Answer: False
Step-by-step explanation: Absolute value means <em>distance from zero</em> on a number line. A common mistake is to assume that absolute value is always positive but that's not necessarily the case.
Take 0 for example.
It's 0 units away from zero on a number line which
means it has an absolute value of zero.
However, all other numbers besides zero will have
an absolute value that is positive.
Answer:
it has one root x=2/5
Step-by-step explanation:
Answer:
Eq: (x+a/2)²+(y+1)²=(a²-8)/4
Center: O(-a/2, -1)
Radius: r=0.5×sqrt(a²-8)
Mandatory: a>2×sqrt(2)
Step-by-step explanation:
The circle with center in O(xo,yo) and radius r has the equation:
(x-xo)²+(y-yo)²=r²
We have:
x²+y²+ax+2y+3=0
But: x²+ax=x²+2(a/2)x+a²/4-a²/4= (x+a/2)²-a²/4
And
y²+2y+3=y²+2y+1+2=(y+1)²+2
Replacing, we get:
(x+a/2)²-a²/4+(y+1)²+2=0
(x+a/2)²+(y+1)²=a²/4-2=(a²-8)/4
By visual inspection we note that:
- center of circle: O(-a/2, -1)
- radius: r=sqrt((a²-8)/4)=0.5×sqrt(a²-8). This means a²>8 or a>2×sqrt(2)
I'm pretty sure the answer is 15 base-ten blocks
Answer:
Step-by-step explanation:
#22
<h3>Given </h3>
- Equation x² -4x + 1 = k(x - 4) with equal roots
<h3>To find</h3>
<h3>Solution</h3>
<u>The equation in standard form is:</u>
- x² -4x + 1 = k(x - 4)
- x² - 4x - kx + 1 + 4 = 0
- x² - (k + 4)x + 5 = 0
<u>When the quadratic equation has equal roots its discriminant is zero</u>
- D = 0
- b² - 4ac = 0
- (k + 4)² - 4*5 = 0
- (k + 4)² = 20
- k + 4 = ± √20
- k = - 4 ± √20
- or
- k = -4 ± 2√5
