Answer:
k = ⅕
Step-by-step explanation:
The slope-intercept equation for a straight line is
y = mx + b, where
m = the slope and
b = the y-intercept
Data:
(3,4) = a point on the line
(3k,0) = x-intercept
(0,-5k) = y-intercept
Calculations:
1. Slope
m = (y₂ - y₁)/(x₂ - x₁) = (-5k - 0)/(0 - 3k) = -5/(-3) = ⁵/₃
This makes the equation
y = ⁵/₃x - 5k
2. k
Insert the value of the known point: (3,4)
4 = (⁵/₃)(3) - 5k
4 = 5 - 5k
-1 = -5k
k = ⅕
The figure below shows your graph passing through (3,4) with intercepts 3k and -5k on the x- and y-axes respectively
.
2p-14=4(p+5)
Step 1, parentheses
2p-14=4p+20
Subtract 20 from each side of the equation
2p-34=4p
Subtract 2p from each side
-34=2p
Divide each side by 2
-17=p
4x+6y=56 and y=4x can be used to determine the number of small cars rented and the number of large cars rented, where x represents number of small cars and y represents number of large cars.
Step-by-step explanation:
Number of people hold by small cars = 4
Number of people hold by large cars = 6
Let,
Number of small cars = x
Number of large cars = y
The students rented 4 times as many large cars as small cars,
y = 4x Eqn 1
which altogether can hold 56 people.
4x+6y=56 Eqn 2
4x+6y=56 and y=4x can be used to determine the number of small cars rented and the number of large cars rented, where x represents number of small cars and y represents number of large cars.
Keywords: linear equations, addition
Learn more about linear equations at:
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Answer:
22 grams
Step-by-step explanation:
loses 50% of it's mass per 22 years
so after 22 years the mass would be 44 grams
22 years later would leave 50% of 44 grams = 22 grams
