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ser-zykov [4K]
3 years ago
7

Find the real or imaginary solutions of the equation by factoring. 6x^2+13x-5=0

Mathematics
1 answer:
beks73 [17]3 years ago
4 0
6x^2+13x-5=0\\
6x^2-2x+15x-5=0\\
2x(3x-1)+5(3x-1)=0\\
(2x+5)(3x-1)=0\\
x=-\dfrac{5}{2} \vee x=\dfrac{1}{3}
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4. find the real number roots. sqrt-0.25
e-lub [12.9K]

Given is square root of a negative real number, i.e. \sqrt{-0.25}

When we find square root of positive real numbers, we get Real answers.

But when we find square root of negative real numbers, we get Imaginary answers. To solve them, we can split the given negative number into product of -1 and the number itself but with positive sign. e.g. -4 = -1 x 4.

For square root of -1, we use english letter 'i' called Imaginary unit i.e. \sqrt{-1} = i

Now we can use -0.25 = -1 x 0.25

\sqrt{-0.25} =\sqrt{-1*0.25} \\\\ \sqrt{-0.25} =\sqrt{-1}*\sqrt{0.25} \\\\ \sqrt{-0.25} =i*0.5 \\\\ \sqrt{-0.25} =0.5i

Hence, "0.5i" is the final answer.

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3 years ago
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Answer:

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Step-by-step explanation:

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A five​-digit number starts with a number between 4​-9 in the first​ position, with no restrictions on the remaining 4 digits. a
Maurinko [17]

Answer:

(a) Pr = 0.3024

(b) Pr = 0.6976

(c) Pr = \frac{^9P_{n-1}}{10^{n-1}}

Step-by-step explanation:

Given

Start = \{5,6,7,8\} i.e. between 4 and 9

n(Start) =4

Digits = 5

Solving (a): Probability that each of the 5 digit are different

Since there is no restriction;

The total possible selection is as follows:

First\ digit = 4 (i.e. any of the 4 start digits)

Second\ digit = 10\\ (i.e. any of the 10 digits 0 - 9)

Third\ digit = 10 (i.e. any of the 10 digits 0 - 9)

Fourth\ digit = 10 (i.e. any of the 10 digits 0 - 9)

Fifth\ digit = 10 (i.e. any of the 10 digits 0 - 9)

So, the total is:

Total = 4 * 10 * 10 * 10 * 10

Total = 40000

For selection that all digits are different, the selection is:

First\ digit = 4 (i.e. any of the 4 start digits)

Second\ digit = 9 (i.e. any of the remaining 9)

Third\ digit = 8 (i.e. any of the remaining 8)

Fourth\ digit = 7 (i.e. any of the remaining 7)

Fifth\ digit = 6 (i.e. any of the remaining 6)

So:

Selection =4 * 9 * 8 * 7 * 6

Selection =12096

So, the probability is:

Pr = \frac{Selection}{Total}

Pr = \frac{12096}{40000}

Pr = 0.3024

Solving (b): At least 1 repeated digit

The probability calculated in (a) is the all digits are different i.e. P(None)

So, using laws of complement

We have:

P(At\ least\ 1) = 1 - P(None)

So, we have:

Pr= 1 - 0.3024

Pr = 0.6976

Solving (c): An expression to model the probability.

<em>Using (a) as a point of reference, we have;</em>

Pr = \frac{Selection}{Total}

Where

Selection =4 * 9 * 8 * 7 * 6 ---- for selection of 5 i.e. n = 5

Total = 4 * 10 * 10 * 10 * 10

Selection =4 * 9 * 8 * 7 * 6

This can be rewritten as:

Selection = 4 * ^9P_4

4 can be expressed as: 5 - 1

So, we have:

Selection = (5-1) *^9P_{5-1}

Substitute n for 5

Selection = (n-1) *^9P_{n-1}

Selection = (n-1)^9P_{n-1}

Total = 4 * 10 * 10 * 10 * 10

This can be rewritten as:

Total = 4 * 10^4

Total = (5-1) * 10^{5-1}

Total = (n-1) * 10^{n-1}

Total = (n-1) 10^{n-1}

So, the expression is:

Pr = \frac{(n-1)^9P_{n-1}}{(n-1)10^{n-1}}

Pr = \frac{^9P_{n-1}}{10^{n-1}}

<em>Where n represents the digit number</em>

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The y-intercept of g(x) in g(x) = 3x - 2 is (0,-2) (0,0) (2/3,0)
Dennis_Churaev [7]
For any y-intercept, the x-coordinate is zero. This is something to bear in mind to start with.

Now to find the y-intercept, find g(0) = -2.

Therefore the answer is (0,-2)
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Cameras R Us has a sale for 25% off camera bags, which is a discount of $20. To find the original cost of the camera bag, Tara c
Vsevolod [243]

Answer:

It will be 2. (B) and 4. (D)

Step-by-step explanation:

I took the assignment and got it right :D

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