Find the value of GM If DM = 35

Given: [tex]cosec[/tex] [tex]A[/tex]  [tex]=\sqrt{2}[/tex]

∴ [tex]A=\frac{\pi }{4} =45^{0}[/tex]

[tex]sin[/tex] [tex]A[/tex] [tex]=sin[/tex] [tex]45^{0}[/tex] = [tex]\frac{1}\sqrt{2}[/tex]

[tex]cot[/tex] [tex]A[/tex] [tex]=cot[/tex] [tex]45^{0}[/tex] [tex]=1,[/tex]

[tex]tan[/tex] [tex]A[/tex] [tex]=[/tex] [tex]tan[/tex] [tex]45^{0}[/tex] [tex]=1[/tex]

[tex]cos[/tex] [tex]A[/tex] [tex]=[/tex] [tex]cot[/tex] [tex]45^{0}[/tex] [tex]=\frac{1}{\sqrt{2} }[/tex]

∴ [tex]=2[/tex]

[tex]\large\underline{\sf{Solution-}}[/tex]

METHOD 1: Using Trigonometric values.

We have given that,

[tex]\sf\cosec\theta=\sqrt2[/tex]

So,

[tex]\sf\theta=45^{\circ}[/tex]

We need to find:

[tex]\sf\dfrac{1+\sin^2\theta+\cos^2\theta}{1+\sec^2\theta-\tan^2\theta}[/tex]

So,

[tex]\sf\longmapsto\dfrac{1+\sin^2(45^{\circ})+\cos^2(45^{\circ})}{1+\sec^2(45^{\circ})-\tan^2(45^{\circ})}[/tex]

[tex]\sf\longmapsto\dfrac{1+\left(\frac{1}{\sqrt2}\right)^2+\left(\frac{1}{\sqrt2}\right)^2}{1+(\sqrt2)^2-(1)^2}[/tex]

[tex]\sf\longmapsto\dfrac{1+\frac{1}{2}+\frac{1}{2}}{1+2-1}[/tex]

[tex]\sf\longmapsto\dfrac{1+1}{2}[/tex]

[tex]\sf\longmapsto\dfrac{2}{2}[/tex]

[tex]\sf\longmapsto\bf1[/tex]

METHOD 2: Using Trigonometric Identities

We need to find:

[tex]\implies\dfrac{1+\sin^2\theta+\cos^2\theta}{1+\sec^2\theta-\tan^2\theta}[/tex]

But, we know that,

[tex]\sf\red⇛ \sin^2\phi+\cos^2\phi=1[/tex]

And,

[tex]\sf\red⇛ \sec^2\phi-\tan^2\phi=1[/tex]

So,

[tex]\sf\longmapsto\dfrac{1+(\sin^2\theta+\cos^2\theta)}{1+(\sec^2\theta-\tan^2\theta)}[/tex]

[tex]\sf\longmapsto\dfrac{1+1}{1+1}[/tex]

[tex]\sf\longmapsto\dfrac{2}{2}[/tex]

[tex]\sf\longmapsto\bf1[/tex]

Therefore, by both methods the answer is 1.

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Similar questions

Prove that:

\cos( \frac{3\pi}{2} + \theta) \cos(2\pi + \theta) [ \cot( \frac{3\pi}{2} - \theta) + \cot(2\pi + \theta) ] = 1...

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Answer:

For the first one put 3/5 then for the other box I THINK its 15

Step-by-step explanation:

Answer:

n=27

Step-by-step explanation:

(n+6)° + (2n+5)° +90° = 180°

3n+9=90

3n=81

n=27

Sorry if I did it wrong

Answer:

isoseles triangle

explanation: none of the sides are the same

hope this helps

Answer: SCALENE

Step-by-step explanation:

All sides are unequal, ISOSELES has 2 equal sides and EQUILATERAL all sides are equal.

Answer: No difference

Step-by-step explanation:

The function f(x)=-2x+6 will produce the very same points in the table.

x y y calculated

2 2 2

5 -4 -4

8 -10 -10

11 -16 -16

The points are all on the line y=-2x+6. They describe the same line, which will have the same intercept.

Answer:

I'm not sure, but I'll try

Step-by-step explanation:

(Side)^2 = (Hypotenuse)^2 - (Side)^2

(Side)^2 = (9)^2 - ( √ 65 )^2

(Side)^2 = (81) - (65)

(Side)^2 = 16

Take root of answer

Side = √16

Side = 4

Answer = 4

_________

[tex] \: [/tex]

a² = c² - b²

a² = 9² - (√65)²

a² = 81 - 65

a² = 16

a = √16

a = 4

Answer:

25%

Step-by-step explanation:

(original value - new value / original value) x 100

So

4 - 3 = 1

1/4 = 0.25

0.25 x 100 = 25

So there was a 25% decrease in the number of apples bought.

Hope it helps :)

Answer:

A (0,0)

Step-by-step explanation:

When a function intersects the y-axis then the point of intersection is called y-intercept of the function,

Also, for y-intercept x = 0.

That is, if f(x) is the function then its y-intercept is (0, f(0) )

By the given table for x = 0, f(x) = 0

Hence, the y-intercept of the given function is (0,0),

Option A is correct.

Answer: The attachment is a bit difficult to read, and long.  I'll make some suggestions and add some detail to a few of the problems, but would ask that these suggestions be applied to other problems to find the answers.

Step-by-step explanation:

9.   Coinciding lines line on top of each other.  I.e., they are the same equation.  If we take A, for example, we can reduce the second expression by dividing by 2:  (2x+4y=6)/2 = (x + 2y = 3).  This matches the first expression (x + 2y = 3).  !   Whoa, that went fast.

10.   (x+8)(x-8) = x² +8x -8x - 64 = x² - 64

11.  I don't have the time to explain how one can factor, but practice is important.  And I don't know if this is completely factored, but it matches one of the options.  Try (n-2)(n²+2n + 4)  [n³ +2n² +4n - 2n² -4n -8 = n³ - 8.  It works.

12.  The denominators are the same, so add the numerators and keep the denominator.  (7x+4y)/x²y

13.  The slope is the "Rise" over the "Run."  (3,4), (8,-1)  Rise = (-1 - 4) = -5.  Run = (8-3) = 5  Slope = -(5/5) = -1

14.  A line with a positive slope will move upwards as x increases.  We can eliminate options C and D immediately.  That leaves A and B.  The line we are looking for is y = 5x + b.  We are not given b, the y-intercept, so determine the slopes of both lines:  I get 4 for A and 5 for B.  To confirm B is correct, we could calculate b for y=5x+b by using given point, (2,3).  3 = 5*2 + b, b = -7.  We can't see this point (0,-7) on the graph, but it appears correct.  B is the best answer.

15.  The line will have the form of y=mx+b.  Calculate m, the slope, from the two points (3,1) and (4,7).  Rise = 6, Run = 1  Slope = 6.  y=6x+b.  Find b by using either of the given poins and solving for b.  I'll choose (3,1).  y=6x+b;  1 = 18 + b; b = -17.  The equation is y=6x-17.  Rearrange option A (y =6x - 17).

16.  The second value in each factor must, when multiplied together, equal the final term of the original expression, -9y².  I see only one option for which that is true, C.  Multiply the two factors in C to be certain, and you'll find they result in the correct expression.

Answer:

Same Side Interior Angles

Step-by-step explanation:

Angle 7 and angle 14 are both inside of the two transversal lines E and M, and are on the same side of the line Q, making them both same side interior angles

-Chetan K

Answer:

15

Step-by-step explanation:

95 - 50 = 45

45/3 = 15

Step-by-step explanation:

28 dollars is the answer

Answer:

n-12= number of cookies left

Answer:

y=n-12

Step-by-step explanation:

y= how many cookies are left

n = number of cookies

-12 = how many his friends ate

Answer:

EF ║ CD and AB ║ CD are the parallel segments.

Step-by-step explanation:

The given question is incomplete without picture; here is the picture attached with the answer.

Since m∠A = m∠D = 42°

Therefore, AB ║ CD and segment AD is the transverse.

Now ∠AEF + ∠IEF = 180° [Supplementary angles]

138° + ∠IEF = 180°

∠IEF = 180 - 138

       = 42°

∠IHG + ∠DHG = 180° [ Supplementary angles ]

∠IHG + 122 = 180

∠IHG = 180 - 122

∠IHG = 58°

But ∠IEF ≠ ∠IHG

Therefore, EF and GH are not parallel.

If the segments AB and GH are parallel then ∠IHG = ∠IAB (By the property of alternate angles)

But ∠IHG ≠ ∠IAB

Therefore, AB and GH are not parallel.

Now ∠IEF ≅ ∠IDC ≅ 42° [alternate angles]

which reveals that EF ║ CD

Therefore, EF ║ CD and AB ║ CD

Answer:

THIS MATH WEBSITE HELPS A LOT, TYPE YOUR QUESTION AND IT'LL ANSWER IT LOL

Step-by-step explanation:

wish you the best! gl!

The attached image is the graph.

Answer:

The Graph Below

Step-by-step explanation:

You would start at 2 on the y-axis and going down 3 on the y-axis and move over 1 on the x-axis

I hope this helps

Answer:

(6,3), (10,5),(14,7)

Step-by-step explanation:

6/3 = 2

10/5 = 2

14/7 = 2

Answer:

Step-by-step explanation:

There are two options as below.

1. JL/JK = 5 : 1

Find the coordinates of L:

The point is L(8, - 10)

2. JL/JK = 1 : 5

Find the coordinates of L:

The point is L(0, 6)

Answer:

5300

Step-by-step explanation:

Round 4619 up to 5000.

Round 288 up to 300.

Add them together!

Answer:

15

Step-by-step explanation:

[tex]x^{2} + 2x = 3^{2} + 3 * 2 = 9 + 6 = 15[/tex]

3 · 2 = 6

2 · 3 = 6

6 + 6 = 12

Have a luvely day!

Answer:

a) 168

b) 3

Step-by-step explanation:

a) 56÷4=14 14×12=168

b) 56÷4=14 56-14=42 42÷14=3

Answer:

[tex]1) \: \: \frac{5x}{2y} \\ a) \: \: x = 8 \: \: and \: \: y = 10 \\ \frac{5x}{2y} \\ \frac{5(8)}{2(10)} \\ \frac{40}{20} \\ 2 \: ans \\ b) \: \: \frac{5x}{2y} \\ \frac{5( \frac{1}{2}) }{2( \frac{2}{3}) } \\ \frac{2.5}{1.3} \\ \frac{25}{13} \\ 1.92 \: \: ans \: \\ \\ 2) \: \: \frac{a {b}^{3} }{c} \\ \\ a) \: \: a = 4 \: .\: b = 3 \: . \: c = 2 \\ \\ \frac{a {b}^{3} }{c} \\ \frac{(4) {(3)}^{3} }{2} \\ \frac{4(27)}{2} \\ \frac{108}{2} \\ 54 \: \: ans \: \\ \\ b) \: \: a = - 2 \: . \: b = - 2 \: . \: c = 2 \\ \\ \frac{a {b}^{3} }{c} \\ \frac{( - 2) {( - 2)}^{3} }{2} \\ \frac{ - 2 { (- 2)}^{3} }{2} \\ \frac{ - 2( - 8)}{2} \\ \frac{16}{2} \\ 8 \: \: ans \: [/tex]

Step-by-step explanation:

question 3 is already answered by me in your question..or you can see attachment.

Answer:

p = 18

Step-by-step explanation:

4(p-7) = 44

The operations in order are to distribute first, 4p - 28 = 44

Isolate the variable, 4p = 72

and divide for the answer, p = 18

P stands for pictures, the number of pictures that can be saved to your photo stream at once is 18.

Answer:

More and more of product AB but limited to the amount of B

Step-by-step explanation:

Adding more of one substance which makes up the reactant will increase the number of product AB that will be obtained but limited by the amount of B.

The amount of reacting substances is directly proportional to the amount of product yield. This means that adding more and more of the substance which makes up the reactant increases the amount of atoms reacting to form a product.

Hence, adding more and more of only substance A will increase the product AB, however, the amount of B in the product will be limited.

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Answer:

25.)Yesss

26.)Yesss she have enough money to buy a popcorn and soda

27.)?

Step-by-step explanation:

#Hopeee it Helpssss

follow me pls.

Answer:

x-intercept = 2

Step-by-step explanation:

Sum = 3

Product = -10

Factors = 5 , (-2)      {5*(-2) = -10  & 5 +(-2) = 3)

Rewrite the middle term using the factors: 3x = 5x - 2x

x² + 3x - 10 = x² + 5x - 2x - 10

                  =x(x + 5) - 2(x + 5)

                  = (x +5)(x - 2)

x² + 8x +15 = x² + 3x + 5x + 15

                  = x(x + 3) + 5(x + 3)

                  = (x + 3)(x + 5)

[tex]f(x) =\dfrac{x^{2}+3x -10}{x^{2}+8x + 15}\\\\=\dfrac{(x+5)(x -2)}{(x+5)(x+3)}\\\\=\dfrac{x-2}{x+3)}[/tex]

At x-intercept, y = o

[tex]\dfrac{x -2}{x + 3}=0\\[/tex]

x - 2 = 0

x  = 2

Answer:

y=-2x+1

Step-by-step explanation:

Just look at photo dap