An observatory is 150 feet high. When a person is standing in the observatory looking at an island, the angle of depression is . What is the approximate horizontal distance from the observatory to the island?
A. 70 feet
B. 166 feet
C. 322 feet
D. 355 feet

When it is asking you to solve a system of equations, it means that it wants you to find the value of the variables, in this case, x and y.

3x + 2y = 1  -- equation 1

y = x - 12 -- equation 2

Put (equation 2)'s value of y into (equation 1)

3x + 2(x-12) = 1

3x + 2x - 24 = 1

5x - 24 = 1

5x = 25

x = 5 -- equation 3

Put (equation 3)'s values of x into (equation 2)

y = 5 - 12 = -7

Thus the solutions are x = 5 and y = -7 and we have solved the system of equations.

Hope that helped!

Answer:

7.5 mm

Step-by-step explanation:

To find the length of the earing,  you need to divide 39 by 2.5
39/2.5=7.5
Hope this helps :)

Answer:

4 sessions.

Step-by-step explanation:

He starts with 10 minutes practiced and has to finish his quota in 20 minute sessions, so we can represent that with the equation 90=20x+10. Then solve for x.

90=20x+10

Subtract 10

80=20x

Divide by 20

x=4

It would take 4 sessions.

Answer:

1 10 min session + x 20 min sessions = 90 min

10+20x=90

20x=80

x=4 sessions

Answer:

8

Step-by-step explanation:

Exponent of x = 6

Exponent of y = 2

Degree of the monomial = 6 + 2 = 8

Answer:

33

Step-by-step explanation:

Using the Intersecting Chords Theorem

For any two Intersecting Chords --->  UC*CW=TC*CV

By Substituting --->  12(2x+5)=14(2x+2)

By Expanding   --->  24x+60=28x+28

Then --> 28x-24x=60-28

Then --> 4x=32

So x=32/4=8

Now to get UW,,  UW=UC+CW=12+(2x+5)=2x+17

By Substituting by x=8

UW=2x+17=2*8+17=33

Answer: 436

Step-by-step explanation: 18,800 divided by .03 equals 564-128=436

Answer:

Step-by-step explanation:

diameter = 4.275"

r = 4.275 ÷ 2 = 2.1375"

Area of circle = πr²

                      = 3.14 * 2.1375 * 2.1375

                      = 14.3463

                     ≈ 14.3 in²

Answer:

x = 10

y = 42

Step-by-step explanation:

The sum of a number and two times a smaller number is 62

2x+y=62

so y=62−2x

Three times the bigger number exceeds the smaller number by 116

x+116=3y

substitute for y:

x+116=3(62−2x)

x+6x=186−116

7x=70

x=10

3y=10+116=126

#y = 126/3 = 42

The chords from the center of the circle will be 5 cm. Apply pythogorous to find the distance of chords from the center of the circle.

It is a point locus drawn equidistant from the center. The radius of the circle is the distance from the center to the circumference.

Given data;

Diameter,d=26 cm

Chord, PQ, = 24 cm

P is the chord from the center of the circle

All the given dimensions shown in the digrame are in the centimeter.

The chords from the center of the circle are found by the pythogorous theorem;

From Δ DCB

The value of the side p is;

h²=p²+b²

13²=p²+12²

169=p²+144

p=5 cm

Hence, the chords from the center of the circle will be 5 cm.

To learn more about the circle, refer to the link: https://brainly.com/question/11833983.

#SPJ1

Answer:

D a n I s h K r o n e ...........

I Think The Answer Is krone

Answer:45 degree angle

Step-by-step explanation: am smart

Answer:

22°

..........

......

......

.....

.....

......

Answer:

the answer is 160 that the answer

Answer:

20

Step-by-step explanation:

To find the median, first, arrange the numbers from smallest to greatest. We have 18, 18, 22, 22. Next, find the number in the center. In this case, there are two numbers in the middle and it doesn't easily fall under one number. In this case, find the average of the two numbers. We have (18+22)/2 = 20. Therefore, the median of 18, 18, 22, 22 is 20.

The solution of inequality shows that the range is x >8.

The domain of a function is the set of input values for which the function is real and defined. In the other words, when you define the domain, you are indicating for which values x the function is real and defined.

While the domain is related to the values ​​of x, the range is related to the possible values ​​of y that the function can have.

Inequality is a mathematical expression that does not present equality between both sides. It is represented by symbols: <, ≤, > and ≥.

For solving this question, you should convert the text of the problem into an algebraic expression. Consequently, you will have:

                                           x+9 > 17

                                           x > 17-9

                                           x > 8

Therefore, the range is x>8.

Learn more about the range here:

https://brainly.com/question/10197594

Answer:

2 of them are perfect numbers and they are 6 and 28

Step-by-step explanation:

because they are one of the first 5 perfect numbers!

Hope this helps :)

Answer:

(0,4)

Step-by-step explanation:

Multiply each point by 1/3

0 x 1/3 = 0

12 x 1/3 = 4

Answer:

slope=0

Step-by-step explanation:

The required slope of the line is zero which implies that the given line is parallel to the x-axis.

The slope of the line is a tangent angle made by line with horizontal. i.e. m =tanx where x in degrees.

here,
The slope of the line that passes through the points (−10,−8) and (−9,−8) is given as,

m = (y₂ - y₁) /  (x₂ - x₁)

Substitute values in the above equation,
m = -8 + 8 / -9 +10
m = 0

Thus, the required slope of the line is zero which implies that the given line is parallel to the x-axis.

Learn more about slopes here:

https://brainly.com/question/3605446

#SPJ2

Answer:

Hope it helps bhhhhbbbbbbhb

Answer:

S234tep-by-step explanation:

36*6.50

=234

Answer:

12%

Step-by-step explanation:

Answer:

3y ≤ 1/2x

Step-by-step explanation:

please give brainliest!!

3 times y is less than or equal to half of x can be written as 3y ≤ x/2 or x ≥ 6y.

Expressions are mathematical statements which consist of two or more terms and terms are connected to each other using mathematical operators like addition, multiplication, subtraction and so on.

Given that,

three times y is less than or equal to half of x can be written.

Three times y means that 3 is multiplied to y.

Half of x means that x is multiplied to 1/2.

This is an inequality expression.

We can write it as,

3y less than or equal to x/2.

3y ≤ x/2

Multiplying both sides by 2,

6y ≤ x

or x ≥ 6y

Hence the inequality expression is x ≥ 6y.

Learn more about Inequality Expressions here :

https://brainly.com/question/17356086

#SPJ7

The code for Escape Room is MCYHW.

Inequalities is a mathematic expression that do not present equalitiy between both sides. It is represented by symbols: <, ≤, > and ≥.

For solving this exercise, firstly, you should solve the inequalities identified by letters: H, W, M, Y and C. After that, you should relate yours anwers with the options given for the exercise.

                       [tex]-11x-4 > -15\\ \\ -11x > -15+4\\ \\ -11x > -11\; *(-1)\\ \\ 11x < 11\\ \\ x < 1[/tex]

Therefore, you should connect H with x<1.

                       [tex]32 > -16x\\ \\ Rewriting \\ \\ -16x < 32 \\ \\ -16x < 32\; *(-1)\\ \\ 16x > -32\\ \\ x > \frac{-32}{16} \\ \\ x > -2[/tex]

Therefore, you should connect W with x>-2.

                       [tex]3+x\leq -9\\ \\ x\leq -9-3\\ \\ x\leq -12[/tex]

Therefore, you should connect M with x≤-12.

                       [tex]-7x+7\leq -56\\ \\-7x\leq -56-7\\ \\ -7x\leq -63\\ \\ -7x\leq -63\; *(-1)\\ \\ 7x\geq 63\\ \\ x\geq \frac{63}{7} \\ \\ x\geq 9[/tex]

Therefore, you should connect Y with x≥9.

                       [tex]-20\geq -5x+15\\ \\Rewriting\\ \\ 5x+15\leq -20\\ \\ -5x\leq -20-15\\ \\ -5x\leq -35\\ \\-5x\leq -35\; *(-1)\\ \\ 5x\geq 35\\ \\ x\geq \frac{35}{5} \\ \\ x\geq 7[/tex]

Therefore, you should connect C with x≥7.

Thus, the sequence is:

M - [tex]x\leq -12[/tex]

C - [tex]x\geq 7[/tex]

Y- [tex]x\geq 9[/tex]

H- [tex]x < 1[/tex]

W- [tex]x > -2[/tex]

Read more about inequalities here.

https://brainly.com/question/25275758

Answer:

792 cm

Step-by-step explanation:

8*9*11=792

72*11=792

72+720=792

Answer:

The answer is 396 i hope it helps!

Answer:

A

Step-by-step explanation:

I agree with Katie because number is legs is directly proportional to the number of ants.

1 ant has 6 legs.

So, 2 ants have 6 *2 = 12

3 ants have 6*3 = 18

Answer:

[tex]\frac{43}{100}[/tex]

Step-by-step explanation:

Think of it as a percentage. 43% is [tex]\frac{43}{100}[/tex] , but it is also 0.43. Any number over 100 will be put into a similar decimal format ([tex]\frac{12}{100}[/tex] = 0.12  and [tex]\frac{4}{100}[/tex] = 0.04)

The fraction with a denominator of 100 is equivalent to 0.43 is,

[tex]\frac{43}{100}[/tex].

Here,

We have to find fraction with a denominator of 100 is equivalent to 0.43.

What is Fraction?

A fraction is used to represent the portion/part of the whole thing.

Now,

Let a fraction with a denominator of 100 is [tex]\frac{x}{100}[/tex].

And, its equivalent to 0.43.

Hence,

[tex]\frac{x}{100} = 0.43[/tex]

[tex]x = 43[/tex]

So, A fraction with a denominator of 100 is [tex]\frac{43}{100}[/tex].

Which is equivalent to 0.43.

Learn more about the Fraction visit:

https://brainly.in/question/5112127

#SPJ2

Answer:

28 square units or 28 units^2

Step-by-step explanation: