What is the value of tan(60°)? One-half StartRoot 3 EndRoot StartFraction StartRoot 3 EndRoot Over 2 EndFraction StartFraction 1 Over StartRoot 3 EndRoot EndFraction
Answers
Answer:
[tex]\sqrt3[/tex]
Step-by-step explanation:
To find:
The value of [tex]tan60^\circ[/tex] = ?
Solution:
Kindly consider the equilateral [tex]\triangle ABC[/tex] as attached in the answer area.
Let the side of triangle = [tex]a[/tex] units
Let us draw the perpendicular from vertex A to side BC.
It will divide the side BC in two equal parts.
i.e. BD = DC = [tex]\frac{a}{2}[/tex]
Using Pythagorean Theorem in [tex]\triangle ABD[/tex]:
[tex]\text{Hypotenuse}^{2} = \text{Base}^{2} + \text{Perpendicular}^{2}[/tex]
Side AD = [tex]\frac{\sqrt3}{2}a[/tex]
Using Trigonometric ratio:
[tex]tan\theta = \dfrac{Perpendicular}{Base}[/tex]
[tex]tanB = \dfrac{AD}{BD}[/tex]
Putting the values of AD and BD:
[tex]tan60^\circ=\dfrac{\frac{\sqrt3}{2}a}{\frac{1}{2}a}\\\Rightarrow tan60^\circ = \bold{\sqrt3}[/tex]
Related Questions
What is the slope of the line that passes through points (-10, -3) and (5, 3)?
Answers
Answer:
m = 6/15
Step-by-step explanation:
Answer:
(-0.4,1)
Have a beautiful day, and stay safe.
The Carey family took a trip in November. Mary is calculating the gas mileage in miles per gallon for her dad's truck. When he fills the tank, her dad records the miles on the truck as 15,345. Her dad pays $53.28 to fill up the empty gas tank of the truck. What is the size of the truck's tank in gallons if it cost $3.33 per gallon? Round your answer to the nearest whole number. Be sure to include the correct units in your final answer. *
Answers
Answer:
The size of the tank is 16 gallons
Step-by-step explanation:
Here, we want to calculate the size of the gas tank of the truck
we simply divide the total amount spent by the price per gallon
Mathematically, that will be;
53.28/3.33 = 16 gallons
PLS PLS PLS HELP MEEEEE HIGH POINTS PLS ANSWER CORRECTLY I NEEEED U
In parallelogram WXYZ, the shorter sides are half the length of the longer sides.
Parallelogram W X Y Z. The length of sides W X and Z Y are 12 inches. Angle Y is 120 degrees. Angle Y is opposite to Angle W.
Which statements are true? CHECK ALL THAT APPLY.
A. Quadrilateral WXYZ is a rectangle.
B. The quadrilateral has opposite sides that are parallel.
C. The quadrilateral has opposite angles that are congruent.
D. If W X = 12 in., then X Y = 6 in.
E. Side WZ must be 12 inches.
F. mAngle Z = measure of angle X
G. Measure of angle W = 120 degrees
H. Measure of angle Z = 120 degrees
Answers
Answer:
B
E
H
I think this is right
For the given parallelogram following statements are true
B. The quadrilateral has opposite sides that are parallel
F. Measure of angle Z = Measure of angle X
G. Measure of angle of W =120 degrees
What is parallelogram?
A parallelogram is a simple quadrilateral with two pairs of parallel sides
Given,
Shorter sides are half the length of the longer sides. Length of he side WX and ZY are 12 inches. Angle Y is 120 degrees. Angle Y is opposite to angle W
Draw the figure using the the data
Using the figure we can say that
The quadrilateral has opposite sides that are parallel
Measure of angle Z = Measure of angle X
Measure of angle of W =120 degrees
Hence, the correct options are B,F and G
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The radio hot 97 plays despacito ft Justin beiber every 5 minutes. Another station Z 100 plays despacito every 7 minutes. Both stations at 3:00 pm and time will it be when despacito at the same time
Answers
Answer:
The next time they would play despacito on both stations is after 35 minutes.
Hence, 3:00pm + 35
= 3:35 pm
Step-by-step explanation:
The radio hot 97 plays despacito ft Justin beiber every 5 minutes. Another station Z 100 plays despacito every 7 minutes. Both stations at start 3:00 pm and what time will it be when despacito at the same time ?
Find and list multiples of time that despacito plays Radio hot 97 and Station Z 100.
Hence, we find the Multiples of 5 minutes and 7 minutes until the first common multiple is found. This is the lowest common multiple.
Multiples of 5:
5, 10, 15, 20, 25, 30, 35, 40, 45
Multiples of 7:
7, 14, 21, 28, 35, 42, 49
Therefore, the first common multiple is found which is the lowest common multiple is 35
LCM(5, 7) = 35
The next time they would play despacito on both stations is after 35 minutes.
Hence, 3:00pm + 35
= 3:35 pm
Answer:
of course they play despacito that much lol
Step-by-step explanation:
You got an A on 6 of your last 8 quizzes in Algebra 2. What is the experimental probability that you will get an A on your next quiz? (Simplify the fraction).
Answers
Not so sure
Really stupid question, but how do you add a comment lol. There’s no enter button or anything (I’m on an iPad) if that helps.
Answers
Answer:
You just do
Step-by-step explanation:
Answer:
just click the thing that says "Ask blah blah about this question..."
Step-by-step explanation:
Write in simplest form: what is 2^-3 in simplest form
Answers
Answer: 1/8
[tex]2^{-3}=\frac{1}{2^{3} }=\frac{1}{8}[/tex]
Step-by-step explanation:
Answer:
1/8
Step-by-step explanation:
The graph of a non-invertible function passes through the points (- 1, 2), (0, 6) and (3, - 4) How is the inverse of this function graphed ? Drag a phrase or group of coordinates into each box to correctly complete the statement.
Answers
Answer:
The order of ordered pairs of a function and its inverse reverse. The graph of the inverse of this function passes through the points (2,-1), (6,0), (-4,3).
Explanation:
I just took the test.
As per the graph, the non-invertible functions pass through the point of (-1, 2)), (0,6), and (3, - 4).
The inverse of the function on the graph will be depicted by the Y = X. The graph of the inverse passes through the vertical line test for the inverse function. While the graph of the inverse function will pass through the (2,-1), (6,0), (-4, 3)Learn more about the graph of a non-invertible function that passes through the point.
brainly.com/question/19894576.
Solve 14+3n=5n−6 . Check your solution.
n= __
Answers
Answer:
N = 10
Step-by-step explanation:
Subtract 3n from both sides
14 = 2n - 6
add 6 to both sides
20 = 2n
divide by 2
n = 10
Answer:
n = 10
I hope this helps!
Write in point-slope form an equation for the line through
the point (2, -3) that has the slope of -2. Use point-slope
form
Answers
Answer:
y=-2x+1
Step-by-step explanation:
y-y=m(x-x1)
y-(-3)=-2(x-2)
y+3=-2x+4
-3 -3
y=-2x+1
Kiera is contacting the poll workers from the last election to see whether they are willing to work in the next election. During the last election, 42\%42%42, percent of the poll workers were under 606060 years old. Let WWW be the number of poll workers Kiera contacts before reaching one that is 606060 years old or older. Assume that each poll worker's age is independent. Find the mean and standard deviation of WWW. Round your answers to one decimal place.
Answers
Answer:
Mean: 1.7 and standard deviation 1.1.
Step-by-step explanation:
42% Of the poll workers are less than 60 years old. In other words, 58% of the poll workers are 60 years old: 1-0.42 = 0.58. So W is a geometric variable where the first "success" is poll worker who is at least 60years old.
Mean: 1/0.58 = 1.7241 poll workers, about 1.7 poll workers.
Standard deviation: sqr(1-p)/p = sqr(1-0.58)/0.58 = 1.1174 poll workers, about 1.1 poll workers.
The required Mean and the standard deviation are given as 1.7 and 1.1 respectively.
Given that,
During the last election, 42%, percent of the poll workers were under 60 years old. Let W be the number of poll workers Kiera contacts before reaching one that is 606060 years old or older.
The mean of the values is the ratio of the total sum of values to the number of values.
here,
42% of poll workers are under the age of 60. Also, 58% of poll workers are above the age of 60.
= 1 - 0.42 = 0.58.
So "W" is a geometric variable with the first success being a poll worker beyond the age of 60.
Mean = 1/0.58
= 1.7 poll workers.
Standard deviation = √[(1-0.58)/0.58]
= 1.1 poll workers.
Thus, the required Mean and the standard deviation are given as 1.7 and 1.1 respectively.
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Tom bought 3 boxes of books at a yard sale. If each box had 2 books how many books did he Buy ?
i will be giving brainliest.
Answers
Answer:
6
Step-by-step explanation:
2 books in each box.
There are three boxes
2 times 3 equals 6
I bet I will mark you as a brainiest if u get this right
To make porridge, Goldilocks mixes together 3 bags of oats with 1 bag containing 20% wheat bran and 80% oats. All the bags have the same volume. What percentage of the volume of Goldilocks' porridge mixture is wheat bran?
5%
6%
20%
26%
60%
15%
8%
Answers
Answer:
6%
Step-by-step explanation:
This is an honest guess just because you are not given the content of 2 out of the 3 bags. When starting at 100 percent of the makeup of the porridge you can then divide that by 3 to get the content of 1 bag. You will get around 33 then you find what 20% of 33 is which is closest to either 6 percent.
What is the solution to the equation above
Answers
Answer:
A = 3/4
Step-by-step explanation:
alternately could equal 0.75
the distance traveled by an object divided by the time in which the distance was traveled is called the__of an object
Answers
Answer:
speed (v)
Step-by-step explanation:
v = d/t
v = speed
d = distance travelled
t = time taken
somebody please help
Answers
Answer:
729
Step-by-step explanation:
hope it helps
Answer: 27/2 = 13 1 2\
also 729
The value of a stock increases 1423 points twice in one week. The other three days the value decreases by 10 points, 813 points, and 1223 points. By how many points did the value of the stock change that week? A. 2/3 points B. 1/3 points C. −1 1/3 points D. −1 2/3 points
Answers
Answer:
Step-by-step explanation:
Remark
Usually the statements are written from your broker's and his accountant's point of view. That being said, he looks at the numbers as a debit for a plus, and a credit as a minus. We'll assume it started out as a new purchase.
Debit Credit Balance
0 0
1423 1423
1423 2846
10 2836
813 2023
1223 800
None of the answers match. I have done it correctly. There is no way you will get a fractional amount from those numbers. You are going to have to take it to your teacher/instructor to find out how it is done.
The sum of two numbers a and b is 7 and the difference between them is 2. What is the value of a x b ? Give your answer as a mixed number in its simplest form.
Answers
Answer:
45/4
Step-by-step explanation:
We can interpret the question to have two equation which can be solve simultaneously
a+b=7------------(1)
a-b=2------------(2)
From eqn(2) make a subject of formula
a=2+b--------(3)
Substitute the (3) into eqn(1)
a+b=7------------(1)
2+b+b=7
2b=7-2
2b=5
b=5/2
From equation (3) substitute value of b to find a
a=2+b--------(3)
a= 2+5/2
a=9/2
Then What is the value of a x b ?
9/2× 5/2
=45/4
Answer:
11 1/4
Step-by-step explanation:
a+b=7
a-b=2
adding equations gives us 2a=9 so a= 9/2
b= 7- 9/2= 14-9/2=5/2
therefore a x b= 9/2 x 5/2 =45/4
45/4 in a mixed number is 11 1/4
What is the slope of a line that passes through these points? (5, 3) and (4, 1).
Answers
9514 1404 393
Answer:
2
Step-by-step explanation:
The slope can be found from the slope formula:
m = (y2 -y1)/(x2 -x1)
m = (1 -3)/(4 -5) = -2/-1
m = 2
The slope of the line is 2.
Answer:
2
Step-by-step explanation:
ΔY = 1 – 3 = -2
ΔX = 4 – 5 = -1
two negatives make a positive
If a watch costs $40 and you must pay 6.5% sales tax, how much will the tax be?
Answers
Answer:
$42.60
Step-by-step explanation:
change 6.5% to. 065 and multiply it by 40. $2.60 is your sales tax. then add 2.60 to $40 which equals $42.60
Jamal's lawn is shaped like a square with an area of 224.9 ft? Which measurement is closest to the side length of his
lawn in feet?
A.15 ft
B.56 ft
C.28 ft
D.11 ft
Answers
Answer:
A. 15 ft
Step-by-step explanation:
I took the test.
By applying formula of area of square we got length of side of Jamal's square shaped lawn is 15 ft.
What is square?A quadrilateral whose all four sides are equal and all four equal angles are equal to 90°is called square .
Given that area of square shaped lawn is224.9 square feet.
We know that area of square is equal to [tex]a^2[/tex] where a is length of side of square .
We can calculate length side of lawn as
Area = [tex]a^2[/tex]
224.9 = [tex]a^2[/tex]
[tex]a= \pm \sqrt{224.9}\\\\\Rightarrow a=\pm 14.9966[/tex]
We know that length of side of square can't be negative so
[tex]a=14.9966\\\\a\approx 15 ft[/tex]
By applying formula of area of square we got length of side of Jamal's square shaped lawn is 15 ft.
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Question 13 (1 point)
03.OSLO
What is the volume of a sphere with a radius of 6 inches?
1120 cubic inches
2880 cubic inches
2900 cubic inches
3000 cubic inches
Answers
Answer:
V=904.78 in^3
Step-by-step explanation:
V=4/3pir^3=4/3.pi.6^3=904.77868in^3
Hurry, I need help and please explain
Answers
Answer:
Question 18
=$3.33
Step-by-step explanation:
i)
26/100 x 4.5
=1.17
(the discount price)
ii)
$4.5-$1.17
=$3.33
Answer:
QUESTION 18
The original price is $4.50
The discount is 26%
They are asking for the sale price which the price after the discount.
So,
The original price means 100% of the cost, like there is no discount at all.
But then we have to apply a 26% discount which means to subtract 26% (the discount) from 100% (the original price)
The new price of the item has to be 74% of the original price.
74% of $4.50 is the same as saying 26% discount.
But what is the number?
To calculate 74% of $4.50, turn 74% into a decimal which is 0.74, then multiply it by 4.50.
0.74 x 4.50 = 3.33
In conclusion, after a 26% discount on an item that is originally $4.50, the new price (sale price) of the item is now $3.33
It cost $510 to get your car fixed. If it was $375 for parts, how much did the mechanic charge for the work to fix your car?
Answers
(6th grade math)
yasiara has 3/4 of cake. she wants to divide it up into 1/12 size pieces. how many pieces will she have? ( can you show work please)
Answers
50 = 2x + 12
Solve step by step.
Answers
Answer:
x=19
Step-by-step explanation:
subtract 12 from each side: 50-12=2x+12-12
38=2x
divide by 2
38/2=2x/2
19=x
Answer:
x=19
Step-by-step explanation:
50=2x+12
50-12=2x+12-12
38=2x
38/2=2x/2
x=19
The base of a skyscraper is a triangle bordered by three streets: Main Street, Elm Street, and Maple Street. The Elm Street side is 2 ft shorter than twice the Maple Street side. The Maple Street side is 12 ft shorter than half the Main Street side. The Main Street side is 210 ft.
Answers
Answer:
Step-by-step explanation:
1. 93
2.184
Solve for y in terms of x: 3x = 15-5y
Helppp
Answers
y=3-3/5x
hope it helps:):)
Answer:
Step-by-step explanation:
3x =15-5y
Add 5y and subtract 3x on both sides
5y=15-3x
y=(15-3x)/5
distribute 3(7x - 8)
Answers
Answer: 21x - 24
Step-by-step explanation:
(3 * 7) x - 3 (8) = 21x - 24
1. 7.35 x 10 6 – 9.42 x 10 8
2. 3.14 x 10 -3+1.59 x 10 -1
3. (2 .8x 10 -9 )(4.75 x 10 -3 )
Answers
Answer:
1) -9.3465 × 10^8
2) 1.6214 × 10^-1
3) 1.33 × 10^-11
Explanation:
When solving arithmetic operations of numbers in scientific notation, there is a strategy that can be used.
First recognize the quotient(division) between the size of the numbers indicated by a multiple of 10 to a certain power. Remember, taking the quotients of like numbers with different powers is the subtraction of powers.
For example, to solve the first expression (problem one):
7.35 x 10^6 – 9.42 x 10^8
Divide 10^8 by 10^6 to get 10^2
So
it is like subtracting 7.35 and 9.42 × 10^2 which is 7.35 - 942, then once this expression is solved, multiply by the lowest multiple of 10 which is 10^6.
7.35 - 942 = -934.65 → -934.65 × 10^6 = (-9.3465 × 10^2) × 10^6 = -9.3465 × 10^8.
Long subtraction may need to be used when dealing with numbers that are far apart. Likewise long addition multiplication or division is used for very big or small numbers.
Anyway for the second expression (problem 2)
Addition in my opinion is much easier because it is really just adding on the bigger number. Subtraction may take a little longer but both processes are all based on the bigger number or the number with the greatest power of the multiple 10.
So 3.14 × 10^-3 + 1.59 × 10^-1
The quotient between 10^-1 and 10^-3 is the the difference between -3 and -1 which is 10^2
So again it is like adding 3.14 and 1.59 × 10^2 which is 3.14 + 159 = 162.14 = 1.6214 × 10^2. Now use the multiple of 10 with the largest contrast which is 10^-3 so 1.6214 × 10^2 × 10^-3 = 1.6214 × 10^(2-3) = 1.6214 × 10^-1.