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Damm [24]
3 years ago
13

Find the solution(s) to 2x2 + 5x – 3 = 0.

Mathematics
1 answer:
iren2701 [21]3 years ago
5 0

Answer:

C and E

Step-by-step explanation:

Let's factor this the "old fashioned" way.  The standard form of a quadratic is

y=ax^2+bx+c

If you're familiar with the quadratic formula I'd say throw it into that, but if not, again, let's do it the "old fashioned" way.  

We need to find the product of our a and c.  Our a = 2 and our c = -3.  So that gives us a -6.  Now we have to find the factors of 6 (the negative right now doesn't matter so much).  The factors of 6 are 1, 6  and 2, 3.  Both of those possibilities will work to give us a +5, which is the linear term.  Puttng in the 2, 3 first:

0=2x^2+3x+2x-3

Now group the terms together into groups of 2:

0=(2x^2+3x)+(2x-3)

The idea is to factor out something common in each term so that what's left over in the parenthesis in both terms is exactly the same.  In the first term we can factor out a common x, and in the second term, the only thing common is a 1.  So that looks like this:

x(2x+3)+1(2x-3)

What's inside those parenthesis are not actually identical, so 2 and 3 won't work.  Lets try 1 and 6.  For those 2 numbers to equal a +5, the 6 is positive and the 1 is negative.  So let's try that:

(2x^2+6x)+(-x-3)

In the first term we can factor out the common 2x and in the second term we can factor out the common -1:

2x(x + 3) - 1(x + 3)

Now what's common is (x + 3), so we can factor THAT out and what is left over is 2x - 1:

(x + 3)(2x - 1) = 0

If x + 3 = 0, then x = -3

and if 2x - 1 = 0, then 2x = 1 and x = 1/2

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<h2><u>Answer with explanation</u>:</h2>

Let \mu be the average life of light bulbs.

As per given , we have

Null hypothesis : H_0 : \mu =5400

Alternative hypothesis : H_a : \mu >5400

Since H_a is right-tailed and population standard deviation is also known, so we perform right-tailed z-test.

Formula for Test statistic : z=\dfrac{\overlien{x}-\mu}{\dfrac{\sigma}{\sqrt{n}}}

where, n= sample size

\overline{x}= sample mean

\mu= Population mean

\sigma=population standard deviation

For n=95,\ \overline{x}=5483\ \&\ \sigma=500, we have

z=\dfrac{5483-5400}{\dfrac{500}{\sqrt{95}}}=1.61796786124\approx1.6180

Using z-value table , Critical one-tailed test value for 0.06 significance level :

z_{0.06}=1.5548

 Decision : Since critical z value (1.5548) < test statistic (1.6180), so we reject the null hypothesis .

[We reject the null hypothesis when critical value is less than the test statistic value .]

Conclusion : We have enough evidence at 0.06 significance level to support the claim that the new filament yields a longer bulb life

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2 2/5

Step-by-step explanation:

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Explain how to find which value is greater (5/6)*81 or (9/10)*81 without multiplying?
8_murik_8 [283]

The value (9/10)*81 is greater than (5/6)*81

<h3>How to determine the greater value?</h3>

The values are given as:

(5/6)*81 and (9/10)*81

Remove the common factor in both values

So, we have:

5/6 and 9/10

Convert to decimals

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0.9 is greater than 0.83

Hence, (9/10)*81 is greater than (5/6)*81

Read more about expressions at:

brainly.com/question/723406

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