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Zarrin [17]
3 years ago
13

What are the easy ways to complete problems like these?

Mathematics
1 answer:
Romashka-Z-Leto [24]3 years ago
4 0

You can think of this whole process as "surgically removing" the repeating part from the decimal to get it into fraction form. I'll break down the steps:

x=0.\overline{12}

We set some variable x equal to our repeating decimal.

100x=12.\overline{12}

We want to move the decimal point <em>just enough </em>to the right so that we can make the "chop" we're going to perform in the next step. Since the decimal starts repeating every two digits, we want to scoot the decimal point two places over, which we can do by multiplying it by 100. We do the same to the x to keep both sides equal.

100x-x=12.\overline{12}-0.\overline{12}

This is the "chop." We're subtracting the original value of x from both sides to get rid of the repeating part of 12.\overline{12}. On the left side, this leaves us with

99x=12

We can then divide either side of the equation by 99 to find that

x=\frac{12}{99}=\frac{4}{33}

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IrinaK [193]

The question can be solved as follows:

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\frac{5.52\times10^3}{1.2\times10^5}=4.6\times10^{-2}

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3 years ago
Diagram below shows the curve of a quadratic function
uranmaximum [27]

Answer:

q = -8, k = 2.

r = -6.

Step-by-step explanation:

f(x) = (x - p)^2 + q

This is the vertex form of a quadratic where the vertex is at the point (p, q).

Now the x intercepts are at -6 and 2 and the curve is symmetrical about the line x = p.

The value of p is the midpoint of  -6 and 2 which is (-6+2) / 2 = -2.

So we have:

f(x) = 1/2(x - -2)^2 + q

f(x) = 1/2(x + 2)^2 + q

Now the graph passes through the point (2, 0) , where it intersects the x axis, therefore, substituting x = 2 and f(x) = 0:

0 = 1/2(2 + 2)^2 + q

0 = 1/2*16 + q

0 = 8 + q

q = -8.

Now convert this to standard form to find k:

f(x) = 1/2(x + 2)^2 - 8

f(x) = 1/2(x^2 + 4x + 4) - 8

f(x) = 1/2x^2 + 2x + 2 - 8

f(x) = 1/2x^2 + 2x - 6

So k = 2.

The  r  is the y coordinate when x = 0.

so r = 1/2(0+2)^2 - 8

=  -6.

3 0
3 years ago
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dmitriy555 [2]

Answer:

Step-by-step explanation:

ΔABD ≅ ΔCBD .

So AD = DC

8x - 4 = 3x + 1       {add 4 to both sides}

     8x = 3x + 1 + 4

     8x = 3x + 5 {subtract 3s from both sides}

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        x = 5/5

x = 1

8 0
3 years ago
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