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kenny6666 [7]
3 years ago
9

Finding the roots by completing the square

Mathematics
1 answer:
Andrej [43]3 years ago
6 0
For y=x^2-6x-11

complete the square

so roots
set y=0
0=x^2-6x-11

group x terms
0=(x^2-6x)-11
take 1/2 of linear coefient (-6) and square it
-6/2=-3, (-3)^2=9
add positive and neative to inside of parenthasees
0=(x^2-6x+9-9)-11
complete square
0=((x-3)^2-9)-11
expand
0=(x-3)^2-9-11
0=(x-3)^2-20
add 20 to both sides
20=(x-3)^2
sqrt both sides
remember positive and negative roots

+/-2√5=x-3
add 3 to both sides
3+/-2√5=x

so
x=3+2√5 and 3-2√5
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Sam watched television the past five nights for 42 minutes, 23 minutes, 56 minutes, 19 minutes, and 67 minutes. What was the med
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Answer:

42 minutes is the median amount of time

Step-by-step explanation:

The Median is the middle value of data set.

If there is "odd" number of numbers, and there are n numbers, the median is:

(n/2) + 1 th  number

If there is "even" number of numbers, and there are n numbers, the median is:

Average of n/2th and (n/2) + 1 th number

Here, we have 5 numbers, so the median would be:

(5/2) + 1 th number

That is

3rd number

But, we need to arrange the numbers from least to greatest. Lets write it:

19, 23, 42, 56, 67

The third number is 42, this is the median

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3 years ago
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Step-by-step explanation:

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4 years ago
What is the constant of proportionality (unit rate) for the following equation:<br> t = 3 · x
shtirl [24]

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Step-by-step explanation:

6 0
3 years ago
Item 18
Nimfa-mama [501]

A mixed number in simplest form, in the box is 40  5/8 cm^3.

We have given that,

The figure contains a right rectangular prism. The length of the prism is labeled 6 and one-half centimeters, the width is labeled 2 and one-half centimeters, and the height is labeled 2 and one-half centimeters.

<h3>What is the volume of the prism?</h3>

The figure is a rectangular prism, so the formula would be Volume = length x width x height.

length = 6 .5cm

width  =  2.5cm

height  =  2.5cm

If you plug everything you have in the problem into the volume equation, you would get

volume = 6.5cm x 2.5cm x 2.5 cm.

Without a calculator first, turn the mixed numbers into improper fractions.

6 .5=13/2

2.5 = 5/2

Volume = 13/2  x 5/2   x 5/2

When you multiply everything together you should get.

As a mixed number, that would be 40 5/8.

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brainly.com/question/23963432

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7 0
2 years ago
Given csc(A) = 60/16 and that angle A is in Quadrant I, find the exact value of sec A in simplest radical form using a rational
Katarina [22]

Answer:

\displaystyle \sec A=\frac{65}{63}

Step-by-step explanation:

We are given that:

\displaystyle \csc A=\frac{65}{16}

Where <em>A</em> is in QI.

And we want to find sec(A).

Recall that cosecant is the ratio of the hypotenuse to the opposite side. So, find the adjacent side using the Pythagorean Theorem:

a=\sqrt{65^2-16^2}=\sqrt{3969}=63

So, with respect to <em>A</em>, our adjacent side is 63, our opposite side is 16, and our hypotenuse is 65.

Since <em>A</em> is in QI, all of our trigonometric ratios will be positive.

Secant is the ratio of the hypotenuse to the adjacent. Hence:

\displaystyle \sec A=\frac{65}{63}

6 0
3 years ago
Read 2 more answers
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