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horsena [70]
2 years ago
8

Please help serious answers only

Mathematics
2 answers:
pishuonlain [190]2 years ago
8 0

Answer:

The first one

Step-by-step explanation:

We want to find the roots of the equation -2x + 3 = -8x²

Step 1: Our first step is to get the equation in quadratic form so we can use the quadratic formula to find the roots

Quadratic form: ax² + bx + c = 0

We can easily get this equation in quadratic form by moving -8x² to the right side. We can do this using inverse operations. The inverse of subtraction is addition so to get rid of -8x² we add 8x² to both sides

After adding -8x² to both sides we acquire 8x² - 2x + 3 = 0

The equation is now in quadratic form meaning we can now use the quadratic formula to find the roots.

Quadratic Formula : \frac{-b+-\sqrt{b^2-4(a)(c)} }{2(a)}

where the values of a, b and c are derived from the equation

Remember that the equation is in quadratic form ax² + bx + c = 0

8x² - 2x + 3 = 0  so a = 8 , b = - 2 and c = 3

We then plug in these values into the quadratic formula ( note that the +- means plus or minus meaning that we have to evaluate this twice, once when the discriminant ( b² - 4(a)(c) is the discriminant ) is being add to -b and once when the discriminant is being subtracted from -b )

First lets evaluate when the discriminant is being added to -b

Recall the quadratic formula : \frac{-b+\sqrt{b^2-4(a)(c)} }{2(a)}

a = 8 , b = - 2 and c = 3

\frac{2+\sqrt{2^2-4(8)(3)} }{2(8)}

Work being done inside of the square root: 2² = 4 , -4 * 8 = -32 , -32 * 3 = -96

4 - 96 = - 92

Work being done at denominator : 2 * 8 = 16

\frac{2+\sqrt{-92} }{16}

The first root is \frac{2+\sqrt{-92} }{16}

We now do this same process but instead we subtract the discriminant.

We would be left with the same thing but it would be \frac{2-\sqrt{-92} }{16} instead of \frac{2+\sqrt{-92} }{16}

In some cases we would get a completely different answer, so evaluating it twice, once  when the discriminant is being add to -b and once when the discriminant is being subtracted from -b may be important in some cases.

We then simplify the two roots. You may notice that there is a negative number under the radical and you might ask how can you square root a negative? well you can't which is when imaginary roots come in. Imaginary roots: i = -1 . We can take out an i from -92 making it 92 because i = -1 and -92/-1 = 92. We would be left with i√92

So we can conclude that the roots of the equation are \frac{2+i\sqrt{92} }{16} and \frac{2-i\sqrt{92} }{16}

Looking at the answer choices we notice that there are two very similar answers. The first and second one. The only difference between the two is that 2 is positive on the first one and 2 is negative on the second one. Looking at the roots we just found, the 2 should be positive therefore the answer is the first one.

Note that ± means plus or minus and it means that the expression can either be added or subtracted and it will be a root. This means that saying the roots are \frac{2+-i\sqrt{92} }{16} is the same as saying the roots are \frac{2+i\sqrt{92} }{16} and \frac{2-i\sqrt{92} }{16}

pentagon [3]2 years ago
4 0

Answer:

The answer is 3/4 and -1/2

\frac{3}{4} and  -  \frac{1}{2}

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Answer: Given a sample of 200, we are 90% confident that the true proportion of people who watched educational TV is between 72.1% and 81.9%.

Step-by-step explanation:

\frac{154}{200} =0.77

1-0.77=0.23

\sqrt{\frac{(0.77)(0.23)}{200} }=0.049

0.77±0.049< 0.819, 0.721

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3 years ago
The expression 3x2−5x2simplifies to −2x2<br><br> is this true?
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I dont think so I would look at it as how did they get the -2

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The two outside pairs of sides are stated as congruent.

The inside side is congruent by reflective property

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A square has a diagonal of 44in. I want to frame the picture, how many inches of frame do I need
dimaraw [331]

The square has a 44-inch diagonal.

The pythagorean equation must be used to obtain the hand.

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Diagonal (d) ^ 2 = 2side (s)^2

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8 0
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1. The number of rabbits on an island is increasing exponentially.
Zina [86]

Answer:

<em>There are approximately 114 rabbits in the year 10</em>

Step-by-step explanation:

<u>Exponential Growth </u>

The natural growth of some magnitudes can be modeled by the equation:

P=P_o(1+r)^t

Where P is the actual amount of the magnitude, Po is its initial amount, r is the growth rate and t is the time.

We are given two measurements of the population of rabbits on an island.

In year 1, there are 50 rabbits. This is the point (1,50)

In year 5, there are 72 rabbits. This is the point (5,72)

Substituting in the general model, we have:

50=P_o(1+r)^1

50=P_o(1+r)\qquad\qquad[1]

72=P_o(1+r)^5\qquad\qquad[2]

Dividing [2] by [1]:

\displaystyle \frac{72}{50}=(1+r)^{5-1}=(1+r)^{4}

Solving for r:

\displaystyle r=\sqrt[4]{\frac{72}{50}}-1

Calculating:

r=0.095445

From [1], solve for Po:

\displaystyle P_o=\frac{72}{(1+r)^5}

\displaystyle P_o=\frac{72}{(1.095445)^5}

P_o=45.64355

The model can be written now as:

P=45.64355(1.095445)^t

In year t=10, the population of rabbits is:

P=45.64355(1.095445)^{10}

P = 113.6

P\approx 114

There are approximately 114 rabbits in the year 10

5 0
3 years ago
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