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3 years ago

X^2-10x+8=0 by completing the square

Mathematics

1 answer:

OverLord2011 [107]3 years ago

4 0

When completing the square <span>x=9.12311 and </span><span>x=<span>0.876894</span></span>

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Each of students reported the number of movies they saw in the past year. Here is what they reported. 6, 13, 13, 19, 16, 4, 5 Fi

Artemon [7]

Answer:10.9

Step-by-step explanation:You add all of the numbers together (76) and then divide by the total of numbers (7). You will get 10.85714286, you have to round to the nearest 10th , so the 5 changes the 8 to a 9.

3 0

3 years ago

in 2013 the population of detroit was 743,204. The population of the city of detroit in the year 1970 was 688,701 greater than i

irina [24]

1 431 905
Just add them together

7 0

3 years ago

Read 2 more answers

You are creating an open top box with a piece of cardboard that is 16 x 30“. What size of square should be cut out of each corne

Arada [10]

Answer:

$\frac{10}{3} \ inches$ of square should be cut out of each corner to create a box with the largest volume.

Step-by-step explanation:

Given: Dimension of cardboard= 16 x 30“.

As per the dimension given, we know Lenght is 30 inches and width is 16 inches. Also the cardboard has 4 corners which should be cut out.

Lets assume the cut out size of each corner be "x".

∴ Size of cardboard after 4 corner will be cut out is:

Length (l)= $30-2x$

Width (w)= $16-2x$

Height (h)= $x$

Now, finding the volume of box after 4 corner been cut out.

Formula; Volume (v)= $l\times w\times h$

Volume(v)= $(30-2x)\times (16-2x)\times x$

Using distributive property of multiplication

⇒ Volume(v)= $4x^{3} -92x^{2} +480x$

Next using differentiative method to find box largest volume, we will have $\frac{dv}{dx}= 0$

$\frac{d (4x^{3} -92x^{2} +480x)}{dx} = \frac{dv}{dx}$

Differentiating the value

⇒ $\frac{dv}{dx} = 12x^{2} -184x+480$

taking out 12 as common in the equation and subtituting the value.

⇒ $0= 12(x^{2} -\frac{46x}{3} +40)$

solving quadratic equation inside the parenthesis.

⇒ $12(x^{2} -12x-\frac{10x}{x} +40)$ =0

Dividing 12 on both side

⇒ $[x(x-12)-\frac{10}{3} (x-12)]$ = 0

We can again take common as (x-12).

⇒ $x(x-12)[x-\frac{10}{3} ]$ =0

∴ $(x-\frac{10}{3} ) (x-12)= 0$

We have two value for x, which is $12 and \frac{10}{3}$

12 is invalid as, w= $(16-2x)= 16-2\times 12$

∴ 24 inches can not be cut out of 16 inches width.

Hence, the cut out size from cardboard is $\frac{10}{3}\ inches$

Now, subtituting the value of x to find volume of the box.

Volume(v)= $(30-2x)\times (16-2x)\times x$

⇒ Volume(v)= $(30-2\times \frac{10}{3} )\times (16-2\times \frac{10}{3})\times \frac{10}{3}$

⇒ Volume(v)= $(30-\frac{20}{3} ) (16-\frac{20}{3}) (\frac{10}{3} )$

∴ Volume(v)= 725.93 inches³

6 0

3 years ago

What does 2:6 = 14:_______

pshichka [43]

Answer:

14:42

Step-by-step explanation:

As we got 2 to get to 14, that means that we need to times by 7. Then we times the 6 by 7 to get the answer of 42.

5 0

2 years ago

Read 2 more answers

Which of these is a simplified form of the equation 7z 2 = 8 2z 1z? 10z = 6 10z = 10 4z = 6 4z = 10.

vodka [1.7K]

Like terms are those terms that are having the same variables and order. The simplified form of the given equation 7z+2=8+2z+1z is 4z=6.

<h3>What are Like terms?</h3>

Like terms are those terms that are having the same variables, also the variables are of the same order as well.

for example, 25x and 5x are like terms; 30xy and 7xy are like terms, 9x³ and 4x² are not like terms, etc.

The given equation to us is 7z+2=8+2z+1z, simplifying the equation we will get,

$7z + 2 = 8 + 2z + 1z\\\\\text{Bring the like terms on the same side of the equation}\\\\7z -2z-1z = 8 -2\\\\7z-3z=6\\\\4z = 6$

Hence, the simplified form of the given equation 7z+2=8+2z+1z is 4z=6.

Learn more about Like Terms:

brainly.com/question/2513478

3 0

2 years ago