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zvonat [6]
2 years ago
11

Solve the inequality x2-x-12 < 0 +

Mathematics
2 answers:
Olin [163]2 years ago
4 0

Step-by-step explanation:

x2-x-12<0

x2-x<12

x=12

Dmitry [639]2 years ago
4 0
The answer is x= 12
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HELP!! Algebra help!! Will give stars thank u so much &lt;333
Anna35 [415]

Answers:

  • Part a)  \bf{\sqrt{x^2+(x^2-3)^2}
  • Part b)  3
  • Part c)   2.24
  • Part d)  1.58

============================================================

Work Shown:

Part (a)

The origin is the point (0,0) which we'll make the first point, so let (x1,y1) = (0,0)

The other point is of the form (x,y) where y = x^2-3. So the point can be stated as (x2,y2) = (x,y). We'll replace y with x^2-3

We apply the distance formula to say...

d = \sqrt{(x_1-x_2)^2+(y_1-y_2)^2}\\\\d = \sqrt{(0-x)^2+(0-y)^2}\\\\d = \sqrt{(0-x)^2+(-y)^2}\\\\d = \sqrt{x^2 + y^2}\\\\d = \sqrt{x^2 + (x^2-3)^2}\\\\

We could expand things out and combine like terms, but that's just extra unneeded work in my opinion.

Saying d = \sqrt{x^2 + (x^2-3)^2} is the same as writing d = sqrt(x^2-(x^2-3)^2)

-------------------------------------------

Part (b)

Plug in x = 0 and you should find the following

d(x) = \sqrt{x^2 + (x^2-3)^2}\\\\d(0) = \sqrt{0^2 + (0^2-3)^2}\\\\d(0) = \sqrt{(-3)^2}\\\\d(0) = \sqrt{9}\\\\d(0) = 3\\\\

This says that the point (x,y) = (0,3) is 3 units away from the origin (0,0).

-------------------------------------------

Part (c)

Repeat for x = 1

d(x) = \sqrt{x^2 + (x^2-3)^2}\\\\d(1) = \sqrt{1^2 + (1^2-3)^2}\\\\d(1) = \sqrt{1 + (1-3)^2}\\\\d(1) = \sqrt{1 + (-2)^2}\\\\d(1) = \sqrt{1 + 4}\\\\d(1) = \sqrt{5}\\\\d(1) \approx 2.23606797749979\\\\d(1) \approx 2.24\\\\

-------------------------------------------

Part (d)

Graph the d(x) function found back in part (a)

Use the minimum function on your graphing calculator to find the lowest point such that x > 0.

See the diagram below. I used GeoGebra to make the graph. Desmos probably has a similar feature (but I'm not entirely sure). If you have a TI83 or TI84, then your calculator has the minimum function feature.

The red point of this diagram is what we're after. That point is approximately (1.58, 1.66)

This means the smallest d can get is d = 1.66 and it happens when x = 1.58 approximately.

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2 years ago
What is the lowest common multiple of 120 160 180
Anna11 [10]
20 it the least common multiple of the numbers given
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3 years ago
What is 15% of $150?'
AleksandrR [38]

Answer:

$22.50

Step-by-step explanation:

15% of 150=22.5

6 0
2 years ago
HELP!!!!!!!!!!!!!!!!!!!!!!!!!!!!<br> Show your work
cestrela7 [59]
Well start with reflecting abc over the y axis
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3 years ago
If the revenue for the week is $2000, and labor cost consist of two workers earning $8 per hour who works 40 hours each, whay is
SVEN [57.7K]
Two workers earning 8 bucks an hour for 40hrs, well, that means each worker is making 8*40 or 320 bucks, now, is two workers, so 320+320 or 640 is the total cost then.

now, the revenue, sales income, is 2,000 bucks, how much is 640 off of?

well, if we take 2000 to be the 100%, what is 640 in percentage off of it?

\bf \begin{array}{ccllll}&#10;amount&\%\\&#10;\text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\&#10;2000&100\\&#10;640&x&#10;\end{array}\implies \cfrac{2000}{640}=\cfrac{100}{x}

solve for "x".
6 0
3 years ago
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