A side of the triangle below has been extended to form an exterior angle of 157°. Find the value of x

Answer:

Step-by-step explanation:

Formulas used:

  [tex]sin( A +B) = 2sin Acos B\\\\sin A= sin (\frac{A}{2} + \frac{A}{2}) = 2 \ sin \frac{A}{2}cos \frac{A}{2}\\\\cos(A + B) = cosA cosB - sinA sinB\\\\cos A = cos(\frac{A}{2} + \frac{A}{2}) = cos \frac{A}{2} cos \frac{A}{2} - sin \frac{A}{2} sin \frac{A}{2}[/tex]

                               [tex]= cos^2 \frac{A}{2} - sin^2 \frac{A}{2}[/tex]

  [tex]1 - sin^2 \frac{A}{2} = cos^2 \frac{A}{2}[/tex]

   [tex]\frac{sin\frac{A}{2}}{cos\frac{A}{2}} = tan\frac{A}{2}[/tex]

Given :

LHS =

             [tex]\frac{sin \frac{A}{2} + sin A }{1 + cos \frac{A}{2} + cosA}\\\\=\frac{sin \frac{A}{2} + 2sin \frac{A}{2} cos \frac{A}{2} }{1 + cos \frac{A}{2} +cos ^2\frac{A}{2} -sin^2 \frac{A}{2} }\\\\= \frac{sin\frac{A}{2}( 1 +2cos \frac{A}{2} ) }{cos \frac{A}{2} + cos ^2 \frac{A}{2} + 1 - sin^2\frac{A}{2} }\\\\= \frac{sin\frac{A}{2}( 1 +2cos \frac{A}{2} ) }{cos \frac{A}{2} + cos ^2 \frac{A}{2} +cos ^2 \frac{A}{2} }\\\\[/tex]

            [tex]=\frac{sin\frac{A}{2}( 1 +2cos \frac{A}{2} ) }{cos \frac{A}{2} + 2cos ^2 \frac{A}{2} }\\\\=\frac{sin\frac{A}{2}( 1 +2cos \frac{A}{2} ) }{cos \frac{A}{2} ( 1 + 2cos \frac{A}{2}) }\\\\=\frac{sin\frac{A}{2}}{cos\frac{A}{2}}\\\\= tan \frac{A}{2}\\\\= RHS[/tex]

Answer: i feel like its C but im not sure

Step-by-step explanation:

Answer:

0

Step-by-step explanation:

Anything times 0 is 0.

Without the 0 it's 3.72966900E+33.

it should be false but its been a while since i did that but the expressions should be multiplied together  

Answer:

a

using a calculator u can see the digits that follow.

Answer:

Option A is correct

Step-by-step explanation:

Answer:

x = 30

Step-by-step explanation:

here 50 is hypotenuse as it is opposite of 90 degree.

x and x + 10 are the two other smaller sides of a right angled triangle respectively.

using pythagoras theorem,

a^2 + b^2 = c^2

x^2 + (x + 10)^2 = 50^2

x^2 + x^2 + 20x + 100 = 2500

2x^2 + 20x + 100 = 2500

2x^2 + 20x + 100 - 2500 = 0

2x^2 + 20x - 2400 = 0

2(x^2 + 10x - 1200) = 0

x^2 + 10x - 1200 = 0

x^2 + (40 - 30) - 1200 = 0

x^2 + 40x - 30x - 1200 = 0

x(x + 40) - 30(x + 40x) = 0

(x + 40)(x - 30) = 0

either x + 40 = 0          OR x - 30 = 0

x = 0 - 40

x = -40

x - 30 = 0

x = 30

x = -40,30

since the length and distance is not measured in negative ur answer will be 30

credit goes to sreedevi102

thank u very much . At first i was wrong and giannathecookie i m really sorry

Answer:

x = 30

Step-by-step explanation:

Using Pythagoras Theorem:

[tex]x^2 + ( x+ 10)^ 2 = 50^2\\\\x^2 + (x^2 + 100 + 20x ) = 2500\\\\x^2 + x^2 + 20x = 2500 - 100 \\\\2x^2 + 20x = 2400\\\\2x^2 + 20x - 2400 = 0\\\\2(x^2 + 10x - 1200) = 0\\\\x^2 + 10x - 1200 = 0\\\\x^2 + 40x - 30x - 1200 = 0\\\\x(x + 40 ) -30(x + 40) = 0\\\\(x+40)(x - 30) = 0\\\\x = -40, \ x = 30[/tex]

Since x is the measurement of a side, it can't be negative. Therefore x = 30

Answer:

[tex]Area =( 4 \times 3) + ( \frac{1}{4} \pi \times 2^2) \\\\[/tex] [tex]\ cm^2[/tex]

Step-by-step explanation:

The figure is a combination of rectangle and a quarter of a circle.

Therefore,

                    Area = Area of rectangle x Area of quarter of the circle

                             [tex]= (Length \times breadth ) + ( \frac{1}{4} \pi r^2)\\\\=( 4 \times 3) + ( \frac{1}{4} \pi \times 2^2) \\\\[/tex]

Bella took the sum of area of rectangle and area of entire circle.

That is why Bella is wrong.

9514 1404 393

Answer:

  B.  91

Step-by-step explanation:

14C12 = 14!/(12!(14-12)!) = 14·13/(2·1) = 7·13 = 91

Answer:

1/3

Step-by-step explanation:

3+3+2+1=9 marbles

3 are red so 3/9

3/9=1/3

Answer:

.

Step-by-step explanation:

Answer:

73.13 m^2

Step-by-step explanation:

1/2(bh)

Pi(d)

Answer:

Step-by-step explanation:

Clara gave (1/2) of formal dresses to her sister. After giving, she has 1/2

of formal dresses (1- 1/2 = 1/2).

Number of formal dresses that Clara has = [tex]\frac{1}{2}*d=\frac{1}{2}d[/tex]

Clara bought 4 more dresses

[tex]\frac{1}{2}d + 4 = 12[/tex]

Answer:

60009=hh

Step-by-step explanation:

Answer:

Step-by-step explanation:

If the numerator is 7 less than its denominator, than the original number in terms of x is

[tex]\frac{x-7}{x}[/tex]. If we triple the numerator, the expression to do this is 3(x - 7); if we increase the denominator, the expression to do this is x + 13. Putting that together along with the fact that after we do this manipulation the new number is 3/2:

[tex]\frac{3(x-7)}{x+13}=\frac{3}{2}[/tex] and distribute:

[tex]\frac{3x-21}{x+13}=\frac{3}{2}[/tex] and cross multiply to get:

2(3x - 21) = 3(x + 13) and

6x - 42 = 3x + 39 and

3x = 81 so

x = 27. Subbing 27 for x into the original number:

[tex]\frac{27-7}{27}=\frac{20}{27}[/tex]

Answer:

7

Step-by-step explanation:

we use Pythagorean theorem for solving x

a^2 + b^2 = c^2

c^2 - a^2 = b^2

(√58)^2 - (3)^2 = b^2

58 - 9 = b^2

49 = b^2

b = 7

Answer:

(- 4, - 12 ) , (4, 12 )

Step-by-step explanation:

Given the 2 equations

y = 3x → (1)

y = x² + 3x - 16 → (2)

Substitute y = x² + 3x - 16 into (1)

x² + 3x - 16 = 3x ( subtract 3x from both sides )

x² - 16 = 0 ( add 16 to both sides )

x² = 16 ( take the square root of both sides )

x = ± [tex]\sqrt{16}[/tex] = ± 4

Substitute these values into (1) for corresponding values of y

x = - 4 : y = 3 × - 4 = - 12 ⇒ (- 4, - 12 )

x = 4 : y = 3 × 4 = 12 ⇒ (4, 12 )

Answer:

5

Step-by-step explanation:

8x^2y^3 24

degree of monomial is power of x + power of x

2 + 3= 5

Answer:

5

Step-by-step explanation:

What is that 24 doing there?

If the monomial is

[tex] 8x^2y^3 [/tex]

then the degree is 5.

The degree of a monomial is the sum of the exponents of all the variables of the monomial.

x^3= 125000 m^3

x=50 m

Answer:

Yes it is biased since they are only survey people in marketing not a random sample of people from and group in the company

Answer:

the answer is a 4 x d = 24 I think

Answer: 11 because it all works out.

Answer:

$150.5

Step-by-step explanation:

CP of an item = $140

sales tax rate = 7.5%

sales tax amount = sales tax rate of CP

=7.5% of CP

= 7.5/100 * $140

=$1050/100

=$10.5

total cost with tax = CP + tax rate

=$140 + $10.5

=$150.5

9514 1404 393

Answer:

  x = -9

Step-by-step explanation:

The value 13-8x apparently is the measure of the arc in degrees. That is the same as the measure of the central angle, shown as 85°. Then we have ...

  85 = 13 -8x

  72 = -8x . . . . . . subtract 13

  x = -9 . . . . . . . . divide by -8

The value of x is -9.

Answer:

a

Step-by-step explanation:

first one i believe

Answer:

[tex]{ \tt{pH = - log[H {}^{ + } ]}} \\ pH = - log(4.2 \times {10}^{ - 5} ) \\ pH = 4.38[/tex]

Step-by-step explanation:

H

pH of a solution is 4.38

"The pH of a solution refers to the strength of solution whether it is acidic or basic in nature It is considered by the concentration of hydrogen ion in the solution."

We have,

Concentration of [tex]4.2[/tex]×[tex]10^{-5}[/tex][tex]MH_{3}O[/tex]

pH = [tex]-log(H^{+})[/tex]

⇒pH = [tex]-log(4.2[/tex]×[tex]10^{-5})[/tex]

⇒pH = 4.38

∴ pH of a solution is 4.38

Learn more about pH of a solution here

https://brainly.com/question/23162505

#SPJ2

Answer:

yes it's ok and I'm sorry I didn't get it

Answer:

812 in²

Step-by-step explanation:

The area (A) is calculated as

A = bh ( b is the base and h the perpendicular height )

Here b = 29 and h = 28 , then

A = 28 × 29 = 812 in²

Answer:

16) 8/X

19) 16x^8

22)81x^8

Answer:

D: (x^2 + 3x + 9) (x^2 - 3x + 9)

-

G: (x^2 + 3x + 5) (x^2 - 3x + 5)

Answer:

[tex]d) \: \: ( {x}^{2} + 3x + 9)( {x}^{2} - 3x + 9)[/tex]

[tex]g) \: \: ( {x}^{2} + 2x + 5)( {x}^{2} - 2x + 5)[/tex]

Step-by-step explanation:

Hope it is helpful....

Answer:

c

Step-by-step explanation:

A scale drawing is a reduced form in terms of dimensions of an original image / building / object

the scale drawing is usually reduced at a constant dimension

scale of the drawing = original dimensions / dimensions of the scale drawing

DEF should be three times as big as ABC

AB = 5 ; DE = 5 x 3 = 15

AC = 3 ; DF = 3x 3 = 9

BC = 4 ; EF = 4 X 3 = 12

the options that correspond to this is option c