All categories

3 years ago

Prove the divisbility of the following numbers.

Mathematics

1 answer:

Anastaziya [24]3 years ago

7 0

Answer:

3^16

Step-by-step explanation:

12^8 * 9^12

Rewrite 12 as 3*4 and 9 as 3*3

(3*4)^8 * (3*3)^12

We know that (ab)^c = a^c * b^c

3^8 4^8 3^12 3^12

We can write 4 as 2^2

3^8 2^2^8 3^12 3^12

We know a^b^c = a^(b*c)

3^8 2^(2*8) 3^12 3^12

3^8 2^(16) 3^12 3^12

We also know that a^b *a^c *a^d = a^(b+c+d)

2^(16) 3^8 3^12 3^12

2^(16) 3^(8+12+12)

2^16 3^(32)

But we need 6 ^16 so we will need a 3^16 3^32 = 3^16 * ^16 (16+16=32)

2^16 *3^16 *3^16

Remember a^b*c^b = (ac)^b

(2*3)^16 3^16

6^16 3^16

You might be interested in

Sarah's family of 4 went camping for 1 week. they each year 3 paper plates a day. how many paper plates did the family use up we

Mama L [17]

Answer:

Step-by-step explanation:

they use 3 plates a day

there are 4 of them

so in one day, they use 12 plates [3x4]

they camp for 7 days, so 12x7.

84!! :D

4 0

3 years ago

A circle is increased to have a circumference that is 4 times larger than the original. Which of the following options best desc

kogti [31]

Area of a circle is directly proportional to the square of radius of the circle while the circumference is proportional to the radius of the circle. This means that if the radius of a circle is increased x times, then its area will be increased to x^2 times the original area, and the circumference will increase to x times the original circumference.

Thus when the radius is doubled, or in other words if radius mad 2 time the original radius, the area of circle will become 2^2 = 4 time the original area. The circumference will become 2 times the original circumference.

We can calculate exact area and circumference of a circle from its radius using the following equations:

Area of circle = (pi/4)*r^2

Circumference of circle = 2*pi*r

Where r is the radius of the circle.

I know this is a lot, sorry.

3 0

3 years ago

the Children's Hospital sponsors a 10k race to raise money. it receives $75 per race entry and $10,000 in donations but it must

masha68 [24]

Answer:

There would need to be at least 1,800 entries in order for them to meet their goal.

Step-by-step explanation:

To find this, we must write an equation that helps solve it. We know that for every entry (x), we gain 75 and lose 25. We can express this as the following.

75x - 25x

Then we can add the number of donations.

75x - 25x + 10,000

Then we can set it as greater than or equal to the goal number.

75x - 25x + 10,000 ≥ 100,000

Now we solve this using the order of operations.

75x - 25x + 10,000 ≥ 100,000 ----> Combine like terms

50x + 10,000 ≥ 100,000 ------> Subtract 10,000

50x ≥ 90,000 -----> Divide by 50

x ≥ 1,800

4 0

3 years ago

Read 2 more answers

Could someone pretty please help me on this. I need explanation.

astraxan [27]

Answer:

In mathematics, the slope or gradient of a line is a number that describes both the direction and the steepness of the line. ... A slope with a greater absolute value indicates a steeper line. The direction of a line is either increasing, decreasing, horizontal or vertical.

Step-by-step explanation:

here are a few more things you might want to know will douing this

How do you know which slope is steeper?

When you look at the two lines, you can see that the blue line is steeper than the red line. It makes sense the value of the slope of the blue line, 4, is greater than the value of the slope of the red line, . The greater the slope, the steeper the line.

Can you create a line segment with infinite steepness?

An infinite slope is simply a vertical line. When you plot it on a line graph, an infinite slope is any line which runs parallel to the y-axis. You can also describe this as any line that doesn't move along the x-axis but stays fixed at one constant x-axis coordinate, making the change along the x-axis 0.

How does rate of change affect the steepness of a line?

The steepness of a line is essentially the slope. ... A negative slope would be depicted by a line going from the upper left to bottom right. Slope values increase the higher the number is: For instance, a line with a slope of 2 is steeper than a line with a slope of 12 . Hope this helps!Jun 20, 2018

What are the 3 slope formulas?

There are three major forms of linear equations: point-slope form, standard form, and slope-intercept form.

What is a 6% grade?

A road sign indicating a 6% grade, or 6% slope. A six percent slope means that the road elevation changes 6 feet for every 100 feet of horizontal distance (Figure 1.3). ... A road climbs at a gradient of 6 percent. The road gains 6 feet in elevation for every 100 feet of horizontal distance.

What does the slope represent?

The slope and y-intercept values indicate characteristics of the relationship between the two variables x and y. The slope indicates the rate of change in y per unit change in x.

IF YOU NEED MORE INFO LET ME KNOW I DID NOW WANT TO PUT TO MUCH IN HERE

3 0

3 years ago

I will give brainliest

Angelina_Jolie [31]

Answer:

A,B,D

Step-by-step explanation:

plz mark brainliest

8 0

3 years ago

Read 2 more answers