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1 answer:
Answer:
1) (x + 3)(3x + 2)
2) x= +/-root6 - 1 by 5
Step-by-step explanation:
3x^2 + 11x + 6 = 0 (mid-term break)
using mid-term break
3x^2 + 9x + 2x + 6 = 0
factor out 3x from first pair and +2 from the second pair
3x(x + 3) + 2(x + 3)
factor out x+3
(x + 3)(3x + 2)
5x^2 + 2x = 1 (completing squares)
rearrange the equation
5x^2 + 2x - 1 = 0
divide both sides by 5 to cancel out the 5 of first term
5x^2/5 + 2x/5 - 1/5 = 0/5
x^2 + 2x/5 - 1/5 = 0
rearranging the equation to gain a+b=c form
x^2 + 2x/5 = 1/5
adding (1/5)^2 on both sides
x^2 + 2x/5 + (1/5)^2 = 1/5 + (1/5)^2
(x + 1/5)^2 = 1/5 + 1/25
(x + 1/5)^2 = 5 + 1 by 25
(x + 1/5)^2 = 6/25
taking square root on both sides
root(x + 1/5)^2 = +/- root(6/25)
x + 1/5 = +/- root6 /5
shifting 1/5 on the other side
x = +/- root6 /5 - 1/5
x = +/- root6 - 1 by 5
x = + root6 - 1 by 5 or x= - root6 - 1 by 5
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Answer:
m = -3
b = 9
y = -3x + 9
Step-by-step explanation:
Let us solve the question
∵ The line passes through points (4, -3) and (3, 0)
∵ The rule of the slope is m =
∵ (x1, y1) and (x2, y2) are 2 points on the line
∴ x1 = 4 and y1 = -3
∴ x2 = 3 and y2 = 0
→ Substitute them in the rule of the slope to find it
∵ m = =
= -3
∴ m = -3
∵ The form of the equation of the line is y = m x + b
→ Substitute the value of m in the form of the equation.
∴ y = -3x + b
→ To find b substitute x and y by the coordinates of the point (3, 0) or (4, -3)
∵ x = 3 and y = 0
∴ 0 = -3(3) + b
∴ 0 = -9 + b
→ Add 9 to both sides
∴ 9 = b
∴ b = 9
→ Substitute the value of b in the equation
∵ y = -3x + 9
∴ The equation of the line is y = 3x + 9