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3 years ago

How do you decompose numbers

1 answer:

8 0

Method 1 Decomposing into Hundreds, Tens, and Ones
Understand the difference between "tens" and "ones." ...

Break apart a two digit number. ...

Introduce the "hundreds" place. ...

Break apart a three digit number. ...

Apply this pattern to infinitely larger numbers. ...

Understand how decimals work. ...

Break apart a decimal number.

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Find the equation of the line that is perpendicular to y=3y-x=7 and contains the point (2,-1).

a_sh-v [17]

First you want to get it into standard form. which would mean you get the x of the side of the y and divide everything by the y's coefficient in this case 3.

3y-x=a

3y=x+a

y=1/3x+a

Now your going to want to turn this into a perpendicular li e which means you flip the coefficient and make it negitive

y=-3x+a

then we fill in the points.

-1=-3(2)+a

Solve

-1=-6+a

-1+6=a

5=a

Now put it in standard form.

y=-3x+5

3 0

4 years ago

Given GHI G (4,-3), H (-4,2), and I (2,4), find the perpendicular bisector of HI in standard form.

Olin [163]

Answer:

$3x+y=0$

Step-by-step explanation:

step 1

Find the slope of segment HI

The formula to calculate the slope between two points is equal to

$m=\frac{y2-y1}{x2-x1}$

we have

H (-4,2), and I (2,4)

substitute the given points

$m=\frac{4-2}{2+4}$

$m=\frac{2}{6}$

simplify

$m=\frac{1}{3}$

step 2

Find the slope of the perpendicular line to segment HI

we know that

If two lines are perpendicular, then their slopes are opposite reciprocal (the product of their slopes is equal to -1)

$m_1*m_2=-1$

we have

$m_1=\frac{1}{3}$

$m_2=-3$

step 3

Find the midpoint segment HI

we know that

The formula to calculate the midpoint between two points is equal to

$M(\frac{x1+x2}{2},\frac{y1+y2}{2})$

we have

H (-4,2), and I (2,4)

substitute

$M(\frac{-4+2}{2},\frac{2+4}{2})$

$M(-1,3)$

step 4

we know that

The perpendicular bisector of HI is a line perpendicular to HI that passes though the midpoint of HI

Find the equation of the perpendicular bisector of HI in point slope form

$y-y1=m(x-x1)$

we have

$m=-3$

$M(-1,3)$

substitute

$y-3=-3(x+1)$

step 5

Convert to slope intercept form

$y=mx+b$

Isolate the variable y

$y-3=-3x-3$

$y=-3x-3+3$

$y=-3x$

step 6

Convert to standard form

$Ax+By=C$

where

A is a positive integer

B and C are integers

$y=-3x$

Adds 3x both sides

$3x+y=0$

see the attached figure to better understand the problem

3 0

4 years ago

A cone has a volume of 3533.5 cubic inches and a radius of 15 inches. What is its height?

tia_tia [17]

Answer:

h=14.9966

Step-by-step explanation:

1. The formula of the volume is:

V= $\frac{ab(h)}{3}$

2. So you have to substitute the the data that you have:

3533.5 $in^{3}$ = $\frac{ab(h)}{3}$

3. To have the area of the base (ab) you have to get the formula of the circle's area and solve:

A= $\pi$ ( $r^{2}$ )

A= $\pi$ ( $15^{2}$ )

A=3.1416(225)

A=706.86in

4. Now you have the area of the base:

3533.5 $in^{3}$ = $\frac{706.86(h)}{3}$

5. In this step you are going to clear the variable which is the heigh (h) and solve as an equation:

3533.5 $in^{3}$ = $\frac{706.86(h)}{3}$

3533.5 $in^{3}$ (3)=706.86(h)

$\frac{10,600.5}{706.86}$ =h

h=14.9966

The result may vary depending on the value of $\pi$ that you use,

7 0

3 years ago

Read 2 more answers

What is the range of this function {(3,4)(5,8),(9,-4),(-2,1),(0,8)}

denis23 [38]

To solve this problem you must apply the proccedure shown below:
1. You have the following information given in the problem above:
 {(3,4)(5,8),(9,-4),(-2,1),(0,8)}
2. Therefore,by definition, you have that the range is the set of all the values of y given. Keeping this on mind, you have that the range is:
Range:{4,8,-4,1,8}
Therefore, as you can see, the answer is: Range:{4,8,-4,1,8}.

4 0

3 years ago

Read 2 more answers

The histogram shows the number of runners who ran a given number of miles each week. How many runners ran 5–6 miles a week?

erma4kov [3.2K]

Answer:

5 runners

Step-by-step explanation:

By looking at the graph, the number of runners in the 5-6 mile category is 5.

6 0

3 years ago

Read 2 more answers