Find the value of x that will make L || M

Answer:  see proof below

Step-by-step explanation:

Given: A + B + C = π                     →  A = π - (B + C)

                                                     → B + C = π - A

Use the Pythagorean Identity: cos² A + sin² A = 1   →  sin² A = 1 - cos² A

Use Double Angle Identities: cos 2A = 2 cos² A - 1 → cos² A = (cos 2A + 1)/2

                                             → cos A = 1 - 2 sin² (A/2)    

Use Sum to Product Identity: cos A + cos B = 2 cos [(A + B)/2] · cos [(A - B)/2]

Use Cofunction Identities:  cos (π/2 - A) = sin (A)

                                             sin (π/2 - A) = cos A

                                             cos (-A) = cos (A)

Proof LHS → RHS:

[tex]\text{LHS:}\qquad \qquad \sin^2\bigg(\dfrac{B}{2}\bigg)+\sin^2 \bigg(\dfrac{C}{2}\bigg)-\sin^2\bigg(\dfrac{A}{2}\bigg)[/tex]

[tex]\text{Pythagorean:}\qquad 1-\cos^2 \bigg(\dfrac{B}{2}\bigg)+1-\cos^2 \bigg(\dfrac{C}{2}\bigg)-\bigg[1-\cos^2 \bigg(\dfrac{A}{2}\bigg)\bigg]\\\\\\.\qquad \qquad \qquad =1-\cos^2 \bigg(\dfrac{B}{2}\bigg)-\cos^2 \bigg(\dfrac{C}{2}\bigg)+\cos^2 \bigg(\dfrac{A}{2}\bigg)[/tex]

[tex]\text{Double Angle:}\quad 1-\bigg(\dfrac{\cos(2\cdot \frac{B}{2})+1}{2}\bigg)-\bigg(\dfrac{\cos (2\cdot \frac{C}{2})+1}{2}\bigg)+\bigg(\dfrac{\cos (2\cdot \frac{A}{2})+1}{2}\bigg)\\\\\\.\qquad \qquad \qquad =1-\dfrac{\cos B}{2}-\dfrac{1}{2}-\dfrac{\cos C}{2}-\dfrac{1}{2}+\dfrac{\cos A}{2}+\dfrac{1}{2}\\\\\\.\qquad \qquad \qquad =\dfrac{1}{2}[1-(\cos B+\cos C)+\cos A][/tex]

[tex]\text{Sum to Product:}\qquad \dfrac{1}{2}\bigg(1-\bigg[2\cos \bigg(\dfrac{B+C}{2}\bigg)\cdot \cos \bigg(\dfrac{B-C}{2}\bigg)\bigg]+\cos A\bigg)[/tex]

[tex]\text{Given:}\qquad \dfrac{1}{2}\bigg(1-\bigg[2\cos \bigg(\dfrac{\pi -A}{2}\bigg)\cdot \cos \bigg(\dfrac{B-C}{2}\bigg)\bigg]+\cos A\bigg)[/tex]

[tex]\text{Cofunction:}\qquad \dfrac{1}{2}\bigg(1-\bigg[2\sin \bigg(\dfrac{A}{2}\bigg)\cdot \cos \bigg(\dfrac{B-C}{2}\bigg)\bigg]+\cos A\bigg)[/tex]    

[tex]\text{Double Angle:}\qquad \dfrac{1}{2}\bigg[1-2\sin \bigg(\dfrac{A}{2}\bigg)\cdot \cos \bigg(\dfrac{B-C}{2}\bigg)+1-2\sin^2 \bigg(\dfrac{A}{2}\bigg)\bigg]\\\\\\.\qquad \qquad \qquad =\dfrac{1}{2}\bigg[2-2\sin \bigg(\dfrac{A}{2}\bigg)\cdot \cos \bigg(\dfrac{B-C}{2}\bigg)-2\sin^2 \bigg(\dfrac{A}{2}\bigg)\bigg]\\\\\\.\qquad \qquad \qquad =1-\sin \bigg(\dfrac{A}{2}\bigg)\cdot \cos \bigg(\dfrac{B-C}{2}\bigg)-\sin^2 \bigg(\dfrac{A}{2}\bigg)[/tex]

[tex]\text{Factor:}\qquad \qquad 1-\sin \bigg(\dfrac{A}{2}\bigg)\bigg[ \cos \bigg(\dfrac{B-C}{2}\bigg)-\sin \bigg(\dfrac{A}{2}\bigg)\bigg][/tex]

[tex]\text{Given:}\qquad \qquad 1-\sin \bigg(\dfrac{A}{2}\bigg)\bigg[ \cos \bigg(\dfrac{B-C}{2}\bigg)-\sin \bigg(\dfrac{\pi -(B+C)}{2}\bigg)\bigg][/tex]

[tex]\text{Cofunction:}\qquad 1-\sin \bigg(\dfrac{A}{2}\bigg)\bigg[ \cos \bigg(\dfrac{B-C}{2}\bigg)+\cos \bigg(\dfrac{B+C}{2}\bigg)\bigg][/tex]

[tex]\text{Sum to Product:}\ 1-\sin \bigg(\dfrac{A}{2}\bigg)\cdot 2 \cos \bigg(\dfrac{(B-C)+(B-C)}{2\cdot 2}\bigg)\cdot \cos \bigg(\dfrac{(B-C)-(B+C)}{2\cdot 2}\bigg)\\\\\\.\qquad \qquad \qquad =1-2\sin \bigg(\dfrac{A}{2}\bigg)\cdot \cos \bigg(\dfrac{B}{2}\bigg)\cdot \cos \bigg(-\dfrac{C}{2}\bigg)[/tex][tex]\text{Cofunction:}\qquad =1-2\sin \bigg(\dfrac{A}{2}\bigg)\cdot \cos \bigg(\dfrac{B}{2}\bigg)\cdot \cos \bigg(\dfrac{C}{2}\bigg)[/tex]

[tex]\text{LHS = RHS:}\quad \checkmark\\\\\quad 1-2\sin \bigg(\dfrac{A}{2}\bigg)\cdot \cos \bigg(\dfrac{B}{2}\bigg)\cdot \cos \bigg(\dfrac{C}{2}\bigg)=1-2\sin \bigg(\dfrac{A}{2}\bigg)\cdot \cos \bigg(\dfrac{B}{2}\bigg)\cdot \cos \bigg(\dfrac{C}{2}\bigg)\quad[/tex]

Answer:

198

Step-by-step explanation:

270/15 gives us 18, his miles per gallon. multiply that by 11, and you get 198.

Answer:

x=36.1

supplementary angle = 143.9 degrees

Step-by-step explanation:

angle: x

supplementary angle: 180-x

x = (180-x)-107.8

2x = 72.2

x = 36.1 degrees

180-x =  143.9 degrees

supplementary angle = 143.9 degrees

x measures 107.8 less than 180-x

x=180-x-107.8

x=72.2-x

Add x to both sides

2x=72.2

Divide both sides by 2

x=36.1

_________________________________

hope this helps, I just solved this so probably should get it fact checked.

Answer:

um, can you make that a bit clearer thanks! (:

Step-by-step explanation:

Slope-intercept form: y = mx + b

m = the slope

y = the y-intercept

In our problem,

y = -4/3x - 1

m = -4/3

The slope is -4/3

Answer:

x/11 = 10/12

x = 10*11/12= 55/6

Step-by-step explanation:

[tex] \huge \pink {\tt { \frac{x}{11} = \frac{10}{12}}} [/tex]

By cross multiplication, we get

12x = 110

or, x = 110/12 = 55/6

Step-by-step explanation:

The concentration of Marcia's solution is:

1.0 kg / 3.0 L = 0.33 kg/L

The concentration of Bobby's solution is:

(2.0 lb × 1 kg / 2.2 lb) / (7.0 pints × 1 L / 2.11 pints) = 0.27 kg/L

Therefore, Marcia's solution is more concentrated.

Answer:

D. 82

Step-by-step explanation:

a^2 + b^2 = c^2

80^2 + 18^2 = c^2

324 + 6400 = c^2

6724 = c^2

82 = c

Answer:

   down 7 1/4 feet

Step-by-step explanation:

4 1/2 + 2 3/4 = 4 2/4 + 2 3/4 = (4+2) +(2/4 +3/4) = 6 +5/4 = 7 1/4

The dolphin is 7 1/4 feet below the surface.

Answer:

Step-by-step explanation:

Answer:

$39.38

Step-by-step explanation:

$36.98 * 6.5%= 2.4037

2.4037 + 36.98= 39. 3837

round up

$39.38

Answer:

39.38

Step-by-step explanation:

if it was negitive I would be -2

Step-by-step explanation:

so 6-4=2 and if you make that negative it would be -2

Answer:

-$6 + $4 = -$2

Step-by-step explanation:

Since Morris borrowed 6 dollars to begin with, the first term in my equation is -6$, representing the debt he has incurred from taking a loan of 6 dollars from his mother. After paying $4 dollars, he would still be in debt of $2 to his mother. Since he is still in debt of 2 dollars, the furthest right term in my aforementioned equation is -$2.

Answer:

hope it helps

plz mark as brainliest

Length of [tex]\boldsymbol{AC}[/tex] is [tex]\boldsymbol{22}[/tex] units.

"To understand the calculation, check below."

Midpoint

The middle point of the a line segment is called the midpoint.

It's really the centroid of both segment and the ends, and it is equidistant from both.

It cuts the portion in half.

[tex]B[/tex] is the midpoint of [tex]

AC[/tex] [tex]\boldsymbol{AB=BC}[/tex][tex]3x-1=x+7[/tex] [tex]2x

AC=8[/tex] [tex]\boldsymbol{x=4}[/tex]

So,[tex]BC=4+7[/tex] [tex]=\boldsymbol{11}[/tex]

Therefore,[tex]AC=2BC[/tex] [tex]=2 \times 11\\=\boldsymbol{22}[/tex]Length of [tex]\boldsymbol{AC}[/tex] is [tex]\boldsymbol{22}[/tex] units.

Find out more information about midpoint here:

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Answer:

Not sure but that's my answer

Answer:

terminating

repeating

terminating

repeating

Step-by-step explanation:

3/5 = 0.6 ; terminating

1/9 = 0.1111... ; repeating

7/10 = 0.7 ; terminating

5/12 = 0.41666666... ; repeating

Answer:

True the absolute value is how many digits away the number is from zero.

Step-by-step explanation:

Answer:

d =2

Step-by-step explanation:

6d+8=14+3d

Subtract 3d from each side

6d-3d+8=14+3d-3d

3d +8 = 14

Subtract 8 from each side

3d +8-8 = 14-8

3d =6

Divide by 3

3d/3 = 6/3

d =2

Answer:

Step-by-step explanation:

B being midpoint of AC means:

BC = AB = 32

Answer:

C

Step-by-step explanation:

First, notice that this is a cubic function.

The standard form for a cubic function is:

[tex]f(x)=a(x-b)^3+c[/tex]

Where a is the vertical stretch, b is the horizontal shift, and c is the vertical shift.

From our graph, we can see that unlike the parent function, x³, this cubic is 3 units to the right and 1 unit up from the standard position.

Therefore, our b is +3 and c is +1. Let's substitute these values. Also, let's assume a is 1. So:

[tex]f(x)=(x-3)^3+1[/tex]

Therefore, our answer is C.

And we're done!

Answer:

3000000

Step-by-step explanation:

:D

The equivalent value of the equation is A = 3000000

Given data ,

Let the equation be represented as A

Now , the value of A is

Let the first number be p = 3000

Let the second number be q = 1000

Now , A = pq

where A = 3000 x 1000

On simplifying the equation , we get

A = 3000 x 1000

So , the left hand side of the equation is equated to the right hand side by the value of ( 3000 x 1000 )

A = 3000000

Therefore , the value of A = 3000000

Hence , the expression is A = 3000000

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5 + 2p is at least 11.

Subtract 5 from both sides.

2p is at least 11.

p > 5

Answer:

Which of the following represents the area of a rectangle whose length is x - 6 and whose width is x - 8? A) x2- 14x - 48. B) x2+ 48. C) x2- 48. D) x2- 14x + 48 . and... for the first one multiply both out to get x^2-14x + 40 8 D 4(8x^3+a million) element out 4 utilising the x^3+y^3 formula, on (2x)^3 + a million^3)

Step-by-step explanation:

Answer:

The total number of pages from page X to page Y is Y minus X plus 1.

So from 1 to 9, there are 9 minus 1 is 8 plus 1 is 9.

Step-by-step explanation:

Answer:

[tex]12x^{2} -5x -2[/tex]

Step-by-step explanation:

We multiply the first term 3x by 4x and then 3x multiplied by one. We proceed to multiply by -2 by 4x and multiplied by -2 +1. We finally add and get the result.

[tex]12x^{2} -5x -2[/tex]

Answer: hope i helped with this answer~

Step-by-step explanation:

The fourth diagram  show lines that must be parallel lines cut by a transversal

A line is an infinitely long object with no width, depth, or curvature.

Parallel lines  refers to two lines which can be found on the same plane, at an equidistance and does not meet.

A transversal is defined as a line that passes through two lines in the same plane at two distinct points in the geometry.

The fourth diagram has two same-side interior angles that are supplementary (add to 180°).

The converse of the same-side interior angle theorem states that if two lines are cut by a transversal and the same side interior angles are supplementary, then the lines are parallel.

Hence, the fourth diagram  show lines that must be parallel lines cut by a transversal

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Exact Form: t = 8/5

Decimal Form: t = 1.6

Mixed Number Form: t = 1 3/5 (one and three fifths)

Answer:

t = 8/5 or t = 1.6

This will be a fraction buh can be turned into a decimal

Step-by-step explanation:

subtract 1 on both sides 5t + 1 - 1 = 9 - 1

then simplify 5t = 8 after det divide both side 5t/5 = 8/5 and den your answer is t = 8/5...

HOPE DIS HELPS YU OR IS RIGHT!!!!!