From the side view, a gymnastics mat forms a right triangle with other angles measuring 60° and 30°. The gymnastics mat extends 5 feet across the floor. How high is the mat off the ground?
Answers
To find the height of the mat off the ground, we can use trigonometry.
Explanation:To find the height of the mat off the ground, we can use trigonometry. Since the angles of the right triangle formed by the mat are 60° and 30°, we can determine the height using the sine function. The sine of an angle is equal to the length of the side opposite the angle divided by the length of the hypotenuse.
In this case, the side opposite the 30° angle is the height of the mat, and the hypotenuse is the length of the mat, which is 5 feet. So, we have sin(30°) = height/5. Solving for the height, we get height = 5 * sin(30°) = 5 * 0.5 = 2.5 feet.
Therefore, the mat is 2.5 feet off the ground.
The correct answer is option B. The height of the gymnastics mat off the ground is [tex]\frac{5\sqrt{3}}{3}}[/tex] feet.
Given that the gymnastics mat extends 5 feet across the floor, this length corresponds to the side opposite the 60° angle in the right triangle.
Let's denote the length of the side opposite the 30° angle as [tex]$x$[/tex].
According to the properties of a 30-60-90 triangle, the side opposite the 60° angle is [tex]\sqrt{3}[/tex] times the side opposite the 30° angle, so we have:
[tex]\[ 5 = x\sqrt{3} \][/tex]
To find [tex]$x$[/tex], we divide both sides of the equation by [tex]$\sqrt{3}$[/tex]:
[tex]\[ x = \frac{5}{\sqrt{3}} \][/tex]
To rationalize the denominator, we multiply the numerator and the denominator by [tex]$\sqrt{3}$[/tex]:
[tex]\[ x = \frac{5\sqrt{3}}{3} \][/tex]
The complete question is:
From the side view, a gymnastics mat forms a right triangle with other angles measuring 60° and 30°. The gymnastics mat extends 5 feet across the floor. How high is the mat off the ground?
A. [tex]\frac{5}{2}[/tex] ft.
B. [tex]\frac{5\sqrt{3}}{3}[/tex] ft.
C. [tex]5\sqrt{3}}[/tex] ft.
D. 10 ft.
Related Questions
A drawer contains 4 red socks, 8 white socks, and 6 blue socks. Without looking, you draw out a sock, return it, and draw out a second sock. What is the probability that the first sock is white and the second sock is red?
Answers
An Octagon has the radius of 56 and an area of 10,391.9 square millimeters.
a1) What is the approximate perimeter of the octagon? Round to the nearest whole number.
A) 93
B) 186
C) 371
D) 1299
a2) What is the approximate length of one side of the octagon? Round to the nearest whole number.
A) 23
B) 46
C) 371
D) 1299
Answers
Answer:
Step-by-step explanation:
Alright, lets get started.
The area of octagon is given [tex]= 10391.9[/tex]
The formula for area of octagon with side a is = [tex]2(1+\sqrt{2} )a^2[/tex]
[tex]10391.9 = 2(1+\sqrt{2} )a^2[/tex]
hence ,
[tex]a^2 = \frac{10391.9}{2(1+\sqrt{2} )}[/tex]
[tex]a^2 = 2152.2329[/tex]
[tex]a = 46.39[/tex]
Hence the length of the side of the octagon is 46 : Answer
Now perimeter of the octagon will be = [tex]8*side length[/tex]
Hence the perimeter = [tex]8*46.39 =371.1[/tex]
hence the perimeter of the octagon is 371 : Answer
Hope it will help :)
Your friend's height is close to 180 centimeters. What is your friend's height close to in meters?
Answers
Answer:
The friend's height close to 1.8 meters.
Step-by-step explanation:
As given in the question
Your friend's height is close to 180 centimeters.
As
1 meter = 100 centimeter
[tex]1\ centimeter = \frac{1}{100}\ meters[/tex]
Now convert 180 centimeters into meters .
[tex]180\ centimeter = \frac{180}{100}\ meters[/tex]
[tex]180\ centimeter = 1.8 meters[/tex]
Therefore the friend's height close to 1.8 meters.
Paul bought a discount card for the bus. The card allows him to buy daily bus passes for $1.70. After one month, Paul bought 12 passes and spent a total of $25.40. How much did he spend on the student discount card?
Answers
Decide if the problems are parallel,perpendicular or neithet and why
1).12x-4y=8
2).3y=-x+5
3).y=1/3x-5
4).12x-10=4y
5).2/3×+2y=8
Answers
1).12x-4y=8 → y = 3.x + 2
2).3y=-x+5 → y = (-1/3)x +5/3
3).y=1/3x-5 → y = (1/3)x -5
4).12x-10=4y → y = 3.x - 5/2
5).2/3×+2y=8 → y = (-1/3).x +4
1) and 4) are parallel since they have the same slope (m=3)
2) and 5) are parallel (m = -1/3 = same)
1) and 2) are perpendicular since the product of their slopes = -1 [(3).(-1/3)]
1) and 5) are perpendicular ((3).(-1/3) = -1
2) and 4) are perpendicular ((3).(-1/3) = -1
4) and 5) are perpendicular ((3).(-1/3) = -1
two wheels are rolled simultaneously. The radius of the smaller wheel is r feet and the radius of the larger wheel 2r feet. If both wheels did a total of 4 rotations, how much further did the large wheel travel? PLEASE SHOW STEPS TYSM
Answers
So if we open the circumference of the circle into a straight line segment, the length of this segment is C=2πR≈2*3.14*R=6.28R
4 rotations mean 4 circumferences that is 4 segments of length 6.28R,
which makes a linear distance of 4*6.28R=25.12R
i: the radius of the smaller wheel is R=r, thus it covers a distance of 25.12r feet
ii: the radius of the smaller wheel is R=2r, thus it covers a distance of 25.12*2r=50.24r (feet)
50.24r is twice 25.12r, thus the larger wheel traveled Twice the distance of the smaller one.
Answer: the larger covered twice the distance of the smaller.
while his bank account balance was -$45 Dylan made 6 withdrawals of 9$ what was his new bank account balance?
Answers
6 withdrawals of 9$
6 times 9 is 54
He withdrew a total of 54$
-45 - 54
Is -99$
His new account balance is -99$
NEED HELP FAST!
1.
(08.05 LC)
A student is trying to solve the system of two equations given below:
Equation P: y + z = 6
Equation Q: 8y + 7z = 1
Which of the following is a possible step used in eliminating the y-term? (1 point)
(y + z = 6) • –8
(y + z = 6) • 7
(8y + 7z = 1) • 7
(8y + 7z = 1) • 8
Answers
Answer:
(y + z = 6) • –8
Step-by-step explanation:
Because in order to eliminate 8 you will need to multiply by a negative number so that you can eliminate a positive number.
Hope this helped!
Given the expression 5a2b – 13ab + 7a3 – 4b, do the following as instructed below:
1. Write the polynomial in descending order.
2. Classify the polynomial by the number of terms.
3. State the degree of the polynomial.
Thank you !!
Answers
A. The descending order of this expression is 7a^3+5a^2b-13ab-4b.
B. This is a polynomial.
C. This is a 3rd degree polynomial.
The given expression is
[tex]5 {a}^{2} b - 13ab + 7 {a}^{3} - 4b[/tex]
To write the polynomial in descending order means we should write in decreasing powers of
[tex]a[/tex]
So in descending order we have,
[tex]7 {a}^{3} + 5 {a}^{2}b - 13ab - 4b[/tex]
ANSWER TO QUESTION 2
When a polynomial is in simplified form and it has one term, we call it a monomial.
If a simplified polynomial has two terms,it is called a binomial.
If a simplified polynomial has three terms, it is called a trinomial.
If a simplified polynomial gas four or more terms, we just call it a polynomial.
The given polynomial
[tex]5 {a}^{2} b - 13ab + 7 {a}^{3} - 4b [/tex]
has four terms and it us in simplified form, so it is classified as polynomial.
ANSWER TO QUESTION 3.
The degree of the polynomial is the highest degree the polynomial has.
We calculate the degree by adding the exponents of the two variables of each term.
For instance the first term is
[tex]7 {a}^{3} = 7 {a}^{3} {b}^{0} [/tex]
[tex]degree = 3 + 0 = 3[/tex]
Since the highest degree is 3, we say the degree of the polynomial 3.
The legs of a right triangle are 3 units and 5 units. What is the length of the hypotenuse? Round your answer to the nearest hundredth.
4.00 units
2.83 units
5.83 units
8.00 units
Answers
Answer:
the answer is 5.83
Step-by-step explanation:
hope it helped :)
Todd and his brother Robert are going to use 512 square feet of their backyard for skateboard ramps. The shape of the backyard is rectangular, with the length twice as long as the width. What are the dimensions of the backyard? A(w) = 2w2 512 = 2w2 The width of the backyard is feet. The length of the backyard is feet.
Answers
Answer:
16ft by 32ft
Step-by-step explanation:
Answer:
The answer is 512 = 2w2 or C
Step-by-step explanation:
I just did the assignment
f(x) = –5x – 4 and g(x) = –3x – 2, find (f – g)(x).
Answers
f(x)-g(x)=
(-5x-4)-(-3x-2)=
-5x-4+3x+2=
-2x-2
(-5x-4)-(-3x-2)
(-5x-4)+3x+2
-5x-4+3x+2
-2x-4+2
-2x-2
Final answer: -2x-2
What is b-r-3,when b=9 and r=2
Answers
Substitute values
9-2-3
9-2=7
7-3=4
Final answer: 4
Want brainliest answer this
Answers
12 x 11 = 132
3*12=36
132+36 = 168 square feet
What is equivalent to this statement:4 is 80% of x
Answers
4/80*100=5
An equivalent statement to '4 is 80% of x' is 'x is 5'.
Explanation:The statement '4 is 80% of x' can be written as the equation 4 = 0.8x. To find an equivalent statement, we can solve this equation for x.
To solve for x, divide both sides of the equation by 0.8: x = 4 / 0.8 = 5.
Therefore, an equivalent statement is: x is 5.
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A rectangular aquarium is 2/3 filled with water and then is tilted on its side until the water level coincides with one edge of the bottom. During the process, 6 quarts of water are poured out. What is the volume of the tank in quarts?
Answers
Answer:
36 Quarts
Step-by-step explanation:
Let the volume of the Aquarium be x quarts.
Hence amount of water filled in it will be
[tex]\frac{2x}{3}[/tex] quarts
Also problem says that the tank is tilted until water level coincides with one edge of the bottom. At this position , the amount of water filled in the tank will be half of the total volume , as the slant water level will be the diagonal of the tank and a diagonal divides the tank in two halves.
Hence current volume of water in the tank will be
[tex]\frac{x}{2}[/tex]
And in this process the amount of water poured out is 6 quarts. It will the difference between the amount of water earlier in the tank and the amount of water in the tank now. Hence
[tex]\frac{2x}{3}-\frac{x}{2}=6[/tex]
[tex]\frac{4x-3x}{6}=6[/tex]
[tex]x=36[/tex]
Hence the volume of the tank is 36 quarts.
estimate 17.5×8.4 need help
Answers
Marneshia walked three over eight of a mile in three over five of an hour. What equation can be used to calculate her unit rate in miles per hour? three eighths over three fifths = five eighths mile per hour three eighths over three fifths = one and three fifths miles per hour three fifths over three eights = one and three fifths miles per hour three fifths over three eights = five eighths mile
Answers
Answer:
A in short is your answer
Step-by-step explanation:
A number, y, is equal to the difference of a larger number and 3. The same number is one-third of the sum of the larger number and 9. Which equations represent the situation?
a)x+y=3 and x-3y=-27
b)x+y=3 and x-3y=-9
c)x-y=3 and x-3y=-27
d)x-y=3 and x-3y=-9
Answers
Answer: x + y = 3 and x - 3 = -9
Step-by-step explanation:
What is the simplified form of 20 times x to the fifth power over 15 times y to the sixth power times the fraction 5 times y to the fourth power over 6 times x squared?
Answers
Lola takes the train from Paris to Nice. The distance between the two cities is about
920,000
920,000
meters. If the train travels at a speed of
230
230
kilometers per hour, how long will it take Lola to travel from Paris to Nice?
Answers
Hope this help you.
If the speed of the train is 230 km per hour. Then the time taken by the train from Paris to Nice will be 4 hours.
What is speed?The distance covered by the particle or the body in an hour is called speed. It is a scalar quantity. It is the ratio of distance to time.
We know that the speed formula
[tex]\rm Speed = \dfrac{Distance}{Time}[/tex]
Lola takes the train from Paris to Nice.
The distance between the two cities is about 920,000 meters.
If the train travels at a speed of 230 kilometers per hour.
Then the time taken by the train from Paris to Nice will be
[tex]\rm Time = \dfrac{Distance}{Speed}\\\\\\\rm Time = \dfrac{920000 \ m}{230\ km/h}\\\\\\Time = \dfrac{920 \ km}{230 \ km/h}\\\\\\Time = 4 \ hours[/tex]
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Only false statements have counterexamples. true or false
Answers
The statement 'Only false statements have counterexamples' is false.
A counterexample is an instance that disproves a statement by providing an example where the premises are true, but the conclusion is false. Thus, only false statements have counterexamples can be considered false. A true statement cannot have a counterexample because that would contradict its truth.
For example, consider the statement 'All swans are white.' A single observation of a black swan would be a counterexample that disproves this statement, showing it is false.
Find two consecutive whole numbers that √46 lies between.
Answers
This is because the square root of 46 is roughly 6.8, so the two nearest whole numbers would be 6 and 7.
Two consecutive whole numbers that √46 lies between are 6 and 7.
The given surd is √46.
We need to find two consecutive whole numbers that √46 lies between.
What are consecutive whole numbers?Numbers that follow each other in a regular counting order or pattern are called consecutive numbers. They are written in a series where the difference between the numbers is fixed and where no numbers are skipped in between.
Now, 46 is lies between the perfect squares 6²=36 and 7²=49.
Therefore, two consecutive whole numbers that √46 lies between are 6 and 7.
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i need help with this problem. thank you so much who ever answer this
Answers
-36/8 = -4.5
-4.5 = -4.5
-9/2 is equal to -4 1/2 or -4.5 as a decimal.
Final answer: =
Side GH = 3, side IG = 5, side JK = 3, and side LJ = 5. What side corresponds to side HI and can be used to show that ΔGHI ≅ ΔJKL by SSS? (Enter your answer using letters only)
Answers
Since it says enter with only letters, you would put KL as the answer
Larry has taken out a $600 loan with a 12 percent interest rate to buy a laptop computer. He needs to repay the loan by the end of two years. He will be paying $28.24 every month for two years. What kind of interest rate is Larry being charged? Explain the reasons for your answer.
Answers
Answer:
Larry is paying the same amount every month for the duration of the loan. So he is being charged a fixed interest rate.
Step-by-step explanation:
plato answer
What fraction of a minute is 42 seconds
Answers
42 seconds is 7/10 of one minute.
______________________________________________
Explanation:
______________________________________________
There are 60 seconds in 1 min.
______________________________________________
So; 42 seconds is: 42/60 of 1 min.
42/ 60 = (42÷6) / (60÷6) = 7/10 .
______________________________________________
The answer is: "7/10".
42 seconds is 7/10 of one minute.
______________________________________________
What's the supplementary angle of 149.9 degrees?
Answers
Please help! find the solution of this system of equations -6x + 2y=38 6x - 8y= -44
Answers
-6x and 6x eliminate each other.
You have -6y=-6
Y=1
Plug this in into another equation and you have x
Solve it by using the elimination method.
-6x and 6x eliminate each other.
You have -6y=-6
Y=1
Plug this in into another equation and you have
-6x+2(1)=38
solve for x to get
X= -6
what is a constant interval and how does it appear on a graph?
Answers
A function is said to have a constant interval if, for any input, the output is the same. The graph of a function with a constant interval is parallel to the axis of the range, i.e., a horizontal line.
A constant interval refers to a specific type of interval that remains the same or constant over its entire length. In other words, the difference between any two consecutive points or numbers in a constant interval is always the same.
Let's assume that f(x) = c is a function with a constant interval.
Then,
for any [tex]x_1\leq x_2[/tex] or [tex]x_1\geq x_2[/tex],
[tex]f(x_1) = f(x_2)[/tex].
Thus, a function whose output remains constant for every input is called a function with constant intervals.
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