Which statement is NOT true about Rational Numbers? *
Whole Numbers are Rational Numbers
Only fractions are Rational Numbers
Integers, Whole Numbers, and Natural Numbers are Rational Numbers
Repeating decimals and terminating decimals are Rational Numbers

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:

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:

   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:

3/4

Step-by-step explanation:

3/5(1+p)-21/20

3/5+3/5p=21/20

3/5p=21/20-3/5

3/5p=21/20-12/20

3/5p=9/20

p=9/20÷3/5

p=9/20*5/3

p=45/60

p=3/4

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

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!!!!!

Answer:

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

Step-by-step explanation:

Answer:

198

Step-by-step explanation:

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

Answer:

Step-by-step explanation:

B being midpoint of AC means:

BC = AB = 32

Answer:

a. Addition & division

Step-by-step explanation:

2x - 4 = 16   (adding 4 to both sides)

2x  = 16 + 4

2x = 20  (dividing both sides by 2)

x = 20/2 = 10

Hence we can see that the two operations are addition and then division

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.

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:

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:

A0.15

Step-by-step explanation:

Answer:

Step-by-step explanation:

The graph is of the equation y = -x^2 +4. It is a polynomial of even degree, so has a domain of all real numbers: (-∞, ∞).

The vertical extent of the graph includes y=4 and all numbers less than that:

  range: (-∞, 4]

The graph is increasing to the left of its vertex at x=0, decreasing to the right.

  increasing (-∞, 0); decreasing (0, ∞)

There is no interval on which the function is constant. It has a horizontal tangent at x=0, but a single point does not constitute an interval.

Answer:

OC 193 lb is correcte!

The person's weight, in pounds, when rounded to the nearest

the whole number is equal to [tex]1.9\times10^{2} pound[/tex]

We have given that, A pound is approximately 0.45 kilogram.

0.45 kg = 1 pound

Thus if 0.45 kg is equal to= 1 pound

87 kg will be equal to [tex]=\frac{1}{0.45} \times 87=1.9 \times 10^2 pound[/tex]

The number of significant digits in an answer should be equal to the least number of significant digits in any one of the numbers being multiplied, divided, etc.

Thus the answer should contain 2 significant digits.

To learn more significant digits visit:

https://brainly.com/question/24491627

#SPJ2

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:

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

Step-by-step explanation:

Answer:

72 cats

Step-by-step explanation:

sum the parts of the ratio, 3 + 8 = 11 parts

Divide the total by 11 to find the value of one part of the ratio.

99 ÷ 11 = 9 ← value of 1 part of the ratio, then

8 parts = 8 × 9 = 72 ← number of cats

Answer:

if i;m right its 45 degrees

Step-by-step explanation:

Answer:

28

Step-by-step explanation:

alternative angle theorem lets you know that angle acb is equal to cae and you can find acb since you know all angles add up to 180. 180-105-47=28