Answer:
To match each functions with the corresponding function formula when h(x) = 5 - 3x and g(x) = -3 x + 5.
1. k(x) = (3h - 5g)(x)
= = 3(5 - 3x)-5(-3 x + 5)
= = 15 - 9x + 15x - 25
K(x) = -10 + 6x
2. k(x) = (h - g)(x)
= = (5 - 3x) - (-3 x + 5)
= = 0
k(x) = 0
3. k(x) = (5g + 3h)(x)
= = 5(-3 x + 5)+3(5 - 3x)
= = -15x + 25 + 15 - 9x
k(x) = - 24x +40
4. k(x) = (3g + 5h)(x)
= = 3 (-3 x + 5) + 5(5 - 3x)
= = -9x + 15 +25 -15x
k(x) = -24x + 40
5. k(x) = (g + h)(x)
= = (-3 x + 5) + (5 - 3x)
k(x) = -6x + 10
6. k(x) = (5h - 3g)(x)
= = 5(5 - 3x) - 3(-3 x + 5)
= =25 - 15x + 9x - 15
k(x) = 10 - 6x
A b c and d r not answers, u need to tell how the different variations would change based on the numbers and where they r
Answer: B) $47/week
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Explanation:
Because the graph goes through the origin, we can simply divide the y value over the x value. Do so for any point on the diagonal line.
For example, picking (x,y) = (2, 94) leads to k = y/x = 94/2 = 47 being the constant of proportionality and also the amount of savings per week.
You can think of it like this:
2 weeks = $94 in savings
2/2 weeks = $94/2 in savings ... divide both sides by 2
1 week = $47 in savings
leading to the savings rate of $47 per week
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Side note: This linear equation is y = 47x. It is in the form y = kx with k = 47. It is a direct proportion equation. The constant of proportionality is also the slope. All direct proportion equations are linear and go through the origin.
Since the tank is 66.06% full, it is (100 - 66.06) = 33.94% empty.
Its capacity is 6,000L. So, in order to fill it to capacity, the service station
must order 33.94% of 6,000L .
33.94% = 0.3394
"of" means "times"
0.3394 x 6,000L = <em>2,036.4 liters</em> needed, to fill the tank to the rim.
