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3 years ago

Is -3.25 irrational or rational ??

Mathematics

2 answers:

Ann [662]3 years ago

7 0

Answer:

yes it is rational number.

Step-by-step explanation:

lorasvet [3.4K]3 years ago

6 0

Answer - rational

Explaination- rational numbers can be decimals and this number is not on going.

Hope this helped :)

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You are creating an open top box with a piece of cardboard that is 16 x 30“. What size of square should be cut out of each corne

Arada [10]

Answer:

$\frac{10}{3} \ inches$ of square should be cut out of each corner to create a box with the largest volume.

Step-by-step explanation:

Given: Dimension of cardboard= 16 x 30“.

As per the dimension given, we know Lenght is 30 inches and width is 16 inches. Also the cardboard has 4 corners which should be cut out.

Lets assume the cut out size of each corner be "x".

∴ Size of cardboard after 4 corner will be cut out is:

Length (l)= $30-2x$

Width (w)= $16-2x$

Height (h)= $x$

Now, finding the volume of box after 4 corner been cut out.

Formula; Volume (v)= $l\times w\times h$

Volume(v)= $(30-2x)\times (16-2x)\times x$

Using distributive property of multiplication

⇒ Volume(v)= $4x^{3} -92x^{2} +480x$

Next using differentiative method to find box largest volume, we will have $\frac{dv}{dx}= 0$

$\frac{d (4x^{3} -92x^{2} +480x)}{dx} = \frac{dv}{dx}$

Differentiating the value

⇒ $\frac{dv}{dx} = 12x^{2} -184x+480$

taking out 12 as common in the equation and subtituting the value.

⇒ $0= 12(x^{2} -\frac{46x}{3} +40)$

solving quadratic equation inside the parenthesis.

⇒ $12(x^{2} -12x-\frac{10x}{x} +40)$ =0

Dividing 12 on both side

⇒ $[x(x-12)-\frac{10}{3} (x-12)]$ = 0

We can again take common as (x-12).

⇒ $x(x-12)[x-\frac{10}{3} ]$ =0

∴ $(x-\frac{10}{3} ) (x-12)= 0$

We have two value for x, which is $12 and \frac{10}{3}$

12 is invalid as, w= $(16-2x)= 16-2\times 12$

∴ 24 inches can not be cut out of 16 inches width.

Hence, the cut out size from cardboard is $\frac{10}{3}\ inches$

Now, subtituting the value of x to find volume of the box.

Volume(v)= $(30-2x)\times (16-2x)\times x$

⇒ Volume(v)= $(30-2\times \frac{10}{3} )\times (16-2\times \frac{10}{3})\times \frac{10}{3}$

⇒ Volume(v)= $(30-\frac{20}{3} ) (16-\frac{20}{3}) (\frac{10}{3} )$

∴ Volume(v)= 725.93 inches³

6 0

3 years ago

Name the corresponding part if ∆RST ≅ ∆WXY ∠R= ∠X ∠W ∠Y

Furkat [3]

The question is asking choose among the following choices that states the angle that is congruent to angle R if triangle RST is congruent to WXY, base on that, the possible answer would angle R is equals to angle W. I hope you are satisfied with my answer and feel free to ask for more

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3 years ago

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What is the probability of flipping 3 coins and having exactly two of them land on tails?

Drupady [299]

Step-by-step explanation:

We can also simply calculate the total number of possible outcomes of 3 coin flips, meaning the overall probability of exactly 2 coin flips out of 3 being tails is 37.5%.

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2 years ago

What is the solution to the system of equations?

zysi [14]

Answer:

x=3, y=-1

Step-by-step explanation:

x+y = 2

x -y =4

I will use elimination to eliminate the variable y. Add the two equations together.

x+y = 2

x -y =4

-------------

2x = 6

Divide each side by 2

2x/2 = 6/2

x = 3

But we still don't know y

x+y =2

Substitute x=3 into the equation

3+y =2

Subtract 3 from each side

3-3 +y =2-3

y =-1

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3 years ago

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Triangles CDE and NOP are similar. The lengths of CD and NO are 53in and 212in, respectively. DE IS 106In long and NP is 318in.

Serggg [28]

Gttenbhgegegdggrggrggggg

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3 years ago