From the observation deck of a skyscraper, Jamal measures a 51° angle of depression
to a ship in the harbor below. If the observation deck is 1123 feet high, what is the
horizontal distance from the base of the skyscraper out to the ship? Round your
answer to the nearest hundredth of a foot if necessary.

Answer:

First triangle: 54.46 degrees

Step-by-step explanation:

For the first problem, solve for the third side, then the third angle, and then subtract from 180.

20^2 + 28^2 = c^2

400 + 784 = c^2

1184 = c^2

34.41 = third side

Find the third angle:

sin(90)/34.41 = sin(x)/20

20 * sin(90)/34.41 = sin(x)

35.54 is the third angle.

180 - 35.54 - 90 = 54.46. The angle with the question mark is 54.46. Do the other 2 problems the same way.

Answer:

17 ft 8 in

Step-by-step explanation:

Answer:

n+3n=$850  n is one person and 3n is the other represented by n

Step-by-step explanation:

Answer:

B, C

Step-by-step explanation:

Step-by-step explanation:

We have that

[tex](x + \frac{1}{x} ) {}^{2} = 3[/tex]

We are trying to find the number value so that we can apply in the later equation.

Qe first simplify.

Remeber that

[tex](a + b) {}^{2} = a {}^{2} + 2ab + {b}^{2} [/tex]

Also remeber that

[tex] \frac{1}{x} = {x}^{ - 1} [/tex]

so

[tex](x + x {}^{ - 1} ) {}^{2} = {x}^{2} + 2x {}^{0} + {x}^{ - 2} = 3[/tex]

We then simply remeber that x^0=1 so

[tex] {x}^{2} + 2 + \frac{1}{ {x}^{2} } = 3[/tex]

Multiply both sides by x^2.

[tex] {x}^{4} + 2 {x}^{2} + 1 = 3 {x}^{2} [/tex]

Subtract both sides by 3x^2

[tex] {x}^{4} - {x}^{2} + 1 = 0[/tex]

Notice that x^4= (x^2)^2.

So our reformed equation is

[tex]( {x}^{2} ) {}^{2} - {x}^{2} + 1 = 0[/tex]

Let a variable , w equal x^2. This means that we subsitute variable, w in for x^2.

[tex]w {}^{2} - w + 1 = 0[/tex]

Now we use the quadratic formula

[tex] w = \frac{ - b + \sqrt{b {}^{2} - 4ac } }{2a} [/tex]

and

[tex]w = - b - \frac { \sqrt{b {}^{2} - 4ac } }{2a} [/tex]

Let a=1 b=-1 and c=1.

[tex]w = \frac{1 + \sqrt{1 - 4(1)} }{2} [/tex]

[tex]w = \frac{1 - \sqrt{1 - 4} }{2} [/tex]

Now, we get

[tex]w = \frac{1}{2} + \frac{i \sqrt{3} }{2} [/tex]

and

[tex]w = \frac{1}{2} - \frac{ i\sqrt{3} }{2} [/tex]

Now since we set both of these to the x^2 we solve for x.

and

[tex] {x}^{2} = \frac{1}{2} + \frac{i \sqrt{3} }{2} [/tex]

and

[tex] {x}^{2} = \frac{1}{2} - \frac{i \sqrt{3} }{2} [/tex]

We can represent both of these as complex number in the form of a+bi. Next we can convert this into trig form which is

[tex] {x}^{2} = 1( \cos(60) + i \: \sin(60) [/tex]

and

[tex] {x}^{2} = 1( \cos(300) + i \: sin(300))[/tex]

Next we take the sqr root of 1 which is 1, and divide the degree by two.

[tex] {x} = 1( \cos(30) + i \: sin \: 30)[/tex]

and

[tex]x = 1( \cos(150) + i \: sin(150)[/tex]

We are asked for the 2nd root so just add 180 degrees to this and we have

[tex]x = 1 \cos(210) + i \: sin \: 210)[/tex]

and

[tex]x = 1( \cos(330) + i \: sin(330)[/tex]

which both simplified to

[tex]x = - \frac{ \sqrt{3} }{2} - \frac{1}{2} i[/tex]

and

[tex]x = \frac{ \sqrt{3} }{2} - \frac{1}{2} i[/tex]

Now we must find

x^18+x^12+x^6+1.

We just use demovire Theorem. Which is a complex number raised to the nth root is

[tex] {r}^{n} (cos(nx) + i \: sin(nx)[/tex]

So let plug in our first root.

[tex]1( \cos(330 \times 18)) + i \: sin \: (330 \times 18))) + 1( \cos(12 \times 330)) + i \: sin(12 \times 330) + 1( \cos(6 \times 330) + i \: sin(6 \times 330))) + 1[/tex]

To save time we multiply the angle and use rules of terminals angle and we get

[tex]1( \cos(180) + i \sin(180) ) + 1( \cos(0) + i \: sin \:( 0) + 1( \cos(180) + i \: sin(180) + 1[/tex]

And we get

[tex] - 1 + 1 + - 1 + 1 = 0[/tex]

So one of the answer is x=0

And the other, let see

[tex]1 \cos(210 \times 18) + i \: \sin(210 \times 18) + 1 \: cos(210 \times 12) + i \: sin(210 \times 12) + 1 \cos(210 \times 6) + \:i sin(210 \times 6) + 1[/tex]

[tex] \cos(180) + i \: sin(180) + 1 \cos(0) + i\sin(0) +1( \cos(0) + i \sin(0) + 1[/tex]

We get

[tex] - 1 + 1 + 1 + 1 = 2[/tex]

So our answer are 2.

So the answer to the second part is

0 and 2.

Answer:

4

Step-by-step explanation:

6 - 2 = 4

Answer:

4

Step-by-step explanation:

Ciara is not my friend but she's my sister

Answer:

It's an obtuse Scalene Triangle

Step-by-step explanation:

Look up triangle angle calculator and enter in the sides

Answer:

The slope is 2/4 or 1/2

Step-by-step explanation:

Readers can learn various information related to an airplane flight.

Fly through the sky is a children's song in which different aspects of an airplane flight are described in a simple and direct way. Some of the aspects that a person can learn by reading the lyrics of the song are:

Learn more about airplane in: https://brainly.com/question/15415980

Answer:

P(x)= x^3 - 4x^2 + 16x - 64

Step-by-step explanation:

First, let’s find all of the zeroes. If the question is asking for a degree 3 polynomial, than there has to be more than 2 zeroes. The complex conjugates theorem states that if a+bi is a zero, than a-bi has to be a zero as well. So if 4i is a zero, than -4i has to be a zero as well. By looking at the zeroes, you can write them as a linear factorization.

(x-4)(x+4i)(x-4i)

If you foil all of it, you will get x^3 - 4x^2 + 16x - 64.

Answer:

5x^5

Step-by-step explanation:

5x^2*4x^3/4

Divide

5x^2*1x^3

Multiply and Calculate

5x^5

answer: [tex]25x^{3}[/tex]

steps to solve:

→ let's write this out as an equation instead of in word form. 5x to the power of 2 times 4x to the power of 3 divided by 4 is [tex]\frac{5^{2} * 4x^{3}}{4}[/tex].

→ first, calculate the power of [tex]5x^{2}[/tex]. [tex]5x^{2} = 25[/tex], so now we have [tex]\frac{25^{2} * 4x^{3}}{4}[/tex]

→ now, multiply the monomials. [tex]25 * 4x^{3} = 100x^{3}[/tex].

→ [tex]\frac{100x^{3}}{4}[/tex]. we need to cross out the common factor, which is 4. 100 divided by 4 is 25. we're now left with [tex]25x^{3}[/tex].

so, [tex]25x^{3}[/tex] is the answer

Answer:

5 : 1

Step-by-step explanation:

Selling price = 37.90

Cost price = 7.58

Selling price : cost price = 37.90 : 7.58

When simplifying, we can first check if one number is a factor of the other:

7.58 * 3 = 22.74

7.58 * 4 = 30.32

7.58 * 5 = 37.9

Perfect. Therefore, selling price = 5 * cost price and selling price: cost price = 5:1

Step-by-step explanation:

[tex]thanks \: you \: the \: point \\ pls \: follow \: me[/tex]

Answer:

3750

Step-by-step explanation:

2250/45=50

50x75=3750

Answer:

18 minutes

Step-by-step explanation:

7.2 litres is 7200ml

each minute 400ml leaves the tank

so the question being asked is how many 400's are there in 7200...

7200 divided by 400 is 18.

Answer:

Look at the screenshots

Step-by-step explanation:

Answer:

Above is the answer, coupled with a detailed step-by-step explanation. Thank you!

Answer:

0.5

Step-by-step explanation:

→ Find the difference in y

7 - 3 = 4

→ Find the difference in x

9 - 1 = 8

→ Divide the results

4 ÷ 8 = 0.5

Answer:

The slope is 1/2 (m=1/2)

Step-by-step explanation:

Use the slope formula: [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex] to solve for the slope. y2 is 7, y1 is 3, x2 is 1, x1 is 9. [tex]\frac{7-3}{9-1}=\frac{4}{8} = \frac{1}{2}[/tex]

We know that the triangle is an isosceles triangle because the base angles are the same.

Therefore, the answer is 'x = 2'

Hoped this helped.

[tex]BrainiacUser1357[/tex]

Answer: I'm not sure what Savvas is, but the answer to your second question is 23.68.

Step-by-step explanation: This can be solved using the stacking method of multiplication, like so:

6.4

x3.7

You would multiply this equation as if there are no decimals, (first doing 7x4, and then 7x6 + 2, then adding a zero to your ones place at the bottom, and doing 3x4, the 3x6 + 1), to get 2348. You then would add the decimals in by moving over 2 places to the left.

Answer: 10230

Step-by-step explanation:

The amount in pound is 1230 pounds.

The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.

For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.

12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.

As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.

This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.

Given:

1 ton is equal to 2,000 pounds.

So, 5 tons  and 230 pounds

= 5 x 2000 + 230

= 1000 + 230

= 1230 pounds.

Learn more about Unitary Method here:

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#SPJ6

Answer:

that depends if it's taken in consideration the pizzas that he ate were from the 40 slices or not

Answer:

he ate 5 slices

Step-by-step explanation:

Step-by-step explanation:

30/4 = 7.5 per hour

now,

7.5 × 19 = 142.5

$142.5

Answer:

$142.50

Step-by-step explanation:

30 divide by 4 = 7.5

So each hour the worker would earn $7.50

7.5 x 19= The worker will earn 142.50 after working 19 hours.

The value of the variable 'y' will be square root 21 that is √21.

The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180 °.

The ratio of the matching sides will remain constant if two triangles are comparable to one another.

The ratio of the corresponding sides of a similar triangle remains constant. Then the equation is given as,

y / 3 = 7 / y

Simplify the equation, then we have

y / 3 = 7 / y

y² = 21

y  = √21

The value of the variable 'y' will be square root 21 that is √21.

More about the triangle link is given below.

https://brainly.com/question/25813512

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The phrases that can be represented as the algebraic expression, 3n - 3 are: Option 3 and Option 5.

Let's translate each of the given phrases to algebraic expressions in order to determine which of them can be represented as 3n - 3.

Option 1:

3 fewer than n is represented as, n - 3

Option 2:

difference between n and 3 is represented as, n - 3.

Option 3:

3 times n is 3n

3 fewer than 3n is represented as 3n - 3.

Option 4:

product of 3 and n is represented as 3n.

Option 5:

3 less than 3n is represented as 3n - 3.

Therefore, the phrases that can be represented as the algebraic expression, 3n - 3 are: Option 3 and Option 5.

Learn more about algebraic expression on:

https://brainly.com/question/2164351

Answer:

x = 4

Step-by-step explanation:

    The angle markings at the bottom of the triangle mean they are congruent. Since they are the only two congruent to each other, that means this triangle is an isosceles triangle.

    In an isosceles triangle, not only are the bottom angles congruent, their opposing sides are congruent as well. In this instance, that means 9x - 8 = 28. Knowing that we can solve for x.

[tex]9x-8=28\\\\9x-8+8=28+8\\\\9x=36\\\\\frac{9x}{9}=\frac{36}{9}\\\\x=4[/tex]

Answer:

Step-by-step explanation:

9x - 8 = 28 ( converse of isosceles triangle )

(If two angles of a triangle are congruent , then the sides opposite to these angles are congruent.)

[tex]9x - 8 = 28 \\ 9x - 8 = 28 + 8 \\ 9x = 36 \\ \frac{9x}{9} = \frac{36}{9} \\ x = 4 \\ [/tex]

Answer:

31

Step-by-step explanation:

Answer:

Answer #3

Step-by-step explanation:

The ratio of sugar to flour is 2:1, so the x values need to be twice as big as the y values in the points.