1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
lubasha [3.4K]
3 years ago
8

June and Armando are each in a hot air balloon. Armando's balloon is at a slightly higher elevation than June's. The two balloon

s are 100 ft apart
June notices she must look up at an angle of 25° to see Armando in his balloon. How much higher is Armando than June?
Mathematics
1 answer:
Mandarinka [93]3 years ago
6 0

Answer:

46.63 ft

Step-by-step explanation:

I've drawn and attached a triangle diagram to represent this elevation and distance of balloons.

Now, from the diagram attached, we can see the angle at which June must look up to see Armando is 25°.

Also, the height of Armando above June is represented by "x".

Thus, using pythagoras theorem, we can find x.

Thus;

x/100 = tan 25

x = 100 × tan 25

x = 100 × 0.4663

x = 46.63 ft

You might be interested in
Calculate the discriminant to determine the number solutions. y = x ^2 + 3x - 10
Nataly_w [17]

1. The first step is to find the discriminant itself. Now, the discriminant of a quadratic equation in the form y = ax^2 + bx + c is given by:

Δ = b^2 - 4ac

Our equation is y = x^2 + 3x - 10. Thus, if we compare this with the general quadratic equation I outlined in the first line, we would find that a = 1, b = 3 and c = -10. It is easy to see this if we put the two equations right on top of one another:

y = ax^2 + bx + c

y = (1)x^2 + 3x - 10

Now that we know that a = 1, b = 3 and c = -10, we can substitute this into the formula for the discriminant we defined before:

Δ = b^2 - 4ac

Δ = (3)^2 - 4(1)(-10) (Substitute a = 1, b = 3 and c = -10)

Δ = 9 + 40 (-4*(-10) = 40)

Δ = 49 (Evaluate 9 + 40 = 49)

Thus, the discriminant is 49.

2. The question itself asks for the number and nature of the solutions so I will break down each of these in relation to the discriminant below, starting with how to figure out the number of solutions:

• There are no solutions if the discriminant is less than 0 (ie. it is negative).

If you are aware of the quadratic formula (x = (-b ± √(b^2 - 4ac) ) / 2a), then this will make sense since we are unable to evaluate √(b^2 - 4ac) if the discriminant is negative (since we cannot take the square root of a negative number) - this would mean that the quadratic equation has no solutions.

• There is one solution if the discriminant equals 0.

If you are again aware of the quadratic formula then this also makes sense since if √(b^2 - 4ac) = 0, then x = -b ± 0 / 2a = -b / 2a, which would result in only one solution for x.

• There are two solutions if the discriminant is more than 0 (ie. it is positive).

Again, you may apply this to the quadratic formula where if b^2 - 4ac is positive, there will be two distinct solutions for x:

-b + √(b^2 - 4ac) / 2a

-b - √(b^2 - 4ac) / 2a

Our discriminant is equal to 49; since this is more than 0, we know that we will have two solutions.

Now, given that a, b and c in y = ax^2 + bx + c are rational numbers, let us look at how to figure out the number and nature of the solutions:

• There are two rational solutions if the discriminant is more than 0 and is a perfect square (a perfect square is given by an integer squared, eg. 4, 9, 16, 25 are perfect squares given by 2^2, 3^2, 4^2, 5^2).

• There are two irrational solutions if the discriminant is more than 0 but is not a perfect square.

49 = 7^2, and is therefor a perfect square. Thus, the quadratic equation has two rational solutions (third answer).

~ To recap:

1. Finding the number of solutions.

If:

• Δ < 0: no solutions

• Δ = 0: one solution

• Δ > 0 = two solutions

2. Finding the number and nature of solutions.

Given that a, b and c are rational numbers for y = ax^2 + bx + c, then if:

• Δ < 0: no solutions

• Δ = 0: one rational solution

• Δ > 0 and is a perfect square: two rational solutions

• Δ > 0 and is not a perfect square: two irrational solutions

6 0
3 years ago
10. For a popular Broadway musical, the theater box office sold 356 tickets at $80 apiece, 275 tickets at $60 apiece, and 369 ti
V125BC [204]
I thank it is B you have to add all the tickets and times that by the the amount of money  
6 0
3 years ago
A backpack is on sale for 30% off. If the sales price is $15.75, what is the original price?
Kryger [21]

Answer:

Your answer is 16.05

Step-by-step explanation:

15.75 + 0.3 = 16.05

16.05 - 0.3 = 15.75

5 0
3 years ago
Una carraca contiene 2’5 decalitros de agua. ¿cuantas botellas de medio litro se necesitan para vaciar la garrafa? SI cada botel
emmainna [20.7K]
English please I can’t understand
8 0
3 years ago
Find a6 for an arithmetic sequence where a1=3x+1 and d=2x+6​
abruzzese [7]

Answer:

a₆ = 13x + 31

Step-by-step explanation:

The nth term of an arithmetic sequence is

a_{n} = a₁ + (n - 1)d

Here a₁ = 3x + 1 and d = 2x + 6 , then

a₆ = 3x + 1 + 5(2x + 6)

    = 3x + 1 + 10x + 30

    = 13x + 31

7 0
3 years ago
Read 2 more answers
Other questions:
  • Matt is showing his work in simplifying (6.2 − 1.6) − 4.4 + 7.8. Identify any error in his work or reasoning.
    13·1 answer
  • Solutions for 2x^2+18x=20, worth a TON, please only 100% answers ! Thank u !
    12·1 answer
  • Jala put $600 in an interest bearing account with a annual compound interest rate of 5%. Jala determined that after seven years,
    9·2 answers
  • Which of the following shows the correct order of the given numbers?<br> 1 5/8, 1 3/10, 1.6
    10·2 answers
  • HELP! Find the missing value for the exponential function represented by the table below.
    8·2 answers
  • Determine the next term in the geometric sequence. -1, -6, -36, -216, ??
    7·2 answers
  • What is the unit rate of the data if two points are (0,0) and (1,4)
    13·1 answer
  • 2 times as many as 8 is 20
    5·1 answer
  • A survey of Micki’s customers showed that 1,800 out of 2,200 of the customers buying carrots would buy organic carrots if the ca
    14·1 answer
  • Consider the function y 2x+3. which is true
    6·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!