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Andru [333]
4 years ago
8

For which interval does this quadratic inequality hold true? 6x − x2 − 8 > 0

Mathematics
2 answers:
xz_007 [3.2K]4 years ago
8 0
6x-x^2-8 \ \textgreater \ 0 \\
-x^2+6x-8\ \textgreater \ 0 \\
-x^2+2x+4x-8\ \textgreater \ 0 \\
-x(x-2)+4(x-2)\ \textgreater \ 0 \\
(-x+4)(x-2)\ \textgreater \ 0 \\ \\
\hbox{the zeros:} \\
(-x+4)(x-2)=0 \\
-x+4=0 \ \lor \ x-2=0 \\
x=4 \ \lor \ x=2

The coefficient of x is negative, so the parabola opens downwards. The values greater than 0 are between the zeros.
The solution set for the inequality is:
x \in (2,4)

The answer is B.
Wittaler [7]4 years ago
4 0
-x²+6x-8>0           a=-1 , b=6    , c=-8
Δ = b² - 4.a.c 
Δ = 6² - 4 . -1 . -8 
Δ = 36 - 32
Δ = 4

x = (-b +- √Δ) / 2a

x' = (-6 + √4) / 2(-1)        x'' = (-6 - √4)/ 2(-1)
x' = -4 / -2                     x'' = -8 / -2
x' = 2                            x'' = 4


2>x>4   ou   (2,4)

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Help me please and don’t give me a unhelpful answer
Rudik [331]

Answer:

8/9 is greater than 5/6

Step-by-step explanation:

Steps for comparing fractions

Find the least common denominator or LCM of the two denominators:

LCM of 9 and 6 is 18

For the 1st fraction, since 9 × 2 = 18,

8 /9  =  

8 × 2 = 16

9 × 2  =  18

Likewise, for the 2nd fraction, since 6 × 3 = 18,

5 /6  =  5 × 3

6 × 3  =  15 /18

Since the denominators are now the same, the fraction with the bigger numerator is the greater fraction

16 /18  >  15 /18  or  8 /9  >  5 /6

6 0
3 years ago
Read 2 more answers
|n/2 − 1/3| −1= 1/6
weqwewe [10]
1. n/2-1/3-1=1/6
n/2=1/6+1/3+1
n/2=1/6+2/6+6/6
n/2=9/6=3/2
n=3/2*2=3

check: abs(3/2-1/3)-1=1/6,    abs(9/6-2/6)-1= 1/6, 7/6-1=1/6, 1/6 =1/6 
3 is a root

2. -(n/2-1/3)-1=1/6
-n/2+1/3-1=1/6
-n/2-2/3=1/6
-n/2=1/6+2/3
-n/2=1/6+4/6
-n/2=5/6
n=-2*5/6=-5/3=-1 2/3  
check :    abs((-5/3)/2-1/3) -1=1/6
abs(-5/6-1/3) -1 =1/6,     abs(-5/6-2/6) -1=1/6, abs (-7/6)-1=1/6,  7/6-1=1/6, 1/6=1/6
so -5/3 or -1 2/3  is also root

so  two roots 3 and -5/3(that can be written as -1 2/3)

5 0
4 years ago
If A(0, 0) and B(2, 5), find AB. If necessary, submit your answer as a decimal to the nearest tenth. (Remember: AB means "the di
Olin [163]
To determine the distance between two points, we use the equation,
                                   distance = √(x₂ - x₁)² + (y₂ - y₁)²
Substituting the known values for the abscissa and ordinates of the points,
                                distance = √(0 - 2)² + (0 - 5)² = √29 ≈ 5.39 
Therefore, the distance between these two points is approximately equal to 5.39. 
8 0
4 years ago
Not sure how to solve this I need help thank you
inessss [21]
5.4 +20% = 5.6
because you are adding 205 or.20 to you bottle
3 0
3 years ago
I need help pls right now
VMariaS [17]

Answer: the answer is 1 in the numerator and r to the 8th power times s to the 5th power in the denominator.

Step-by-step explanation:

4 0
4 years ago
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