Point-slope form: y - y₁ = m(x - x₁)
[m is the slope, x₁ and y₁ ---> (x₁, y₁) is the point]
Since you know:
m = 5
(2, 6) = (x₁, y₁) Substitute/plug in the values into the equation
y - y₁ = m(x - x₁)
y - 6 = 5(x - 2) The 1st option is your answer
Points (1, 7) and (-3, 2)
Slope for a line between (x₁, y₁) and (x₂, y₂) , m = (y₂ -y₁) / (x₂- x₁)
The slope for the line joining the two points = (2 - 7) / (-3 - 1) = -5/-4
Slope = 5/4
Hence the perpendicular bisector would have a slope of -1/(5/4) = -4/5
By condition of perpendicularity
For points (1, 7) and (-3, 2),
Formula for midpoints for (x₁, y₁) and (x₂, y₂) is ((x₁ +x₂)/2 , (y₁+ y₂)/2)
Midpoint for (1, 7) and (-3, 2) = ((1+ -3)/2 , (7+2)/2) = (-2/2, 9/2)
= (-1, 9/2)
Since the slope of perpendicular bisector is -4/5 and passes through the midpoint (-1, 9/2)
Equation y - y₁ = m (x - x₁)
y - 9/2 = (-4/5) (x - -1)
y - 9/2 = (-4/5)(x + 1)
5(y - 9/2) = -4(x + 1)
5y - 45/2 = -4x - 4
5y = -4x - 4 + 45/2
5y + 4x = 45/2 - 4
5y + 4x = 22 1/2 - 4 = 18 1/2
5y + 4x = 37/2
10y + 8x = 37
The equation of the line to perpendicular bisector is 10y + 8x = 37
90 x 135% = 90 x 1.35 = 121.5 (notice that instead of finding 35% and adding it on, I included the 90 by mutliplying by 1.xx) - in this case xx - 35 since it was a 35% increase.
Answer:
204
Step-by-step explanation:
90-5 (9-5 (9- (14-12) 3 ) ÷5
▪︎ First we have to solve the ones in the brackets ___ ( 14-12 ) which is e equal to 2
90-5 (9-5 (9- 2×3 ) ÷5 "the 3 comes inside the bracket coz we solved the previous one"
▪︎then we have to solve ( 9-2×3 ) which is equal to 3 _____ is 3 because if we go in the BODMAS way it will be
( 2×3 =6) , then... (9-6=3)
▪︎at the same time we can subtract 9-5 because we are done with the first bracket ( 9-5=4 )
90-5 (4×3)÷5
▪︎at the same time we can subtract 90-5 as well coz we are done with the first bracket ( 90-5=85)
▪︎then we can multiply (4×3) coz it's in the brackets (4×3=12)
85×12÷5
▪︎so then we hv to multiply 85 by 12 , then the answer is 1020
1020÷5
▪︎then divide (1020÷5=204)
☆90-5 (9-5 (9- (14-12) 3 ) ÷5
=90-5(9-5(9-2×3)÷5
=90-5(4×3)÷5
=85×12÷5
=1020÷5
=204
hope this helps☆☆☆
( sorry fr the long answer )
Answer:
it takes 24 hours for the bacteria cells to increase to 300
Step-by-step explanation:
WE use the formula

Where A is the initial amount of bacteria= 100
bacteria doubles every 15 hours so b=2
d= 15 because d is the time taken to double the number
t is the number of hours
c is the number of bacteria after t hours = 300
Plug in all the values and solve for 't'

Divide both sides by 100

Now we take log on both sides

As per log property we can move the exponent before log
log a^m = m log(a)

Divide both sides by log(2)

Multiply both sides by 15

t = 23.77
So its approximately 24 hours