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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Answer:
4
Step-by-step explanation:
You want a cookie?
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Step-by-step explanation:
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A plane is pointed S 15° E, with indicated speed 500 mph. It flies through a wind
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Step-by-step explanation:
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Step-by-step explanation:
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Answers
Answer:
D
Step-by-step explanation:
Commutative switchs the numbers but not with subtraction or divion
Answer:
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Answers
Answer:
Step-by-step explanation:
The shadow length will be proportional to height
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h = 12(32)/60 = 6.4 ft or 6 ft 4.8 inches
answer.plsssssssssssssssssssssssssssssssssss
Answers
Answer:
see explanation
Step-by-step explanation:
(1)
4(m + 7) = 4 ( divide both sides by 4 )
m + 7 = 1 ( subtract 7 from both sides )
m = - 6
(2)
let the number be n , then
[tex]\frac{3}{5}[/tex] n - 2 = 40 ( multiply through by 5 to clear the fraction )
3n - 10 = 200 ( add 10 to both sides )
3n = 210 ( divide both sides by 3 )
n = 70
The required number is 70
(3)
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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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A spherical tank has a circular orifice in its bottom through which the liquid flows out. The following data is collected for the flow rate through the orifice as a function of time:
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Hi small cats and cats and dogs have a great experience with the evening of the evening of 6th century the morning of this
Introduction to Dividing Whole Numbers
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Answer:
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Step-by-step explanation:
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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.
Need help with this
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Answer:
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Step-by-step explanation:
nope
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Answers
Answer:
I think it is b I’m not quite sure though. Sorry if wrong…
Step-by-step explanation:
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.
The Ferrari Sports Car is a tenth second slower than the Lamborghini Sports Car.
The Renault Sports Car is three tenths of a second faster than the McLaren Sports Car.
What time does the Renault Sports Car displays to reache a maximum speed of 200km/h?
Answers
The Renault Sports Car displays 15.70 seconds to reache at maximum speed of 200km / h.
Since 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 Ferrari Sports Car is a tenth second slower than the Lamborghini Sports Car, and the Renault Sports Car is three tenths of a second faster than the McLaren Sports Car, to determine what time does the Renault Sports Car displays to reache a maximum speed of 200km / h the following calculation must be performed:
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Therefore, the Renault Sports Car displays 15.70 seconds to reache at maximum speed of 200km / h.
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Answers
Answer:
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Step-by-step explanation:
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A swimming coach needs to choose a team for a relay race. The coach must select 4 of 6 available swimmers
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Answers
The number of unique ways is given by the number of possible
combination having distinct members.
The number of unique ways there are to arrange 4 of the 6 swimmers are 15 ways.
Reasons:
The given parameters are;
The number of swimmers available = 6 swimmers
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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free 100 xp answer with fav movies pls for 100 free xp , 100 free xp always is given by algebros every day. Please do enjoy this plentiful amount of free xp I care about how you are feeling introduce yourself with telling me about your fav movie and why it is your fav. Enjoy! Please answer
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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.
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FREE XPFREE XPFREE XPFREE XPFREE XPFREE XPFREE XPFREE XPFREE XPFREE XPFREE XPFREE XPFREE XPFREE XPFREE XPFREE XPFREE XPFREE XPFREE XPFREE XPFREE XPFREE XPFREE XPFREE XPFREE XPFREE XPFREE XPFREE XPFREE XPFREE XPFREE XPFREE XPFREE XPFREE XPFREE XPFREE XPFREE XPFREE XPFREE XPFREE XPFREE XPFREE XPFREE XPFREE XPFREE XPFREE XPFREE XPFREE XPFREE XPFREE XPFREE XPFREE XPFREE XPFREE XPFREE XPFREE XPFREE XPFREE XPFREE XPFREE XPFREE XPFREE XPFREE XPFREE XPFREE XPFREE XPFREE XPFREE XPFREE XPFREE XP
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Answer:
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Step-by-step explanation:
In a parallelogram the diagonals bisect each other , then
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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
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add both sides by 20 and we get 25x=200°
divide both sides by 25 and we get x=8°
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=> 25x = 200
=> x = 8
Ok done. Thank to me:>
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Answers
Answer:
a 'term'
Step-by-step explanation:
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Answers
Answer:
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Step-by-step explanation:
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HELPPPP
Answers
Step-by-step explanation:
I'm not sure if I'm using substitution method but I guess it's x = 12.4
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Answers
Answer:
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Step-by-step explanation:
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If the area of a rectangle is 12[tex]b^{7}[/tex]b[tex]b^{4}[/tex] and the width of the rectangle is 4[tex]a^{2}[/tex][tex]b^{2}[/tex] , what is the length of the rectangle?
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]
The rabbit will never go over 75 pounds. If this rabbit is bom in July weighing 2 pounds, in which month will it weigh around 46 pounds?
Answers
Christa sells bracelets during the summer months to earn some extra money. She
made this pictograph to represent her sales for last summer.
Bracelets Sold
June
July
August
=4 bracelets
How many bracelets did Christa sell in June and July?
8
32
12
40
Answers
Answer:
32 bracelets
Step-by-step explanation:
First multiply each bracelet by 4 to get the correct amount:
3x4=12
4x5=20
Then, add the two.
12+20=32
f(x)=x^2-(7/2)x-.5 and g(x)= 2-(2/x)
Answers
Answer:
23
Step-by-step explanation:
help ??? on edu math review
Answers
Answer:
It must be C.
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.