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The tangent or tanθ in a right angle triangle is the ratio of its perpendicular to its base. The distance from point A to point B is 763.752ft.

The tangent or tanθ in a right angle triangle is the ratio of its perpendicular to its base. it is given as,

[tex]\rm Tangent(\theta) = \dfrac{Perpendicular}{Base}[/tex]

where,

θ is the angle,

Perpendicular is the side of the triangle opposite to the angle θ,

The base is the adjacent smaller side of the angle θ.

A.) The distance between the boat and the lighthouse when the angle of depression is 10°.

Tan(10°) = Height of lighthouse/ distance between the boat and the lighthouse

Distance between the boat and the lighthouse

= 145/Tan(10°) = 822.336ft

B.) The distance between the boat and the lighthouse when the angle of depression is 68°.

Tan(68°) = Height of lighthouse/ distance between the boat and the lighthouse

Distance between the boat and the lighthouse

= 145/Tan(68°) = 58.584ft

The distance between point A and B = 822.336ft - 58.584ft = 763.752 ft

Hence, the distance from point A to point B is 763.752ft.

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Answer:

764

Step-by-step explanation:

Rounded. Just did the question

Answer:

It is B kid you need to study this is basic shhhhhiz

Step-by-step explanation:

Answer:

it is B kid you need to study

Answer:

Step-by-step explanation:

4^-3

= 1/4^3

4^-18

= 1/4^18.

Answer:

2, 9 , 16 , 23 , 30 ......

Step-by-step explanation:

[tex]a_n = 7n - 5[/tex]

       [tex]a_1 = 7*1 - 5 = 7-5 = 2\\\\a_2 = 7*2 - 5 = 14 - 5 = 9\\\\a_3 = 7*3 - 5 = 21 - 5 = 16\\\\a_4= 7*4 - 5 = 28 - 5 = 23\\\\a_5= 7*5 - 5 = 35 - 5 = 30[/tex]

Answer:

200 feet of the ground at a thirty degrees angle does not make a difference .

u need to know whether it is the top or bottom of it, the kite

Answer:

the aa similarity postulate

Step-by-step explanation:

no sides are given and we can not simply assume the sides are congruent, however we do know two of the angles on both triangles are the same allowing us to know that the third therefore must also be the same.

both traingles share angle MAN

and AMN and ABC are equal so therefore

angle ANM and ACB must also be the same

Answer:

Step-by-step explanation:

Answer:

No, this isn't a right triangle.

Step-by-step explanation:

To check if the triangle is right we can use Pythagorean Theorem. If the equation turns out as true, the triangle is right.

Pythagorean Theorem

[tex]c^2 = a^2 + b^2[/tex]

c ... hypotenuse

a ... one leg

b ... another leg

The longest side in a right triangle is always hypotenuse, therefore we use the side which is 13 cm long as hypotenuse.

[tex]c^2 = a^2 + b^2\\13^2 = 4^2 + 12^2\\169 = 16 + 144\\169 = 160[/tex]

Number 169 isn't equal to 160 so the equation is false. That means that the triangle is not right.

Answer:

12

Step-by-step explanation:

22n + 17(20 - n) = 400 ← distribute parenthesis and simplify left side

22n + 340 - 17n = 400

5n + 340 = 400 ( subtract 340 from both sides )

5n = 60 ( divide both sides by 5 )

n = 12

there are 12, 22 cent stamps in the book

The angle that will be formed by the cable based on the information given will be 15°.

From the complete information, it's important to divide the total angle by 12. This will be:

= 360°/12 = 30°

Then, the relations that will be used will be:

= 1/2(60° - 30°)

= 1/2 × 30°

= 15°

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Answer:

∠FDE or ∠GDA

Step-by-step explanation:

The adjacent angle refers to the angle which lies right next to an angle, and the sum of the angles is 180, meaning they are supplementary.

Here, in this diagram, there are 2 adjacent angles for ∠FDG :

Answer:

monomial

Step-by-step explanation:

it is correct

Step-by-step explanation:

sqrt(5x - 2) <= 3

5x - 2 <= 9

5x <= 11

x <= 11/5

but also : 5x -2 >= 0

otherwise the square root is not valid for real numbers.

5x >= 2

x >= 2/5

so the solution is for all x out of R (real numbers), where

2/5 <= x <= 11/5

Answer:

6

explanation

[tex]since \: they \: are \: similar \\ \frac{x + 2}{32} = \frac{3}{12} \\ crossmultiplying \\ 32 \times 3 = 12(x + 2) \\ 96= 12x + 24 \\ 12x = 96 - 24 \\ 12x = 72 \\ dividing \: bothsides \: y \: 12 \\ x = \frac{72}{12} \\ x = 6[/tex]

Answer: No solutions

Step-by-step explanation:

    There are no solutions to 0 = x² - x + 1.

[Method One]

   We can solve this by rewriting the equation, but it is quicker to graph it when there are no solutions. See attached.

[Method Two]

 I said we can solve this by solving an equation, here it is. We will use the quadratic formula since the equation given is already in the proper form.

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

[tex]\displaystyle x=\frac{1\pm\sqrt{(-1)^2-4(1)(1)} }{2(1)}[/tex]

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

   -> Negative numbers don't have real square roots, so there is no solution

Answer:

Yes, it is in the tenth place, and it is 5 thousand is 10,000 times more than the 5 in the tenth place

Step-by-step explanation:

3 = ones place

.5 = tenths place

.04 = hundredths place

.005 = thousandth place

for the second question all you need to do it

5000 divided by .5 = 10000 (because they both have 5, don't try this if there are :example: 4 in the hundreds place to 3 in the one's place).

Answer:

The value of the 5 in the tenths place of 3.545 is 10 times the value of the 5 in the thousandths place

Step-by-step explanation:

i did the end of the year test for k12. good luck on your grade and i hope that this is right!

Answer:

Area of the paper required =7000 cm²

Step-by-step explanation:

Dimensions of an Aquarium:

Length (l) = 80 cm,

Breadth (b) = 30 cm,

Height (h) = 40 cm

/* According to the problem given,

Area of the paper required =

Area of the base + 2×Area of two side faces + Area of the back side

(Front side should be visible,So, it is not covered )

= lb+2×bh+lh

= 80×30+2×(30×40)+80×40

= 2400+2×1200+3200

= 2400+2400+3200

= 7000 cm²

Therefore,

Area of the paper required =7000 cm²

Step-by-step explanation:

Answer:

98°

142°

83°

97°

Step-by-step explanation:

m(arc)JL = 2 × 49° = 98°

m(arc)MJ = 360° - 120° - 98° = 142°

m<KJM = (120° + 46°)/2 = 83°

m<KLM = (360° - 120° - 46°)/2 = 97°

Answer:

  all are NO

Step-by-step explanation:

No integer ratio with 8 in the denominator can be equal to any integer ratio with 3 in the denominator.

__

The denominators 8 and 3 are relatively prime, so equivalent fractions using them cannot be formed with integers.

The equivalent to 4/3 has a mixed-number numerator that is greater than 8.

  [tex]\dfrac{4}{3}=\dfrac{10\frac{2}{3}}{8}[/tex]

This matches none of the offered choices.

Answer: what is the question? I will gladly sovle it

Step-by-step explanation:

tell me your questions and i will solve it asap. i know the area is 40 square millmetres but if you have a question i will gladly answer it.

Answer:

one time

Step-by-step explanation:

because after that you would subtract by 20

Answer:

2 : 3

Step-by-step explanation:

Given :

Solving :

8 red cards have been removed from the pack.

So, now the ratio is :

Answer:

  (a)  1 and 8

  (d)  64 and 125

Step-by-step explanation:

In addition to the cubes of 2 through 11 that you found in question 1, it is convenient to add 1³ = 1 to the list for the purpose of answering this question. The cubes of the first 11 integers are ...

  1, 8, 27, 64, 125, 216, 343. 512, 729, 1000, 1331

__

This question is asking you to find the numbers on either side of any that are not on the list:

  (a)  2 is between 1 and 8

  (d)  100 is between 64 and 125

Answers:  

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

Explanation:

Each term is separated by a plus sign or a minus sign. We could rewrite the 4ab-5b portion as 4ab + (-5b) to help get everything separated by a plus sign.

The five terms are

The coefficients are the numbers just to the left of the variable. For a term like 4ab, the coefficient is 4. For the term "m", we can think of it as 1m so we can see it has a coefficient of 1.

The constant term is the term that doesn't have any variable attached to it. That would be the "3" as the first term.

Answer: 3*(2x+y)

Step-by-step explanation:

Answer:

Centre (5,-9) and radius is 14

Step-by-step explanation:

The circle equation is of form,

[tex] = > {(x - a)}^{2} + {(y - b)}^{2} = {r}^{2} [/tex]

where centre is (a,b) and radius is 'r'.

Answer:

17/20

Step-by-step explanation:

1/4 +3/5 simplify into:

5/20 + 12/20= 17/20

Answer:

80%

Step-by-step explanation:

9 + 4 + 7 = 20

1 out of 20 = 5%

4 plums = 20%

Answer:

4/5 or 80%

Step-by-step explanation:

So u add up all the fruits which is 20. And then then u make a fraction which is all fruits but not plums over all fruits. So it is 16/20. The 16 came from not having the plums bc there are 4 plums and 20 - 4 = 16. Simplified of 16/20 is 4/5 or %80.

The conditional probabilities that are correct are P(D | F) =  6/34, P(E | D) = 7/25 and P(F | E) = 8/18

The formula to compute the conditional probability P(A|B) is:

P(A | B) = P(A and B)/P(B)

The above means that the probability of event A such that the event B has already occurred

When the above formula is applied to the give data in the complete, we have:

P(D | F) = 6/34

P(E | D) = 7/25

P(D | E) = 7/18

P(F | E) = 8/18

P(E | F) = 8/34

Hence, the conditional probabilities that are correct are P(D | F) =  6/34, P(E | D) = 7/25 and P(F | E) = 8/18

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Answer: a,b,d

Step-by-step explanation:

trust