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3 years ago

How do you factor this equation? 7x²+5x-3

Mathematics

1 answer:

svetoff [14.1K]3 years ago

8 0

Answer:

Step-by-step explanation:

This is a quadratic expression. Use the quadratic formula to find the roots, and then once you have the roots, write the corresponding factors.

The coefficients of this quadratic expression are a = 7, b = 5 and c = -3

The discriminant is b^2 - 4ac, or 5^ - 4(7)(-3), or 25 + 84 = 109. Because this is positive, we know that the expression has two unequal, real roots.

Using the quadratic formula, we now find these roots:

-b ± √(discriminant)

x = -------------------------------- which here is:

-5 ± √109

x = -----------------

The factors can be found from these two roots. The first one is

-5 - √109 5 + √109

(x - ---------------- ) = (x + ---------------- )

14 14

and the second is

5 - √109

(x + ---------------- )

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3 years ago

12, 9, 15, 19, 20, 15<br><br> Mean <br><br> Median <br><br> Mode

Ede4ka [16]

Answer:

Mean: 15

Median: 15

Mode: 15

Step-by-step explanation:

<h2>Definitions:</h2>

<u>Mean</u>: It represents the average value of a given data set. The formula for finding the mean of a given set of numbers by taking the quotient of all numbers and the number of values. In other words:

$\displaystyle\mathsf{Mean\:=\:\frac{Sum\:of \:all\: values}{Number\:of\:values \:in\: a \:given \:data\:set}}$

<u>Median:</u> It represents the middle value in a given set of numbers. In order to determine the median, it is essential to arrange the given data either in <em>ascending</em> or <em>descending</em> order (although it is customary to arrange the numbers into ascending order).

If there is an odd number of values in a given set, then the <u>middle number</u> is the median of that set.

If a given list comprises of an even number of items, then we must take the <em>average</em> of the two middle numbers.

<u>Mode</u>: It represents the number that <u>occurs most often</u> on a list of items or data.

<h2>Solution:</h2><h3><u>Find the Mean:</u></h3>

Using the formula provided in the previous section for finding the mean:

$\displaystyle\mathsf{Mean\:=\:\frac{Sum\:of \:all\: values}{Number\:of\:values \:in\: a \:given \:data\:set}}$

$\displaystyle\mathsf{Mean\:=\:\frac{12+9+15+19+20+15}{6}\:=\:\frac{90}{6}\:=\:15}$

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Arrange the given data set in <u><em>ascending order</em></u>:

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Next, since there is an even number of items on our given data set, we must <u>take the average of the</u><u> two middle numbers</u> (which are 15 and 15):

$\displaystyle\mathsf{Median\:=\:\frac{15+15}{2}\:=\:\frac{30}{2}\:=\:15}$

Therefore, the median is 15.

As described in the previous section of this post, the mode is the number that occurs most often on our given data. The only repeating number on our list is 15, hence it is the mode.

Therefore, the <em>mean</em>, <em>median</em>, and <em>mode</em> of the given data set is <u>15</u>.

6 0

2 years ago

Let alpha and beta be conjugate complex numbers such that frac{\alpha}{\beta^2} is a real number and alpha - \beta| = 2 \sqrt{3}

miskamm [114]

Answer:

$-3+i\sqrt{3} , 1+\sqrt{3}$

Step-by-step explanation:

Given that alpha and beta be conjugate complex numbers

such that frac{\alpha}{\beta^2} is a real number and alpha - \beta| = 2 \sqrt{3}.

Let

$\alpha = x+iy\\\beta = x-iy$

since they are conjugates

$\alpha-\beta = x+iy-(x-iy)\\= 2iy= 2i\sqrt{3} \\y =\sqrt{3}$

$\frac{\alpha}{\beta^2} }\\=\frac{x+i\sqrt{3} }{(x-i\sqrt{3})^2} \\=\frac{x+i\sqrt{3}}{x^2-3-2i\sqrt{3}} \\=\frac{x+i\sqrt{3}((x^2-3+2i\sqrt{3}) }{(x^2-3-2i\sqrt{3)}(x^2-3-2i\sqrt{3})}$

Imaginary part of the above =0

i.e. $\sqrt{3} (x^2-3)+2x\sqrt{3} =0\\x^2+2x-3=0\\(x+3)(x-1) =0\\x=-3,1$

So the value of alpha = $-3+i\sqrt{3} , 1+\sqrt{3}$

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3 years ago

A scientist has two solution which she labelled, solution A and solution B, each continue salt,she knows that solution A is 65%

Lorico [155]

A = oz of the solution A

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~I hope this helped~

If it doesn't make since, I can try to switch up the wording ^^

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3 years ago