The sum of three consecutive integers is 42 . Let x be the middle of the three integers.transcribe the statement accordingly
1 answer:
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Answer:
a. -⅓
b. 3
c. y = 3x - 10
Step-by-step explanation:
a. Gradient of line AB:
A(1, 3), B(7, 1)
Gradient (m) = -⅓
b. The of the line that is perpendicular to line AB would be the negative reciprocal of the gradient of line AB.
Thus, the negative reciprocal of -⅓ = 3
Gradient of the line perpendicular to line AB = 3
c. Equation of the line that passes through (4, 2) and is perpendicular to line AB:
We can write the equation using the point-slope form equation, y - b = m(x - a), where,
(a, b) represents a point on the line, and,
m = gradient/slope
We know that the gradient/slope (m) = 3
Also, a point, (a, b) = (4, 2).
Therefore, substitute a = 4, b = 2, and m = 3 into y - b = m(x - a)
Thus:
y - 2 = 3(x - 4)
y - 2 = 3x - 12
Add 2 to both sides
y = 3x - 12 + 2
y = 3x - 10
Hey there!☺
Equation
−4(10 − a) = 36 Simplify both sides
(−4)(10) + (−4)(−a) = 36 Distribute
−40 + 4a = 36
4a − 40 = 36
4a - 40 + 40 = 36 + 40 Add 40 to both sides
4a = 76
4a/4 = 76/4 Divide both sides by 4
76/4 = 19 Simplify 76/4
a = 19
Hope this helps!