MATHEMATICS HIGH SCHOOL

Jack is taking medications for a recent illness. Every 6 hours he takes an antibiotic, every 4 hours he takes a pain reliever, and every 3 hours he drinks a glass of water. If he starts this regime at 10 am, at what time will he be taking both medicines and a glass of water?

Answers

Answer 1

Answer:

At 10p.m that is after 12 hours of time gap he be taking both medicines and a glass of water.

What is least common multiple?

" Least common multiple is defined as the smallest number which is a multiple of given set of numbers."

According to the question,

Given,

Time to start regime = 10am

Time to take antibiotic =Every 6hours

Time to take pain reliever =Every 4hours

Time to drink a glass of water =Every 3hours

Least common multiple of ( 6, 4, 3) = 12

After 12 hours Jack is taking both medicines and a glass of water.

Start regime at 10am

Time after 12hours is 10pm.

Hence, at 10p.m that is after 12 hours of time gap he be taking both medicines and a glass of water.

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Answer 2

Answer: he'd take the antibiotics at 4pm, the pain reliever at 2pm and water at 1pm

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Solve for x. -ax+4b>9

Answers

-ax+4b>9
-ax>9-4b
-x>(9-4b)/a
x<-(9-4b)/a
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Answer: x<-(9-4b)/a or x<(4b-9)/a

Let's solve for a.(−a)(x)+4b>9Step 1: Add -4b to both sides. −ax+4b+−4b>9+−4b −ax>−4b+9
Step 2: Divide both sides by -x. −ax−x>−4b+9−x a<4b−9x

The ticket price for the ice hockey match was £14.50. The price has increased by 7%. How much is a ticket after the increase?

Answers

7%= $\frac {7}{100}$ = 0.07
14.5 × 0.07 = 1.015
Add this number to the original:
14.5+1.015 = £15.515

There is another way, whenever they give us an increased Percentage, they provide us with a hint!
we add that increased percent to 100
100+7=107%
107%= $(107)/(100)$ = 1.07
14.5×1.07= £15.515, it can also be rounded to 15.52
£15.515≈£15.52

Place 1/5 on the number line below .

Answers

right next to the zero van I heht brainleist please

Seventy-three million nine thousand in numbers

Answers

Answer:

73,009,000

Step-by-step explanation:

Answer:

73,009,000

Step-by-step explanation:

seventy three million so 73,000,000

nine thousand so 9,000

fill in blanks = 73,009,000

If A, B,C are the angles of a triangle then prove: (the following in picture)Please help me to prove this.

Answers

Answer: see proof below

Step-by-step explanation:

Given: A + B + C = π → A + B = π - C

→ C = π - (A + B)

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

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

Use the Double Angle Identity: cos 2A = 1 - 2 sin² A

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

Proof LHS → RHS:

LHS: cos A + cos B + cos C

= (cos A + cos B) + cos C

$\text{Sum to Product:}\qquad 2\cos \bigg((A+B)/(2)\bigg)\cdot \cos \bigg((A-B)/(2)\bigg)+\cos C$

$\text{Given:}\qquad 2\cos \bigg((\pi -C)/(2)\bigg)\cdot \cos \bigg((A-B)/(2)\bigg)+\cos C\n\n\n.\qquad \qquad =2\cos \bigg((\pi)/(2) -(C)/(2)\bigg)\cdot \cos \bigg((A-B)/(2)\bigg)+\cos C$

$\text{Cofunction:}\qquad 2\sin \bigg((C)/(2)\bigg)\cdot \cos \bigg((A-B)/(2)\bigg)+\cos C$

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

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

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

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

$\text{Product to Sum:}\qquad 1+2\sin \bigg((C)/(2)\bigg)\bigg[2\sin \bigg((A)/(2)\bigg)\cdot \sin\bigg((B)/(2)\bigg)\bigg]\n\n\n.\qquad \qquad \qquad \qquad =1+4\sin \bigg((C)/(2)\bigg)\bigg[\sin \bigg((A)/(2)\bigg)\cdot \sin\bigg((B)/(2)\bigg)\bigg]\n\n\n.\qquad \qquad \qquad \qquad =1+4\sin \bigg((A)/(2)\bigg)\sin \bigg((B)/(2)\bigg) \sin\bigg((C)/(2)\bigg)$

$\text{LHS = RHS:}\ 1+4\sin \bigg((A)/(2)\bigg)\sin \bigg((B)/(2)\bigg) \sin\bigg((C)/(2)\bigg)=1+4\sin \bigg((A)/(2)\bigg)\sin \bigg((B)/(2)\bigg) \sin\bigg((C)/(2)\bigg)\quad \checkmark$

The proof for this is simple. Let's say that A + B + C = π. From here on we require several trigonometric identities that must be applied.

$\cos \left(A\right)+\cos \left(B\right)+\cos \left(C\right) \n= 2 * cos((A + B) / 2) * cos((A - B) / 2) + \cos C \n= 2 * cos((\pi /2) - (C/2)) * cos((A - B) / 2) +\cos C \n= 2 * sin(C/2) * cos((A - B) / 2) + (1 - 2 * sin^2 (C/2)) \n= 1 + 2 sin (C/2) * cos((A - B) / 2) - sin (C/2) \n= 1 + 2 sin (C/2) * cos((A - B) / 2) - sin((\pi /2) - (A + B)/2 ))\n= 1 + 2 sin (C/2) * cos((A - B) / 2) - cos((A + B)/ 2)\n= 1 + 2 sin (C/2) * 2 sin (A/2) * sin(B/2) \n= 1 + 4 sin(A/2) sin(B/2) sin(C/2)$

Hope that helps!

5. To rent a van, a moving company charges a daily fee plus a fee per mile.The table shows the total cost, c, and the number of miles driven, d.
Write an equation in slope intercept form to represent this situation

Answers

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