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Ad libitum [116K]
3 years ago
5

Solve x2 + 5x = −6. x = 5 and x = 1 x = −5 and x = −1 x = 3 and x = 2 x = −3 and x = −2

Mathematics
1 answer:
fomenos3 years ago
8 0

Answer:

x = −3 and x = −2

Step-by-step explanation:

x^2 + 5x = −6

Add 6 to each side

x^2 + 5x+6 = −6+6

x^2 +5x+6 =0

Factor

What 2 number multiply to 6 and add to 5

3*2 =6

3+2 =5

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

Using the zero product property

x+3 =0             x+2 =0

x+3-3=0-3         x+2-2=0-2

x=-3                       x=-2

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Step-by-step explanation:

<u>Given </u><u>:</u><u>-</u><u> </u>

A semicircle is given with radius of 3cm .

And we need to find the perimeter of the semicircle . We know the perimeter as ,

:\implies Perimeter = πr

:\implies Perimeter = 3cm × π

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Now there is the diameter of circle is 6cm . Hence totally the perimeter is ,

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We were supposed to give answers in terms of π .

<h3>Hence the perimeter is ( 3π + 6 ) cm</h3>
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Step-by-step explanation:

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Solve sin 0 + 1 = cos20 on the interval 0 ≤ 0 &lt; 2pi. Show work please!
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Answer:

\theta=\frac{\pi}{2},\frac{3\pi}{2}\frac{2\pi}{3}\frac{4\pi}{3}

Step-by-step explanation:

You need 2 things in order to solve this equation:  a trig identity sheet and a unit circle.

You will find when you look on your trig identity sheet that

cos(2\theta)=1-2sin^2(\theta)

so we will make that replacement, getting everything in terms of sin:

sin(\theta)+1=1-2sin^2(\theta)

Now we will get everything on one side of the equals sign, set it equal to 0, and solve it:

2sin^2(\theta)+sin(\theta)=0

We can factor out the sin(theta), since it's common in both terms:

sin(\theta)(2sin(\theta)+1)=0

Because of the Zero Product Property, either

sin(\theta)=0 or

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The next equation needs to first be solved for sin(theta):

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Go back to your unit circle and find the values of theta where the sin is -1/2 in the interval.  They are:

\theta=\frac{2\pi}{3},\frac{4\pi}{3}

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