Answer:
y = 8
Step-by-step explanation:
Given that y is directly proportional to x² then the equation relating them is
y = kx² ← k is the constant of variation
To find k use the condition y = 2 when x = 3, then
2 = k × 3² = 9k ( divide both sides by 9 )
= k
y = x² ← equation of proportion
When x = 6, then
y = × 6² = × 36 = 2 × 4 = 8
Answer:
the area of the mat = total area added minus the original area of the water color painting.
length of the mat is:
L = 21 in + 3 in + 3 in because 3 in is added to each side
L = 27 inwidth of the mat is:w = 11 in + 3 in + 3 inw = 17in
Area mat = (27 in x 17 in) - ( 21 in x 27 in)
area mat = 108 sq in is the area of the mat
Answer:
one possible solution is 5/6
Step-by-step explanation:
Solving for x
0 < 3x - 2 < 1
Add 2 to each side
0+2 < 3x - 2+2 < 1+2
2 < 3x<3
Divide each side by 3
2/3 < 3x/3 < 3/3
2/3 < x < 1
X must be between 2/3 and 1
Getting a common denominator
4/6 < x < 6/6
So x can be 5/6
Step-by-step explanation:
i)=
m=2/3
x=-3
y = 5
now
y=mx+c
or, 5 = 2/3× -3 + c
or, 5 = -2+c
c =7
now,
y= mx + c
or, y = 2/3×x+7
or, y = 2x/3+7
or, 3y = 2x+21
so, 3y-2x=21
equation would be 3y-2x=21.
now
ii)=
if slope of 3y-2x=21 and 2x-3y = 0 are same, they are parallel.
2x-3y = 0
2x = 3y
lets suppose x is 9
now
2x=3y
2×9 = 3y
or, 18 = 3y
so, y = 6
one coordinate would be (9,6) now
lets again suppose x is 3
2x=3y
2×3 = 3y
or, 6 = 3y
so, y = 2
another coordinate is (3,2)
now lets find slope
x1=9,y1=6
x2=3,y2=2
slope = (y2-y1)/(x2-x1)
= (2-6)/(3-9)
= -4/-6
= 2/3
Since, slope of 3y-2x=21 and 2x-3y has same slope 2/3, they are parallel.
Answer:
18 Possible outcomes
For every number one the dice you can get three different marbles so its
6 x 3 + 18