power27

then what number base is 3.444444 supposed to be converted from

put 31/9 into a calculator, it is equal to 3.444444

is the base 10 part supposed to mean something? i just assumed it meant that it didn't want the fraction to be in base 7 or anything.

to start, we will ignore the 3 and come back to it later

we are left with the fraction .4444444444444

i see this and reconize that it is 4/9, but if you dont there is a way we can get there algabraicly

x=.444444444

multiply by 10

10x=4.44444444444

subtract the original equation

9x=4

divide by 9, and you get x=4/9

coming back to the 3

4/9+3=(3(9)+4)/9

=31/9

(r*s)(t) means r(s(t)), where you plug t into the function s, and then put the value you get from that into r.

for option a, substituting s(t)=t+f into r is 2(t+5)+1

=2t+10+1

=2t+11

this is the result we were looking for, so the answer is a

The probability you draw all blue is 6/15 * 5/14 * 4/13= 120/2730

all white: 5/15 * 4/14 * 3/13= 60/2730

all red: 4/15 * 3/14 * 2/13= 24/2730

add them together to get probability of any one of them happening: (120+60+24)/2730

=204/2730

=34/455

Let the length and with be l and w, respectivly.

l=3w-4

lw=55

Substitute for l

(3w-4)w=55

Looking at 55, an obvious factor pair is 5 and 11. This works.

w=5 and l=11

In this case, it might be easier to count the number of total words and subtract the number of words that do not contain A.

There are 4*4*4=64 total words

There are 3 letters excluding A, so 3*3*3=27 words w/o A

64-27=37 possible words that contain A.

There are 6*6=36 possible rolls, and while some of these are the same they need to be counted multiple times because they have a higher chance of occuring.

Rolls that sum to 4, with frequency:

(1,3) x3

(3,1) x3

(2,2) x1

Sum to 5:

(1,4) x3

(4,1) x3

(3,2) x1

(2,3) x1

Sum to 6:

(3,3) x1

(2,4) x1

(4,2) x1

Sum to 7:

(3,4) x1

(4,3) x1

8:

(4,4) x1

Adding up the frequencies gets 21

The probability is 21/36=7/12

Because the triangles are similar, 4:15 is in the same ratio as 5: height of the house.

To get from 4 to 5 you increast by 25%, increasing 15 by 25% means the height of the house is 18.75 feet tall.

\(2x^2+2y^2+10x-6y-18=0\)

First, you want to put this equation in a form that you can get information about the circle from.

Rearrange a bit:

2x²+10x+2y²-6y=18

Factor

2(x²+10x)+2(y²-3y)=18

Divide by 2

(x²+10x)+(y²-3y)=9

Add numbers to turn into perfect squares, making sure to add the same to both sides

(x²+10x+25)+(y²-3y+2.25)=9+25+1.5

Factor

(x+5)²+(y-1.5)²=36.25

(-5,1.5) is the center and 36.25 is the radius squared, so 36.25pi is the area.