The angles in a quadrilateral are 103.8° , 77° , 111.4° and p°. Calculate the value of p.

Explanation:

On taking LHS

Cos[(3π/2)+θ]Cos(2π+θ)[Cot{(3π/2)-θ}+Cot(2π+θ)]

We know that

π = 180°

2π = 2×180° = 360°

3π/2 = (3×180°)/2 = 540°/2 = 270°

Now

LHS becomes

Cos(270°+θ)Cos(360°+θ)[Cot(270°-θ)+Cot(360°+θ)]

We know that

Cos (270°+θ) = Sin θ

Cos (360°+θ) = Cos θ

Cot (270°-θ) = Tan θ

Cot (360°+θ) = Cot θ

→ Sin θ Cos θ [Tan θ + Cot θ]

→ Sinθ Cosθ[(Sinθ/Cosθ)+(Cosθ/Sinθ)]

→ Sinθ Cosθ[(Sin²θ+Cos²θ)/(SinθCosθ)]

→ Sin θ Cos θ [1/(Sin θ Cos θ)]

Since Sin²θ+Cos²θ = 1

→ (Sin θ Cos θ)/(Sin θ Cos θ)

→ 1

→ RHS

→ LHS = RHS

Hence, Proved.

Here are the formulae that I have used:

→ π = 180°

→ Cos (270°+θ) = Sin θ

→ Cos (360°+θ) = Cos θ

→ Cot (270°-θ) = Tan θ

→ Cot (360°+θ) = Cot θ

Here are the Trigonometric Identities that I have used:

→ Sin²θ+Cos²θ = 1

Hope this helps!!

Answer:

None of the above

Step-by-step explanation:

20 x 4 = 80

20 + 20 +20 =20 = 80

Answer:

arc VW = 66°

Step-by-step explanation:

The inscribed angle WXY is half the measure of its intercepted arc WY, so

WY = 2 × 57° = 114°

Arc YX = 180° ( semi- circle ) , then

VW = YX - WY = 180° - 114° = 66°

Answer:

66°

Step-by-step explanation:

1) m(WY)=2*57=114°;

2) m(WX)=180-m(WY)=180-114=66°

Answer:

6 and 9 are the two numbers that have a sum of 15 and when multiplied + 54

Step-by-step explanation:

Answer:

y = 2x - 1

Step-by-step explanation:

Slope = (5-1) / (3-1) = 4/2 = 2

y-intercept = 1 - (2)(1) = - 1

y = 2x - 1

Answer:

[tex]x=55[/tex]

Step-by-step explanation:

To solve this question you need to know some properties of a parallelogram which is the shape given.

Firstly, remember that in a parallelogram opposite angles are equal.

Secondly, remember that the diagonals of a parallelogram bisect each other.

Lastly, remember that the sum of the interior angles of a quadrilateral or a parallelogram is 360°.

So, by using the first property we can see that because [tex]<[/tex]PQR=70° then [tex]<[/tex]PSR must be equal to 70° as well.

Now, we can use the last property to find [tex]<[/tex]SPQ then, use the second property to find [tex]x[/tex].

Let's name [tex]<[/tex]SPQ, [tex]y[/tex].

and That gives:

[tex]2y+140=360[/tex]

Subtract 140 from both sides:

[tex]2y=360-140[/tex]

[tex]2y=220[/tex]

[tex]y=\frac{220}{2}[/tex]

[tex]y=110[/tex]

So, [tex]<[/tex]SPQ=110 and

Now using the second property we can find that:

[tex]<[/tex]SPQ=[tex]2x[/tex]

And [tex]2x=110[/tex]

[tex]x=\frac{110}{2}[/tex]

[tex]x=55[/tex]

Hope this helped.

Find the price of 1 wing:

9.50 / 5 = 1.90 per wing

Divide total spent by price per wing:

26.60 / 1.90 = 14

Answer: 14

Answer:

14

Step-by-step explanation:

$9.50 / 5 = $1.90

$26.60 / $1.90 = 14

Answer:

D(t) = 2,280 - 60t

for D(15) compare the eqns and substitute the value of t.

D(15) = 2,280 - 60(15)

D(15) = 1,380 miles.

In the context of the qn, the Chang family travels 1,380 miles in 15 hours.

Answer:

1/3125 or, 5^-5

Step-by-step explanation:

5^-1 = blank * 5^4

1/5/625= blank   or,     5^-1/5^4=blank

blank=1/3125               5^-5=blank

Answer:

-4 - 8-=-4

Step-by-step explanation:

Answer:

y = x-7

Step-by-step explanation:

Slope intercept form is

y = mx+b  where m is the slope and b is the y intercept

2y -2x = -14

Add 2x to each side

2y-2x+2x= 2x-14

2y = 2x-14

Divide by 2

2y/2 = 2x/2 -14/2

y = x-7

Answer:

166,400,000

Got the same one today and figured it out! Yw!❤

Answer:

28125

Step-by-step explanation:

300÷20=15

15×1875=28125

Answer:

3x + 4y = - 24

Step-by-step explanation:

Answer:

45°

4 units

Step-by-step explanation:

Rotation changes nothing about the geometric relationships within the figure. Angle measures are unchanged; side lengths are unchanged.

The acute angles of an isosceles right triangle are (180° -90°)/2 = 45°. This is true regardless of the orientation of the triangle with respect to any coordinate axes.

The measures of the legs of your triangle are 0 -(-4) = 4 = (1 - (-3)). Rotating the figure any amount in any direction around any center doesn't change that.

Answer:

Q1 b = 105 c= 75 D=105

Step-by-step explanation:

A aNd C are the same and B and D are the same as they are opposite angles. So , 75 +75 = 150 . Then , 360 - 150 = 210 . 210÷ 2 = 105

Hence,

A= 75 B = 105 C=75 D = 105

1. 3n - 5

Five less = -5

Than thrice (three times) a number = 3n

2. 7n + 3

The product of 7 and a number = 7n

Added to 3 = + 3

3. 1/2(3n - 4)

One-half = 1/2

The difference of thrice a number and 4 = 3n - 4

Hope this helps!! :)

Answer:

1. 5-x

2. (7*x)+x

3. 1/2(3x-4)

Step-by-step explanation:

(4s + 2) × (5s² + 10s +3)

we know immediately the first and the last term of the result, because there is only one operation to build them :

20s³ and 6.

so, the first answer option is already eliminated.

let's multiply

4s×5s² + 4s×10s + 4×3s + 10s² + 20s + 6

20s³ + 40s² + 12s + 10s² + 20s + 6

20s³ + 50s² + 32s + 6

so, the last answer option is correct.

Answer:

Step-by-step explanation:

g(-4) = 4   ,  x < -2

g(-2) = (x - 1)²     ; -2≤x< 1

        = (-2-1)²

         = (-3)²

g(-2) = 9

g(0) = (x -1)²      ;  -2 ≤ x < 1

      = (0 -1)²

       = (-1)²

       = 1

Answer:

x = 42 degrees

y = 37 degrees

Step-by-step explanation:

Those are right angle triangles. So you know the right angles are 90 degrees, and each triangle gives you the measurement of another angle.

So, take the triangle in the top left (x):

180 - 90 - 48 = x

Same with the other triangle (y)

180 - 90 - 53 = y

Answer:

84,350

Step-by-step explanation:

843.5 x 10^2 = answer

Answer:

84350

Step-by-step explanation:

Answer:

6 is this answers to find

Answer:

9 omelets

Step-by-step explanation:

She used 12 eggs in the morning so 39-12= 27 then 27/3 = 9

Hope that helps!

Answer:

1/27

have a lovely day <3

Answer:

[tex]\frac{1}{27}[/tex]

Step-by-step explanation:

[tex]\frac{1}{3} ^3[/tex]

[tex]\frac{1}{3}[/tex] × [tex]\frac{1}{3}[/tex] × [tex]\frac{1}{3}[/tex]

[tex]\frac{1}{27}[/tex]

Answer:

(0,4) and (1,2)

Step-by-step explanation:

The standard equation of a straight line is given as y = mx + b

Given the equation y = -2x + 4

Is x = 0, then;

y = -2(0) + 4

y = 4

One of the point on the graph is (0,4)

If x = 1, then;

y = -2(1) + 4

y = -2 + 4

y = 2

Hence the second point is (1, 2)

Learn more on equation of a line here: https://brainly.com/question/19417700

Answer:

152558.75*5%=7627.9

Step-by-step explanation:

Answer: The rule (x,y)=(y,-x) describes the

transformation

Step-by-step explanation:.........bc