

4x=32

So x = 8

So the value of x will be 8

So answer will be 8

5 0
3 years ago
Cell phone plan A costs 79 per month and comes with a free 500 phone. Cell phone plan B costs 50 per month but does not come wit
meriva

Answer: it will take 25 months

Step-by-step explanation:

Let x represent the number of months that it will take for the cost of both plans to be the same.

Cell phone Plan A costs $70 per month and comes with a free $500 phone. This means that the total cost of x months with plan A would be

70 × x = $70x

Cell phone plan B costs 50 per month but does not come with a phone. If you buy the 500 phone and choose plan B, then the total cost of x months with plan B would be

500 + 50 × x = 500 + 50x

To determine the number of months until your cost is the same as Plan A's, we would equate both costs. It becomes

70x = 500 + 50x

70x - 50x = 500

20x = 500

x = 500/20 =25

8 0
3 years ago
How many extraneous solutions does the equation below have?
aev [14]

Answer:

A solution is said to be extraneous, if it is a zero of the equation, but it does not satisfy the equation,when substituted in the original equation,L.H.S≠R.H.S. 

The given equation consisting of  variable , m is

   \frac{2 m}{2 m+3} -\frac{2 m}{2 m-3}=1\\\\ 2 m[\frac{1}{2 m+3} -\frac{1}{2 m-3}]=1\\\\ 2 m\times \frac{[2 m-3 -2 m- 3]}{4m^2-9}=1\\\\ -6 \times 2 m=4 m^2 -9\\\\ 4 m^2 +1 2 m -9=0\\\\m=\frac{-12 \pm\sqrt{12^2-4 \times 4 \times (-9)}}{2\times 4}\\\\m=\frac{-12 \pm \sqrt {144+144}}{8}\\\\m=\frac{-12 \pm \sqrt {288}}{8}\\\\m=\frac{-12 \pm 12 \sqrt{2}}{8}\\\\m=\frac{3}{2}\times(-1 \pm \sqrt{2})

None of the two solution

m=\frac{3}{2}\times(-1 +\sqrt{2}) and , m=\frac{3}{2}\times(-1 -\sqrt{2}), is extraneous.

Here, L.H.S= R.H.S

Option A: 0→ extraneous

8 0
3 years ago
Read 2 more answers
Could you solve it What is _____+______+______=30 Using 1,3,5,7,9,11,13 ,15 what are the numbers ​
wariber [46]

Answer:

We want to solve:

___ + ___ + ____ = 30

using the numbers:

1, 3, 5, 7, 9, 11, 13, 15.

Now, 30 is an even number.

And the given numbers are all odd.

A random even number is written as:

2*n  (where n is an integer)

A random odd number is written as:

2*k + 1 (where k is an integer)

If we add 3 odd numbers, we get:

(2*k + 1) + (2*c + 1) + (2*j + 1) = 2*(k + c + j) + 3

= 2*(k + c + j + 1) + 1

(k + c + j + 1) is an integer, then we can write this as p

then the sum of 3 odd numbers can be written as:

2*p + 1

This means that the sum of 3 odd numers is always an odd number.

Then we can not find 3 odd numbers such that their sum is equal to 30.

if instead, we could use 4 numbers, like:

___ + ___ + ___ + ___ = 30

Then we could select:

15, 1, 5 and 9.

because:

15 + 1 + 5 + 9 = 15 + (1 + 5) + 9 = 15 + 6 + 9 = 15 + (6 + 9) = 15 + 15  = 30

6 0
3 years ago
Can someone please help how do u do this
sasho [114]
Hey, I suggest checking out tiger algebra, this is the answer I got from the site :

8 0
3 years ago
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