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SVEN [57.7K]
3 years ago
14

Solve for x: −3|x 7| = −12 x = 5 over 3, x = −19 over 3 x = −3, x = −11 x = −3, x = 11 no solution

Mathematics
1 answer:
const2013 [10]3 years ago
5 0
-3|x + 7| = -12
|x + 7| = -12/-3 = 4
x + 7 = 4 and x + 7 = -4
x = 4 - 7 and x = -4 - 7
x = -3 and x = -11
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A dolphin is swimming 20 feet below the surface. It descends another 10 feet before rising 2
andrezito [222]

Answer:

28 feet

Step-by-step explanation:

20 + 10 = 30 - 2 = 28 feet

The dolphin is 20 feet below the surface, goes down another 10 feet, so 30 feet below the surface, and raises two feet, so 28 feet below the surface.

8 0
3 years ago
A discuss moves from P1 (4,8) to P2 (15,17). What is the lincar displacement in the horizontal and vertical directions? What is
Yakvenalex [24]

Answer:

The horizontal displacement is 11 units, the vertical displacement is 9 units, and the projection angle is 39.3 degrees.

Step-by-step explanation:

We can start using the definition of displacement in one dimension between any 2 points which is the difference between them, so we have

\Delta s = s_2-s_1

And apply it to get the horizontal and vertical displacements.

Once we have found them, we can use trigonometric functions to find the projection angle with respect the horizontal.

Linear displacements.

Using the definition of displacement, we can write the horizontal displacement as

\Delta x = x_2-x_1

So we can use the given points P1:(x_1,y_2)  \text{  and  } P_2: (x_2,y_2) on the displacement formula

\Delta x = 15-4\\\Delta x = 11

In the same manner we can look at the y components of those points to find the vertical displacement

\Delta y = 17-8\\\Delta y =9

Thus the horizontal displacement is 11 units and the vertical displacement is 9 units.

Projection angle.

The projection angle with respect the horizontal is the angle that is made between the line that connects the points P1 and P2 and the horizontal, so we can use the linear displacements previously found to write

\tan(\theta) = \cfrac{\Delta y}{\Delta x}

Solving for the angle we get

\theta = \tan^{-1}\left(\cfrac{\Delta y}{\Delta x}\right)

Replacing values

\theta = \tan^{-1}\left(\cfrac{9}{11}\right)

Which give us

\theta = 39.3^\circ

So the projection angle is 39.3 degrees.

7 0
3 years ago
Identify the perfect cube contained as a factor in 54
erastova [34]

Answer:

27.

Step-by-step explanation:

54 = 2 * 3 * 3 * 3.

3 occurs 3 times so the perfect cube is 27.

8 0
2 years ago
8. A triangle has sides with lengths of 6, 8, and 10 units, and a square has a
svet-max [94.6K]

Difference between the area of the triangle and square is 25

Step-by-step explanation:

  • Step 1: Find the area of the triangle given its 3 sides using the Heron's formula.

Area of the triangle = \sqrt{s (s-a)(s-b)(s-c)} where s = \frac{a + b + c}{2}

⇒ s = (6 + 8 + 10)/2 = 24/2 = 12

\sqrt{s(s-a)(s-b)(s-c)} = \sqrt{12(12-6)(12-8)(12-10)}

                                    = \sqrt{12(6)(4)(2)} = \sqrt{576} = 24 sq. units

  • Step 2: Find the area of the square with perimeter = 28 units.

Perimeter of the square = 4 × side = 28

⇒ Side of the square = 28/4 = 7 units

⇒ Area of the square = (side)² = 7² = 49 sq. units

  • Step 3: Find the difference between the area of the square and triangle.

Difference = 49 - 24 = 25

8 0
3 years ago
The table below shows the number of tickets sold, t, at a high school basketball game, and the amount of money collected, m.
Tresset [83]
m = t2.5

So money equals to tickets sold*2.5

2.5 is each tickets price

If you ask how I found;

$100 / 40 tickets = $2.5
3 0
3 years ago
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