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Alekssandra [29.7K]
2 years ago
10

Greg stands at a horizontal distance 35 feet from the base of the building. The angle of elevation Craig stands out a horizontal

distance 35 feet from the base of the building. The angle of elevation from grade to the top of the building it’s 38° what is the height of the building to the nearest foot

Mathematics
1 answer:
ValentinkaMS [17]2 years ago
8 0
Because X is opposite of the 38° angle and 35 is adjacent to the 38° angle, you would use tan. To set up the equation you would put X over 35 and set an equal to 38(tan). Then you would multiply both sides by 35 to cancel out the 35 on the bottom of the X. When you multiply 38(tan) by 35, you get X equals 27.

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Let $a$ and $b$ be nonzero real numbers such that
algol [13]
<h3>Answer:   -7/2</h3>

=========================================================

Explanation:

Let's expand out (2 - 7i)(a + bi) using the FOIL rule

(2 - 7i)(a + bi) = 2a + 2bi - 7ai - 7bi^2

(2 - 7i)(a + bi) = 2a + 2bi - 7ai - 7b(-1)

(2 - 7i)(a + bi) = 2a + 2bi - 7ai + 7b

(2 - 7i)(a + bi) = (2a+7b) + (2bi-7ai)

(2 - 7i)(a + bi) = (2a+7b) + (2b-7a)i

We're told the result is purely imaginary. What this means is that the real part (2a+7b) is zero, while the imaginary part (2b-7a) is nonzero. If both are zero, then we have 0+0i = 0 which is purely real.

For example, the complex numbers 0-7i and 0+2i are purely imaginary.

Let's use the fact that 2a+7b must be zero to do the following steps:

2a+7b = 0

2a = -7b

a = -7b/2

a/b = -7/2 which is the final answer

We must check to see if 2b-7a is nonzero

2b - 7a = 2b - 7(-7b/2)

2b - 7a = 2b + 24.5b

2b - 7a = 26.5b

The result is nonzero if and only if b is nonzero. Luckily we're told b is nonzero at the top of the problem. So we don't have any worries that (2b-7a) is zero.

Therefore, (2a+7b) + (2b-7a)i will be purely imaginary with a/b = -7/2

------------------

A concrete example:

Let a = -14 and b = 4

a/b = -14/4 = -7/2

(2-7i)(a+bi) = (2-7i)(-14+4i) = 0 + 106i which is purely imaginary.

I'll let you do the steps in expanding that out using the FOIL rule.

4 0
1 year ago
8.45 At some point in the season, the Unicorns had won 60% of their basketball games. After that point, they won 8 more games an
ololo11 [35]

Answer:

The total number of games won by Unicorn is 40.

Step-by-step explanation:

  • We are given with a word problem
  • We are asked to find the number of unicorns played during the season
  • We can do this in two steps

         Step 1: Finding the win percentage

         Step 2: Finding the number of unicorns played during the season

Step 1 of 2

Let the number of games played by unicorn be x.The unicorn won 60% of the first x-10 games That is $\frac{60}{100} \times(x-10)$

Combining the 8 games we get,

$$\begin{gathered}\frac{60}{100}(x-10)+8=\frac{60}{100} \times x-\frac{60}{100} \times 10+8 \\0.6 x-6+8=0.6 x+2\end{gathered}$$

Step 2 of 2

The unicorn totally won 65% of the games played.

That is $\frac{65}{100} \times x=0.65 x$

Equating both the equation gives

$$\begin{gathered}0.6 x+2=0.65 x \\2=0.65 x-0.6 x \\2=0.05 x \\\frac{2}{0.05}=x \\40=x\end{gathered}$$

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2 years ago
Lines c and d are perpendicular. if the slope of line c is -4, what is the slope of line d?
torisob [31]
The slope of line d is 1/4.
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2 years ago
What is is the value of x if -18/6x=-22
blagie [28]

Answer:

x=22/3 is your answer


7 0
3 years ago
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(02.03)Figure ABC is reflected about the x-axis to obtain figure A'B'C':
faust18 [17]

Answer:

B.(–2, –7)

Step-by-step explanation:

5 0
3 years ago
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