Solve the inequality and express your answer in interval notation.
x2 - 12x + 5 <0
Answers
Answer:
([tex]6 - \sqrt{31}[/tex], [tex]6 + \sqrt{31}[/tex])
Step-by-step explanation:
[tex]x^{2}-12x+5 < 0[/tex]
To solve this inequality, we can start by completing the square. To do this, we divide the x coefficient (-12) by 2 and then square it. We then add the result to the left side of the equation. To ensure the inequality remains true, we also subtract it.
[tex]x^{2}-12x+(-6^{2})-(-6^{2}) + 5 < 0\\x^{2}-12x+36-36 + 5 < 0\\[/tex]
We can then express the first trinomial as a perfect square.
[tex](x-6)^{2} - 31 < 0[/tex]
Add 31 to both sides:
[tex](x-6)^{2}< 31[/tex]
Then take the square root of both sides:
[tex]x-6<[/tex] ± [tex]\sqrt{31}[/tex]
Finally, add 6 to both sides:
x < 6 + [tex]\sqrt{31}[/tex]
x > 6 - [tex]\sqrt{31}[/tex]
The solution to the inequality in interval notation is shown by option A
What is inequality?
An inequality in mathematics describes how two expressions relate to one another by indicating whether one expression is greater, smaller, equal to, or not equal to the other. Inequalities are denoted by symbols.
We have to use the quadratic formula that states that;
x < (-b ± √([tex]b^2[/tex] - 4ac)) / 2a
So we have that;
x < [12 ± √([tex](-12)^2[/tex] - 4 * 1 * 5)] / 2 * 1
Thus we would obtain in the end;
6 - √31 < x < 6 + √31
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Suppose Steve changed $250 into 200 Euros. How many Euros did he receive per US dollar?
Answers
Answer:
0.8 Euros
Step-by-step explanation:
Per US Dollar means its a proportion that the question is asking for. So, you can do 200/250 and get the answer.
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Step-by-step explanation:
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Answers
Answer:
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Step-by-step explanation:
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Answers
Answer:
x=8°
Step-by-step explanation:
Let's make an equation with this problem, since all side have to add up to 180 degrees we can solve it
(5x-2)+(9x+3)+(11x-21)=180°
lets add up light terms
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Original price of a puppy $159.95 Discount 15% Tax 8.725%?
Answers
Answer:
$124.095
Step-by-step explanation:
Discounted Price= $159.95- 15%of $159.95=$135.9575
Final Price= Discounted price + Tax
= $135.9575+ 8.725% of $135.9575
= $135.9575-$11.8622
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Simplify your answer completely.
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Answers
Answer:
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Step-by-step explanation:
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Answers
Answer:
Step-by-step explanation:
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Answers
Answer:
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Step-by-step explanation:
Exterior angle property: Exterior angle equals sum of opposite interior angles
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x = 46/2
x = 23
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Answer:
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Step-by-step explanation:
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Answer:
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Step-by-step explanation:
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Answer:
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Answer:
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Step-by-step explanation:
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Step-by-step explanation:
Use substitution to determine which value of x makes the equation x– 5 = 7.4 true
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Answers
Step-by-step explanation:
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Answer:
see explanation
Step-by-step explanation:
(1)
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m + 7 = 1 ( subtract 7 from both sides )
m = - 6
(2)
let the number be n , then
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The Lamborghini Sports Car reaches a maximum speed of 200km/h in 15.50s
The McLaren Sports Car displays the same time as the Ferrari Sports Car.
The Renault Sports Car is small in size.
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The Renault Sports Car is three tenths of a second faster than the McLaren Sports Car.
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Answers
The Renault Sports Car displays 15.70 seconds to reache at maximum speed of 200km / h.
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Answers
Answer:
D
Step-by-step explanation:
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Answer:
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Answers
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Step-by-step explanation:
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Answers
[tex]\text{Given that,}\\\\\text{Area} = 12 b^7 b b^4 =12 b^{12}\\\\\text{Width} = 4a^2 b^2\\\\\text{Now,}\\\\\text{Length} \times \text{Width} =\text{Area} \\\\\implies \text{Length} = \dfrac{\text{Area}}{\text{Width}}=\dfrac{12b^{12}}{4a^2 b^2} = \dfrac{3b^{10}}{a^2}[/tex]
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Answers
The number of unique ways is given by the number of possible
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The number of unique ways there are to arrange 4 of the 6 swimmers are 15 ways.
Reasons:
The given parameters are;
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The number of swimmers the coach must select = 4 swimmers
Required:
The number of unique ways to arrange 4 of the 6 swimmers.
Solution:
The number of possible combination of swimmers is given as follows;
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Therefore, the coach can select 4 of the 6 available swimmers in 15 unique ways
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360
Step-by-step explanation:
6!/(6-4)!
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Answers
Answer:
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Step-by-step explanation:
x² - 9 = 16
=> 16 + 9 = x²
=> 25 = x²
=> x = 5
Referring to the options, C is the only one that is accurate to me. Hoped this helped.
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Step-by-step explanation:
My favorite movie would have to be the Pirates of the Caribbean collection. Captain Jack sparrow aka Johnny Depp is is just great at his character.
Answer:
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Step-by-step explanation:
Guided Practice
The graph of y = 2(x + 1)2 − 4 is a translation 1 unit horizontally and 4 units vertically of the function y = 2x2. Graph this function in your notebook.
Type your answer and then click or tap Done.
The vertex of the parabola is (Fill in the blank text field 1
, Fill in the blank text field 2
( , )
Answers
Answer:
Step-by-step explanation:
hmm
The graph of a quadratic function is always a parabola. The vertex of the parabola after transformation is (-1,-4).
What is a quadratic equation?A quadratic equation is an equation whose leading coefficient is of second degree also the equation has only one unknown while it has 3 unknown numbers. It is written in the form of ax²+bx+c.
The graph of the two functions can be made as shown below. Therefore, the two functions are,
y=2x² → Drawn by the red line
y = 2(x + 1)² − 4 → Drawn by the blue line
Now, the vertex of a quadratic function or a parabola is the point at which the function or the parabola changes its slope, it's either the maximum of the function or the minimum of the function, depending on which side the parabola opens.
Hence, The vertex of the parabola after transformation is (-1,-4).
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f(x)=x^2-(7/2)x-.5 and g(x)= 2-(2/x)
Answers
Answer:
23
Step-by-step explanation: