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wlad13 [49]
3 years ago
14

Simplify: 5z^7⋅6z thanks

Mathematics
1 answer:
Deffense [45]3 years ago
4 0

Answer:

30z^8

Step-by-step explanation:

5z^7.6z

= 5 x z^7 x 6 x z

= 5 x 6 x z^7 x z

= 30 x z^(7+1)

=30z^8

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Solve the following equations by factorisation method.Only factorisation not dharacharya.​
Luba_88 [7]

Hello, please consider the following.

When x_1 and x_2 are two roots, we can factorise as

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So for the first equation, we can say that the sum of the zeros is

\dfrac{a^2+b^2}{2}=\dfrac{a^2}{2}+\dfrac{b^2}{2}

and the product is

\dfrac{a^2b^2}{4}=\dfrac{a^2}{2}\dfrac{b^2}{2}

So we can factorise as below.

4x^2-2(a^2+b^2)x+a^2b^2=(2x-a^2)(2x-b^2)=0

And the solutions are

\boxed{\sf \n\bf  \ \dfrac{a^2}{2} \ \ and \ \ \dfrac{b^2}{2}}

For the second equation, we will complete the square and put the constant on the right side and take the root.

Let's do it!

9x^2-9(a+b)x+2a^2+5ab+2b^2=0\\\\9(x-\dfrac{a+b}{2})^2-9\dfrac{(a+b)^2}{4}+2a^2+5ab+2b^2=0\\\\9(x-\dfrac{a+b}{2})^2=\dfrac{9(a+b)^2-8a^2-20ab-8b^2}{4}\\\\9(x-\dfrac{a+b}{2})^2=\dfrac{9a^2+18ab+9b^2-8a^2-20ab-8b^2}{4}\\\\9(x-\dfrac{a+b}{2})^2=\dfrac{a^2+b^2-2ab}{4}=\dfrac{(a-b)^2}{4}\\\\(x-\dfrac{a+b}{2})^2=\dfrac{(a-b)^2}{2^2\cdot 3^2}

We take the root, and we find the two solutions

\begin{aligned}x_1&=\dfrac{a+b}{2}-\dfrac{a-b}{6}\\\\&=\dfrac{3a+3b-a+b}{6}\\\\&=\dfrac{2a+4b}{6}\\\\&\boxed{=\dfrac{a+2b}{3}}\end{aligned}

\begin{aligned}x_1&=\dfrac{a+b}{2}+\dfrac{a-b}{6}\\\\&=\dfrac{3a+3b+a-b}{6}\\\\&=\dfrac{4a+2b}{6}\\\\&\boxed{=\dfrac{2a+b}{3}}\end{aligned}

Thank you.

6 0
3 years ago
The Pacific Crest Trail is a hiking trail that extends from Mexico to Canada and is about 2650 miles long. Suppose Xin hikes one
seraphim [82]

Answer:

Xin has hiked 2.65 miles of the trial.

Step-by-step explanation:

Given:

Distance of the trial hike = 2650 miles

portion of the trial Xin hikes = \frac{1}{1000} of the trial.

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Solution:

Now we can say that;

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framing in equation form we get;

Distance Xin hike = \frac{1}{1000}\times 2650 = 2.65 \ miles

Hence Xin has hiked 2.65 miles of the trial.

8 0
4 years ago
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