4. A hot air balloon hovers 100 feet about the ground. The balloon is tethered to the ground with a
rope that is 250 feet long. At what angle of elevation, is the rope attached to the ground? Round
you answer to the nearest degree.
Answers
Answer:
[tex]\theta=24^\circ[/tex]
Step-by-step explanation:
Trigonometry and Right Triangles:
The ratios of the sides of a right triangle are called trigonometric ratios. Any angle or side length can be calculated using the appropriate trigonometric ratio.
Please refer to the image below. The balloon is 100 feet high and the rope has a length of 250 feet. The right triangle formed allows us to apply a trigonometric ratio that relates the two given side lengths: the hypotenuse and the opposite leg to angle θ.
The sine ratio is defined as:
[tex]\displaystyle \sin\theta=\frac{\text{opposite leg}}{\text{hypotenuse}}[/tex]
[tex]\displaystyle \sin\theta=\frac{100}{250}=0.4[/tex]
[tex]\displaystyle \sin\theta=0.4[/tex]
Calculating θ:
[tex]\theta=\arcsin 0.4[/tex]
[tex]\theta=23.6^\circ[/tex]
To the nearest degree:
[tex]\mathbf{\theta=24^\circ}[/tex]
Related Questions
solve the equation or inequality.
5t - 3 (7t + 1) < 93
Answers
Step-by-step explanation:
5t-3(7t+1) < 93
Remove the parentheses
5t-21t-3 < 93
-16t < 93+3
-16t < 96
Divide both sides by 16
-t<96/16
-t<6
t > -6
Answer: The inequality t < 6 is the correct answer.
Step-by-step explanation:
5t - 3 (7t + 1) < 93 <--- This is the original equation.
5t + (7t + 1) - 3 < 93 <---- Use commutative property.
16t - 3 < 93 <--- Simplify
16t - 3 + 3 < 93 + 3 <---- Add 3 to both sides,
16t < 96 <--- Simplify and do addition.
[tex]\frac{16t}{16}[/tex] < [tex]\frac{96}{16}[/tex] <--- Divide both sides by 16.
t < 6 <--- is the answer to the inequality.
Hope this helps! :D
find the number that belongs in the green box.
round your answer to the nearest tenth.
Answers
Step-by-step explanation:
By Sine Rule, 13/sin96° = x/sin25°.
Hence, x = 13sin25°/sin96° = 5.5.
-2y - 3y + 8 = 8 -5y - 12
solve this equation fast please
Answers
What we need to do is cancel both like terms on both sides of this equation which is
8=8 and you remove them.
Then you are left with -2y-3y=-5y-12
What you need to do is add -2y-3y because they are like terms
Now you have -5y
Then you put -5y=-5y-12
So you have to now cancel equal terms on both sides of this equation which were “-5y=-5y”, then you turn them into a 0
Now you are left with 0=-12
Therefore the statement is false for any value of y.
7th grade math help lol
Answers
Step-by-step explanation:
F and C, I think those are the only ones
Solve the system of equations.
y=4x
y = x^2 + 3
A. (-1, -4) and (3, 12)
B. (0, 3) and (1, 4)
C. (1, 4) and (3, 12)
D. (-3, -12) and (-1, -4)
Answers
Answer:(1,4) and (3,12)
Step-by-step explanation
If 15 ounces of candy cost $3.75 what is the price per unit
Answers
Answer:
$0.25 per ounce
Step-by-step explanation:
3.75 divided by 15 is 0.25
Answer:
0.25 per ounce
Step-by-step explanation:
3.75 divided by 15 is 0.25
Two years ago Juanita bought 2 shirts for $15 and last year she bought 4 shirts for $45. Assuming the prices will increase linearly, how much will 8 shirts cost Juanita this year?
Answers
Answer:
This year, Juanita will have to use $75.
Step-by-step explanation:
Because if 2 shirts is $15, 4 shirts will be $30. $45 is $15 more than $30, so the increase is $15. 2*4 is 8, so that will make it 15*4=60. 60+15=75.
Given: x + y = 10.
If x = -21, what is y?
Answers
You have to work backwards to isolate y. You would at 21 to both sides and get y = 31
Answer:
31.
Step-by-step explanation:
-21 + 31 = 10
x + y = 10
y = 31
Duane recorded the temperature outside his window one morning. On the second day, the temperature went up 7 degrees. On the third day, the temperature went down 10 degrees. On the fourth day, the temperature went down 6 degrees, and it was 1°F. What was the temperature on the first day?
Answers
Answer:
The temperature on the first day was 10 °F.
Step-by-step explanation:
Let's find the temperature in every single step starting from the fourth day:
[tex]T_{4} = T_{3} - 6 F = 1 F[/tex]
[tex] T_{3} = 1 F + 6 F = 7 F [/tex]
Then, the temperature of the third day was 7 °F
On the third day:
[tex] T_{3} = T_{2} - 10 F = 7 F [/tex]
[tex] T_{2} = 7 F + 10 F = 17 F [/tex]
Hence, the temperature on the second day was 17 °F.
Now, on the second day:
[tex]T_{2} = T_{1} + 7 F = 17 F[/tex]
[tex] T_{1} = 17 F - 7 F = 10 F [/tex]
Therefore, the temperature on the first day was 10 °F.
I hope it helps you!
7. The lifetime of a certain brand of tires is approximately normally distributed, with a
mean of 40,000 miles and a standard deviation of 2,500 miles under normal driving conditions.
Tire wear is greatly affected by road, weather and driver conditions along with proper
maintenance of the tires. A driver who aggressively accelerates or makes quick stops, for
example, will wear out a tire much more quickly. The brand carries a warranty of 33,000 miles
under normal driving conditions, i.e., the company will replace a tire if it wears out before this
mileage limit is reached.
Answers
Answer:
0.0025551
Step-by-step explanation:
Given that:
Mean (m) = 40000
Standard deviation (s) = 2500
P(x < 33,000) :
USing the relation to obtain the standardized score (Z) :
Z = (x - m) / s
Z = (33000 - 40000) / 2500 = - 2.8
p(Z < -2.8) = 0.0025551 ( Z probability calculator)
Probability of Tyre wagering out before mileage limit is reached = 0.0025551
A cork has a mass of 3 grams and a volume of 16 cm3
. Calculate the density.
Answers
Answer:
0.1875, or 3/16
Step-by-step explanation:
The formula for density is mass/volume.
I hope this helps :)
Answer:
[tex]{\boxed {\sf \frac{3}{16} \ g/cm^3}}[/tex]
or
[tex]\boxed {\sf 0.1875 \ g/cm^3}}[/tex]
Step-by-step explanation:
Density can be found by dividing the mass by the volume.
[tex]\rho= \frac{m}{v}[/tex]
The mass of the cork is 3 grams and the volume is 16 cubic centimeters.
[tex]m= 3 \ g\\v= 16 \ cm^3[/tex]
Substitute the values into the formula.
[tex]\rho = \frac{3 \ g }{16 \ cm^3}[/tex]
Divide.
[tex]\rho=\frac {3}{16} \ g/cm^3[/tex]
[tex]\rho=0.1875 \ g/cm^3[/tex]
The density of the cork is 3/16 or 0.1875 grams per cubic centimeter.
Write a real-world problem that can be solved using the equation 9+4x=21−2x.
Answers
1. you have to subtract 9 from both sides. 21-9= 12
2. you have to add 2x to both sides. 4x+2x= 6x
3. 6x divided by both sides =
4.x=2
Wahts the value of N
Answers
Answer:
n=7
Step-by-step explanation:
33-19÷2= 7
sorry if my answer is wrong
8x-17+5x+19
Solve for x & find the converse
Answers
Answer:
4 if rong so so sorry
Step-by-step explanation:
What are the variables in each graph? Describe how the variables are related at various
points on the graph.
Answers
9514 1404 393
Answer:
variables: time, volumepoints show volume at a given timeStep-by-step explanation:
The axes labels give you a clue as to the variables: time, volume.
__
The graph is a plot of volume versus time. That is, each point is the volume at a particular time.
help needed!!! OVER DUE ASSIGNMENT! click picture!!
Answers
Answer:
Step-by-step explanation:
x= 6/2=3 ; y = 59° ( it opposes the side that is 10/2=5)
2) x= 6/2 =3
Use the information to answer the question.
Liz types at a rate of 25 words per minute. The graph shows the number of words typed over time by 4 other students.
Which student types at the same unit rate of words per minute as Liz?
please help!
Answers
This is because if she types 25 words in one minute then that means she can type 50 words in 2 minutes (just multiply by 2). The only person on the graph who can type 50 words in 2 minutes is Britt.
Hope this helps! Any questions let me know :)
Subtract the sum of −7 and 13 from the sum of −2 and −9 *
Answers
Answer:
-17
Step-by-step explanation:
The sum of -2 and -9 is (-2) + (-9) = -2 - 9 = -11.
The sum of -7 and 13 is 13 - 7 = 6.
Hence, subtracting 6 from -11 would be -11 - 6 = -17.
Hope this helped!
Norman is a sunflower farmer. He uses a plot of
land that is 3 km by 4.3 km. How much land
does he use for his sunflowers
Answers
Answer: 12.9 square km
Step-by-step explanation: 4.3 x 3 =12.9
What information can be used to compare linear relationships? Explain why.
Answers
Answer:the slope and the y intercept (you can tell there linear if the slope is the same and the y-intercepts are different).
Step-by-step explanation:
Answer:
Sample Response: Linear relationships can be compared using their initial values, or y-intercepts, and their rates of change, or slopes. Initial values can tell you which relationship started with a greater value. Comparing slopes can tell you which relationship is rising or falling faster.
Step-by-step explanation:
tree+snowman+tree=17
raindeer+raindeer+snowflake=12
raindeer=snowflake
raindeer-3=snowman
then what does tree equal
Answers
Answer:
Step-by-step explanation:
Monke
Define a variable. Write and solve each equation.
9. Anna wants to take horseback riding lessons.
She is given $200 for her birthday to cover the
cost. She has to pay $20 for grooming supplies.
If the lessons are $30 an hour, how many lessons
can Anna take?
Answers
The answer is x = 6
Let us first define x to be the number of hours of riding lessons she can take.
X = Hours of lessons
Now, she has $200, she needs to pay $20 for grooming supplies, and the lessons cost $30 an hour. We to find the maximum amount of hours of lessons she can take, so in other words, we want to make her broke. To do this, we first convert the words into an equation:
200 - 20 - 30x = 0
Simplifying, we get
180 = 30x
x=6
In which story is the answer to the question 0?
1:
Neil felt sick, so his grandma took his temperature. She said his temperature
was 2°F above the normal human body temperature. At dinner time, his
temperature was 2°F higher than it was that morning. What is the difference
between Neil's temperature now and the normal human body temperature?
2:
Neil felt sick this morning, so his grandma took his temperature. She said his
temperature was 2°F above the normal human body temperature. At dinner
time, his temperature was 2°F lower than it was that morning. What is the
difference between Neil's temperature now and the normal human body
temperature?
Answers
Answer:
2
Step-by-step explanation:
It was +2 in the morning. -2 would make it 0.
the second story is the answer
Does anyone wanna help ya girl out?? I’ll give brainliest for best answer (it’ll go who answers first, and how helpful the answer is)... you’ll also get 20 points teehee :)
Answers
Answer: 1, 2, and 4
Step-by-step explanation:
An iPhone is on sale for $450. It originally cost $500. What percent off is the sale offering?
Answers
Answer:
10% off
Step-by-step explanation:
A sports store is having a 20% off sale on skis. The original price of the ski is $560.00
The tax rate is 8.5%. What is the total cost of the skis?
Answers
Answer:
Total cost: 486.080$
Step-by-step explanation:
Original Price: 560.000$
Sale: 20%
Discount: 560.000$ * 20% = 112.000$
Discounted Price: 560.000$ - 112.000$ = 448.000$
Tax Rate: 8.5%
Tax: 448.000$ * 8.5% = 38.080$
Tax after Tax: 448.000$ + 38.080$ = 486.080$
The point-slope form of a line that has a slope of Two-thirds and passes through point (6, 0) is shown below.
y minus 0 = two-thirds (x minus 6)
What is the equation in slope-intercept form?
Answers
Answer:
c
Step-by-step explanation:
(x+1)-6(x+1)+8 how to factorise it?
Answers
Answer:
Step-by-step explanation:
If you have written the question correctly, then you don't need to factor it. You only need to remove the brackets.
x + 1 + 6x + 6 + 8
7x + 15 is your final answer.
However, I think the question is
(x + 1)^2 + 6(x + 1) + 8
Let y = x + 1
y^2 + 6y + 8
(y + 2)(y + 4)
(x + 1 + 2 ) ( x + 1 + 4)
(x + 3)(x + 5)
HELP PLZ TEXT MESSAGE: The cost of a text message increases from $0.10 per messages to $0.25 per message. What is the percent increase in the cost of sending a text message?
Answers
0.2x+40=50
0.2x = 10
5(0.2x) = 5(10)
x = 50
Therefore, 50 text messages would have to be sent or received in order for the plans to cost the same each month.
write an equation in slope intercept form for the line that passes through (1,-1) and is parallel to the line described by y=2x-4
PLEASE HELP:(((((
Answers
If 2 lines are parallel, their slopes are the same, so all we need to do is plug in the given point and slope in the equation y = mx + b and solve for b.
[tex]-1 = 2(1) + b\\\\-1 = 2 + b\\\\-3 = b[/tex]
The equation of a line in slope-intercept form that goes through (1, -1) and is parallel to the line y = 2x - 4 is [tex]y = 2x - 3[/tex].