Prove using the trigonometric identities the following equation

Answer:

[tex]\sqrt{205}[/tex]

Step-by-step explanation:

Using the pythagorean theorem, [tex]x^{2} +18^{2} =23^{2} \\[/tex] so that means [tex]x^{2} = 23^{2} -18^{2} =205[/tex] so x = [tex]\sqrt{205}[/tex]

Answer:

a) 10/3  

b) hyperbola

c) x = ± 6/5

Step-by-step explanation:

a) A conic section with a focus at the origin, a directrix of x = ±p where p is a positive real number and positive eccentricity (e) has a polar equation:

[tex]r=\frac{ep}{1\pm e*cos\theta}[/tex]

Given the conic equation: [tex]r=\frac{12}{3-10cos\theta}[/tex]

We have to make it to be in the form [tex]r=\frac{ep}{1\pm e*cos\theta}[/tex]:

[tex]r=\frac{12}{3-10cos\theta}\\\\multiply\ both\ sides\ by\ \frac{1}{3} \\\\r=\frac{12*\frac{1}{3}}{(3-10cos\theta)*\frac{1}{3}}\\\\r=\frac{12*\frac{1}{3}}{3*\frac{1}{3}-10cos\theta*\frac{1}{3}}\\\\r=\frac{4}{1-\frac{10}{3}cos\theta } \\\\r=\frac{\frac{10}{3}(\frac{6}{5} ) }{1-\frac{10}{3}cos\theta }[/tex]

Comparing with  [tex]r=\frac{ep}{1\pm e*cos\theta}[/tex]

e = 10/3 = 3.3333, p = 6/5

b) since the eccentricity = 3.33 > 1, it is a hyperbola

c) The equation of the directrix is x = ±p = ± 6/5

Answer:

  7.7 seconds

Step-by-step explanation:

Put the given height into the formula and do the arithmetic.

  t = √(290.57/4.9) = √59.3 ≈ 7.7 . . . seconds

The object will take 7.7 seconds to hit the ground.

Answer:

-1, -0.5, 0, 0.4, 1/5, 11/2

Step-by-step explanation:

Answer:

1) x = 6

2) 129

Step-by-step explanation:

For equation 1:

[tex]7x=42\\\\\frac{7x=42}{7}\\\\ \boxed{x=6}[/tex]

Expression 2:

Apply PEMDAS Rule.

[tex]8^2+9((12/3)*2)-7\\\\8^2+9(4*2)-7\\\\8^2+9(8)-7\\\\64+9(8)-7\\\\64+72-7\\\\136-7\\\\\boxed{129}[/tex]

Hope this helps.

Answer:

y = -2x + 1

Step-by-step explanation:

First, find the slope with rise/run (y2 - y1) / (x2 - x1)

We can use the points (-1, 3) and (0, 1)

Plug in the points:

(1 - 3) / (0 + 1)

-2/1

= -2

The y-intercept is (0, 1) because that is the point where the line intercepts the y axis. So, we can plug in the slope and y-intercept into the equation:

y = mx + b

y = -2x + 1

Answer:

[tex]\Large \boxed{\mathrm{A) \ 7}}[/tex]

Step-by-step explanation:

The triangle is a right triangle.

We can use trigonometric functions to solve the problem.

tan(θ) = opp/adj

tan(35) = x/10

Multiply both sides by 10.

10 tan(35) = x

x = 7.00207538...

Answer:

0.2146

Step-by-step explanation:

From the picture:

The radius of the circle = r. This means that the area of the circle = πr²

Also For the square, the length of the square = 2r, Therefore the area of the square = Length × length = 2r × 2r = 4r²

The area inside the square but outside the circle = Area of square - Area of circle = 4r² - πr² = r²(4 - π) = 0.8584r²

The ratio of the area inside the square but outside the circle to the area of the square =  r²(4 - π) / 4r² = (4 - π) / 4 = 1 - π/4 = 0.2146

Answer: Hi!

Option I is correct. 3(2x + 4) = 6x + 12

When you use the distributive property, you multiply the term outside of the parentheses (in this case, 3) by the terms inside of the parentheses (in this case, 2x and 4.)

Hope this helps!

Hello, please consider the following.

[tex](\forall x \in \mathbb{R}) \\ \\ x=(f^{-1}of)(x)\\\\=(fof^{-1})(x)\\\\=f(f^{-1}(x))\\\\=6\left( f^{-1}(x) \right) ^3-8 = x\\\\\text{We need to express }f^{-1}(x) \text{ in function of x.}\\\\\text{Let's do it!}[/tex]

[tex]6\left( f^{-1}(x) \right) ^3-8 = x\\\\\left( f^{-1}(x) \right) ^3 =\dfrac{x+8}{6}\\\\\Large \boxed{\sf \bf \ \ f^{-1}(x)=\sqrt[3]{\dfrac{x+8}{6}}\ \ }[/tex]

Thank you

Answer:

-i

Step-by-step explanation:

[tex]\sqrt{-1}[/tex] * [tex]\sqrt{-1}[/tex] * [tex]\sqrt{-1}[/tex] = -i

Answer:

8

Step-by-step explanation:

Numbers divisible by 12 and 30:

So, numbers should be divisible by 60

To find the greatest one divide 586 by 60 and take whole part of quotient, which is 9, so there are 9 multiples of 60 smaller than 586.

Excluding 60 which is less than 75.

So required number is 9 - 1 = 8.

Answer:

826×3569=2947994 ans

Answer:

178° 35'

Step-by-step explanation:

∠ACB and ∠ACD are supplementary, so they add up to 180°.

First, convert to degrees (there are 60 minutes in a degree).

∠ACB = 1°25' = 1° + (25/60)° = 1.4167°

Now find the supplementary:

∠ACD = 180° − 1.4167°

∠ACD = 178.5833°

∠ACD = 178° 35'

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

Explanation:

If angle x is the reference angle, then the side 9 is the adjacent side (it is the closer leg to angle x). The hypotenuse is 17 as it is opposite the largest angle. The largest side is always opposite the largest angle in a triangle.

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

cos(angle) = adjacent/hypotenuse

cos(x) = 9/17

x = arccos(9/17)

x = 58.034281249203

x = 58

Arccosine is the same as inverse cosine, written as [tex]\cos^{-1}[/tex]

Make sure your calculator is in degree mode.

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

Edit:

After finding x, we can find y

x+y = 90

58+y = 90

y = 90-58

y = 32

Answers reflection (b)

Step-by-step explanation:

it’s right on 8th grade khan ywwww

So he tried to reflect(b) map one figure onto the other using transformations.

If a quadrilateral is a parallelogram, then its opposite sides are congruent. If a quadrilateral is a parallelogram, then its opposite angles are congruent. If a quadrilateral is a parallelogram, then its diagonals bisect each other.

Both the theorems are proved now which states that quadrilaterals are congruent to one another. Note: Each diagonal of a parallelogram divides the parallelogram into two congruent triangles and the opposite sides of a parallelogram are congruent.

Learn more about the quadrilaterals are not congruent at

https://brainly.com/question/20429

#SPJ2

Answer:

2x - 2

Step-by-step explanation:

Order of Operations: BPEMDAS

Step 1: Distribute parenthesis

2x - 6 + 4

Step 2: Combine like terms

2x - 2

And we have our answer!

Answer:

[tex]2( x -3) + 4 \\ 2x - 6 + 4 \\ [/tex]

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

Explanation:

The fancy or strange looking E symbol is the greek uppercase letter sigma, to mean sum. So they want you to add the terms in the form x^2. The x values are from the list given to us.

x = 16 leads to x^2 = 256

x = 13 leads to x^2 = 169

etc etc

After squaring all the x values, we have this new list {256, 169, 25, 400, 196}

Lastly, you add up all the squared values to get the final answer of 256+169+25+400+196 = 1046

Answer:

10°

Step-by-step explanation:

The angle subtended at the circumference is half the angle subtended at the centre of the circle i.e. 20°÷2=10°

Answer:

Ms. Steiner

Step-by-step explanation:

Mr. Coelho

science = 25 / 50 = 1/2

math  = 30 / 40 = 3/4

not the same rate

Ms. Steiner

science = 20 / 50 = 2/5

math  = 12 / 30 = 2/5

It is the same rate, so they are proportional

Mr. Coelho:  Science: 50 minutes / 25 tests = 2 minutes per test

                     Math: 40 minutes / 30 tests = 1.33 minutes per test.

Ms. Steiner: Science: 50 minutes / 20 tests = 2.5 minutes per test.

                     Math: 30 minutes / 12 tests = 2.5 minutes per test.

The answer is Ms. Steiner.

Answer:

Step-by-step explanation:

Here, we'll use an apostrophe to signify the complement of a set.

__

(a) The shaded portion is two disjoint (non-overlapping) sections, so must be the union of something. The shaded space on the left is that part of A that is not in B, so it is A∩B'. Similarly, the shaded space on the right is that part of set B that is not in set A: A'∩B. Then the shaded area altogether is the union of these sets:

  (A∩B')∪(A'∩B)

__

(b) For this one, it might be easier to identify the unshaded area. That is where the sets A and B overlap, so it is A∩B. Then the area that is not that area is the complement of this:

  (A∩B)'

Answer:

No solution

Step-by-step explanation:

[tex]-38 - 7y = 2 - 7(y + 6)\\\\\mathrm{Expand\:}2-7\left(y+6\right):\quad -7y-40\\-38-7y=-7y-40\\\\\mathrm{Add\:}38\mathrm{\:to\:both\:sides}\\-38-7y+38=-7y-40+38\\\\Simplify\\-7y=-7y-2\\\\\mathrm{Add\:}7y\mathrm{\:to\:both\:sides}\\-7y+7y=-7y-2+7y\\\\Simplify\\\\0=-2\\\mathrm{The\:sides\:are\:not\:equal}\\No\: solution[/tex]

Answer:

No solution

Step-by-step explanation:

First do distribute property

-38-7y=2-7y-42

then combine like terms the 2 and the -42

-38-7y=-40-7y add 7y from both sides

-38+y=-40 add 38 to -40 you get -2

0=-2 no solution

Answer:

Cost of the item sold= $1,223

Step-by-step explanation:

Let

x= cost of the item sold

$97.84=commission on the item

Percentage of the commission=8%

To find the cost of the item sold

Commission=8% of cost of the item

97.84=0.08 * x

97.84=0.08x

Divide both sides by 0.08

97.84 / 0.08 = 0.08x / 0.08

1,223=x

x=$1,223

Therefore, cost of the item sold= $1,223

Answer:

8 inches

Step-by-step explanation:

The computation of the length, in inches of Segment line G prime A prime is shown below:-

Data provided

In two quadrilateral GAME and G'A'M'E',

ME = 35 inches

AM = GE = 56 inches

M'E' = 14 inches

Also, the perimeter of quadrilateral GAME = 167 inches

GA + AM + ME + GE = 167

Now we will put the values into the above equation

GA + 56 + 35 + 56 = 167

GA + 147 = 167

So,

GA = 20 inch

Therefore

GAME is closely related to G'A'M'E'

Now,

By the property of similar figures,

[tex]\frac{M E}{M' E'} = \frac{GA}{G'A'}[/tex]

[tex]G'A' = \frac{M'E'\times GA}{ME} \\\\ = \frac{14\times 20}{35}[/tex]

= 8 inches

Answer:

o the nearest tenth of ft

Length of one of the side= 14.6 ft

Step-by-step explanation:

Reed wants to have a square garden plot in his backyard. He has covered enough compost to cover an area of 214 square feet.

His square garden is a square one, and the area of a square is the square of one of it's sides .

So if the area= 214 ft²

Length of one of the side = √(214 ft²)

Length of one of the side= 14.6287 ft

To the nearest tenth of ft

Length of one of the side= 14.6 ft

Answer:

4y

Step-by-step explanation:

[tex]y- (-3y)\\\\\mathrm{Apply\:rule}\:-\left(-a\right)=a\\=y+3y\\\\=4y[/tex]

Hello there! :D

I love showing people how to use this concept, so lets get right to it! If you have trouble with negative (-) signs and how they interact with each other, I suggest you watch some Khan academy videos, it could realy help you in the future! :)

Alright, so here's the general rule: (multiplication and division)

-,-= +

-,+ = -

+,+=+

So, with this rule, I think we can solve!

Firstly, remember PEMDAS.

Let's look at the signs first. Two negatives equal a positive. Make the 3y in the parenthesis positive. Think of the negative sign as a -1 that is being multiplied by the (-3y) and the y.

That would look like this:

(y) (-1) (-3y)

Now we have:

y*(3y)

So when multiplying a variable by a variable, it becomes squared.

So, we would have 3y^2 or [tex]3y^{2}[/tex]

If you have any questions about this problem feel free to comment on this answer.

I hope this helped you and you have a wonderful day,

Kai xx

Answer:

Step-by-step explanation:

A. Data of the study: All 45 exercise times there were recorded from the participants in the study

B. Parameter of the study: The average amount of time that all clients exercise in one week.

C. Variable of the study: The amount of time that any given client from the fitness center exercises.

D. Population for the study: All clients at the fitness center.

E. Sample of this study: The 45 client from the fitness center who participated in the study.

F. Statistics of the study: The average amount of time that a sample of clients exercises in one week

Answer:

Rs 30800

Step-by-step explanation:

The formula for compound interest is

A = P[1 + (r/100)]^t, where

A = amount of compounded interest

P = principal amount

r = interest rate

Applying this to our question, we have

A = 25000 [1 + (10/100)] [1 + (12/100)]

A = 25000 (1 + 0.1) (1 + 0.12)

A = 25000 * 1.1 * 1.12

A = 25000 * 1.232

A = 30800