Answers
Answer:
√3
Step-by-step explanation:
To recall trigonometric ratios, there is a special acronym known as sohcahtoa which stands for
sin(x)=opposite/ hypotenusecos(x)=adjacent/hypotenuse tan(x)=opposite /hypotenuseFinding the angle [tex]\theta[/tex]
We are given that,
[tex] \displaystyle \sin( \theta) = \frac{ \sqrt{3} }{2} [/tex]
To find the angle [tex]\theta[/tex] , take inverse of sin of both sides,
[tex] \displaystyle { \sin}^{ - 1}( \sin( \theta) )= { \sin}^{ - 1} \bigg(\frac{ \sqrt{3} }{2} \bigg )[/tex]
with the help of unit circle,we acquire:
[tex] \displaystyle \boxed{\theta= {60}^{ \circ} }[/tex]
Finding [tex]\tan\theta[/tex]
simply plug in the value of theta:
[tex] \tan( {60}^{ \circ} ) [/tex]
using unit circle,we get:
[tex] \implies \tan( {60}^{ \circ} ) = \boxed{\sqrt{3} }[/tex]
and we're done!
Let's solve
[tex]\\ \rm\Rrightarrow sin\theta=\dfrac{\sqrt{3}}{2}[/tex]
[tex]\\ \rm\Rrightarrow \theta=sin^{-1}\left(\dfrac{\sqrt{3}}{2}\right)[/tex]
[tex]\\ \rm\Rrightarrow \theta=\dfrac{\pi}{3}[/tex]
Now
[tex]\\ \rm\Rrightarrow tan\theta=tan\dfrac{\pi}{3}[/tex]
[tex]\\ \rm\Rrightarrow tan\theta=\sqrt{3}[/tex]
Related Questions
does anyone know the answer?
Answers
Have a nice day
Answer:
C
Hope This Helps! :)
Suppose that there are two types of tickets to a show advance and same day the combined cost of one advance ticket and one same-day ticket is $70 for one performance 20 advance tickets and 35 same day tickets were sold.The total amount paid for the tickets was $1850.what was the price of each kind of ticket
Answers
The price of the advance ticket is $40 and the price of the same day tickets is $30.
What are the linear equations that reperesent the question?a + b = $70 equation 1
20a + 35b = 1850 equation 2
Where:
a = cost of one advance ticket
b = cost of one same day ticket
What is the cost of one same day ticket?
Multiply equation 1 by 20
20a + 20b = 1400 equation 3
Subtract equation 3 from equation 2
15b = 450
Divide both sides by 15
b = $30
What is the cost advance ticket?
Subtract $30 from $70.
$70 - $30 = $40
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What is half of 72 in math?
Answers
Answer:
36
Step-by-step explanation:
Answer:
36
Step-by-step explanation:
Divide 72 by 2, and you get 36
Rollie borrowed some money from his sister. Their brother wanted to know how much Rollie borrowed, but Rollie wouldn’t tell him. Instead, Rollie gave his brother a riddle.
“Each month, I paid our sister one-third of the amount I still owed her plus an additional $3. At the end of 3 months, I still owed her $3.”
Solve the riddle to find out how much money Rollie borrowed from his sister.
Explain how you arrived at your solution.
Answers
By working with fractions, we will see that the amount that Rollie borrowed from his sister is $31.50.
How much Rollie borrowed?Let's say that Rollie borrowed a quantity x.
The first month, Rollie returns one third of x + $3, so now he owes:
x - x/3 - 3 = (2/3)*x - 3
the second month returns another third of what he owes plus $3, so now he returns:
(1/3)*((2/3)*x - 3) + 3 = (2/9)*x + 2
So no he owes:
(2/3)*x - 3 - (2/9)*x - 2 = (4/9)*x - 5
Finally, on the third month he returns:
(1/3)*((4/9)*x - 5) + 3 = (4/27)*x - 5/3 + 3 = (4/27)*x + 4/3
Now he owes:
(4/9)*x - 5 - (4/27)*x - 4/3 = (8/27)*x - 19/3
And that is equal to $3, what he owes at the end of the third month, so we need to solve:
(8/27)*x - 19/3 = 3
(8/27)*x = 3 + 19/3 = 28/3
Solving for x, we get:
x = (27/8)*(28/3) = 31.5
So Rollie borrowed $31.5 from his sister.
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only question 5 parts a and b PLEASE HELP!!
Answers
the slope means for every 3 cm that grow 2 weeks will pass
hope this helps :3
If a1 = 7 and an = an-1 + 4 then find the value of a4.
Answers
Answer:
[tex]a_4=19[/tex]
Step-by-step explanation:
Given:
[tex]a_1=7[/tex][tex]a_n=a_{n-1}+4[/tex][tex]\implies a_2=a_{1}+4=7+4=11[/tex]
[tex]\implies a_3=a_{2}+4=11+4=15[/tex]
[tex]\implies a_4=a_{3}+4=15+4=19[/tex]
Put values get answer
a_n=a_(n-1)+4a_4=a_3+4a_4=a_2+4+4a_4=a_1+4+4+4a_4=7+12a_4=19Find the side ratio given
pls show work<3 :)
Answers
Answer:
5/2 See below
Step-by-step explanation:
L x W x H = 125/8
for a CUBE L W and H are the same
L^3 = 125/8
L = 5/2
Hep quickly for the brainliest answer quickly please no time
Answers
The 6 and 9 look the same up side down and so do the HOH
Which two terms in (3+14) +27 could you add to get a multiple of ten?
Answers
Answer:
3 and 27
Step-by-step explanation:
Step 1: Determine which two terms we can use
We have the following numbers to choose from: 3, 14, 27
Adding two numbers to get a multiple of ten means that the number that we come up with needs to be divisible by ten. For example: 20, 30, 50, 100 are all multiples of ten.
In this example the only one that would add up to create a multiple of ten is 27 and 3 which would give us 30 which is a multiple of 10.
Answer: 3 and 27
On Monday, Andrew ate some grapes. On Tuesday, he ate 2 more grapes than what he ate on Monday. On Wednesday, He ate 2 more grapes than what he ate on Tuesday. Each day of that week he ate 2 more grapes than what he ate the day before. By the end of Friday, He had eaten 30 grapes in total. How many grapes did Andrew eat on Monday?
Answers
Answer: I think It's 38
Step-by-step explanation:
you can multiply or add all of them together
Answer: Andrew ate 22 grapes on Monday.
Step-by-step explanation:
From Monday to Friday it is 4 days. since he ate 2 more grapes every day. You multiply 2 by 4. To get 8 and subtract 30 by 8 to get 28.
someone pls help me
Answers
Answer:
It should be
likes dislikes
teens 96% 4%
adults 21% 79%
senior 18% 82%
citizens
Step-by-step explanation:
100 people
100%
so 1 person = 1%
i guess
solve for m m/5 + 9 = 11
Answers
Answer:
10
Step-by-step explanation:
10
Answer:
10
Step-by-step explanation:
1) -9 on both sides
2) m/5=2
3) multiply both sides by 5
4) m=10
how many gallons of paint are needed for one coat on the entire exterior of the barn, including roof?
Answers
A bran with the dimensions shown is to be painted. One gallon of pain covers 400 square feet. 23 gallons of pain is need for the one coat of the barn. Option B is correct.
Given that,
A bran with the dimensions shown is to be painted.
One gallon of pain covers 400 square feet.
We have to find how much gallon of paint for one coat on the entire external of the bran, including the roof.
So,
We can see in the picture
1 side of the barn is rectangle with length and breath that is 24 feet and 60 feet.
1 side of the barn is square with side 40 feet.
The front upper side has a triangle with height 21 feet.
Now, We find the area of the rectangle.
Area of rectangle is length × breath
=24feet×60 feet
=1440 square feet
1440 square feet divided by 400 square feet
1440/400=3.6
So, the bran has 2 rectangular sides so 3.6+3.6=7.2
Now, we find the area of square.
Area of square is side × side
=40 feet ×40 feet
=1600 square feet
1600 square feet divided by 400 square feet.
1600/400=4
So, the barn has 2 square side so 4+4=8
Now, we find the area of triangle.
Area of triangle is 1/2×breath ×height.
=1/2×40 feet×21 feet
=1/2×840 square feet
=420 square feet
420 square feet divided by 400 square feet.
420/400=1.05
So, the barn has 2 triangles back and front so 1.05+1.05=2.1
Now, we find the area of roof
Roof is in rectangle with breath 60 feet and height 21 feet
Area of rectangle is length × breath
=60 feet ×21 feet
=1260 square feet
1260 square feet divided by 400 square feet.
1260/400=3.15
So, the barn has 2 rectangle roof so 3.15+3.15=6.3
Now, Adding all the areas we get
=7.2+8+2.1+6.3
=23.6
Therefore, approximately 23 gallons of pain is need for the one coat of the barn. Option B is correct.
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Answer: 23 gallons
Step-by-step explanation: ANSWER ON EDMENTUM
What is the radian equivalent for 180°? 2 pi radians pi radians startfraction pi over 2 endfraction radians
Answers
Answer:
180° = pi radians
Step-by-step explanation:
360° = 2pi radians
90° = pi/2 radians
see image
180° is pi radians.
pi radians is equivalent to 180 degrees, option B is correct.
What is Trigonometry?Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.
The radian equivalent of 180° is pi radians.
This is because a full circle is 360°, which is equivalent to 2 pi radians. Therefore, half of a circle or an angle of 180° is equivalent to half of 2 pi radians, which is pi radians.
Hence, pi radians is equivalent to 180 degrees, option B is correct.
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Use a system of equations to solve the following problems
1) Find the value of two numbers if their sum is 11.9 and their difference is 0.5.
Answers
Answer:
The answer is x= 6.2 and y= 5.7
Step-by-step explanation:
Let the two numbers be x and y.
1st condition:
x+y= 11.9 --- (1)
2nd condition:
x-y=0.5--- (2)
Solving 1 and 2
x+y= 11.9 --- (1)
x-y=0.5--- (2) (here +y and -y will get cancelled)
_____________
2x= 12.4
x= 12.4/2 = 6.2
∴x= 6.2
Now, put x= 6.2 in equation (1) ( u can put in eqn 2 also)
6.2+y= 11.9
y= 11.9-6.2= 5.7
∴y= 5.7
To recheck you can put the value of x and y in any of the eqns.
The LHS will be equal to RHS if the values we got are correct.
Hope it helps.
The diameter of a circle is 8 inches. What is the angle measure of an arc 37 pie inches long?
Answers
Answer:
135 degrees.
Step-by-step explanation:
Circumference of the circle
= 8pi inches.
8pi equals 360 degrees
So 3pi = (3pi / 8pi) * 360
= 3/8 * 360
= 135 degrees.
Find the value of x
x =
Answers
Answer:
[tex]\large\boxed{\tt x^{\circ}= 90^{\circ}}[/tex]
Step-by-step explanation:
[tex]\textsf{We are asked to find the value of x.}[/tex]
[tex]\textsf{The value of x is an angle for this triangle.}[/tex]
[tex]\textsf{Note that we are given 2 other angles, we can use what is given to us to solve for x.}[/tex]
[tex]\large\underline{\textsf{What is a Triangle?}}[/tex]
[tex]\textsf{A Triangle is a shape with 3 sides, and 3 angles. Sometimes these can be congruent,}[/tex]
[tex]\textsf{other times, and most of the time they're not. These are called Equilateral}[/tex]
[tex]\textsf{Triangles. Every Triangle consists of 3 angles that add up to 180}^{\circ}. \ \textsf{If the angles}[/tex]
[tex]\textsf{don't add up to 180}^{\circ}, \ \textsf{then the shape is not a triangle.}[/tex]
[tex]\textsf{Now that we know a Triangle has 3 angles that add up to 180}^{\circ}, \ \textsf{we can create an}[/tex]
[tex]\textsf{equation where x is the \underline{subject}.}[/tex]
[tex]\large\underline{\textsf{Solving;}}[/tex]
[tex]\textsf{All 3 angles add up to 180}^{\circ}, \ \textsf{let's create an equation.}[/tex]
[tex]\tt 180^{\circ} = 37^{\circ} + 53^{\circ} + x^{\circ}[/tex]
[tex]\textsf{To make x the subject, move x to the other side of the equation by subtracting x.}[/tex]
[tex]\tt 180^{\circ} - x^{\circ}= 37^{\circ} + 53^{\circ} + x^{\circ} - x^{\circ}[/tex]
[tex]\textsf{We should also move 180}^{\circ} \ \textsf{to the other side of the equation as well.}[/tex]
[tex]\tt 180^{\circ} - 180^{\circ} - x^{\circ}= 37^{\circ} + 53^{\circ} -180^{\circ}[/tex]
[tex]\underline{\textsf{We should have;}}[/tex]
[tex]\tt- x^{\circ}= -180^{\circ} + 37^{\circ} + 53^{\circ}[/tex]
[tex]\textsf{We should remove the negative for x by dividing the whole equation by -1.}[/tex]
[tex]\frac{\tt- x^{\circ}= -180^{\circ} + 37^{\circ} + 53^{\circ}}{-1} \rightarrow \tt x^{\circ}= 180^{\circ} - 37^{\circ} - 53^{\circ}[/tex]
[tex]\underline{\textsf{Simplify the right side of the equation;}}[/tex]
[tex]\large\boxed{\tt x^{\circ}= 90^{\circ}}[/tex]
Find the inverse function of y=7x.
Answers
Answer:
f^−1(x)=x7
Step-by-step explanation:
To find the inverse , inerchange the variable and slove for Y
Mr. Ramos's monthly mileage allowance for a company car is 750 miles. He drove 8 miles per day for 10 days, then went on a 3-day trip. The table shows the distance he drove on each day of the trip.
Trip Mileage
Day Miles Driven
Tuesday 156.1
Wednesday 240.8
Thursday 82.0
After the trip, how many miles remain in Mr. Ramos's monthly allowance? Record your answer in the box.
Answers
Answer:
558.9 miles total
Step-by-step explanation:
See attached spreadsheet.
Why is this a right triangle? A) Two angles are acute. B) One angle measures exactly 90°. C) All three angles are less than 90°. D) All three sides are of equal length.
Answers
Answer:
B)
Step-by-step explanation:
The main feature in a right triangle is that it has a right angle (90°)
Hope this helps
I WILL MARK BRAINLIEST
Answers
Answer:
21.5
Step-by-step explanation:
19+24=43
43/2=21.5
15+25+16+19+24+23+29+21=172
172/8=21.5
it cost 60$ to for 4 apples how much would 60 apples cost
Answers
Answer:
$900
Step-by-step explanation:
60/4 = 15
60 x 15 = 900
Answer:
900
Step-by-step explanation:
900 it's not that hard 60/4 15x60
2. Which expression is equivalent to 3x - (2x+4)+5?
b. x+9
c. 5x+9
d. 5x+1
Answers
Answer:
x + 1
Step-by-step explanation:
[tex]3x - (2x+4)+5[/tex]
[tex]3x-2x-4+5[/tex]
[tex]3x-2x+1[/tex]
[tex]x+1[/tex]
Find the surface area of the prism.
A cube with side edges of 7 yards.
yd2
Answers
Answer:
To find the surface area of a cube, use the formula: surface area = 6s^2, where s is the length of one of the sides. If you don't know the length of the sides, you can find the surface area using volume. Just find the cube root of the volume, which is equal to the length of one side of the cube.
Step-by-step explanation:
write 6.04*10-3 as an ordinary number
Answers
Answer:
0.00604
Step-by-step explanation:
the exponent - 3 means move the decimal point 3 places to the left
A positive exponent + 3 means move the decimal point 3 places to the right.
6.04 × [tex]10^{-3}[/tex] = 0.00604
What is the value of x in the equation 1/3x − 2/3 =− 18?
Answers
Answer:
x = -52
Step-by-step explanation:
[tex]\frac{1}{3}x-\frac{2}{3}=-18[/tex]
Let us solve for x.
[tex]\frac{1}{3}x=-18+\frac{2}{3}[/tex]
[tex]\frac{1}{3}x=-\frac{18*3}{1*3} +\frac{2}{3}[/tex]
[tex]\frac{1}{3}x=-\frac{54}{3} +\frac{2}{3}[/tex]
[tex]\frac{1}{3}x=\frac{-54+2}{3}[/tex]
[tex]\frac{1}{3}x=\frac{-52}{3}[/tex]
Use cross multiplication to find the value of x.
[tex]\frac{1x}{3}=\frac{-52}{3}[/tex]
[tex]3*1x=3*-52[/tex]
[tex]3x=-156[/tex]
Divide both sides by 3.
x = - 52
Which number is closest to
68?
9
64
8
34
Answers
Answer:
64
Step-by-step explanation:
I need help with this question really confused
Answers
Answer:
7.722[tex]cm^2[/tex]
Step-by-step explanation:
Work out the area of the circle
By the length of the square, you know the diameter of the circle is 12 cm so the radius is 6cm. Then you can calculate the area of the circle by doing
[tex]6^{2}[/tex]π =36π [tex]cm^{2}[/tex]
Work out the area of the square
12 x 12 = 144 [tex]cm^{2}[/tex]
So the bit not occupied by the circle will be 144- 36π = 30.888 [tex]cm^2[/tex]
However, the shaded area is just 1/4 of this bit so 30.888 / 4 = 7.722 [tex]cm^2[/tex]
Which of the following numbers are greater than or equal to 1.75?
Choose all answers
A) 1 4/11
B) 1.6
C) 7/4
Answers
Answer:
Only C
Step-by-step explanation:
1 4/11 is 1+4/11 and 4/11 is less than 1/2 so it has to be less than 1.5, which is less than 1.75
1.6 is less than 1.75 because 1.75-1.6 is 0.15 which is a positive number
4/7 is 1 3/4 which is 1.75
Answer:
a and c
Step-by-step explanation:
they are over 1
Segment AB has point A located at (4, 2). If the distance from A to B is 3 units, which of the following could be used to calculate the coordinates for point B? 3 = square root of the quantity of x minus 2 all squared plus y minus 4 all squared 3 = square root of the quantity of x minus 4 all squared plus y minus 2 all squared 3 = square root of the quantity of x plus 2 all squared plus y plus 4 all squared 3 = square root of the quantity of x plus 4 all squared plus y plus 2 all squared
Answers
The equation that can be used to find the coordinates of B given the coordinates of A and the length of the line segment AB is given by: Option B: 3 =√[(x-4)² + (y-2)²]
What is the distance between two points ( p,q) and (x,y)?The shortest distance(length of the straight line segment's length connecting both given points) between points ( p,q) and (x,y) is:
[tex]D = \sqrt{(x-p)^2 + (y-q)^2} \: \rm units.[/tex]
For this case, we're specified that:
The coordinates of A are (4,2)
The distance from A to B = 3
Let the coordinates of B be (x,y), and (p,q) = (4,2), then we get;
[tex]D = \sqrt{(x-p)^2 + (y-q)^2}\\\\or\\\\3 = \sqrt{(x-4)^2 + (y-2)^2}\\[/tex]
Thus, the equation that can be used to find the coordinates of B given the coordinates of A and the length of the line segment AB is given by: Option B: 3 =√[(x-4)² + (y-2)²]
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