help please!!
[tex]\text{solve the following equation : }[/tex]
[tex] \sf\tan^{2}(\theta)-(1+\sqrt{3})\tan(\theta)+\sqrt{3} = 0[/tex]

Answers

Answer 1
tan²( θ ) - (1 + √3) tan (θ) + √3 = 0

tan²( θ ) - (tan (θ) + √3 tan (θ)) + √3 = 0

tan²( θ ) - tan (θ) - √3 tan (θ) + √3 = 0

tan( θ ) ( tan (θ) - 1) - √3 ( tan (θ) - 1 ) = 0

( tan( θ ) - 1 ) ( tan( θ ) - √3 ) = 0


tan( θ ) - 1 = 0

θ = π/₄

tan( θ ) - √3 = 0


θ = π/₃


so θ = π/₄ and θ = π/₃
Answer 2

Answer:

[tex] \huge \boxed{ \red{ \boxed{\begin{cases} \theta = {45}^{ \circ} \\ \theta= {60}^{ \circ} \end{cases} }}}[/tex]

Step-by-step explanation:

to understand thisyou need to know about:trigonometryPEMDASlet's solve:

distribute tan(θ):

=>tan²(θ)-(tan(θ)+√3tan(θ))+√3=0

remove parentheses:

=>tan²(θ)-tan(θ)-√3tan(θ)+√3=0

so this equation is now in standard form i.e ax²+bx+c=0

we can solve by factoring as we solve quadratic equation

factor out tanθ:

=>tan(θ)(tan(θ)-1)-√3tan(θ)+√3=0

factor out -√3:

=>tan(θ)(tan(θ)-1)-√3(tan(θ)-1)=0

group:

=>(tan(θ)-√3)(tan(θ)-1)=0

separate it as two different equation:

[tex] \implies \begin{cases} \tan( \theta) - 1 = 0 \\ \tan( \theta) - \sqrt{3} = 0 \end{cases}[/tex]

add 1 and √3 to both sides to first and second equation respectively:

[tex] \implies \begin{cases} \tan( \theta) - 1 + 1 = 0 + 1 \\ \tan( \theta) - \sqrt{3} + \sqrt{3} = 0 + \sqrt{3} \end{cases} [/tex]

[tex] \implies \begin{cases} \tan( \theta) = 1 \\ \tan( \theta) = \sqrt{3} \end{cases} [/tex]

[tex] \therefore \begin{cases} \theta = {45}^{ \circ} \\ \theta= {60}^{ \circ} \end{cases} [/tex]


Related Questions

TOURS The table shows the activities of two visitors at a park. You want to take the boat tour for 2 hours and the walking tour for 3 hours. Can you determine how much you will pay? Explain.

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Answer:

Step-by-step explanation:

State if the triangle is acute, obtuse, or right ​

Answers

Answer:

right angle triangle

obtuse, using the Pithagorean Theorem we can deduce it is not a right triangle and since the result is bigger than that of a right triangle it is not acute

A total of 50,000 contestants are chosen for a survey. A
computer randomly eliminates 20% of the participants
each day.
Which function models the survey?

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Answer:

you are correct do not say any other answer

Answer:

The answer is either

y=50000 x 0.8^x

or

y=50000(20%)^x but this just seems wrong

Step-by-step explanation:

I NEED HELP PLEASE !!

Answers

Answer:

all 3 sides are the same length

SOMEONE PLEASE HELP!
Figures 1 and 2 below show two polygonal regions used to approximate the area of the given shape. Find the average area, in square units, of the given shape using figures 1 and 2.

Answers

Answer:

figure 1 is 8.5 units^2 and figure 2 is 3 units^2 and the average are is 5.25 units^2

The overestimated area, the underestimated area, and the average area will be 8.5 units², 3 units², and 2.75 units², respectively.

What is an area?

The area of a 2D form is the amount of space within its perimeter. It is measured in square units such as cm², m², and so on. To find the area of a square formula or another quadrilateral, multiply its length by its width.

Since the area is covered with either a square or a triangle. Therefore, we can write the area of this two as,

Area of a square = 1 unit × 1 unit = 1 unit²

Area of triangle = 0.5 × 1 unit × 1 unit = 0.5 units²

The overestimated area, the number of square and triangles are,

Number of square = 6

Number of triangle = 5

Total overestimated area = (6×1unit²) + (5×0.5unit²) = 8.5 unit²

The under estimated area, the number of square and triangles are,

Number of square = 2

Number of triangle = 2

Total Underestimated area = (2×1unit²) + (2×0.5unit²) = 3 unit²

Furthermore, the average area is,

Average area = (Total overestimated area - Total Underestimated area)/2

                       = (8.5 units² - 3 units²) / 2

                       = 5.5  units² / 2

                       = 2.75 units²

Hence, the overestimated area, the underestimated area, and the average area will be 8.5 units², 3 units², and 2.75 units², respectively.

Learn more about Area here:

https://brainly.com/question/1631786

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What percent of 54 is 28?
52%
192%
19%
0.52%
?

Answers

Answer:

52%

happy to hep ya :)

Step-by-step explanation:

52%

Explanation: 28/54 = x/100
2800 = 54x
2800/54 = 51.85
round to 52%

halp me pleaze................

Answers

i’m pretty sure it’s c it’s seem like the only reasonable answer
You are right and it’s c

factorise fully :

4(x - y)^2 - 9(x + y)^2​

Answers

Answer:

- ( 5x + y ) ( x + 5y )

or

-5x^2 - 5y^2 - 26xy

Answer:

Step-by-step explanation:

4(x^2-2xy+y^2)-9(x^2+2xy+y^2)

4x^2-8xy+4y^2-9x^2-18xy-9y^2

-5x^2-26xy-5y^2

-5x^2-xy-25xy-5y^2

-x(5x+y)-5y(5x+y)

(-x-5y)(5x+y) or you can also remove the negative one to get

-(x+5y)(5x+y)

What is the equation of the line that goes through the points (4,-1) and
(2,3)?

Answers

Answer:

y = -2x + 7

Explanation:

y = mx + b

m = slope

b = y-intercept

y = a given y coordinate

x = a corresponding x coordinate

First, we need to find the slope (m).

1) (4, -1)

2) (2/3)

m = slope = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex] = [tex]\frac{3-(-1)}{2-4}[/tex] = [tex]\frac{4}{-2}[/tex] = -2

plug in the values to the equation y = mx + b

-1 = -2(4) + b

-1 = -8 + b

7 = b

now, we can substitute in m and b into the equation y = mx + b

y = -2x + 7

please also answer this one rlly fast!!

Answers

Answer:

4

Step-by-step explanation:

1 ÷ 0.25 = 4

HELP giving brainlest for first person that answers and extra points

Answers

thanks for the extra points i most definitely needed it

Given right triangle ABC with altitude BD drawn to hypotenuse AC. If BC=6 and DC=4, what is the length of AC ?

Answers

Step-by-step explanation:

BC^2 + DC^2 = AC^2

6^2 + 4^2 =AC^2

36 + 16 = AC^2

52=AC^2

√52=AC

AC=7.2111

May someone please help me with this :)

Answers

so to find the answer you would use the formally 1/2bh
1/2(3.5)(1.5)
which give you 2.625

I really need help!!!!

Answers

Answer:

No

Step-by-step explanation:

You can't use the perpendicular bisector theorem because it doesn't intersect it at a right angle, (meaning it isn't perpendicular)

Your friend Alex has won a scholarship to study abroad. (Congratulations!) Alex has only 8 weeks to earn enough money to buy a plane ticket, and he wants to work at an amusement park over the summer to acheive this goal

Answers

What’s the question?

Step-by-step explanation:

?

what's
[tex] \sqrt{45 + 36} [/tex]

Answers

the square root is 81

help
What is an equation of the line that passes through the points (-4, 4) and (8.1)?

Answers

Answer:

y = -1/4x +3

Step-by-step explanation:

Hope this helps!

quick test 2+2x68(8)=y

Answers

2176

Step-by-step explanation:

2+2=4 68(8)= 544

4× 68×8= 2176

Eight years ago, Manny was 4 years old. Let m equal Manny's age now. Circle every equation that shows Manny's age now.

Answers

Answer:

4+8=M or 4+8=12 or just 12

Step-by-step explanation:

there isnt anything to circle so but since he was 4, 8 years ago, you would add 4 and 8.

which graph represents the function

Answers

I believe the answer is C

A golf course has 18 holes. A guidebook provided to golfers includes useful information about each hole, as shown below. A 4-column table with 6 rows. Column 1 is labeled hole number with entries 1, 2, 3, 4, 5, 6. Column 2 is labeled yards with entries 312, 530, 147, 350, 410, 185. Column 3 is labeled bunkers with entries 2, 5, 1, 0, 2, 1. Column 4 is labeled difficulty level with entries moderate, moderate, easy, moderate, hard, moderate. What are the individuals in this data set? holes yards bunkers difficulty levels

Answers

Answer:

Holes got it right :)

Step-by-step explanation:

Answer

difficulty levels

Step-by-step explanation:

took the test

sorry different question

Write the following FRACTIONS in order of size (SMALLEST to LARGEST)
70% , 2/3 , 0.62 , 13/20 , 0.6

Answers

Answer:

is this helpful?? i guess it is

Answer: 6/10, 62/100, 13/20, 2/3, 7/10

Explanation:

First make all of them decimals:

.7, .667, .62, .65, .6

Then order least to greatest:

.6, .62, .65, .667, .7

Finally put them into fraction form

6/10, 62/100, 13/20, 2/3, 7/10

6 - 4 (6n + 7 ) > 122 giving brainlest to whoever shows work

Answers

Answer:

n<-6

Step-by-step explanation:

6-24n-28>122

-22-24n>122/:(-2)(devide the whole equation by (-2), when u devide by a negative number > changes to <)

11+12n>-61

12n<-72

n<-6

Can u help me with my work pls

Answers

Answer:

The mountain is 8.

The map is 96.

The compass is 6.

The hiker is 54.

The train is 14.

The a corn is 26

Hope this helps.

36-4=32/4=8

24+24=48

48/16=3

4(9)=36

20-15=5

31-12=19

Trees=8
Map=48
Compass=3
Hiker=36
Backpack=5
Acorn=19

Help me please thanks

Answers

Answer:

3.64 × 10¹⁵

Step-by-step explanation:

Hey!

==================================================================

We always follow these rules when we are Multiplying and Dividing numbers with Scientific Notation.

1. If the numbers are not in scientific notation, convert them.

2. Regroup the numbers using the commutative and associative properties of exponents.

3. Now multiply the two numbers written in scientific notation, you work out the coefficients and the exponents separately.

             -Use the product rule; aⁿ × aᵇ = a⁽ⁿ⁺ᵇ⁾  to multiply the bases.

4. If the product of the coefficients is greater than 9, convert it to scientific notation and multiply by the new power of 10.

5. Join the new coefficient to the new power of 10 to get the answer.

--------------------------------------------------------------------------------------------------------------

Let's start!

Our equation:

                                  (5.2 × 10⁶)(7 × 10⁸)

--------------------------------------------------------------------------------------------------------------

1. If the numbers are not in scientific notation, convert them.

They are in scientific notation, so we go on to step 2.

2. Regroup the numbers using the commutative and associative properties of exponents.

(5.2 × 7)(10⁶ × 10⁸)

3. Now multiply the two numbers written in scientific notation, you work out the coefficients and the exponents separately.

             -Use the product rule; aⁿ × aᵇ = a⁽ⁿ⁺ᵇ⁾  to multiply the bases.

5.2 × 7 = 36.4

10⁶ × 10⁸= 10⁽⁶⁺⁸⁾ = 10¹⁴

4. If the product of the coefficients is greater than 9, convert it to scientific notation and multiply by the new power of 10.

36.4 = 3.64 × 10¹

5. Join the new coefficient to the new power of 10 to get the answer.

3.64 × 10¹ × 10¹⁴

3.64 × 10⁽¹⁺¹⁴⁾ = 3.64 × 10¹⁵

==================================================================

3.64 × 10¹⁵

Hope I Helped, Feel Free to ask any questions to clarify :)

Have a fantastic day!

           -Aadi x

24 college students were hired as ushers for a concert. This is 30% of the students who applied for the job. How many college students applied to be ushers

Answers

Answer:

80 students applied

Explanation:

24 ÷ 30 × 100

= 0.8 × 100

= 80

i hope this helps! :D do comment if you need any clarification.

Answer:

80 students

Step-by-step explanation:

if 30%=24

100%=?

100%/30%*24

=80

Find area of circle circumference or area

Answers

Answer:

closest option B (50.24)

Step-by-step explanation:

A=πr²

= π×4×4

=π×16

=50.265m²

Area:

50.24 m^2

Explanation:

The formula for the area of a circle is A = πr²,

where:

A = area, r = radius

Diagram:

[tex]\setlength{\unitlength}{1cm}\begin{picture}(0,0)\thicklines\qbezier(2.3,0)(2.121,2.121)(0,2.3)\qbezier(-2.3,0)(-2.121,2.121)(0,2.3)\qbezier(-2.3,0)(-2.121,-2.121)(0,-2.3)\qbezier(2.3,0)(2.121,-2.121)(-0,-2.3)\put(0,0){\line(1,0){2.3}}\put(0.5,0.3){\bf\large 4\ m}\end{picture}[/tex]

Plug in the data. I'll use 3.14 for pi.

[tex]\bf{A=\pi \times4^2}\\\bf{A=3.14\times16}\\\bf{A=50.24\:m^2}[/tex]

Hence, area = 50.24 m^2

ALEGBRA 1 ! help. me. please. this. is. so. hard. i dont. understand it.

Answers

Answer:

Part a) to find the maximum height of the snowball, you have to differentiate the function. Therefore you get ----> dh/dt= -32x-8 . Now equate this to zero and solve for x. x= (-1)/4 now sub this value in to find h(x) [note: i'm talking about the original function] . I got h max = h((-1)/4) = 9 which is the max height.

Step-by-step explanation:

I'm not too sure about the other questions. Sorry

Solve for x
Literally forgot how to do this..

Answers

Answer:

x = 114 ur welcome

Step-by-step explanation:

Answer:

x = 114

Step-by-step explanation:

Given

[tex]\frac{x+18}{4}[/tex] = 33 ( multiply both sides by 4 to clear the fraction )

x + 18 = 132 ( subtract 18 from both sides )

x = 114

15 is 20% of what number? Enter your answer in the box. ​

Answers

Answer:

75

Step-by-step explanation:

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