Answer:
see explanation
Step-by-step explanation:
If 2 lines are perpendicular then the product of their slopes equals - 1
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Consider the given equations
3x - 4y = 12 ( subtract 3x from both sides )
- 4y = - 3x + 12 ( divide terms by - 4 )
y = 
x - 3 ← in slope- intercept form
with slope m =
3y = 12 - 4x = - 4x + 12 ( divide terms by 3 )
y = - 
x + 4 ← in slope- intercept form
with slope m = -
Then
× - = - 1
Since the product of their slopes = - 1 then the lines are perpendicular
Answer:
i) pi×4500 cm³
ii) pi×600 cm²
iii) 14 liters
Step-by-step explanation:
in general : the diameter is 30 cm, the radius is half of that (15 cm)
i)
the volume of a cylinder is base area times height.
Vc = pi×r²×h = pi×15²×20 = pi×225×20 = pi×4500 cm³
ii)
similar to volume, the side "mantle" area of the cylinder is the circumference of the base area times height.
surface area of the cylinder mantle is
Scm = 2×pi×r×h = 2×pi×15×20 = pi×30×20 = pi×600 cm²
iii)
for this we need now to do the multiplication with pi and then convert the cm³ to liters.
1 liter = a cube of 10 cm side length = 10×10×10 = 1000 cm³
pi×4500 = 14137.17 cm³ = 14.13717 liters or rounded 14 liters
It takes them 12 seconds to eat the whole sausage.
<h3>What is speed?</h3>
Speed is the rate of change of distance.
Analysis:
If kitten eats x cm, then puppy will eat 14 - x cm
speed = d/t
speed of kitten = 1/2
speed of puppy = 2/3
1/2 = x/t
2/3 = 14 - x / t
t = 2x--------1
2t = 3(14 - x ) -------- 2
substitute t in equation 2
2(2x) = 3(14 - x)
4x = 42 - 3x
7x = 42
x = 42/7 = 6cm
substitute value of x in equation 1
t = 2(60 = 12 seconds.
In conclusion, it takes the both animals 12 seconds to finish the sausage.
Learn more about speed: brainly.com/question/4931057
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Answer:
a = 9
Step-by-step explanation:
2(a + 7) = 5a - 13
We want to bring a to one side, I will choose to bring it to the right
First, expand the bracket by multiplying 2 with a + 7
2a + 14 = 5a - 13
Bring the -13 to the left by adding 13 to both sides
2a + 14 + 13 = 5a - 13 + 13
Simplify
2a + 27 = 5a
Bring the 2a to the right by subtracting 2a from both sides
2a - 2a + 27 = 5a - 2a
Simplify
27 = 5a - 2a
27 = 3a
Bring the 3 to the left by dividing both sides by 3
27÷3 = a
Simplify
a = 9
Answer:
b. The greater the number of independent variables measured, the more difficult it is to interpret higher-order interactions.
