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PolarNik [594]
3 years ago
5

Find the value of the variable. If your answer is not an integer, leave it in simplest radical form.

Mathematics
1 answer:
tester [92]3 years ago
8 0

So this is considered a "special triangle." The 30-60-90 triangle states that if the short leg is x, then the hypotenuse is 2x and the long leg is x√3.

Since we have the short leg, to find the hypotenuse, or y in this case, multiply the short leg by 2:

17 × 2 = 34

Next, to find the long leg, or x in this case, multiply the short leg by √3:

17 × √3 = 17√3

<u>In short, x = 17√3 and y = 34. The correct option is the last option.</u>

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How many solutions exist for the given equation? 3(x – 2) = 22 – x zero one two infinitely many
coldgirl [10]

Answer:

one solution

Step-by-step explanation:

Given

3(x - 2) = 22 - x ← distribute parenthesis on left side

3x - 6 = 22 - x ( add x to both sides )

4x - 6 = 22 ( add 6 to both sides )

4x = 28 ( divide both sides by 4 )

x = 7

5 0
3 years ago
Read 2 more answers
<img src="https://tex.z-dn.net/?f=-3%5Csqrt%7B45y%C2%B3%7D" id="TexFormula1" title="-3\sqrt{45y&sup3;}" alt="-3\sqrt{45y&sup3;}"
GarryVolchara [31]

Answer:

-9A · √(5yA)

Step-by-step explanation:

The coefficient -3 stays the same.

45 factors into 5·9, which is helpful because 9 is a perfect square.

Thus, √45 = 3√5.

y cannot be factored.  It stays under the radical.

A³ can be factored into A² (a perfect square) and A.

Thus,

-3√(45yA³) = -3 · 3√5 · √y · A · √A, or

                   = (-3)(3)(A) · √(5yA), or

                    = -9A · √(5yA)

4 0
3 years ago
Determine whether the geometric series 27 + 18 + 12 + 8 + ... converges or diverges, and identify the sum if it exists.
Ne4ueva [31]

The given geometric series as shown in the question is seen to; Be converging with its' sum as 81

<h3>How to identify a converging or diverging series?</h3>

We are given the geometric series;

27 + 18 + 12 + 8 + ...

Now, we see that;

First term; a₀ = 27

Second Term; a₁ = 2(27/3)

Third term; a₂ = 2²(27/3²)

Fourth term; a₃ = 2³(27/3³)

Thus, the formula is;

2ⁿ(27/3ⁿ)

Applying limits at infinity gives;

2^(∞) * (27/3^(∞)) = 0

Since the  terms of the series tend to zero, we can affirm that the series converges.

The sum of an infinite converging series is:

S_n = a/(1 - r)

S_n = 27/(1 - (2/3)

S_n = 81

Read more about converging or diverging series at; brainly.com/question/15415793

#SPJ1

6 0
2 years ago
Is 12:8 and 18:12 equivalent?
tia_tia [17]

Answer:

no

Step-by-step explanation:

18 is not a multiple of 12

and 12 is not a multiple of 8

8 0
3 years ago
What does ≤ mean? Danke
Svetlanka [38]

Answer:

It means less than or equal to

Step-by-step explanation:


6 0
3 years ago
Read 2 more answers
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