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 1

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]

What Is The Value Of Tan(60)? One-half StartRoot 3 EndRoot StartFraction StartRoot 3 EndRoot Over 2 EndFraction

Related Questions

Identify the independent variable (domain).

5x+2y= 150

Answers

Answer:

The independent variable is x

Step-by-step explanation:

In the equation y = m x + b

m is the rate of change ⇒ constantb is the initial value ⇒ constantx is the domain ⇒ inputy is the range ⇒ output

x is the independent variable because it does not depend on any value

y is the dependent variable because it depends on the value of x

Let us solve the question

∵ 5x + 2y = 150

→ Put it in the form above by subtracting 5x from both sides

∵ 5x - 5x + 2y = 150 - 5x

∴ 2y = 150 - 5x

→ Divide each term by 2 to make the coefficient of y equal 1

∴ y = 75 - 2.5x

y = -2.5x + 75

→ Compare is by the form above

∴ m = -2.5 and b = 75

x is the independent variable (domain)

∴ y is the dependent variable (range)

in order to solve for x which trig function would be used cosine sine or tangent​

Answers

Answer:

Cosine

Step-by-step explanation:

I took the test

In order to solve for x , we use the trigonometric function cosine

What are trigonometric relations?

Trigonometry is the study of the relationships between the angles and the lengths of the sides of triangles

The six trigonometric functions are sin , cos , tan , cosec , sec and cot

Let the angle be θ , such that

sin θ = opposite / hypotenuse

cos θ = adjacent / hypotenuse

tan θ = opposite / adjacent

tan θ = sin θ / cos θ

cosec θ = 1/sin θ

sec θ = 1/cos θ

cot θ = 1/tan θ

Given data ,

Let the triangle be ΔABC , where ∠B = 90°

Let the side AB be x

So , the adjacent side = x

The angle of the triangle ∠A is = 72°

So , θ = 72°

The hypotenuse AC = 8

And , by trigonometric relations , we get

cos θ = adjacent / hypotenuse

Substituting the values in the equations , we get

cos 72° = x / 8

Multiply by 8 on both sides , we get

x = cos 72° × 8

Now , cos 72° = 0.30901

Substituting the value of cos 72° , we get

x = 0.30901 × 8

x = 2.472

Hence , the value of x is determined by cosine function

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Martin Lukarevski, a super-hard problem published by Cambridge:

Let m be an arbitrary integer and let k=3m+1. Find all integer solutions x and y of the equation
(x + y − k)(x + y + k)=1+xy.

Answers

Answer:

Yagub Muallim is watching, grave is loading .

Step-by-step explanation:

Which situation could be represented by the equation 38.25 = 3x?

A group of 3 friends each had $38.25. What is x, the total amount of money the friends had all together?

A group of friends had $38.25. They decided to triple their money by working for a neighbor. What is x, the total amount of money the friends had all together after working for a neighbor?

A group of 3 friends had $38.25 all together. Each friend had the same amount of money. What is x, the amount of money each friend had?

A group of friends had $38.25. They earned $3 more. What is x, the amount of money the friends have all together?

Answers

Answer:

A

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

Find the distance between each pair of parallel lines with the given equations y=3x, y=3x+10

Answers

Answer:

sqrt10

Step-by-step explanation:

Since the closest distance between two parallel lines is a line that is perpindicular to them, we first find the line of the slope that is perpindicular to both lines. Since slope of line y = 3x+10 is 3, the slope of the line that is perpinduclar is -1/3. Therefore y = -1/3x is perpindicluar to both lines. We then find the intersection point of each line. We find said points by setting the lines equal to each other. 3x+10=-1/3x, x = -3 therefore y = 1. For the second line we get we find the origin is the intersection. Therefore since this forms a right triangle with the x axis, we find that the distance is 3^2+1^2 = sqrt10

Evaluate each value expression for the given value of the variable : x+x+5 when x=7
QUICK PLSSSSSS

Answers

Answer:

19

Step-by-step explanation:

x = 7, so we have:

7 + 7 = 14

14 + 5 = 19

Answer:

19

Step-by-step explanation:

you replace the x with a seven. so it will look like

7+7+5= 19

The altitude to the hypotenuse of a right triangle divides the hypotenuse into two segments measuring 11 cm and 5 cm. To the nearest tenth, what is the length of the shorter leg of the triangle?

Answers

Answer:

8.4 cm

Step-by-step explanation:

Given that:

A right angled triangle, let [tex]\triangle ABD[/tex]. Right angled at [tex]\angle A[/tex].

Altitude AC to the hypotenuse BD.

Length of side BC = 5 cm

Length of side CD = 11 cm

We have to find the value of shorter leg of triangle. i.e. side AB = ?

Using the concept of similarity, we can say the following:

[tex]\dfrac{AB}{BC} = \dfrac{BD}{AB}\\\Rightarrow AB^2=BC.BD\\\Rightarrow AB^2=5\times (5+11)\\\Rightarrow AB^2=5\times 16\\\Rightarrow AB^2=80\\\Rightarrow AB=\sqrt{80}\\\Rightarrow \bold{AB\approx 8.4\ cm}[/tex]

The length of shorter leg of the triangle = 8.4 cm

Complete the equation of the line through (3,-8)(3,−8)left parenthesis, 3, comma, minus, 8, right parenthesis and (6,-4)(6,−4)left parenthesis, 6, comma, minus, 4, right parenthesis.

Answers

Answer:

[tex]y = \frac{4}{3}x - 12[/tex]

Step-by-step explanation:

Given

[tex](x_1,y_1) = (3,-8)[/tex]

[tex](x_2,y_2) = (6,-4)[/tex]

Required

Determine the equation

First, we need to determine the slope (m):

[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

[tex]m = \frac{-4 - (-8)}{6 -3}[/tex]

[tex]m = \frac{-4 +8}{3}[/tex]

[tex]m = \frac{4}{3}[/tex]

Next, we determine the line equation using:

[tex]y - y_1 = m(x - x_1)[/tex]

Where

[tex]m = \frac{4}{3}[/tex]

[tex](x_1,y_1) = (3,-8)[/tex]

[tex]y - (-8) = \frac{4}{3}(x - 3)[/tex]

[tex]y +8 = \frac{4}{3}(x - 3)[/tex]

[tex]y +8 = \frac{4}{3}x - 4[/tex]

[tex]y = \frac{4}{3}x - 4 - 8[/tex]

[tex]y = \frac{4}{3}x - 12[/tex]

The equation of the line that passes through  (3, -8)(6, -4) is y = - 1 / 2 x - 1

The slope intercept equation is as follows:

y = mx + b

where

m = slope

b = y-intercept

Therefore,

The line passes through (3, -8)(6, -4)

m = -4 - 3 / 6 + 8 = -7 / 14 = - 1 / 2

y = - 1 /2 x + b

let's find b using (6, -4)

-4 = - 1 /2 (6) + b

-4 + 3 = b

b = -1

Therefore,

y = - 1 / 2 x - 1

learn more:

which set of the numbers is equivalent to 75%? (0.75 3/5), (7.5 75/100), (3/4 0.075), (15/20 0.75)

Answers

Answer:

0.75

Step-by-step explanation:

it has to be 0.75 because to make a percentage you move decimal to the left twice and its a %. But i am sorry i do not know the second one, maybe someone else can help :)

Answer:

75.0

Step-by-step explanation:

5 and 2/3 divided by 4?

Answers

Make them into fractions
17/3 divided by 4/1
Divide = multiply reciprocal
17/3 * 1/4 = 17/12
The answer is 17/12

Answer:

1.41 it’s a infinity answer

Step-by-step explanation:

3.
Lakpa buys 20 items for Rs 6000. He sells them at Rs 390 each. Calculate:
(a)
His total profit on the deal.
(b)
His percentage of profit on the deal​

Answers

Your answer is a your welcome

2x-3y=4 x+3y=29
A. ( - 11, 3)
B. (11, - 3)
C. (3, 11)
D. (11, 3)

Answers

Answer:

Step-by-step explanation:

2x-3y=4 x+3y=29

Hmmm I got (11,6) and I did it two different ways. Are these the only answers?

Answer:

(11, 6)

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDASEquality Properties

Algebra I

Solving systems of equations using substitution/eliminationSolving systems of equations by graphing

Step-by-step explanation:

Step 1: Define systems

2x - 3y = 4

x + 3y = 29

Step 2: Rewrite systems

2x - 3y = 4

x = 29 - 3y

Step 3: Solve for y

Substitute in x:                    2(29 - 3y) - 3y = 4Distribute 2:                        58 - 6y - 3y = 4Combine like terms:           58 - 9y = 4Isolate y term:                     -9y = -54Isolate y:                              y = 6

Step 4: Solve for x

Define:                         x + 3y = 29Substitute in y:            x + 3(6) = 29Multiply:                       x + 18 = 29Isolate x:                      x = 11

Step 5: Check

Graph the systems of equations to verify the solution set.

Rounding decimals. 0.01426; thousandths

Answers

Answer:

0.014

Step-by-step explanation:

help I'll give brainliest and 5 starts and heart thanks​

Answers

Answer:

can you expand on what you're talking about?

Answer:

Question isn't complete dude ...

What is the probability of rolling at least one six on a pair of fair
dice?

Answers

It is a 67% percent chance.

Mr. Thompson plans to invest $7,500 in a savings account that earns 2.75% simple annual interest. If he makes no other deposits or withdrawals, how much money will Mr. Thompson's account be worth after 10 years.

Answers

Answer:

Mr. Thompson's account be worth $9,562.50 after 10 years

Step-by-step explanation:

Simple Interest

Interest is calculated on the original principal only of a loan or on the balance of an account.

Unlike compound interest where the interest earned in the compounding periods is added to the new principal, simple interest only considers the principal to calculate the interest.

The interest earned is calculated as follows:

I=P.r.t

Where:

I = Interest

P = initial principal balance

r = interest rate

t = time

Mr. Thompson plans to invest P=7,500 in a savings account that earns r=2.75% = 0.0275.

The interest earned in t=10 years is calculated now:

I=7,500*0.0275*10

I=2,062.50

Now we add the interest to the principal:

A = $7,500 + $2,062.50

A = $9,562.50

Mr. Thompson's account be worth $9,562.50 after 10 years

Kathryn owns a video store. She rents games for 4 and moves for 4 She must rent at least 84 to make a profit She does not have anymore than 20 games Write and solve the system

Answers

Answer:

Katherine will rent at least 64 movies and 20 games to make a profit

Step-by-step explanation:

The given parameters are;

The amount for which she rents games = 4

The amount for which she rents movies = 4

The number of games and movies she most rent to make profit = 84

The number of games she ≤ 20

Let x represent the number of games, let y represents the number movies, we have;

x + y ≥ 84

x ≤ 20

64 ≤ y ≤ 84

The graph of the inequality created with Microsoft Excel showing the feasible region is included

help! i'm not sure how do this so if someone can explain that would be nice :) ​

Answers

Answer:

In slope intercept form it would be y=-1/2x+3

Step-by-step explanation:

THIS IS AN EXAMPLE ON HOW TO GET SLOPE INTERCEPT FORM. start with the point slope form y-y1=m(x-x1) and solve for y. y-8=2(x-6) so y-8=2x-12, add 8 to end up with y=2x-4. 2) start with slope intercept form and solve for b, then substitute that back in: y=mx + b, so 8=2(6)+b, 8=12+b, subtract 12 to get b=-4, therefore equation is y=2x-4.

Which ordered pair is a solution of the equation -4x + 7 = 2y - 3

Answers

Answer:

(0,5) (1,3) (2,1)

Step-by-step explanation:

y+4= 2/3 (x+3) written in standard form​

Answers

2x-3y=6 is correct:)

A phone company charges a base fee of $25 per month plus an additional charge per minute. The monthly phone cost can be represented by this equation: C=25+ a·m/4, where a is the additional charge per minute, and m is the number of minutes used. How can we re-write this equation to solve for the additional charge per minute?
PLZ HURRY

Answers

Answer:

C=25+(a*m)

just simplyfy what it was doing

Formula One race cars can reach speeds of approximately 100 meters per second. What is this speed in meters per minute?

0.6 meters per minute
1.67 meters per minute
600 meters per minute
6,000 meters per minute

Answers

Answer:

6,000 meters per minute

Step-by-step explanation:

Answer:

D. 6,000 meters per minute

Step-by-step explanation:

It's right on edg 2020

hope it helps (;

Have a good day and good luck !!!!!!!!!!!!!!!!!!!!!!!!!!!!!

The selling price of an item is ​$480. It is marked down by ​10%, but this sale price is still marked up from the cost of ​$. Find the markup from cost to sale price.

Answers

Answer:

Markup = [(Revenue – COGS) / COGS] X 100.

Markup = (Gross Profit / COGS) X 100.

Markup = [(Revenue – COGS) / COGS] X 100.

Markup = [($400 – $250) / $250] X 100.

Selling Price = [(Markup X COGS) + COGS] X 100.

Selling Price = (Markup X COGS) + COGS.

Selling Price = (0.50 X $100) + $100.

Step-by-step explanation:

um i think this is the answer

Answer: can someone help with my question really need help its a test.

Step-by-step explanation:

9999999

PLZ ANSWER WILL GIVE BRAINLIST 15 POINTS AND PLUS THREE FOR CORRECT ANSWER!!!!!!

Answers

Answer:

22

Step-by-step explanation:

just simple deduction

i think 22 i’m not positive

Which are are solutions for x^2 + 5x – 1 > 6

Answers

Answer:

it might be b and d

Step-by-step explanation:

A rental car cost 36 for one day plus additional 0.42 per mile. Simplify the expression 36 + 0.42( 78) to determine the cost of renting a car and driving it 78 miles

A. 68.76
B.70.08
C. 93.12
D. 2,808.42

Answers

Answer:

The Answer is A

Step-by-step explanation: What you do is multiply 0.42 by 78 since that is what it costs per mile which is 32.76.

And then you add 36 and you get 68.76

Secant and Tangent Angles in circles.
Solve for x.

Answers

Answer:

x = 1

Step-by-step explanation:

5x + 17 = 1/2[(73x + 5) - (23x - 5)]

5x + 17 = 1/2[37x + 5 - 23x + 5]

5x + 17 = 1/2[14x + 10]

5x + 17 = 1/2 * 2(7x + 5)

5x + 17 = 7x + 5

5x - 17x = 5 - 17

-12x = - 12

x = - 12/-12

x = 1

A circle is a curve sketched out by a point moving in a plane. The value of x that will make the Secant and Tangent Angles true for the circle is 17/25.

What is a circle?

A circle is a curve sketched out by a point moving in a plane so that its distance from a given point is constant; alternatively, it is the shape formed by all points in a plane that are at a set distance from a given point, the centre.

For the given circle, as per the Secant and Tangent Angles theorem, the measure of the angle formed by two tangents can be written as,

∠WVU = (arc WU + arc WU)/2

5x + 17 = [(37x + 5) + (23x - 5)]/2

2(5x + 17) = (37x + 5) + (23x - 5)

10x + 34 = 37x + 5 + 23x - 5

10x - 37x - 23x = 5 - 5 - 34

-50x = -34

x = 34/50

x = 17/25

Hence, the value of x is 17/25.

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how long is a meter
you can not use google

Answers

1 km=1000 m

1 m=100 cm

please mark as brainliest

I will give brainliest
4 = u/10
what is the value of u?

Answers

u = 40

40/10 is 4

Hope this helps!

(-20, -3) U (0,00)
what is the inequality notation?

Answers

Answer:

-20 < x < -3

Step-by-step explanation:

*math*

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