Which ordered pair is not a point on the graph of y=1/2x-7

Please prove this........

Crazy boy [7]

Answer: see proof below

<u>Step-by-step explanation:</u>

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

→ sin C = sin(π - (A + B)) cos C = sin(π - (A + B))

→ sin C = sin (A + B) cos C = - cos(A + B)

Use the following Sum to Product Identity:

sin A + sin B = 2 cos[(A + B)/2] · sin [(A - B)/2]

cos A + cos B = 2 cos[(A + B)/2] · cos [(A - B)/2]

Use the following Double Angle Identity:

sin 2A = 2 sin A · cos A

<u>Proof LHS → RHS</u>

LHS: (sin 2A + sin 2B) + sin 2C

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

$\text{Double Angle:}\qquad 2\sin\bigg(\dfrac{2A+2B}{2}\bigg)\cdot \cos \bigg(\dfrac{2A - 2B}{2}\bigg)-2\sin C\cdot \cos C$

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

$\text{Given:}\qquad \qquad \quad 2\sin C\cdot \cos (A - B)+2\sin C\cdot \cos (A+B)$

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

$\text{Sum to Product:}\qquad 2\sin C\cdot 2\cos A\cdot \cos B$

$\text{Simplify:}\qquad \qquad 4\cos A\cdot \cos B \cdot \sin C$

LHS = RHS: 4 cos A · cos B · sin C = 4 cos A · cos B · sin C $\checkmark$

7 0

4 years ago

Of the 420 students enrolled in basic math only 41% are first-year students. How many

Luba_88 [7]

Answer:

Step-by-step explanation:

There are 420 students.

41% are first year students.

41% = 41/100

420 * 41/100 = 172.4

What do you do about the 0.4? I would just round to the nearest whole number which is 172.

There are 420 - 172 = 248 who are not first year students.

8 0

3 years ago

John has gross biweekly earnings of $743.61. By claiming 1 more withholding allowance, John would have $19 more in his take home

Afina-wow [57]

Answer:

Total withholding allowances are 39.

Step-by-step explanation:

Given the gross earning of John = $743.61

It is given that 1 withholding allowance = $19

Now we have to find the total number of withholding allowances. Here, the number of withholding allowances can be determined by dividing the total earnings with $19.

Number of withholding allowances = 743.61 / 19 = 39.14 or 39 (round off).

4 0

3 years ago

Helps plzzzzzzzzzzzzzzzzzz

DanielleElmas [232]

1 answer. 9876500
2 answer. 12350

3 answer 2468250

4 answer 135800

5 0

3 years ago

Read 2 more answers

Ben was walking in Manhattan at a constant speed. He went along 5th avenue from 4th to 98th street. At 3:00 he was on 15th stree

muminat

Answer: The starting time is 2:27 and finishing time is 7:09.

Step-by-step explanation: It is given that Ben started from 4th street and he finished at 98th street.

Also, at 3:00, he was on 15th street and at 4:30, he was on 45th street.

That is, time taken to cover (45-15), i.e., 30 streets is 90 minutes, so the time taken to cover 1 street is 3 minutes.

Therefore, Ben covers distance from one street to second in 3 minutes. Since he started from 4th street, and there are 11 streets to cover between 4 and 15, so Ben's starting time was (3:00 - 3×11 min) = 2:27.

And his finishing time was (4:30 + 3×53 min) = 7:09.

Again, the equation that tells us on what street 'N' he was after time 'T' of his starting can be written as

$N=4+\dfrac{T}{3.}$

Thus, the starting and finishing time was 2:27 and 7:09 respectively.

3 0

4 years ago