Find x in the kite below

Answer:

- [tex]\frac{2\sqrt{3} }{3}[/tex]

Step-by-step explanation:

Using the identity and the exact value

csc x = [tex]\frac{1}{sinx}[/tex]  and sin60° = [tex]\frac{\sqrt{3} }{2}[/tex]

- 120° is in the third quadrant where sin < 0 , then

csc - 120° = - sin60° , then

csc - 120°

= [tex]\frac{1}{-sin60}[/tex]

= - [tex]\frac{1}{\frac{\sqrt{3} }{2} }[/tex]

= - [tex]\frac{2}{\sqrt{3} }[/tex] ( rationalise the denominator )

= - [tex]\frac{2}{\sqrt{3} }[/tex] × [tex]\frac{\sqrt{3} }{\sqrt{3} }[/tex]

= - [tex]\frac{2\sqrt{3} }{3}[/tex]

The equivalent value of the trigonometric relation cosec ( -120 )° = 2√3/3

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 ,

We know that the cosecant function is defined as the reciprocal of the sine function:

cosec (θ) = 1 / sin(θ)

Therefore, to evaluate cosec(-120°), we first need to find sin(-120°).

We know that sine is an odd function, which means that sin(-θ) = -sin(θ). Therefore,

sin(-120°) = -sin(120°)

We can now use the fact that the sine function has a period of 360 degrees, which means that sin(120°) is the same as sin(120° - 360°) = sin(-240°).

Using the same logic as before, we get:

sin(-240°) = -sin(240°)

Now , from the trigonometric relations , we get

Now, we can use the fact that sin(240°) = sin(240° - 360°) = sin(-120°), which means that:

sin(-240°) = -sin(-120°)

Therefore, we have:

sin(-120°) = -sin(120°) = -sin(-240°) = sin(240°)

Now, we can use the unit circle or trigonometric identities to find sin(240°). One way to do this is to draw a 30-60-90 degree triangle in the third quadrant of the unit circle, with the angle of 240° as the reference angle:

In this triangle, the opposite side (O) has a length of √3, the adjacent side (A) has a length of -1, and the hypotenuse (H) has a length of 2.

Therefore, sin(240°) = O/H = (√3)/2.

Finally, we can use the definition of the cosecant function to find cosec(-120°):

cosec(-120°) = 1/sin(-120°) = 1/sin(240°) = 1/((√3)/2) = 2/√3 = (2√3)/3.

Hence , cosec(-120°) is equal to (2√3)/3.

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Answer:

In order:

Distributive Property

Subtraction Property of Equality

Division Property of Equality or Reciprocal Property

Step-by-step explanation:

Answer:

[tex] \rm Numbers = 4 \ and \ -3.[/tex]

Step-by-step explanation:

Given :-

The sum of two numbers is 1 .

The product of the nos . is 12 .

And we need to find out the numbers. So let us take ,

First number be x

Second number be 1-x .

According to first condition :-

[tex]\rm\implies 1st \ number * 2nd \ number= -12\\\\\rm\implies x(1-x)=-12\\\\\rm\implies x - x^2=-12\\\\\rm\implies x^2-x-12=0\\\\\rm\implies x^2-4x+3x-12=0\\\\\rm\implies x(x-4)+3(x-4)=0\\\\\rm\implies (x-4)(x+3)=0\\\\\rm\implies\boxed{\red{\rm x = 4 , -3 }}[/tex]

Hence the numbers are 4 and -3

Step-by-step explanation:

[tex]numbers \: = x \: and \: y \\ x \times y = - 12......(1) \\ x + y = 1..... ..(2) \\y = 1 - x \\ put \: this \: in \: (1) \\ x(1 - x) = - 12 \\ x - {x}^{2} = - 12 \\ - x + {x}^{2} - 12 = 0 \\ factorise \\ {x}^{2} - 4x + 3x - 12 = 0 \\ x(x - 4) + 3(x - 4) = 0 \\ (x - 4)(x + 3) = 0 \\ x = + 4 \: or \: - 3 \\ thank \: you[/tex]

Answer:

Hey

Step-by-step explanation:

Answer:

9

Step-by-step explanation:

because i said so

Answer:

x = -3

Step-by-step explanation:

Here, this is a vertical line

What this mean here is that the x-value remains constant irrespective of the y value

For all the y values, we have a single x-value

so what this mean is to simply locate the x-axis. value and equate it to x

We have this as;

x = -3

Hello,

Answer B : -0.8=-0.8

[tex]n=-2\\1.4*n+2=2*n+3.2\\\\so:\\1.4*(-2)+2=?\ 2*(-2)+3.2\\\\-2.8+2=\ ? -4+3.2\\\\-0.8=-0.8\\[/tex]

The last line of the justification is –0.8 = –0.8

Given the following equation

1.4n + 2 = 2n + 3.2.

Collect the like terms

1.4n - 2n = 3.2 - 2

Substitute n = -2 into the expression

1.4(-2) + 2 = 2(-2) + 3.2
-2.8 + 2 = -4 + 3.2
-0.8 = -0.8

Hence the last line of the justification is –0.8 = –0.8

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Answer:

Step-by-step explanation:

An angle is cut in half by the bisector.

Since the given angle is 172, its bisector creates 2 equal angles.

2x = 172                 Divide both sides by 2

x = 172/2

x = 86

Answer:

Step-by-step explanation:

From the picture attached,

ΔDEF is a right triangle with two sides,

EF = 17 units

DF = 20 units

By applying Pythagoras theorem in the given triangle,

DE² = DF² + EF²

(20)² = DF² + (17)²

DF² = 400 - 289

DF = √111

Trigonometric ratios for the ∠F,

sin(F) = [tex]\frac{\text{Opposite side}}{\text{Hypotenuse}}[/tex]

[tex]\text{sin}F=\frac{\sqrt{111}}{20}[/tex]

[tex]\text{cosF}=\frac{\text{Adjacent side}}{\text{Hypotenuse}}[/tex]

[tex]\text{cos}F=\frac{17}{20}[/tex]

[tex]\text{tan}F=\frac{\text{Opposite side}}{\text{Adjacent side}}[/tex]

[tex]\text{tan}F=\frac{\sqrt{111}}{17}[/tex]

Choose the correct option.

Given:

Number of flower pots = 6

To find:

The number of ways of the gardener to arrange the flower pots.

Solution:

Number of ways to arrange n items is n!.

So, the number of ways to arrange 6 pots is:

[tex]6!=6\times 5\times 4\times 3\times 2\times 1[/tex]

[tex]6!=720[/tex]

Therefore, there are total 720 ways of the gardener to arrange the flowerpots.

Answer:

Step-by-step explanation:

The area of a sector has the formula

[tex]A_s=\frac{\theta}{360}*\pi r^2[/tex] Hopefully, this looks somewhat familiar to you. Theta is the central angle given as 75, r is the radius given as 4. Filling in:

[tex]A_s=\frac{75}{360}*(3.14)(4)^2[/tex] and simplifying that a bit to look less threatening, but not by much:

[tex]A_s=\frac{5}{24}(3.14)(16)[/tex] and

[tex]A_s=\frac{251.2}{24}=\frac{157}{15}=10.466666666...[/tex] Not sure how you're supposed to express your answer so I gave both the fraction and its decimal equivalency.

Answer:

solution

Step-by-step explanation:

ADC = Sum of triangle

AD+ AC = 2.25+3 =5.25

Step 2:

BCD = Sum of acute angled triangle = a+b+

c

BCD= 2.25+4+3

BCD = 9.25

The value of x =ADC+BCD

= 5.25+ 9.25

= 14.5

Answer:

Vmax = 192.33 cm³

Step-by-step explanation: An error in the problem statement. The sides of the box could not be 12 cm. We assume 1.5 cm

Inside dimensions of the box:

Outer dimensions :          12          10         8

 2 *  1.5   =  3                      3            3         3

Inside dimensions:            9            7         5

The volume of a right circular cylinder is:

V(c)  =  π*r²*h              r is the radius of the base and  h the height

By simple inspection is obvious that volume maximum will occur when r is maximum, and r is maximum, only when the base of the cylinder is in the rectangle 12*10. ( Inside  dim  9*7 ) In that case r  =  7/2   r = 3.5 cm

Then the height is 5 cm.

And the maximum volume of the cylinder is:

Vmax = 3.14* ( 3.5)²*5

Vmax = 192.33 cm³

Answer:

n=5

Step-by-step explanation:

by using

n=(an-a)/a+1

substituting values

n= 7.2-(-7.2)/3.6 +1

n=5

Answer:

same after 3 years

because .............................

Answer:

The populations of orangutans will be same after 3 years

Step-by-step explanation:

Let the populations or orangutans is the same after n years

Decrease in population of oragnutans in the first study

=784-25n=784−25n

Decrease in population of oragnutans in the second study

=817-36n=817−36n

According to the question

784-25n=817-36n784−25n=817−36n

\implies 36n-25n=817-784⟹36n−25n=817−784

\implies 11n=33⟹11n=33

\implies 11n=33⟹11n=33

\implies n=\frac{33}{11}⟹n=

11

33

\implies n=3\text{ years}⟹n=3 years

Therefore, the populations of orangutans will be equal after 3 years

Hope this is helpful.

Answer:

find the positive square root of 7.3441 Which of the following equations is equivalent to 6(3p – 2) = 20? 18p – 2 = 20 18p – 12 = 20 9p – 8 = 20 9p – 4 = 20 Three less than 3 times a number, n, is 19 more than twice the number.

Step-by-step explanation:

Answer:

(a) $ 30000 + 1500 t

(b) $ 52500

Step-by-step explanation:

Initial profit = # 30,000

Profit increases every year by 5 %.

(a) Let the profit after t year is

P = $ 30,000 + 5% of 30,000 t  = $ 30000 + $ 1500 t

(b) t = 15 years

P = $ 30000 + $ 1500 x 15 = $ 52500  

Using exponential function concepts, it is found that:

a) The model is: [tex]A(t) = 30000(1.05)^t[/tex]

b) The prediction for her profits in 15 years is of $62,368.

An increasing exponential function is modeled by:

[tex]A(t) = A(0)(1 + r)^t[/tex]

In which:

Item a:

Then, the model is:

[tex]A(t) = A(0)(1 + r)^t[/tex]

[tex]A(t) = 30000(1 + 0.05)^t[/tex]

[tex]A(t) = 30000(1.05)^t[/tex]

Item b:

In 15 years, the estimate for the profits is of:

[tex]A(15) = 30000(1.05)^{15} = 62368[/tex]

The prediction for her profits in 15 years is of $62,368.

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Answer:

m = 5, n = - 1

Step-by-step explanation:

Given

x² + 4x - 5

Consider the factors of the constant term (- 5) which sum to give the coefficient of the x- term (+ 4)

The factors are + 5 and - 1 , since

5 × - 1 = - 5 and 5 - 1 = + 4 , then

x² + 4x - 5 = (x + 5)(x - 1)

with m = 5 and n = - 1

Answer:

0.6

Step-by-step explanation:

cos H = GH/FH

FH^2=20^2+15^2

FH^2=400+225=625

FH=25

cos H= 15/25=3/5=0.6

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

Explanation:

Before we can apply a trig ratio, we need to find the length of the hypotenuse. Use the pythagorean theorem.

a^2 + b^2 = c^2

c^2 = a^2 + b^2

c = sqrt(a^2 + b^2)

c = sqrt(15^2 + 20^2)

c = 25

The hypotenuse is 25 units long, which is the length of segment FH.

Now we can find the cosine ratio

cos(angle) = adjacent/hypotenuse

cos(H) = GH/FH

cos(H) = 15/25

cos(H) = 3/5

cos(H) = 0.6

Answer:

5 / 648

Step-by-step explanation:

Given tbe sample space for a pair of dice attached below :

Sample space for a pair of dice = 6² = 36

Rolling a 3 first :

Recall, probability = required outcome / Total possible outcomes

P(rolling a 3). = 2 / 36 = 1 /18

Probability of rolling a 6 (second roll)

P(rolling a 6) = 5 / 36

Hence,

P(3) then P(6) ;

1 / 18 * 5/36 = 5 / 648

Answer:

I don't understand this

Step-by-step explanation:

0.7 decimeter =

70,000,000 nanometers

Answer:

D = 51, other = 30

Step-by-step explanation:

d = | 5  1 |

     |-1  10|

D = (5 x 10) - ( 1 x -1) = 50 + 1 = 51

| 2   4|

|-3   9|

(2 x 9) - (4 x -3) = 18 + 12 = 30

Answer:

[tex]x^2 + ( y + 4)^2 = 52[/tex]

Step-by-step explanation:

Equation of circle with center (a , b) and radius, r is :

[tex](x -a)^2 + ( y -b)^2 = r^2[/tex]

Given :  a = 0 , b = - 4

Step 1 : Find the radius.

       Given ( 6 , 0 ) lies on the circle. Therefore the distance between the center (0 , - 4) of the circle and ( 6 , 0 ) gives the radius of the circle.

   [tex]r = \sqrt{( 0 - 6)^2 + ( -4 - 0)^2} \\\\[/tex]

     [tex]= \sqrt{ 36 + 16 } \\\\= \sqrt{52}[/tex]

Step 2 : Equation of circle.

  [tex](x - 0)^2 + (y -( - 4))^2 = (\sqrt{52})^2\\\\x^2 + ( y+ 4)^2 = 52[/tex]

Answer:

-32 shall be multiplied to get the answer.

Step-by-step explanation:

DON'T MIND MY WRITING!!

Answer:

135g

Step-by-step explanation:

[tex]\boxed{mass = density \times volume}[/tex]

Given: density= 5g/cm³, volume= 27cm³

Mass

= 5 ×27

= 135g

Answer:

y = 6x + 22

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = 6x - 1 ← is in slope- intercept form

with slope m = 6

Parallel lines have equal slopes, then

y = 6x + c ← is the partial equation

To find c substitute (- 3, 4 ) into the partial equation

4 = - 18 + c ⇒ c = 4 + 18 = 22

y = 6x + 22 ← equation of parallel line

Answer:

A. Definition of angle bisector

Step-by-step explanation:

Given that ΔABC is an isosceles triangle where AB = BC, and that BD bisects ∠ABC, then by the definition of angle bisection of ∠ABC, we have;

m∠ABD = m∠CBD

The correct option is option A. Definition of angle bisector

Also, given that ΔABC is an isosceles triangle and BD is the angle bisector of ∠ABC, we get;

AD = CD and BD = BD

We can therefore, also find that ΔABD ≅ ΔCBD by Side Side Side (SSS) rule of congruency

4. MIke divided the group into 5 groups. If there were 28 people in each group how big was the original group?

a. What are they asking for?

how big was the original group?

b. identify all the necessary numbers.

28,5

c. write the equation or problem in numeric form.

x=28*5

d. solve the math.

x=140

e.write the answer

. the original group contains 140 people.

5. If he difference is 589 and the subtrahend is 339,what is the minuend?

a. What are they asking for?

what is the minuend?

b. identify all the necessary numbers.

589,339

c. write the equation or problem in numeric form.

x=589-339

d. solve the math.

x=250

e.write the answer.

minuend=250

6. If the quotient is 17 and the dividend 765, what is the divisor?

a. What are they asking for?

what is the divisor?

b. identify all the necessary numbers.

17,765

c. write the equation or problem in numeric form.

x=765/17

d. solve the math.

x=45

e.write the answer.

divisor is 45.

4. Solution

a. How big was the original group?

b. 28 and 5

c. x = 28×5

d. x = 140

e. There are 140 people in original group.

5. Solution

a. What is the minuend?

b. 589 and 339

c. x = 589-339

d. x = 250

e. The minuend is 250.

6. Solution

a. What is the divisor?

b. 17 and 765

c. x = 765/17

d. x = 45

e. Hence, 45 is the divisor.