<h3>Answer:</h3>
±12 (two answers)
<h3>Explanation:</h3>
Suppose one root is <em>a</em>. Then the other root will be -3<em>a</em>. The product of the two roots is the ratio of the constant coefficient to the leading coefficient:
(<em>a</em>)(-3<em>a</em>) = -27/4
<em>a</em>² = -27/(4·(-3)) = 9/4
<em>a</em> = ±√(9/4) = ±3/2
Then the other root is
-3<em>a</em> = -3(±3/2) = ±9/2 . . . . . . the roots will have opposite signs
We know the opposite of the sum of these roots will be the ratio of the linear term coefficient to the leading coefficient: b/4, so ...
-(a + (-3a)) = b/4
2a = b/4
b = 8a = 8·(±3/2)
b = ±12
_____
<em>Check</em>
For b = 12, the equation factors as ...
4x² +12x -27 = (2x -3)(2x +9) = 0
It has roots -9/2 and +3/2, the ratio of which is -3.
For b = -12, the equation factors as ...
4x² -12x -27 = (2x +3)(2x -9) = 0
It has roots 9/2 and -3/2, the ratio of which is -3.
<h2>Answer:
The line from the question [ y = -8x + 3 ] passes through the point ( -1, 11 ). </h2>
<h3 /><h3>Step-by-step explanation:
</h3>
<u>Find the slope of the parallel line</u>
When two lines are parallel, they have the same slope.
⇒ if the slope of this line = - 8
then the slope of the parallel line (m) = - 8
<u>Determine the equation</u>
We can now use the point-slope form (y - y₁) = m(x - x₁)) to write the equation for this line:
⇒ y - 11 = - 8 (x - (-1))
∴ y - 11 = - 8 (x + 1)
We can also write the equation in the slope-intercept form by making y the subject of the equation and expanding the bracket to simplify:
since y - 11 = - 8 (x + 1)
y = - 8 x + 3
The line from the question [ y = -8x + 3 ] passes through the point ( -1, 11 ).
Answer:
The length of the shortest side of the triangle is 10 units.
Step-by-step explanation:
Let <em>a</em> be the shortest side of the isosceles triangle and <em>b</em> be the two congruent sides.
The congruent sides <em>b</em> are each one unit longer than the shortest side. Hence:
The perimeter of the isosceles triangle is given by:
This is equivalent to the perimeter of a square whose side lengths are two units shorter than the shortest side of the triangle. Let the side length of the square be <em>s</em>. Hence:
The perimeter of the square is:
Since the two perimeters are equivalent:
Substitute for <em>b: </em>
<em />
<em />
Solve for <em>a</em>. Distribute:
Simplify:
Hence:
The length of the shortest side of the triangle is 10 units.
Answer:
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Step-by-step explanation:
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