Answer:
y = negative four-thirds x + StartFraction 31 Over 3 EndFraction
y = 2 x + 7
Step-by-step explanation:
Let x denote the smaller number and y denote the larger number.
Part 1
The equation presented indicates that four times some number added to three times a larger number equals 31.
This translates to:
From here, solving for y yields:
- 4x + 3y=31 ⇒ 3y= -4x+31 ⇒ y= (-4x+31)/3 = - 4/3x + 31/3
⇒ y= - 4/3x + 31/3
This indicates the correct response for this scenario:
y = negative four-thirds x + StartFraction 31 Over 3 EndFraction
Part 2
The statement that seven subtracted from the larger number equals twice the smaller number translates to:
y-7= 2x
Further, solving for y yields:y-7= 2x ⇒
y= 2x+ 7
The correct answer for this equation is:
y = 2 x + 7
Answer:
D.
Step-by-step explanation:
This function is piece-wise, meaning you will have two equations along with distinct domains. The equation x squared plus 3 illustrates a parabolic curve, while x plus 4 is depicted as a linear function. There is a specific reason why the point on the parabola is open at x equals 4; this signifies that the value does not satisfy the equation. Therefore, x cannot equal 4 for the parabola, so its domain is x less than 4. The closed point on the linear function indicates that when x is 4, it is part of the solution for that equation and graph. Consequently, the domain for the linear function is x greater than or equal to 4. Hope this clarifies things!
You will achieve this in 15 days. Both 5 and 3 have a least common multiple of 15.
Answer:
2.5 hours
Step-by-step explanation:
Distance equals speed multiplied by time. For constant distance, time varies inversely with speed. When traveling at 60/50 = 6/5 times the original speed, the return journey takes 5/6 of the initial duration:
(5/6)(3 hours) = 2.5 hours... return trip duration
