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2 years ago

If |lm and m<6 = 4x - 15 and m<7 = x+30, then m<6 = 35 45 39 15

Mathematics

1 answer:

pentagon [3]2 years ago

4 0

Answer:

∠ 6 = 45°

Step-by-step explanation:

∠ 6 and ∠ 7 are alternate angles and are congruent, thus

4x - 15 = x + 30 ( subtract x from both sides )

3x - 15 = 30 ( add 15 to both sides )

3x = 45 ( divide both sides by 3 )

x = 15

Thus

∠ 6 = 4x - 15 = 4(15) - 15 = 60 - 15 = 45°

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For questions 3 – 5, an airplane is heading south at an airspeed of 540 km/hr, but there is a wind blowing from the northeast at

GuDViN [60]

First, let's calculate the horizontal and vertical components of the wind speed (W) and the airplane speed (A), knowing that south is a bearing of 270° and northeast is a bearing of 45°:

$\begin{gathered} W_x=W\cos45°\\ \\ W_x=50\cdot0.707\\ \\ W_x=35.35\\ \\ \\ \\ W_y=W\sin45°\\ \\ W_y=50\cdot0.707\\ \\ W_y=35.35 \end{gathered}$ $\begin{gathered} A_x=A\cos270°\\ \\ A_x=540\cdot0\\ \\ A_x=0\\ \\ \\ \\ A_y=A\sin270°\\ \\ A_y=540\cdot(-1)\\ \\ A_y=-540 \end{gathered}$

Now, let's add the components of the same direction:

$\begin{gathered} V_x=W_x+A_x=35.35+0=35.35\\ \\ V_y=W_y+A_y=35.35-540=-504.65 \end{gathered}$

To find the resultant bearing (theta), we can use the formula below:

$\begin{gathered} \theta=\tan^{-1}(\frac{V_y}{V_x})\\ \\ \theta=\tan^{-1}(\frac{-504.65}{35.35})\\ \\ \theta=-86° \end{gathered}$

The angle -86° is equivalent to -86 + 360 = 274°.

Therefore the correct option is b.

8 0

1 year ago

The amount of gas that a helicopter uses is directly proportional to the number of hours

AleksandrR [38]

Answer:

60 gallons

Step-by-step explanation:

We can create a ratio for this. If we consider 2 as the 1 in the ratio, we have a ratio of 1 : 2.5. Therefore, we just need to multiply 24 by 2.5, which equals 60.

7 0

2 years ago

The product of two of three numbers is 7.8. if one number is 3/5, find the other number ( if you don't know please don't answer)

yarga [219]

Answer: 13,I

Step-by-step explanation:

set the 3 number is 3/5, x,y

product of them

3 /5 xy = 7:6

xy = 7:6 x 5 /3

Xy = 13

So the two number is 13, 1

Step-by-step explanation: hope this helped, Meow!

3 0

2 years ago

A bag contains 10 red marbles, 15 yellow marbles, 5 green marbles, and 20 blue marbles. Two marbles are drawn from the bag.

kherson [118]

Answer:

It is the third option: (10C1) (20C1( / 50C2.

Step-by-step explanation:

The number of ways of selecting 2 marbles = the number of combination of any 2 marbles in the 50 marbles in the bag and this is 50C2. It is combinations because the order of drawing the marbles does not matter.

The number of combinations of one being red and the other blue = 10C1 times 20C1.

So the answer is (10C1) (20C1( / 50C2.

6 0

3 years ago

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Musya8 [376]

Answer:

(0,3)

Step-by-step explanation:

The parent function's vertex is at (0,0) and this function is being translated 3 units up, so the vertex is at (0,3)

4 0

2 years ago