Step-by-step explanation:
First solve for y
given equation is 3x-2y ≥ 12
subtract 3x on both sides of the equation which would result with: -2y ≥ 12-3x
divide by -2 on both sides of the equation, flip the sign to ≤ because you are dividing by a negative, then you should get the result y<u> </u><u>≤</u><u> </u>-6 + 3x/2 (should look like a fraction)
y-intercept is at -6
slope is 3/2 (or three halves)
start at -6 on the y-axis, go up 3 across 2 and plot your point, keep repeating when going up and down the graph
Answer:
The ball will reach a height of 5 ft by the 4th time.
Step-by-step explanation:
The initial height of the ball is 40 ft, when it bounces from the floor once the height will be 20 ft, the second time it'll be 10 ft, and so on. The sequence that can represent the maximum height of the ball after each bounce is:
{40, 20, 10,...}
This kind of sequence is called a geometric progression, in this kind of progression the next number is related to the one before it by the product of a constant called ratio, in this case 1/2. To calculate a specific position in this sequence we only need the ratio and the first number, using the formula below:
a_n = a*r^(n-1)
Where n is the position we want to know, a is the first number and r is the ratio. In this case we have:
a_4 = 40*(1/2)^(4-1) = 40*(1/2)^3 = 40/8 = 5
The ball will reach a height of 5 ft by the 4th time.
let's firstly convert the mixed fractions to improper fractions, and then subtract.
![\bf \stackrel{mixed}{10\frac{1}{3}}\implies \cfrac{10\cdot 3+1}{3}\implies \stackrel{improper}{\cfrac{31}{3}}~\hfill \stackrel{mixed}{13\frac{1}{2}}\implies \cfrac{13\cdot 2+1}{2}\implies \stackrel{improper}{\cfrac{27}{2}} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \cfrac{27}{2}-\cfrac{31}{3}\implies \stackrel{\textit{using the LCD of 6}}{\cfrac{(3)27~~-~~(2)31}{6}}\implies \cfrac{81~~-~~62}{6}\implies \cfrac{19}{6}\implies 3\frac{1}{6}](https://tex.z-dn.net/?f=%5Cbf%20%5Cstackrel%7Bmixed%7D%7B10%5Cfrac%7B1%7D%7B3%7D%7D%5Cimplies%20%5Ccfrac%7B10%5Ccdot%203%2B1%7D%7B3%7D%5Cimplies%20%5Cstackrel%7Bimproper%7D%7B%5Ccfrac%7B31%7D%7B3%7D%7D~%5Chfill%20%5Cstackrel%7Bmixed%7D%7B13%5Cfrac%7B1%7D%7B2%7D%7D%5Cimplies%20%5Ccfrac%7B13%5Ccdot%202%2B1%7D%7B2%7D%5Cimplies%20%5Cstackrel%7Bimproper%7D%7B%5Ccfrac%7B27%7D%7B2%7D%7D%20%5C%5C%5C%5C%5B-0.35em%5D%20%5Crule%7B34em%7D%7B0.25pt%7D%5C%5C%5C%5C%20%5Ccfrac%7B27%7D%7B2%7D-%5Ccfrac%7B31%7D%7B3%7D%5Cimplies%20%5Cstackrel%7B%5Ctextit%7Busing%20the%20LCD%20of%206%7D%7D%7B%5Ccfrac%7B%283%2927~~-~~%282%2931%7D%7B6%7D%7D%5Cimplies%20%5Ccfrac%7B81~~-~~62%7D%7B6%7D%5Cimplies%20%5Ccfrac%7B19%7D%7B6%7D%5Cimplies%203%5Cfrac%7B1%7D%7B6%7D)
Answer:
Edit: This is incorrect, it might actually be the 3rd answer, draw arcs on either side of a given point on the line?
Draw arcs on either side of a given point off of the line I believe.
Step-by-step explanation:
Bisect a Segment:
Step 1 - open up your compass so that it is slightly larger than the segment. Put the compass on point A on the given segment and swing an arc above and below the lines. Do the same on point B. Create the points where the circle intersects.
Step 2 - Draw a line going through the points. That’s the bisector.
