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3 years ago

Find all numbers whose absolute value is 5.

Mathematics

1 answer:

melamori03 [73]3 years ago

3 0

Answer:

5 , -5

Step-by-step explanation:

c'mon this is easy. the absolute value of a number is that numbers distance away from zero on the number line. 5 and -5 are the only numbers that are five intergers away from zero.

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What is the surface area of a unit cube?

lisabon 2012 [21]

Answer:

6 units

Step-by-step explanation:

The total area that the surface of a 3-dimensional object would cover if its sides were laid flat is called it's surface area. Surface area is measured in square units. The surface area of a unit cube is 6 square units.

8 0

3 years ago

Evaluate -2x2 y, if x = -3 and y = -1

Gre4nikov [31]

The answer is -12
these are the steps on how to find that
-2x2y
-2(-3)2(y)
6 times -2
-12

6 0

3 years ago

Enter the number that belongs in the green box

Brilliant_brown [7]

Answer:

Step-by-step explanation:

Hi!

First we need to translate 2 units down. That means we need to subtract 2 from the y value. So now we have (-1,1).

For a 270 degree counterclockwise rotation the rule is to go from (x,y) to (y,-x)

So now we have (1,1). Since they're only asking for the x value, the answer is 1.

6 0

3 years ago

A cardboard box without a lid is to have a volume of 19,652 cm3. Find the dimensions that minimize the amount of cardboard used.

Effectus [21]

Answer:

The dimension of the cardboard is 34 cm by 34 cm by 17 cm.

Step-by-step explanation:

Let the dimension of the cardboard box be x cm by y cm by z cm.

The surface area of the cardboard box without lid is

f(x,y,z)= xy+2xz+2yz.....(1)

Given that the volume of the cardboard is 19,652 cm³.

Therefore xyz =19,652

$\Rightarrow z=\frac{19652}{xy}$ ......(2)

putting the value of z in the equation (1)

$f(x,y)=xy+2x(\frac{19652}{xy})+2y(\frac{19652}{xy})$

$\Rightarrow f(x,y)=xy+\frac{39304}{y})+\frac{39304}{x}$

The partial derivatives are

$f_x=y-\frac{39304}{x^2}$

$f_y=x-\frac{39304}{y^2}$

To find the dimension of the box set the partial derivatives $f_x=0$ and $f_y=0$ .Therefore $y-\frac{39304}{x^2}=0$

$\Rightarrow y=\frac{39304}{x^2}$ .......(3)

and $x-\frac{39304}{y^2}=0$

$\Rightarrow x=\frac{39304}{y^2}$ .......(4)

Now putting the x in equation (3)

$y =\frac {39304}{(\frac{39304}{y^2})^2}$

$\Rightarrow y=\frac{y^4}{39304}$

$\Rightarrow y^3= 39304$

⇒y=34 cm

Then $\Rightarrow x=\frac{39304}{34^2}$ =34 cm.

Putting the value of x and y in the equation (2)

$z=\frac{19652}{34 \times 24}$

=17 cm.

The dimension of the cardboard is 34 cm by 34 cm by 17 cm.

4 0

3 years ago

Which statements are true about the toolbox? Select two options.

Amanda [17]

Answer:

Option A and E.

Step-by-step explanation:

It is mentioned that Chiyo has a toolbox having a rectangular prism shape with a length of 8 inches, width of 15 inches, and height of 6 inches.

In addition to this, A triangular prism with a triangular base with base 8 inches and height 3 inches. The prism has a height of 15 inches.

So here the shape can be broken into a triangular prism and rectangular prism

Therefore the first option is correct

Now as we know that

Volume of the rectangular prism is

= l×b× h

= 8 × 15 × 6

= 720

And, the volume of the triangular prism is bh

And, the area of the triangular prism is 1 ÷ 2 × b × h

= 1 ÷ 2 × 8 × 3

= 12

Now the volume is

= 12 × 15

= 180

So, the volume of the tool box is

= 720 + 180

= 900

Hence, the last option is correct

8 0

3 years ago