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jenyasd209 [6]
3 years ago
12

Which of the following is the solution set of x² + 8x + 12 = 0?

Mathematics
1 answer:
raketka [301]3 years ago
4 0

Answer:

\fbox{\begin{minipage}{9em}x = -2 and x = -6\end{minipage}}

Step-by-step explanation:

Given:

x^{2} + 8x + 12 = 0

Solve for:

x

Solution:

Step 1: Select the formula to solve for x

There are some ways to solve quadratic equations.

One of the simple way (if possible) is performing the factorization.

Another way is using the quadratic formula.

Here, we are going to use factorization.

Step 2: Perform factorization

      x^{2} + 8x + 12 = 0

<=>x^{2}  +  2x + 6x  + 12 = 0

<=>(x^{2} + 2x) + (6x + 12) = 0

<=>x(x + 2) + 6(x + 2) = 0

<=>(x + 2)(x + 6) = 0

<=> x = -2 or x = -6

Hope this helps!

:)

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Five bags of chips cost $7.
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1. $1.40 2. $8.40

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7 0
3 years ago
A boat traveled north for 28 miles, then turned x° southwest and traveled for 25 miles before stopping. When it stopped, the boa
zavuch27 [327]

Law of cosine is applicable to all the triangles. The value of the angle by which the boat turns is 39.195°.

<h3>What is the law of cosine?</h3>

Law of cosine helps us to find the third side of the triangle when 2 sides and an angle are known. It is formulated as,

c=\sqrt{a^{2}+b^{2}-2 a b \cdot \cos \gamma}

a, b, c is the sides of the triangle and,

\gamma = angle opposite c

A.)

Given to us

A boat traveled north for 28 miles, then turned x° southwest and traveled for 25 miles before stopping.

When it stopped, the boat was 18 miles from its starting point.

According to the given statements, sides and angles can be written,

a = 25 miles

b = 28 miles

c = 18 miles

\theta = x^o

Substitute the values,

c=\sqrt{a^{2}+b^{2}-2 a b \cdot \cos \gamma}

18=\sqrt{25^{2}+28^{2}-2(25)(28) \cdot \cos \theta}\\\\\theta = 39.195^o

Hence, the value of the angle by which the boat turns is 39.195°.

B.)

Given to us

Starting at the dock, it travels 18 miles to the left, then 25 miles up and to the right, and then 28 miles down and back to the dock.

The angle between 25 miles and 28 miles is x degrees.

According to the given statements, sides and angles can be written,

a = 25 miles

b = 28 miles

c = 18 miles

\theta = x^o

Substitute the values,

c=\sqrt{a^{2}+b^{2}-2 a b \cdot \cos \gamma}

18=\sqrt{25^{2}+28^{2}-2(25)(28) \cdot \cos \theta}\\\\\theta = 39.195^o

Hence, the value of the angle by which the boat turns is 39.195°.

Learn more about the Law of cosine:

brainly.com/question/17289163

5 0
2 years ago
nina wants to enclose a sqare root garden with fencing. It has an area of 141 square feet. To the nearest foot, how much fencong
leonid [27]

The side length (in feet) of the square that is Nina's garden is √141. The four sides of the square are the same length, so add to ...

... 4×√141 = 4×11.874 ≈ 47.497

Rounding to the nearest foot, we find Nina needs 47 feet of fencing.

_____

The answer digit in the tenths place is less than 5, so we round down to the next lower foot.

Note that if you actually multiply 11.874 by 4, you get 47.496. When you're working a problem like this, you always want to maintain full calculator precision until the end. The number we actually used in that multiplication was 11.874342087... (my calculator carries 32 digits). The number that gets rounded is 47.4973683482.... Enough digits are shown here to show how close the number is to being rounded to 48.

If you have your calculator set to show only two decimal digits, you will get the wrong answer. Your calculator will show you 47.50, which you would appropriately round to 48.

5 0
3 years ago
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