Answer:
1) y=⅚x -2⅓
2) y=8/3x -5
Step-by-step explanation:
<u>Point-slope form:</u>
y=mx+c, where m is the gradient and c is the y-intercept.
Parallel lines have the same gradient.
Gradient of given line= 
Thus, m=⅚
Susbt. m=⅚ into the equation,
y= ⅚x +c
Since the line passes through the point (4, 1), (4, 1) must satisfy the equation. Thus, substitute (4, 1) into the equation to find c.
When x=4, y=1,
1= ⅚(4) +c
Thus the equation of the line is 
.
The gradients of perpendicular lines= -1.
Gradient of given line= -⅜
-⅜(gradient of line)= -1
gradient of line
= -1 ÷ (-⅜)
= -1 ×(-8/3)
= 
When x=3, y=3,
Thus the equation of the line is 
.
Answer:
B
Step-by-step explanation:
Since you are trying to find out half the number of students in a PE class, dividing would be most appropriate since you would be trying to find half.
The correct answer is:
[C]: "
" .
____________________________________________________Explanation:____________________________________________________Given:
____________________________________________________ 2 / (9x) = 4 / 7 ; solve for "x" ;
____________________________________________________Cross-multiply:
→ (9x)*4 = 2 * 7 ;
→ 36x = 14 ;
Divide each side of the equation by "36" ;
to isolate "x" on one side of the equation; & to solve for "x" ;
→ 36x / 36 = 14 / 36 ;
x = 14/ 36 ;
→ x = 14/36 = (14÷2) / (36÷2) = 7/18 ;
______________________________________________________
The answer is: "
" ;
→ which is:
Answer choice: [C]: "
" .
______________________________________________________
Let t = number of hours
The first candle starts at 8 inches.
It burns at 7/10 inch per hour, so in t hours it burns (7/10)t inches.
After t hours, its length is 8 - (7/10)t
The second candle starts at 6 inches.
It burns at 1/5 inch per hour, so in t hours it burns (1/5)t inches.
After t hours, its length is 6 - (1/5)t
You want the lengths to be equal, so the equation is
8 - (7/10)t = 6 - (1/5)t
Answer:
31.4 in³
Step-by-step explanation:
The box is just big enough to hold the 3 balls, so it must have a length 6 times the radius of each ball, a width 2 times the radius, and a height 2 times the radius.
The volume of the box is:
V = (6r)(2r)(2r)
V = 24r³
The volume of the 3 balls is:
V = 3 (4/3 π r³)
V = 4πr³
So the volume of the air is:
V = 24r³ − 4πr³
V = (24 − 4π) r³
Since r = 1.4 inches:
V = (24 − 4π) (1.4 in)³
V ≈ 31.4 in³
