In ΔIJK, the measure of ∠K=90°, KJ = 63, IK = 16, and JI = 65. What ratio represents the sine of ∠I?

By using trigonometry, it can be calculated that The measure of the angle is 53.13° First option is correct.

What is Trigonometry?

Trigonometry is a branch of mathematics that studies relationships between the sides and angles of triangles. It is used to calculate lengths, angles, and other geometric figures. Trigonometry has applications in many fields, including engineering, astronomy, and navigation. The most common trigonometric functions are sine, cosine, and tangent. These functions are used to solve problems related to triangles, circles, and other geometric figures. Trigonometric identities are also used to solve algebraic equations. Trigonometry is an important tool for studying the physical world, as it allows us to calculate the position and motion of objects in space.

There are six trigonometrical functions. They are

[tex]sin\theta, cos\theta, tan\theta, cot\theta, sec\theta, cosec\theta[/tex]

[tex]sin\theta = \frac{perpendicular}{hypotenuse}\\cos\theta = \frac{baser}{hypotenuse}\\tan\theta = \frac{perpendicular}{base}\\cot\theta = \frac{base}{perpendicular}\\sec\theta = \frac{hypotenuse}{base}\\cosec\theta = \frac{hypotenuse}{perpendicular}\\[/tex]

Trigonometry is a very important tool in mathematics.

Here, the trigonometric function given is

[tex]cos\theta = \frac{3}{5}[/tex]

[tex]\theta = cos^{-1}(\frac{3}{5})[/tex]

[tex]\theta = 53.13^{\circ}[/tex]

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Answer:

22.2x²

Step-by-step explanation:

3.7x = 3.7 × x

6x = 6 × x

Multiplication of 3.7x and 6x

= 3.7 × 6 × x × x

= 22.2 × x²

= 22.2x²

Answer:

C. 22.2x^2

Step-by-step explanation:

Answer:

93 minutes

Step-by-step explanation

23/68 x/275= 93 min

The like terms to make a simpler expression is   19 x^2-6 x+9 n-6

Group like terms

What is simpler expression?

Solving a math problem is the same thing as simplifying an expression. You basically strive to write an expression as simply as you can when you simplify it. At the conclusion, there shouldn't be any more multiplication, dividing, adding, or subtracting to be done.

[tex]=12 x^2+7 x^2+7 x-3 x-11 x+3 n+6 n-7+1+5-5[/tex]

Add similar elements[tex]: $12 x^2+7 x^2=19 x^2$[/tex]

[tex]=19 x^2+7 x-3 x-11 x+3 n+6 n-7+1+5-5[/tex]

Add similar elements: [tex]$7 x-3 x-11 x=-7 x$[/tex]

[tex]=19 x^2-7 x+3 n+6 n-7+1+5-5[/tex]

Add similar elements: [tex]$3 n+6 n=9 n$[/tex]

[tex]=19 x^2-7 x+9 n-7+1+5-5[/tex]

Add the numbers: [tex]$-7+1+5-5=-6$[/tex]

[tex]=19 x^2-7 x+9 n-6[/tex]

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There is an effective change of 50% in the school.

What is Percentage?

A percentage is a relative figure that represents the hundredth part of any amount. One percent (symbolised 1%) is one hundredth part; consequently, 100 percent denotes the complete amount and 200 percent defines twice the supplied amount.

Solution:

To find the net/effective change we can the use the formula:

(a + b + ab/100)

here a and b are the rate of change

a = 25% and b = 20%

Net change = (25 +20 + 500/100) = 45 + 5 = 50%

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Answer:

$1916.73

Step-by-step explanation:

[tex]I=Prt=P(0.0401)(13/12) \\ \\ \implies P+P(0.0401)(13/12)=2000 \\ \\ P=\frac{2000}{1+(0.0401)(13/12)} \approx \$1916.73[/tex]

Answer:

R = (3, 14 )

Step-by-step explanation:

given endpoints (x₁, y₁ ) and (x₂, y₂ ) then the midpoint M is

( [tex]\frac{x_{1}+x_{2} }{2}[/tex] , [tex]\frac{y_{1}+y_{2} }{2}[/tex] ) ← midpoint formula

calculate the midpoint of PR using this formula and equate x and y coordinates to the coordinates of the given midpoint

let coordinates of R be (x, y ) and P = (- 15, 4 ) , then

[tex]\frac{x-15}{2}[/tex] = - 6 ( multiply both sides by 2 )

x - 15 = - 12 ( add 15 to both sides )

x = 3

and

[tex]\frac{y+4}{2}[/tex] = 9 ( multiply both sides by 2 )

y + 4 = 18 ( subtract 4 from both sides )

y = 14

the coordinates R = (3, 14 )

im not sure if you made a mistake and meant hundredths or not but if you are adding hundreds it would be 59.031 but if you adding hundredths is would be 0.621.

The average of the provided numbers is calculated by dividing the total number of values by the sum of all the values that different socioeconomic classes are affected differently by religion membership.

The middle number, which is determined by dividing the sum of all the numbers by the total number of numbers, is the average value in mathematics. When determining the average for a collection of data, we add up all the values and divide this sum by the total number of values. a single number (such as a mean, mode, or median) that encapsulates or depicts the overall importance of a collection of disparate data. unkind sense 1b.: a calculation that approximates the arithmetic mean. an intellectual level that is characteristic of a group, class, or series. superior than average.

[tex]65, 85, 70, 90, 105.[/tex]

Average =

[tex](65+85+70+90+105)/5\\= 415/5\\= 83\\[/tex]

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The equations that are equivalent are (b) 8k ÷ 4 = 20 ÷ 4, (c) 8k × 3 = 20 × 3 and (d) 8k + 10 = 20 + 10

From the question, we have the following parameters that can be used in our computation:

8k = 20.

Divide both sides of the equation by 4

So, we have the following representation

8k ÷ 4 = 20 ÷ 4

Multiply both sides of the equation by 3

So, we have the following representation

8k × 3 = 20 × 3

Add 10 to both sides of the equation

So, we have the following representation

8k + 10 = 20 + 10

Hence, the equivalent equation is 8k + 10 = 20 + 10

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Because Pisaster is a keystone species, the proportion of living mussels was comparable to the control after Nucella removal.

Sea otters and sea gulls hunt for and eat Pisaster ochraceous. Its function as a keystone species has been well researched. When it was gone from Washington's intertidal regions, the area's species diversity declined.

Sea otters and sea gulls hunt for and eat Pisaster ochraceous. Its function as a keystone species has been well researched. When it was gone from Washington's intertidal regions, the area's species diversity declined.

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36% of the animals in the shelter are hamsters.

[tex]\frac{27}{75}= 0.36[/tex]

0.36 = 36%.

36% of the animals in the shelter are hamsters.

To calculate how much money David will have in this account after 5 years, we first need to find out how much interest the account earns each year. To do this, we need to multiply the interest rate by the amount of money in the account. In this case, the interest earned each year would be $800 * 0.023 = $18.40.

Next, we need to calculate how much interest the account earns over the 5-year period. Since the interest is compounded semiannually, this means that the interest is earned twice per year. Therefore, the total amount of interest earned over 5 years would be $18.40 * 2 * 5 = $184.

Finally, we need to add the interest to the original amount of money in the account to find out how much money David will have after 5 years. In this case, the total amount of money David will have after 5 years is $800 + $184 = $984.

Therefore, if David keeps the money in this account for 5 years, he will have $984.

Answer:

$897

Step-by-step explanation:

We know:

P = 800

n = 2

r = 2.3

t = 5

Write Equation:

[tex]F = 800(1+\frac{\frac{2.3}{100} }{2} )^{2(5)}[/tex]

Evaluate:

896.9

Thus the answer is $897

Answer:

For the first one x= 60 degrees

Second one x= 125 degrees

Step-by-step explanation:

a) To figure out this we can see that the total of angles in a 5- angled shape is 540 degrees.

So (2x X 4) + x = 540 degrees

= 9x= 540

= x = 60

b) To figure out this we can see that the total of angles in a 7- angled shape is 900 degrees.

So 60+2x+x+x+x+x+90= 900

= 150 +6x= 900

= 6x= 750

= x= 125

a) The phasor form of E-field = xˆ 2cos(wt - kz) - yˆ 4cos(wt - kz) is 2√5 L(-63.43).

Polarization type is linearly polarised.

b) The phasor form of E-field = ?

E(z,t) = xˆ 2cos(wt + kz) - yˆ 4sin(wt + kz) is E(z,t) =2√5 L(-143.43). polarization type is elliptical.

We have given that

E⃗(z,t) =2xˆcos(wt - kz) - 4 yˆcos(wt - kz)

|r⃗ | = √((2cos(wt - kz))² + (- 4cos(wt - kz))²)

= √(4cos²(wt - kz) + 16cos²(wt - kz))

= √(20cos²(wt - kz))

= 2√5 cos(wt - kz)

φ = 4cos(wt - kz)/(2cos(wt - kz))

= tan⁻¹ 1(-2) = -63.43°

So, E(z,t) = 2√5 L(-63.43)

b) E(z,t) = xˆ 2cos(wt + kz) - yˆ 4sin(wt + kz)

= xˆ 2cos(wt + kz) - yˆ 4cos(wt + kz -π/2)

|r| = √((2cos(wt + kz))² + (- 4sin(wt -+kz))²)

= √20

phi = tan⁻¹(- 4cos(wt - kz)/(2cos(wt - kz)) - π/2

= tan⁻¹( -2) + π/2 = - 143.43

so, E(z,t) =2√5 L(-143.43)

E(z,t) = xˆ 2cos(wt - kz) - yˆ 4cos(wt - kz)

if wt = 0°

E(z,t) = xˆ 2cos(0 - kz) - yˆ 4cos(0- kz)

= 2xˆ - 4yˆ

wt = 30° , E(z,t) = xˆ 2cos( - kz) - yˆ 4cos(0- kz)

E(z,t) = √3/2(2) xˆ - √3/2(4) yˆ

= √3xˆ - 2√3yˆ

for wt = 45°

E(z,t) = √2 xˆ - 2√2 yˆ

for wt = 90° =>E(z,t) = 0

for wt = 60° , E(z,t) = xˆ - 2 yˆ as seen in above graph that is linear polarised

For part (b) ,

E(z,t) = 2 xˆcos(wt - kz) - 4yˆ sin(wt + kz)

From graph elliptical polarised,

for wt = 0 , E(0,t) = 2 xˆ

for wt = 90° , E(0,t) = -4yˆ

for wt =180° , E(0,t) = -2 xˆ

for wt = 270° , E(0,t) = -4yˆ

Hence, we get the answer of both parts.

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Answer:

Yes, your answer would be correct.

Step-by-step explanation:

That graph intersects at (0, 2), is a solid line, and the slope is -2.

Step-by-step explanation:

whenever you see a variable ( a letter )  without a number in front of it, add a 1 ! It means the same thing...

y is the same as 1y

1). 3y + y = ?

Add that 1!

3y + 1y = ?

This problem is the same as 3 + 1

3y + 1y = 4y

2). b + b = ?

Add those 1's !

1b + 1b = ?

this is the same as 1 + 1

1b + 1b = 2b

Remember to keep the variable !

Part B is like a puzzle and the instructions give us hints.

It is telling us, when we see an r, we replace it with the number 3

and when we see t , we replace it with the number 9

Let's solve these puzzles!

8). [tex]\frac{r}{t} = ?[/tex]

We see and r and a t, let's plug in 3 and 9

Now we have ...

[tex]\frac{3}{9} = ?[/tex]

Divide using a calculator!

We get ....

[tex]\frac{3}{9} = \frac{1}{3}[/tex] or 0.33

9). [tex]rt = ?[/tex]

When variables are right next to each other, this means they are being MULTIPLIED!

Let's replace r and t with 3 and 9 and multiply them together!

[tex]rt =[/tex] 3 × 9

3 × 9 = 27

We do similar things for Part C

12). [tex]ab = ?[/tex]

It tells us a = 5 and b = -4

Let's plug it in

[tex]ab =[/tex]  5 × -4

5 × - 4 = -20

USE THESE EXAMPLES AND TIPS TO COMPLETE THE REST OF THE PROBLEMS AND I WILL CHECK THEM FOR YOU.

COMMENT THEM BELOW

Answer:

7/12

Step-by-step explanation:

I set up the equation, but I first had to find the common denominator which is 12 so I multiplied 3/4 by 3 (top and bottom) and I multiplied 1/6 by 2   (also top and bottom) So I got 9/12-2/12 and when I subtracted I got 7/12

(hope you understood how I got my answer..)

Answer: -5/3

Down -5

right 3

Step-by-step explanation: count the distance between the 2 dots looking from the y axis (up and down)and from the x axis (left to right)

Answer:

684.

Step-by-step explanation:

Answer: 3/5

Step-by-step explanation:

Let x be the required solution:

so, x= 3- (12/5)

⇒ 5x = 15-12 (Multiplying both sides 5 so that the denominator is the same)

⇒ 5x = 3

∴ x = 3/5

The magnitude of the acceleration of the particle is zero when the velocity of the particle is zero.

What is Acceleration ?

Acceleration is the rate of change of velocity. Usually, acceleration means the speed is changing, but not always. When an object moves in a circular path at a constant speed, it is still accelerating, because the direction of its velocity is changing.

Given,

Velocity  v= x² − 5x + 4

now, the acceleration

a = dv/dt

​a = 2x (dx/dt) - 5x(dx/dt)

​

given that, v= dx/dt =0

so, a = 2x*0−5*0

a=0 m/sec²

so, the acceleration is zero ,when the velocity is zero.

Hence ,The magnitude of the acceleration of the particle is zero when the velocity of the particle is zero.

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Answer:

Z

Step-by-step explanation:

Angle V is congruent to angle z because they have the same placement in the letter order.

Answer:

x = 3.66

Step-by-step explanation:

Area of a rectangle = length * width

In this case:

(x+10)x = 50

x*x + x*10 = 50

x² + 10x - 50 = 0

x = {-10±√((10²) -(4*1*-50))} / (2*1)

x = {-10±√(10² + 200)} / 2

x = {-10±√(100+200)} / 2

x = {-10±√300} / 2

x = {-10±17.321} /2        aprox,

It is a geometric figure so only the positive value is taken.

x = {-10+17.321} / 2

x = 7.321/2

x = 3.66

Check:

3.66(3.66+10) = 50

3.66*13.66 = 50

Answer:

CHECKING

let W = 10

C = W/2

C = 10/2

C = 5

C = 5     W = 10

Step-by-step explanation:

The ordered pairs to the system of linear inequality are (-1, 5), (0, 4), (-6, 7)

A system of linear inequalities in two variables consists of at least two linear inequalities in the same variables. The solution of a linear inequality is the ordered pair that is a solution to all inequalities in the system and the graph of the linear inequality is the graph of all solutions of the system.

In the problem given;

x + 5y > 8 ...eq(i)

4x - y < 6 ...eq(ii)

From eq(i)

x + 5y > 8

x > 8 - 5y ...eq(iii)

however, this can easily be solved using a graph.

Plotting the inequality in a graph line;

The ordered pairs are (-1, 5), (0, 4), (-6, 7)

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