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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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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: D; B

Step-by-step explanation: 1 and 4 are alternate exterior angles if you use process of elimination, all the other pairs are, alternate exterior, corresponding or same side interior angles. angles 1 and 4 are in between lines a and b when lines a and b have the transversal of c. with process of elimination, c is the only logical answer, as 1 and 4 both lie on that line. which leaves you with two answers. if you draw out lines a and b with a transversal of c and the lines b and e with the transversal of c, then B is the only logical answer. goodluck :) i just finished this unit :D

Answer:

400=(×+20)× is the equation or

400=×^2+20×

(×+10)= square root of 500

×+10=10 radical 5

final answer -10 + or - 10 radical 5=×

the coefficient of term 4 is 2

Answer:

3rd option

Step-by-step explanation:

3(x + 8) - 9x = 6(4 - x) ← distribute parenthesis on both sides

3x + 24 - 9x = 24 - 6x , collect like terms on left side )

24 - 6x = 24 - 6x

Since both sides are the same then any value of x will make the equation true.

That is all real numbers are solutions

Answer: C g(x) is a function because f(x) is one-to-one.

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

to answer this algebraic question use BDMAS rule

first solve bracket then division, multiplication,addition then subtraction.

6+8-12

14-12

2

Answer:

9.8

Step-by-step explanation:

convert your decimal into a fraction so 2.3= 23/10

23/10 + 8 - 1/2

then calculate your sum or difference

leaving you with

49/5

meaning your answer is

9.8

Answer:

204

Step-by-step explanation:

Answer:

2,4

Step-by-step explanation:

Answer:

B. the slope of the graph of y = mx + b

Step-by-step explanation:

m is the slope.

y is the y value

x is the x value

b is the y intercept

the answer is

d. none of these

A) multiply the price of the game by 5%

42.99 x 0.05 = 2.1495 rounds to 2.15

Amount of tax = $2.15

B) add the amount of tax to the price of the game:

42.99 + 2.15 = 45.14

Total cost = $45.14

Answer:

10+10=1010

Step-by-step explanation:

brainliest?

Answer:

20 lol

And hi!

Answer:

m∠1 = 107 degrees

m∠2 = 73 degrees

Step-by-step explanation:

1. ∠1 and the angle with 107 degrees are corresponding angles, which are located in the same relative position. They're congruent in measures, so m∠1 = 107 degrees.

2. ∠1 and ∠2 are a linear pair, meaning their angle measures add up to 180 degrees. Given m∠1 = 107 degrees, we just have to subtract 107 from 180 to get m∠2.

Therefore, m∠2 = 73 degrees.

Answer:

meat = $2.40

vegetables = $ 2.40

fruit = $2.40 + X

= 2.40 ÷ 2

= 1.2

therefore 2.40 + 1.2

=$3.6 (For fruits )

= $3.6 + $2.40 + $2.40

= $ 8.4

Hope this helps .Plzz mark me brainliest

The total cost of the meat, vegetables and fruit is $8.4.

The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity.

Given that, the costs of the meat, vegetables and fruit are in the ratio meat : vegetables : fruit = 2:2:3.

The cost of the meat is $2.40.

Let the total cost of the meat, vegetables and fruit be x.

Now, 2+2+3=7

So, 2/7 ×x=2.40

2x=2.40×7

2x=16.8

x=8.4

Therefore, the total cost of the meat, vegetables and fruit is $8.4.

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Answer:

(x, y) = (-5/13, -41/13)

Step-by-step explanation: (Assuming the following corrections:)

y = 3x-2

-7x-2y = 9

-7x-2(3x-2) = 9

-7x-6x+4 = 9

-13x = 5

x = -5/13

y = -5/13(3) - 2

y = -15/13 - 2 = -41/13

Step-by-step explanation:

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solving for the inverse of y = x² + 12x

Line 1:    x = y² + 12 x.      

Line 2    y² = x - 12 x.  

Line 3 is y²= - 11 x.

Line 4 is y = √(- 11x)  for x ≥ 0.

The error lies in Line 1. All x's have to be switched with y's and vice versa for the method to work.

As such Line 1 should be  x = y² + 12y  NOT (x = y² + 12 x)

Since Line one is wrong, it messes with all the other lines.

The equation with only one unique solution is 9 − |2x − 1| = 9, with the solution x = 1/2. D.

To determine which equation has only one unique solution, let's analyze each equation:

|3 − x| = 3

In this equation, the absolute value term represents a distance.

By setting up two cases, where the absolute value is positive and negative, we can find the solutions.

Case 1:

3 - x = 3

Solving for x, we have x = 0.

Case 2:

x - 3 = 3

Solving for x, we have x = 6.

Thus, this equation has two solutions.

|x − 2| − 7 = 7

Similar to equation A, the absolute value term represents a distance.

By adding 7 to both sides, we have |x - 2| = 14.

This equation implies that the distance between x and 2 is 14.

There are two possible values for x: x = 2 + 14 = 16 and x = 2 - 14 = -12.

This equation has two solutions.

-4|x| + 1 = -3

To solve this equation, we isolate the absolute value term:

-4|x| = -4

Dividing both sides by -4:

|x| = 1

The absolute value of any number is always positive or zero.

The equation |x| = 1 has two solutions: x = 1 and x = -1.

9 − |2x − 1| = 9

The absolute value term represents a distance.

Subtracting 9 from both sides, we have |2x - 1| = 0.

The only way the absolute value of a real number can be equal to zero is if the number inside the absolute value is zero.

Thus, we set 2x - 1 = 0 and solve for x:

2x - 1 = 0

2x = 1

x = 1/2

Equation D has only one unique solution: x = 1/2.

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Given :-

To find :-

Solution :-

As we know that ,

Substitute ,

Answer:16/20 equals 4/5

Step-by-step explanation:they are asking what is the probability that it is green so we know that 16 counters is green and total counters is 20 so it’s 16/20 and then you simplify it the answer is 4/5

The solution to the system of equations is x≤ -4 and x > 2. Find the number line attached below:

Given the set of inequalities expressed as;

x + 1 ≤ -3 or -4x < -8

For the inequality expression x + 1  ≤ -3

x  ≤ -3 - 1

x ≤ -4

For the inequality expression:

-4x < -8

Divide both sides by -4

-4x/-4 > -8/-4

x > 2

Hence the solution to the system of equations is x≤ -4 and x > 2. Find the number line attached below:

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The domain is the set of x-values for which the equation is true.

Answer:

Look when angle 3= angle B

It would make AD parallel to BC

Step-by-step explanation:

So go with

AD//BC

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1.6 cups of vinegar used for 4 cups of soap.

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

Given:

For  5 cups of soap = 2 cups of vinegar

For 1 cups of soap = 2/5 cups of vinegar used.

Now we have to find how much vinegar required for 4 cups of soap.

So, for 4 cups of soap

=2/5 * 4

=8/5

=1.6 cups of vinegar used.

Hence, 1.6 cups of vinegar used.

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Answer:

[tex]x = \sqrt{3} [/tex]

Step-by-step explanation:

4x^2=12

x^2=12/4

x= root 3

Answer:

In the given equation we need to find out the value of x to make this equation true.

Answer:

$12,400

Step-by-step explanation:

Interest = Principal x Rate x Time (in years)

I = 31000 x .08 x 5

I = 12,400

i would say y + 2/5y is the equivalent expression of 7/5y and y - 2/5y is the quivalent expression of 3/5y but im not sure

Answer:

-2, 1.5

Step-by-step explanation:

(y1 + y2)/2 = y midpoint formula

so, (-1 + 4) = 3

3 / 2 = 1.5

y = 1.5

Step-by-step explanation:

To find the midpoint:

Use the formula;

d = (x2 + x1)/2, (y2 + y1)/2 where x2 = -2, x1 = -2, y1 = -1, y2 = 4

Substitute the values into the equation above. This gives;

d = (-2 + -2)/2, (4 + -1)/2

= (-4/2), (3/2)

=(-2, 1.5) <<<<<<< ✓ Ans

I hope this helps. Thank you

Answer:

c

Step-by-step explanation:

The solution is, C. AB = WX, must to be true to prove AABC= AWXY by the AAS theorem.

A polygon with three edges and three vertices is called a triangle. It is one of the fundamental geometric shapes. Triangle ABC is the designation for a triangle with vertices A, B, and C. In Euclidean geometry, any three points that are not collinear produce a distinct triangle and a distinct plane.

here, we have,

We are given,

Triangles ABC and WXY having ∠A=∠W and ∠B=∠X

Now, it is give that the triangles hold AAS theorem.

Since, we already have two corresponding angles equal i.e. ∠A=∠W and ∠B=∠X.

So, by AAS Theorem, the corresponding sides between these angles must be  equal.

Thus, we have, AB = WX.

Hence, option C is correct. C. AB = WX, must to be true to prove AABC= AWXY by the AAS theorem.

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