Rearrange the equation into slope intercept form
7x+3y=18
3y=-7x+18
y=-7x/3+18/3 so the slope of the reference line is -7/3
To be perpendicular to this line the slope must be the negative reciprocal of this...mathematically m1*m2=-1. So the slope of our perpendicular line is:
-7m/3=-1
-7m=-3
m=3/7 so our line so far is:
y=3x/7+b, using point (6,8) we can solve for b, the y-intercept
8=3(6)/7+b
8=18/7+b
56/7-18/7=b
38/7=b so our line is:
y=3x/7+38/7 or if you prefer
y=(3x+38)/7
If the budget is $12 and each can is $3 the ratio is 3/4
Answer:
The general rule for the nth term of this sequence will be:
Step-by-step explanation:
Given the sequence
12a, 15a, 18a, 21a, 24a,...
An arithmetic sequence has a constant difference 'd' and is defined by
Here,
a₁ = 12a
computing the differences of all the adjacent terms
d = 15a-12a = 3a, d = 18a-15a=3a, d=21a-18a=3a, d=24a-21a=3a
using the nth term formula
substituting a₁ = 12a, d = 3a
Therefore, the general rule for the nth term of this sequence will be:
Answer:
1. a^mn= (a^m)^n
2. a^m+n= a^m • a^m
3. 1= a^0
4. a^m • b^m = ab^ m
5. 1/a^n = (a)^m
Step-by-step explanation:
^ means exponent
• means multiply
Square H"G"F"E" is 6/4 or 3/2 times the size of square EFGH.
Use the following 4 transformations to map EFHG onto its image E"F"G"H":
1. Invert EFGH about y=1 so that it's numbering becomes HGFE, in the same order as its image.
2. Dilate EFGH by 3/2. This will make EFGH of the same area as E"F"G"H". Its center will be at (-4, 1).
3.Translate EFGH along x (horizontally to the left) by 2 units. This will line up EFGH with E"F"G"H" but it will be 10 units above its image.
4. Translate EFGH along y (vertically downward) by 10 units. This will map EFGH onto its image E"F"G"H".
