The diagram shows a 5 cm x 5 cm x 5 cm cube.

Using the numbers -4, 10, 8, 2, -3, -5 create two expressions that equal six

docker41 [41]

Answer:

8-2 and 10-3

Step-by-step explanation:

3 0

3 years ago

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Calculate the average rate of change for given function, from x=2 to x=7

LenaWriter [7]

"When you calculate the average rate of change of a function, you are finding the slope of the secant line between the two points. f(x) = x2 and f(x + h) = (x + h) Therefore, the slope of the secant line between any two points on this function is 2x + h."

8 0

3 years ago

Can you pls put in order I need help ASAP :3 thanks if you can. I will make Brainly

Brums [2.3K]

Answer:

This might get confusing but bear with me.

The top two are correct, leave them where they are. The 6th one down is step three, the 8th one down is step four, the 3rd one down is step five, the 4th one down is step six, the 7th ne down is step seven so leave it alone, and the 5th one down is step 8.

7 0

3 years ago

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

The roster form of The set of odd natural numbers greater than or equal to 5 and less than or equal to 11 .

Lunna [17]

Answer:

{5, 7, 9, 11}

Step-by-step explanation:

Roster form just means list the elements of the set in the brackets.

It says the elements are greater than or equal to five and less than or equal to 11. So we start at 5 and end at 11.

We list {5, 7, 9, 11} because these elements follow the rule that they must be odd natural numbers. Natural numbers are the numbers you can count starting from 0 like {0, 1, 2, 3, ...}.

4 0

3 years ago