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Verdich [7]
3 years ago
9

Please help!!!!!!!!!

Mathematics
2 answers:
Naddika [18.5K]3 years ago
6 0

The answer would be x=245 cm


Lyrx [107]3 years ago
3 0

Answer:

3.14 cm

Step-by-step explanation:

∆DEG is similar to ∆DFH, so

          DE/DG = DF/DH

         3.0/2.3 = (3.0 + 4.1)/(2.3 + x)

         3.0/2.3 = 7.1/(2.3 + x)     Divide each side by 7.1

         2.3/3.0 = (2.3 + x)/7.1     Multiply each side by 7.1

(2.3 × 7.1)/3.0 = 2.3 + x     Subtract 2.3 from each side

                   x = (2.3 ×7.1)/3.0 – 2.3

                     = 5.443 – 3.0

                     = 3.14 cm

<em>Check: </em>

3.0/2.3 = (3.0 + 4.1)/(2.3 + 3.14)

  1.304 = 7.1 /5.44

  1.304 = 1.305

The numbers check to the nearest hundredth.

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Divide, and then round the answer to two decimal places:<br><br> 0.6256108÷0.527
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Answer:

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Part A: Find a rational number that is between 7.7 and 7.9. Explain why it is rational. (2 points)
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Part A:
An easy choice that makes sense is 7.8, right in the middle. To prove that it's rational we need to write it as a ratio. In this case we have 7.8=\frac{78}{10}

Part B:
We need a number that can't be written as a ratio (because it neither terminates nor repeats). Some common ones are \sqrt{2}, e, \phi and \pi so it makes sense to try and use those to build our number. In this case \frac{11\sqrt{2}}{5}\approx7.78 works nicely. 
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4 years ago
Find all the zeros of the polynomial function p(x) = x3 – 5x2 + 33x – 29
hram777 [196]

Answer:

\large \boxed{\sf \ \ x=1, \ \ x=2+5i, \ \ x=2-5i \ \ }

Step-by-step explanation:

Hello,

I assume that we are working in \mathbb{C}, otherwise there is only one zero which is 1. Please consider the following.

First of all, <u>we can notice that 1 is a trivial solution</u> as

   p(1) = 1^3-5\cdot 1^2 + 33\cdot 1-29=1-5+33-29=0

It means that (x-1) is a factor of p(x) so we can find two real numbers, a and b, so that we can write the following.

p(x)=(x-1)(x^2+ax+b)=x^3+ax^2+bx-x^2-ax-b=x^3+(a-1)x^2+(b-a)x-b

Let's identify like terms as below.

a-1 = -5 <=> a = -5 + 1 = -4

b-a = 33

-b = -29 <=> b = 29

So

\boxed{ \ p(x)=(x-1)(x^2-4x+29) \ }

Now, we need to find the zeroes of the second factor, meaning finding x so that:

x^2-4x+29=0 \ \text{ complete the square, 29 = 25 + 4}  \\ \\  x^2-2\cdot 2 \cdot x+2^2+25=0 \\ \\ (x-2)^2=-25=(5i)^2 \ \text{ take the root } \\ \\x-2=\pm 5i \ \text{ add 2 } \\ \\  x = 2+5i \ \text{ or } \ x = 2-5i

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

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