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4 years ago

What is 63 as the product of prime factors in ascending order?

1 answer:

6 0

When we arrange the numbers in such an order that it starts from the smallest number and goes towards the largest number, that order is called ascending order.
Prime factors of 63 are : 3, 3, 7
As 3 repeats and 3 is smaller than 7 so, when we write this in ascending order as the product of these, we write in such a way;
63 = 3 x 3 x 7 = 3² x 7
Now 3² = 9 and 9 is greater than 7,so,
63 = 7 x 9

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7.4.PS-6

Sedaia [141]

Answer:

The area of the given polygon is:

232 cm^2

Step-by-step explanation:

To find the area of the polygon in the picture, you can divide the polygon in three rectangles: a 3 cm by 14 cm, a 5 cm by 14 cm rectangle, and the last rectangle must have a base of 12 cm (20 cm - 3 cm - 5 cm), and a height of 10 cm (14 cm - 4 cm). We can calculate the area of the rectangles with the formula below:

Area of a rectangle = Base * height

Now, we're gonna replace the measurements in the formula.

First rectangle:

Area of a rectangle = 3 cm * 14 cm
Area of a rectangle = 42 cm^2

Second rectangle:

Area of a rectangle = 5 cm * 14 cm
Area of a rectangle = 70 cm^2

Third rectangle:

Area of a rectangle = 12 cm * 10 cm
Area of a rectangle = 120 cm^2

By last, we must add the area of the rectangles:

Area of the polygon = 42 cm^2 + 70 cm^2 + 120 cm^2
Area of the polygon = 232 cm^2

As you can see, the area of the polygon in the picture is 232 cm^2.

5 0

3 years ago

If two of the cations have similar rf values how will you be aple to determine the difference

marshall27 [118]

それでも、日本人の食生活も急速に変化してきています。それでも、日本人の食生活も急速に変化してきています。

7 0

3 years ago

Determine the length the 6 meter side and the 12 meter side will be in the drawing.

vladimir2022 [97]

Answer:

x=2,x=4

So, the 6-meter side will be 2 centimeters and the 12-meter side will be 4 centimeters in the drawing.

Step-by-step explanation:

Solve for x by using cross multiplication

6=3x

x=2

12=3x

x=4

8 0

3 years ago

45,000 mL= I really need this answer just one more Time lol

ArbitrLikvidat [17]

Answer:

45,000 mL (Milliliters) = 45 L (Liters)

Explanation:

The word milliliters is made up of two words, "milli" and "liter"

"Milli" means a thousand, chiefly denoting a factor of one thousandth.

That means one milliliter is one thousandth of a liter

8 0

3 years ago

A rectangular box with a volume of 272ft^3 is to be constructed with a square base and top. The cost per square foot for the bot

ASHA 777 [7]

Answer:

The dimensions of the box is 3 ft by 3 ft by 30.22 ft.

The length of one side of the base of the given box is 3 ft.

The height of the box is 30.22 ft.

Step-by-step explanation:

Given that, a rectangular box with volume of 272 cubic ft.

Assume height of the box be h and the length of one side of the square base of the box is x.

Area of the base is = $(x\times x)$

$=x^2$

The volume of the box is = area of the base × height

$=x^2h$

Therefore,

$x^2h=272$

$\Rightarrow h=\frac{272}{x^2}$

The cost per square foot for bottom is 20 cent.

The cost to construct of the bottom of the box is

=area of the bottom ×20

$=20x^2$ cents

The cost per square foot for top is 10 cent.

The cost to construct of the top of the box is

=area of the top ×10

$=10x^2$ cents

The cost per square foot for side is 1.5 cent.

The cost to construct of the sides of the box is

=area of the side ×1.5

$=4xh\times 1.5$ cents

$=6xh$ cents

Total cost = $(20x^2+10x^2+6xh)$

$=30x^2+6xh$

Let

C $=30x^2+6xh$

Putting the value of h

$C=30x^2+6x\times \frac{272}{x^2}$

$\Rightarrow C=30x^2+\frac{1632}{x}$

Differentiating with respect to x

$C'=60x-\frac{1632}{x^2}$

Again differentiating with respect to x

$C''=60+\frac{3264}{x^3}$

Now set C'=0

$60x-\frac{1632}{x^2}=0$

$\Rightarrow 60x=\frac{1632}{x^2}$

$\Rightarrow x^3=\frac{1632}{60}$

$\Rightarrow x\approx 3$

Now $C''|_{x=3}=60+\frac{3264}{3^3}>0$

Since at x=3 , C''>0. So at x=3, C has a minimum value.

The length of one side of the base of the box is 3 ft.

The height of the box is $=\frac{272}{3^2}$

=30.22 ft.

The dimensions of the box is 3 ft by 3 ft by 30.22 ft.

7 0

3 years ago