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Answer:
2x -3y = -19
Step-by-step explanation:
Taking the differences between the given points, we have ...
(Δx, Δy) = (4, 9) -(-2, 5) = (6, 4)
The equation of the line can be written ...
Δy·x -Δx·y = Δy·(x1) -Δx·(y1) . . . . . for point (x1, y1) on the line
4x -6y = 4(-2) -6(5) = -38
Dividing by 2 gives the standard form equation ...
2x -3y = -19
_____
<em>Additional comment</em>
The original equation 4x-6y=-38 satisfies the requirements of this problem. However, "standard form" requires the numbers in the equation be mutually prime (in addition to the problem requirements). That is, they must have no common factors. Hence, we must remove the common factor of 2 in order to have true "standard form."
The range of f is the set of all real numbers and the range of f would not change if the value of n is changed
<h3>The range of f when n = 5</h3>
The function is given as:
When n = 5, we have:
The domain of the function is:
x < 5 and x ≥ 5
This means that the domain is the set of all real numbers.
The function is a linear piece wise function, and the range of a linear function is the set of all real numbers.
Hence, the range of f is the set of all real numbers.
<h3>Does changing the value of n change the range?</h3>
As stated in (a) the range of a linear function is the set of all real numbers.
This means that irrespective of the value of n; the range would remain the same
Hence, the range of f would not change if the value of n is changed
Read more about piecewise functions at:
brainly.com/question/18859540
#SPJ1
Answer:
The answer is C
Step-by-step explanation:
I took the test on Illuminate
The rule that we will use to solve this question is:
M1V1 + M2V2 = M3V3
where:
M1 is the concentration of the first solution = 80% = 0.8
V1 is the volume of the first solution = 3 gallons
M2 is the concentration of the second solution = 20% = 0.2
V2 is the volume of the second solution = 1 gallon
M3 in the final concentration that we want to calculate
V3 is the final volume = 3 gallons + 1 gallon = 4 gallons
Substitute with the givens in the above equation to get the final concentration as follows:
M1V1 + M2V2 = M3V3
(0.8)(3) + (0.2)(1) = (4)M3
2.4 + 0.2 = 4M3
2.6 = 4M3
M3 = 2.6/4
M3 = 0.65
To get the percentage, we will multiply the concentration by 100 as follows:
% of concentration = 0.65 * 100 = 65%
Answer:B
Step-by-step explanation:
DeShawn would have more money in the long run if he invested in the 20-year endowment
DeShawn already makes $45,000 yearly, which makes him rich enough to purchase the 20 year endowment plans, the 20 year life plan won't be wise, because it last for 20 years, and this will end before he retires, 38 + 20 = 58 and once it ends, no payment will be made if he's still alive, so what if something happens to him in the 2 years inbetween the end of the 20 year term plan and his retirement? That's where the plan doesn't favor him and his family, but the 20 year endowment plan once it's finished, he will be paid the sum assured to him, plus bonuses, and his family will be covered if something happens to him in the 2 years inbetween the end of the 20 year endowment plan and his retirement
