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Airida [17]
3 years ago
9

Solve for x. round your answer to the nearest tenthTrigonometry ​

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

Answer:

\displaystyle x \approx 16.5

General Formulas and Concepts:

<u>Pre-Algebra</u>

Order of Operations: BPEMDAS

  1. Brackets
  2. Parenthesis
  3. Exponents
  4. Multiplication
  5. Division
  6. Addition
  7. Subtraction
  • Left to Right  

Equality Properties

  • Multiplication Property of Equality
  • Division Property of Equality
  • Addition Property of Equality
  • Subtraction Property of Equality<u> </u>

<u>Trigonometry</u>

  • [Right Triangles Only] SOHCAHTOA
  • [Right Triangles Only] tanθ = opposite over adjacent

Step-by-step explanation:

<u>Step 1: Define</u>

Angle θ = 70°

Opposite Leg = <em>x</em>

Adjacent Leg = 6

<u>Step 2: Solve for </u><em><u>x</u></em>

  1. Substitute in variables [tangent]:                                                                     \displaystyle tan70^\circ = \frac{x}{6}
  2. [Multiplication Property of Equality] Isolate <em>x</em>:                                                \displaystyle 6tan70^\circ = x
  3. Rewrite:                                                                                                             \displaystyle x = 6tan70^\circ
  4. Evaluate:                                                                                                           \displaystyle x = 16.4849
  5. Round:                                                                                                               \displaystyle x \approx 16.5
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Write an explicit formula for an, the nth term of the sequence 112, -28, 7, ....
MA_775_DIABLO [31]

Answer:

a_n=112\left(-\frac{1}{4}\right)^{n-1}

Step-by-step explanation:

<u>Geometric Sequences</u>

There are two basic types of sequences: arithmetic and geometric. The arithmetic sequences can be recognized because each term is found as the previous term plus a fixed number called the common difference.

In the geometric sequences, each term is found by multiplying (or dividing) the previous term by a fixed number, called the common ratio.

We are given the sequence:

112, -28, 7, ...

It's easy to find out this is a geometric sequence because the signs of the terms are alternating. If it was an arithmetic sequence, the third term should be negative like the second term.

Let's find the common ratio by dividing each term by the previous term:

\displaystyle r=\frac{-28}{112}=-\frac{1}{4}

Testing with the third term:

\displaystyle -28*-\frac{1}{4}=7

Now we're sure it's a geometric sequence with r=-1/4, we use the general equation for the nth term:

a_n=a_1*r^{n-1}

a_n=112\left(-\frac{1}{4}\right)^{n-1}

6 0
3 years ago
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Arturiano [62]

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Step-by-step explanation:

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5 0
3 years ago
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3 years ago
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Answer:

<u>Option 3</u> satisfies the equation y = -2x + 1.

Step-by-step explanation:

7 = -2*-3 + 1 makes sense

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Have a nice day!

6 0
3 years ago
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