|a-i|= the square root of 37

Answer:  see proof below

Step-by-step explanation:

Use the following Sum to Product Identities:

[tex]\sin x+\sin y=2\sin \bigg(\dfrac{x+y}{2}\bigg)\cos \bigg(\dfrac{x-y}{2}\bigg)\\\\\\\sin x-\sin y=2\cos \bigg(\dfrac{x+y}{2}\bigg)\sin \bigg(\dfrac{x-y}{2}\bigg)\\\\\\\cos x+\cos y=2\cos \bigg(\dfrac{x+y}{2}\bigg)\cos \bigg(\dfrac{x-y}{2}\bigg)\\\\\\\cos x+\cos y=-2\sin \bigg(\dfrac{x+y}{2}\bigg)\sin \bigg(\dfrac{x-y}{2}\bigg)[/tex]

Proof LHS → RHS

[tex]\text{LHS:}\qquad \qquad \qquad \dfrac{\sin 5-\sin 15+\sin 25 - \sin 35}{\cos 5-\cos 15- \cos 25 + \cos 35}[/tex]

[tex]\text{Reqroup:}\qquad \qquad \qquad \dfrac{(\sin 25+\sin 5)-(\sin 35 + \sin 15)}{(\cos 35+\cos 5)-(\cos 25 + \cos 15)}[/tex]

[tex]\text{Sum to Product:}\quad \dfrac{2\sin \bigg(\dfrac{25+5}{2}\bigg)\cos \bigg(\dfrac{25-5}{2}\bigg)-2\sin \bigg(\dfrac{35+15}{2}\bigg)\cos \bigg(\dfrac{35-15}{2}\bigg)}{2\cos \bigg(\dfrac{25+15}{2}\bigg)\cos \bigg(\dfrac{25-15}{2}\bigg)-2\cos \bigg(\dfrac{35+5}{2}\bigg)\cos \bigg(\dfrac{35-5}{2}\bigg)}[/tex][tex]\text{Simplify:}\qquad \qquad \dfrac{2\sin 15\cos 10-2\sin 25\cos 10}{2\cos 20\cos 15-2\cos 20\cos 5}[/tex]

[tex]\text{Factor:}\qquad \qquad \dfrac{2\cos 10(\sin 15-\sin 25)}{2\cos 20(\cos 15-\cos 5)}[/tex]

[tex]\text{Sum to Product:}\qquad \dfrac{\cos 10\bigg[2\cos \bigg(\dfrac{15+25}{2}\bigg)\sin \bigg(\dfrac{15-25}{2}\bigg)\bigg]}{\cos 20\bigg[-2\sin \bigg(\dfrac{15+5}{2}\bigg)\sin \bigg(\dfrac{15-5}{2}\bigg)\bigg]}[/tex]

[tex]\text{Simplify:}\qquad \qquad \dfrac{\cos 10[2\cos 20\sin (-5)]}{\cos 20[-2\sin 10\sin 5]}\\\\\\.\qquad \qquad \qquad =\dfrac{-2\cos10 \cos 20 \sin 5}{-2\sin 10 \cos 20 \sin 5}\\\\\\.\qquad \qquad \qquad =\dfrac{\cos 10}{\sin 10}\\\\\\.\qquad \qquad \qquad =\cot 10[/tex]

LHS = RHS:  cot 10 = cot 10   [tex]\checkmark[/tex]

Answer:

Im not sure but hiiiiiiiiii.

Step-by-step explanation:

Answer:

2 and 4.

Step-by-step explanation:

(x+2)^2 - x^2 = 12

x^2 + 4x + 4 - x^2 = 12

4x + 4 = 12

4x = 8

x = 2.

Hence the integers are 2 and 4.

Answer:

2+2=4

Step-by-step explanation:

Answer:

It has 1 solution

[tex]x=5[/tex]

Step-by-step explanation:

Given

[tex]x - 5 = 5 - x[/tex]

Required

Determine the number of solution

[tex]x - 5 = 5 - x[/tex]

Collect Like Terms

[tex]x + x = 5 + 5[/tex]

[tex]2x = 10[/tex]

Divide both sides by 2

[tex]\frac{2x}{2} = \frac{10}{2}[/tex]

[tex]x = \frac{10}{2}[/tex]

[tex]x = 5[/tex]

Since the value of x is 5, then the equation has 1 solution

[tex]x = 5[/tex] is its only value

Answer:

B. 3

Step-by-step explanation:

Start with the inside brackets where we have g(3). As seen, g(3) is given to be =2 so g(3) inside the bracket is now replaced with 2, giving us f(2). F(2) is given as 3, therefore the answer is B. 3

Hope this helped!

Answer:

[tex] 3^2 \times 3^5 = 3^7 [/tex]

3^2 * 3^5 = 3^7

Step-by-step explanation:

I assume you mean this:

[tex] 3^2 \times 3^5 [/tex]

If so, then the rule is that when you multiply two numbers with the same base, you give the same base and add the exponents.

[tex] 3^2 \times 3^5 = 3^{2 + 5} = 3^7 [/tex]

Answer:

X = 5

Step-by-step explanation:

multiply what is in the ( )

-2 ( -2)

-2 ( 9)

3x -5 +2x -18 = 2

combine like terms

5x -23 = 2

add 23 to both sides

5x = 25

divide 25 by 5

X = 5

Answer:

105

Step-by-step explanation:

LN = 6x

LN = LM + MN ➡ LN = 4x + 8 + 27 so 6x = 4x + 8 + 27

2x = 35 and x = 17.5

6 × 17.5 = 105

Answer:

105

Step-by-step explanation:

4x+8+27=6x

subtract 4x from both sides you get 35 = 2x

divide and get x= 17.5

you know LN = 6(x), so substitute 17.5 in for x and you get 6(17.5)= 105

Answer:

Option (B)

Step-by-step explanation:

There are two lines PS and QT intersecting each other at a point M.

It's given that m∠PMT = 128° and m∠QMR = 90°

Since ∠PMT and ∠QMS are the vertical angles so these angles will be equal in measure.

∠PMT = ∠QMS

128° = m∠QMR + m∠RMS

128° = 90° + m∠RMS

m∠RMS = 128° - 90°

m∠RMS = 38°

Therefore, Option (B) will be the answer.

Answer:

Option C

Step-by-step explanation:

[tex]f(x) = 40( \frac{1}{4} )^{x} [/tex]

Answer: its a

Step-by-step explanation:

[tex]-5*(-7)=35[/tex]

[tex]|35|=35[/tex]

[tex]-1*35=-35[/tex]

Hope this helps.

頑張って!

Answer:

  6 minutes

Step-by-step explanation:

'a' in the formula represents altitude in feet. You are told the altitude is 21000 feet, so put that into the formula:

   21000 = 3400t +600

You can solve this for t:

  20400 = 3400t . . . . . subtract 600 from both sides

  6 = t . . . . . . . . . . . . . . . divide both sides by 3400

The problem statement tells you that t represents minutes after lift off, so this solution means the altitude is 21000 feet 6 minutes after lift off.

The question is asking for the number of minutes after lift off that the plane reaches an altitude of 21000 feet, so this answers the question directly:

  The plane is at an altitude of 21000 feet 6 minutes after lift off.

Answer:

a). Cards (1) and (4)

b). Cards (3) and (5)

Step-by-step explanation:

(a). From the cards attached,

  If card (1) is rotated by an angle of 180° counterclockwise, we get the image given in card (4).

  Therefore, card (4) will be the image of card (1) after a rotation.

(b). If we reflect card (3) across a horizontal line (or x- axis) image card (4) is obtained.

   Therefore, card (3) and card (5) is the pair of cards.

Answer:

14300

Step-by-step explanation:

12500-26800

Answer:

1) 3

2) 7

3) 4

4) 13

5) 5

6) 6

7) 11

8) 8

9) 7

10)80*

11)45*

12) Can't really see sorry

13) Is that the whole question? If not just comment the whole thing and Il'l try answer it ☺ Hope that helped!

Answer:

1. RS = - 2-(-5) = 3

2. R5 = 2 -(-5) = 7

3. ST = 2- (-2) = 4

4. RU = 8-(-5) = 13

5. PQ is a straight line with the length of 5 units.

6. QR is a straight line with the length of 6 units.

7. PR is a straight line with the length of 11 units.

8. AC = 24

4x=24

x=6

AB=6

9. BC = 15

3x=15

BD = 3x + 4x - 13

= 22

I might be wrong

Answer:

4:18, 6:27, etc

Step-by-step explanation:

Basically, anything x 2 and x 9 would be equivalent as a ratio

Answer:

4:18

Step-by-step explanation:

times them both by two

Answer:

5

Step-by-step explanation:

g(x) = 3 - 2x

Let x= -1

g(-1) = 3 - 2*-1

      = 3 - -2

     = 3+2

     = 5

Answer:

5

Step-by-step explanation:

g(-1)=3-(2(-1))

g(-1)=3+2

g(-1)=5

Answer:

1.618

Step-by-step explanation:

Also known as the golden ratio.Golden ratio, also known as the golden section, golden mean, or divine proportion, in mathematics, the irrational number (1 + Square root of√5)/2, often denoted by the Greek letter ϕ or τ, which is approximately equal to 1.618.

HOPE THIS HELPED!

Answer: March to April shows the least increase of average temperature.

Answer:

It’s d

Step-by-step explanation:

Answer:

g = 14

Step-by-step explanation:

g + 3 = 17

minus 3 from both sides

g = 14

Answer:

BC, BD

Step-by-step explanation

If right please brainly

Answer:

Well, in this case all the students selected live in the dorms, so it is actually likely that they eat in the cafeteria regularly.

For example, a student that lives in a house (with family, friends, etc) may have access to eat in his own place or may have larger economic freedom, so maybe they go and eat out. In this group, you may find that the probability for a randomly selected student eats in the cafeteria regularly may be smaller than in the group of the students that live in the dorms.

So the sample will be biassed towards eating regularly in the cafeteria.

Answer:

3

Step-by-step explanation:

18/6 = 3

Answer:

Step-by-step explanation:

Given the speed of an object to be 4metres/month, we are to express the speed in inches/hour.

First we will need to convert 4meters to inches

From the conversion factors given,

1 foot (ft) = 0.305 meters (m)

x ft = 4metres

cross multiply

x * 0.305 = 4*1

x = 4/0.305

x = 13.115ft

4 metres = 13.115ft

Then we will convert 13.115ft to inches

From the conversion factors,

1 foot (ft) = 12 inches (in)

13.115ft = y

cross multiply

y = 13.115*12

y = 157.377 inches

Hence 4 metres = 157.77inches.

For 1 month to hour

First we need to convert month to days and from the conversion factor

1 month = 30 days

Next is to convert 30days to hours

Since 1 day = 24hours

30days = z

z = 30* 24

z = 720hours

Hence 1 month = 720hours

On converting 4metres/month to inches/hour

4metres/month = 157.77inches/720hours

4metres/month = 0.219inches/hour

Hence the speed of the object in inches per hour to the nearest hundredth is 0.22inches/hour