if sin theta=1/root 3, then find the value of (tan theta + 1/cos theta)^2 + (tan theta - 1/cos theta)^2

Answers

Answer 1

Answer:

4

Step-by-step explanation:

[tex]sin(\theta)=\frac{opposite}{hypotenuse}=\frac{1}{\sqrt{3} }\\ \\Therefore, opposite= 1, hypotenuse=\sqrt{3}. \ using \ Pythagoras:\\\\Hypotenuse^2=Adjacent^2+Opposite^2\\\\(\sqrt{3})^2 =Adjacent^2+1^2\\\\3=Adjacent^2+1\\\\Adjacent^2=3-1=2\\\\Adjacent=\sqrt{2}[/tex]

[tex]cos(\theta)=\frac{adjacent}{hypotenuse}=\frac{\sqrt{2} }{\sqrt{3}}\\ \\tan(\theta)=\frac{opposite}{adjacent } = \frac{1}{\sqrt{2}} \\\\Therefore:\\\\(tan(\theta)+\frac{1}{cos(\theta)})^2+ (tan(\theta)-\frac{1}{cos(\theta)})^2=( \frac{1}{\sqrt{2}}+\frac{1}{ \frac{\sqrt{2} }{\sqrt{3}}} )^2+( \frac{1}{\sqrt{2}}-\frac{1}{ \frac{\sqrt{2} }{\sqrt{3}}} )^2\\\\=( \frac{1}{\sqrt{2}}+ \frac{\sqrt{3} }{\sqrt{2}} )^2+( \frac{1}{\sqrt{2}}- \frac{\sqrt{3} }{\sqrt{2}} )^2[/tex]

[tex]=(\frac{1+\sqrt{3} }{\sqrt{2} } )^2+(\frac{1-\sqrt{3} }{\sqrt{2} } )^2=\frac{1+2\sqrt{3}+3 }{2} +\frac{1-2\sqrt{3}+3 }{2} =\frac{1+1+2\sqrt{3}-2\sqrt{3}+3+3 }{2} =\frac{8}{2}=4[/tex]


Related Questions

after leaving home for school, it had taken you 15 minutes to walk 1000 feet. if your destination is a total of 1200 feet from home, about how many minutes do you have left to walk?

Answers

Answer: 3 min

Step-by-step explanation:

Step 1. Find the constant speed

you walked 1000 feet in 15 min

1000 ft/ 15min=200/3 ft / min

Step 2. Apply the constant speed to the left distance

You already walked 1000 feet and it is total 1200 feet

1200-1000=200 feet left

distance ÷ speed=time

200 ÷ (200/3)=3 min

Hope this helps!! :)

Please let me know if you have any question

A 11/16-inch-long bolt is used in a machine. What is the length of the bolt written as a decimal? (Please help)

Answers

Answer:

0.6875

Step-by-step explanation:

11 divide 16 and you get 0.6875

Answer:

The answer is 11/16=0.6875.

Which graph shows the solution to the system of inequalities below?

Answers

Is there a picture to the problem?

Some one help? Im confused with this part of geometry just tell me what answer

Answers

Answer:

the answer is actually PS (7x - 7)

Hoped that I helped

A two-digit number is 3 times the sum of the digits. If the digits are reversed, the new number formed is 9 less than three times the original number. What is the two-digit number?

Answers

Answer:

27

Step-by-step explanation:

2+7=9.

9x3=27

72+9=81

27x3=81

What is 2x-6 = 3x+1-X-7 and you have to regroup/ divide by number next to x?

Answers

Answer:

infinite solutions

Step-by-step explanation:

2x-6 = 3x+1-X-7

Combine like terms

2x-6 = 3x-x +1-7

2x-6 = 2x -6

subtract 2x from each side

-6 = -6

Since this is a true statement, x can be any real number

What is x in these equations a) x+4= 7² - 6 b) x+ √4 + 19= 4x +9

Answers

Answer:

a) 39

b) 4

Step-by-step explanation:

[tex] {7}^{2} = 7 \times 7 = 49[/tex]

the answer to the question would be 4

19. Write the perimeter of the rectangle as a
simplified expression.
x - 3
7x + 1

Answers

Answer:

16x - 5

Step-by-step explanation:

2(x-3) + 2(7x+1) since there are 4 sides, 2 which have the same dimensions

2x - 6 + 14x + 1 = 16x - 5

The simplified expression of the perimeter of the rectangle should be 16x - 4.

Given that

x - 37x + 1

We know that

The perimeter of the rectangle be

= 2(length + breadth)

= 2(x - 3 + 7x +1)

= 2x - 6 + 14x + 2

= 16x - 4

Therefore we can conclude that the simplified expression of the perimeter of the rectangle should be 16x - 4.

Learn more about the rectangle here: brainly.com/question/20733283

given a20=100 and a50=400 identify the common difference “d”

Answers

Answer:

a20=a+19d

or,100=a+19d

or, a=100-19d--------(I)

again,

a50=a+49d

or, 400=a+49d

or, a=400-49d--------(ii)

equating equations,we get

100-19d=400-49d

or, 30d=300

so, d=10

Step-by-step explanation:

plz mark it as brainliest

Si una llave vierte 6 1/3 litros de agua por minuto, ¿cuánto tiempo tardará en llenar un depósito de 88 2/3 litros de capacidad?

Answers

Answer: 14 minutes

Step-by-step explanation:

Given: A tap pours [tex]6\dfrac13[/tex] liters of water per minute.

To find : Time taken to fill an[tex]88 \dfrac23[/tex] liters capacity tank.

which is given by :-

Time = [tex]88 \dfrac23\div 6\dfrac13[/tex] minutes

[tex]=\dfrac{3\times88+2}{3}\div\dfrac{3\times6+1}{3}[/tex]  minutes

[tex]=\dfrac{266}{3}\div \dfrac{19}{3}[/tex] minutes

[tex]=\dfrac{266}{3}\times\dfrac{3}{19}[/tex]  minutes

[tex]=\dfrac{266}{19}=14\text{ minutes}[/tex]

Hence, it will take 14 minutes to fill an[tex]88 \dfrac23[/tex] liters capacity tank.

A certain right triangle with integer side lengths has perimeter $72$. What is its area?

Answers

Answer: 216 square units

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

Explanation:

A common pythagorean triple you may be familiar with is the 3-4-5 right triangle. This has two legs of 3 and 4, and a hypotenuse of 5. The perimeter is 3+4+5 = 7+5 = 12. Note how this is a factor of 72.

If we multiply the perimeter (12) by 6, then 12*6 = 72. So we have scaled the triangle by a factor of 6. Each length is 6 times longer

the side length 3 becomes 3*6 = 18

the side length 4 becomes 4*6 = 24

the side length 5 becomes 5*6 = 30

The new perimeter is 18+24+30 = 42+30 = 72

The last step is to find the area. The two legs of this triangle are the base and height

area = 0.5*base*height

area = 0.5*18*24

area = 9*24

area = 216

-----

Or you could find the area of the 3-4-5 right triangle to get

area = 0.5*base*height = 0.5*3*4 = 6

then multiply by 36 to get 6*36 = 216. The 36 is the square of the scale factor 6 we applied above. The new lengths are 6 times longer, so the new area is 6^2 = 36 times larger.

Write each equation in standard form. Identify A, B, and C.

43. y=12x

44. -4y=3x-24

45. 4x=8y-12

46. Word problem: The distance the Green family traveled during their family vacation is given by the equation y=65x, where x represents the number of hours spent driving. How far does the Green family travel in 8 hours?

Answers

Answer:  The answers are in the steps.

Step-by-step explanation:

A standard form equation says that Ax + By=C

SO we have to set all the equations to be like that.

43.  y = 12x     Subtract 12x from both sides.

    -12x + 1y = 0      In this case -12  is A, 1 is B , and 0 is C.

44 .  -4y =3x -24      subtract 3x from both sides

     -3x - 4y = -24     A is -3 , B is -4, and  C is -24  

45. 4x = 8y - 12         Subtract 8y from both sides.  

   -8y     -8y

  4x - 8y = -12         A is 4, B is -8 and C  is -12  

46. If we are given the equation y=65x and x represent the number of hours spent driving. And it says that how far do you travel in 8 hours then plot 8 into the equation for x and solve for y.

y = 65(8)

y= 520  

They traveled 520 miles in 8 hours .

convert 8 7/8 to an improper fraction

Answers

Answer:

71/8

Step-by-step explanation:

8 ⅞ = 71/8

How?

8 × 8 + 7 = 71

Which is 71/8.

Answer:

Hey there! :)

Step-by-step explanation:

~ Answer is 71/8 ~

There is two ways you can do this, they are provided below :)

Steps in order to solve this question!:

~1. First you have to multiply the denominator by the whole number

(The denominator is 8, and the whole number is 8 too)

So, 8x8=64

~2. Next you have to take the 64 and add it to the 7 which is the numerator of 8 7/8.

64+7=71

~3. The answer is 71/8. The denominator is 8 because the denominator never changes.

………………………………………………………………………………………………

Another way you can do this:

8x8+7

_____ <= And this is how we get 71/8

8

~Therefore the answer is 71/8.

~Hope this helps!

(If you still don’t understand than ask for help! You can ask me if you don’t understand any of the steps!)

I would be glad to answer any questions you have about this problem. :D

6x – у = -9
—12х – 4 y = 0

Answers

Answer:

-15

3

Step-by-step explanation:

6x-y=-9

6x-(15)=-9

-12x-4y=0

-12x-4(3) =0

-12-12=0

I need help please.ASAP

Answers

Answer:

20

Step-by-step explanation:

I do not know how to explain it for you thanks

The answer is 20 hope it helps

Terrance makes $12.50 per hour doing landscaping and earned $275 this
week. How many hours did he work?

Answers

Answer:

22 hours

Step-by-step explanation:

pay rate = (amount of money)/time

(pay rate) * time = amount of money

time = (amount of money)/(pay rate)

time = $275/($12.50/hour)

time = 22

Answer: 22 hours

Answer:

22 hours

Step-by-step explanation:

We know that Terrance makes $12.50 per hour and he made $275 a week. We can divide 275 by 12.50 :

275 ÷ 12.50 = 22

So Terrance worked 22 hours

Check answer:

22 x 12.50 = 275

Un terreno ha sido cultivado con tres variedades de claveles. La sexta parte ha sido sembrada por
claveles rojos, la cuarta parte por claveles amarillos y el resto por claveles blancos.
Actividad 1

1 ¿Qué parte del terreno se sembró con claveles rojos y amarillos? Utilice el espacio para hacer
el proceso.

Answers

Answer:

1) Se siembra cinco doceavas partes del terreno con claveles rojos y amarillos, 2) Se siembra siete doceavas partes del terreno con claveles blancos.

Step-by-step explanation:

El enunciado se encuentra incompleto. La pregunta faltante es:

2 ¿Qué parte del terreno corresponde a los claveles blancos?

1) Sea [tex]A[/tex] el área total sembrada con los tres tipos de claveles. Entonces, las áreas sembradas con claveles rojos y claveles amarillos son [tex]\frac{1}{6}\cdot A[/tex] y [tex]\frac{1}{4} \cdot A[/tex], respectivamente.

El área sembrada con claveles rojos y amarillos se obtiene al sumar las áreas correspondientes, es decir:

[tex]x = \frac{1}{6}\cdot A + \frac{1}{4}\cdot A[/tex]

[tex]x = \left(\frac{1}{6}+\frac{1}{4}\right)\cdot A[/tex]

[tex]x = \left(\frac{4+6}{24} \right)\cdot A[/tex]

[tex]x = \frac{10}{24}\cdot A[/tex]

[tex]x = \frac{5}{12}\cdot A[/tex]

Se siembra cinco doceavas partes del terreno con claveles rojos y amarillos.

2) El área sembrada con claveles blancos se obtiene al sustraer el área obtenida en el punto anterior del área total. Esto es:

[tex]x = A - \frac{5}{12}\cdot A[/tex]

[tex]x = \left(1-\frac{5}{12} \right)\cdot A[/tex]

[tex]x = \left(\frac{12}{12}-\frac{5}{12} \right)\cdot A[/tex]

[tex]x = \left(\frac{12-5}{12} \right)\cdot A[/tex]

[tex]x = \frac{7}{12}\cdot A[/tex]

Se siembra siete doceavas partes del terreno con claveles blancos.

Answer:

Step-by-step explanation:

>:C

Select the expression equivalent to(6x + 5)-(4x – 6).

Answers

the answer is 2x+11 good luck

Write the sentence as an equation the product of 187 and n is the same as 264

Answers

Answer:

i would like to  say you divide but not shure im just starting 8th grade but good luck

Step-by-step explanation:

In circle C, r = 32units what is the area of circle C

Answers

Answer:

1024π, 3215.36

Step-by-step explanation:

The formula for the area of a circle is πr^2

R is the radius, which is already given to us. We need to find r^2

32x32=1024

1024π

We can leave it in terms of pi or we can solve it out.

1024x3.14=3215.36

1024π, 3215.36

Answer:

see below

Step-by-step explanation:

The area of a circle is given by

A = pi r^2

A = pi * 32^2

A =1024 pi units^2

If we use pi = 3.14

A = 3215.36 units^2

If we use the pi button

A =3216.990877 units^2

Given: AB ∥ DC , m CB =62°, m∠DAB=104° Find: m∠DEA, m∠ADB

Answers

Answer:

Step-by-step explanation:

sum of angles of parallelogram=360 degrees

adjacent angles add up to 180 degrees (supplementary angles)

Angle A=104 (DAB=104)

Angle D=180-104=76 degrees (angle ADB)

Angle B=60 degrees

Angle C=180-60=120 (DCB)    

Binomial (x - 6) and trinomial (-2x2 + x + 9) are the factors of which of the
following polynomials?
2x^3+12x-3x+54
-2x^2+15
-2x^3+13x^2+3x-54
O 2x^2-3

Answers

Answer:

Option (3)

Step-by-step explanation:

If binomial (x - 6) and trinomial (-2x² + x + 9) are the factors of a polynomial then their multiplication will be equal to the polynomial.

(x - 6)(-2x² + x + 9) = x(-2x² + x + 9) - 6(-2x² + x + 9)

                              = -2x³ + x² + 9x + 12x² - 6x - 54

                              = -2x³ + 13x² + 3x - 54

Therefore, Option (3) will be the correct option.

Referring to the Fig. in Question #3, evaluate the expression shown when a = 3, b = 8, c = 4 Please help.

Answers

Answer:

[tex]\huge\boxed{4}[/tex]

Step-by-step explanation:

=> [tex]\sqrt{b^2-4ac}[/tex]

Given that a = 3 , b = 8 and c = 4

=> [tex]\sqrt{(8)^2-4(3)(4)}[/tex]

=> [tex]\sqrt{64-48}[/tex]

=> [tex]\sqrt{16}[/tex]

=> 4

Help needed ASAP will give brainliest!

Answers

The third one is correct bc 59g weighs more than 25g which will need to be pushed with more force


The temperature is -3°F at 7 A.M. During the next three hours, the temperature increases 13°F. What is the temperature at 10 AM?

A -16°F
B-16°F
C- 10°F
D-10°F

Answers

10 degrees F, which would be C if the - didn’t represent a negative

Given the following three points, find by hand the quadratic function they represent.
(-1,-8), (0, -1),(1,2)
(1 point)
O f() = -5x2 + 8x - 1
Of(x) = -222 +50 - 1
O f(x) = -3.x2 + 4.0 – 1
O f() = -3x2 + 10x - 1​

Answers

Answer:

The equation is;

f(x) = -2·x² + 5·x - 1

Step-by-step explanation:

The general form of a quadratic equation  or function f(x) is, f(x) = y = a·x² + b·x + c

Given that the points representing the quadratic function are;

(-1, -8), (0, -1), (1, 2) which  are of the form (x, y)

When x = -1, f(x) = y = -8

Plugging in the above values into the general form of a quadratic function, we have;

-8 = a·(-1)² + b·(-1) + c = a - b + c

-8  = a - b + c.........................(1)

When x = 0, y = -1, we have;

-1 = a·(0)² + b·(0) + c = c

c = -1.......................................(2)

When x = 1, y = 2, which gives;

2 = a·(1)² + b·(1) + c = a + b + c

2 = a + b + c........................(3)

Adding equation (1) to equation (3), we have;

-8 + 2 = a - b + c + a + b + c

-8 + 2 = 2·a + 2·c

From equation (2) c = -1, we get;

-8 + 2 = -6 = 2·a + 2·c = 2·a + 2 × (-1)

-6 = 2·a - 2

-4 = 2·a

a = -2

From equation (3), we have

2 = a + b + c

Substituting the values of a, and c gives;

2 = -2 + b - 1

b = 2 + 2 + 1 = 5

b = 5

The equation is therefore;

f(x) = -2·x² + 5·x - 1.

Answer:

b

Step-by-step explanation:

PLEASE ANSWER QUICKLY! MATH: mr. Sanford left half of hi fortune to April, his daughter. he left half of the remaining half to his Uncle Jed. He left half of the remaining half to charity. He left the remaining $30,000 to the local animal shelter. What was the total amount of Mr. Sanford’s fortune.

Answers

Answer:

$240,000

Step-by-step explanation:

Mr. Sanford's fortune is x

He left 1/2x to daughterHe left 1/2*1/2x = 1/4x to Uncle JedHe left 1/2*1/4x = 1/8x to charityHe left the remaining $30,000 to the local animal shelter.

Then we got the equation:

x = 1/2x + 1/4x + 1/8x + 30000x = 7/8x + 300001/8x = 30000x= 8*30000x= $240000

Mr. Sanford’s fortune was $240,000

WILL MARK BRAINLIEST AND 20 POINTS Determine algebraically whether each of the following functions is even, odd, or neither. f(x) = x^2 - x

Answers

Answer:

Neither

Step-by-step explanation:

The function is neither because if it was even it would follow the rules of:

[tex]f(-x)=f(x)[/tex]

and if it was odd it would follow the rules of:

[tex]-f(x)=f(-x)[/tex]

but instead it follows the rule:

[tex]-f(x)\neq f(-x))\\[/tex]

Which of the following best describes the term constructions in geometry?
A: Combining two or more figures together to create a new figure or shape.
B: A way to draw precise figures using a compass and a straightedge.
C: Creating a figure or shape by hand.
D: Places where things are being built that often slow down traffic.

Answers

Answer:

B: A way to draw precise figures using a compass and a straightedge.

Step-by-step explanation:

In geometry, the term 'construction' refers to the draw geometrical shapes and figures accurately. The lines, angles, figures, and shapes are drawn with the help of a compass, ruler, and pencil. Arcs and lines are drawn neatly and angles are constructed. The lines and shapes are constructed without known lengths or angles with the help of the compass, pencil, and ruler.

A sequence is defined below.
f(0) = 7
f(n) = 2f(n - 1) - 3 for n > 1, where n is an integer
What is the third number in the sequence?

Answers

Answer:

35

Step-by-step explanation:

f(0) = 7

f(1) = 2f(0) - 3 = 11

f(2) = 2f(1) - 3 = 19

f(3) = 2f(2) - 3 = 35

i think the answer is 35
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