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Jobisdone [24]
3 years ago
10

Solve for x. Enter your answer in interval notation using grouping symbols. x2 + x < 20

Mathematics
2 answers:
Rus_ich [418]3 years ago
6 0

Answer:

x<18

Step-by-step explanation:

2+x<20

Karo-lina-s [1.5K]3 years ago
3 0

Answer:

(-5, 4)

Step-by-step explanation:

x^2 + x < 20 can be rewritten as a quadratic in standard form:  x^2 + x - 20 < 0.  Recognize that the graph of x^2 + x - 20 is that of a parabola that opens up.  Because the y-intercept (0, -20) is below the x-axis, we know for certain tht the graph intersects the x-axis in two places.  Our job is to determine the two horizontal intercepts, which in turn determine the solution set.

x^2 + x - 20 = 0 factors as follows:  (x + 5)(x - 4) = 0, whose roots are -5 and 4.

These two roots form 3 intervals:  (-infinity, -5), (-5, 4) and (4, infinity).   We now must identify on which intervals x^2 + x - 20 is less than 0 (that is, on which intervals the graph is below the x-axis).  Choose three test values for x:  the first could be -6 (which is in the set (-infinity, -5) ); x^2 + x - 20 is + there, and so the graph is above the x-axis and x^2 + x - 20 is positive.  Reject this.  

Next, test x = 0; x^2 + x - 20 is negative there, meaning that x^2 + x - 20 < 0 and that x^2 + x < 20.  Thus, the solution is (-5, 4).  It can be shown that x^2 + x - 20 is positive again for x-values within the interval (4, infinity).

Evaluating

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Vlad [161]

Answer:

\large\boxed{-4\dfrac{7}{8}=-4.875}

Step-by-step explanation:

To add two fractions, they must have the same denominator.

LCD = 8

1\dfrac{1}{4}=1\dfrac{1\cdot2}{4\cdot2}=1\dfrac{2}{8}

-6\dfrac{1}{8}+1\dfrac{1}{4}=-6\dfrac{1}{8}+1\dfrac{2}{8}=-\left(6\dfrac{1}{8}-1\dfrac{2}{8}\right)=(*)\\\\\text{We know}\ 1=\dfrac{8}{8},\ 6=5+1=5+\dfrac{8}{8}=5\dfrac{8}{8}.\\\\\text{Therefore}\ 6\dfrac{1}{8}=5\dfrac{8+1}{8}=5\dfrac{9}{8}\\\\(*)=-\left(5\dfrac{9}{8}-1\dfrac{2}{8}\right)=-\bigg((5-1)+\dfrac{9-2}{8}\bigg)=-\bigg(4+\dfrac{7}{8}\bigg)=-4\dfrac{7}{8}

You can convert the fractions to the decimals.

6\dfrac{1}{8}=8.125\\\\1\dfrac{1}{4}=1.25\\\\-6\dfrac{1}{8}+1\dfrac{1}{4}=-6.125+1.25=1.25-6.125=-4.875

5 0
3 years ago
How do i calculate:<br><br> ((6 x y−2 x y)−x2y2)+10 x y
alex41 [277]
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3 years ago
Read 2 more answers
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Karo-lina-s [1.5K]

Answer:

5 hours

Step-by-step explanation:

So what you have to do is set the two equal to one another and solve for x

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8 0
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dexar [7]

Answer:

<em>14.5 pounds of apples.</em>

Step-by-step explanation:

$3.77 ÷ $.26 = 14.5

Apples = <em>14.5 pounds</em>

<em />

Hope this helps! :)

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Step-by-step explanation:

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