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Hitman42 [59]
3 years ago
8

Solve for x: |2x + 12| = 18

Mathematics
2 answers:
Mashcka [7]3 years ago
7 0
2x + 12 = 18
18 - 12 = 6
2x = 6
x = 3
kumpel [21]3 years ago
7 0
So you want to drop the absolute value signs and you need to make two equations:

2x + 12 = 18 OR 2x + 12 = -18
subtract both sides by 12 for both equations
2x = 6 OR 2x = -30
divide both sides by 2 for both equations
x = 3 OR x = -15

i hope this helps!!

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A ball is thrown into the air. The path it takes is modeled by the equation: -3t+24t = h, where t is the time in seconds and h i
astra-53 [7]

Given:

The given equation is:

-3t^2+24t=h

Where, t is the time in seconds and h is the height of the ball above the ground, measured in feet.

To find:

The inequality to model when the height of the ball is at least 36 feet above the ground. Then find time taken by ball to reach at or above 36 feet.

Solution:

We have,

-3t^2+24t=h

The height of the ball is at least 36 feet above the ground. It means h\geq 36.

-3t^2+24t\geq 36

-3t^2+24t-36\geq 0

-3(t^2-8t+12)\geq 0

Splitting the middle term, we get

-3(t^2-6t-2t+12)\geq 0

-3(t(t-6)-2(t-6))\geq 0

-3(t-2)(t-6)\geq 0

The critical points are:

-3(t-2)(t-6)=0

t=2,6

These two points divide the number line in 3 intervals (-\infty,2),(2,6),(6,\infty).

Intervals      Check point           -3(t-2)(t-6)\geq 0           Result

(-\infty,2)               0                       (-)(-)(-)=(-)         False

(2,6)                    4                       (-)(+)(-)=+>0            True

(6,\infty)                  8                        (-)(+)(+)=(-)        False

The inequality is true for (2,6) and the sign of inequality is \geq. So, the ball is above 36 feet between 2 to 6 seconds.

6-2=4

Therefore, the required inequality is -3t^2+24t\geq 36 and the ball is 36 feet above for 4 seconds.

3 0
3 years ago
If x = 10, y = 5, and z = 11, what is the tangent ratio for g°?
loris [4]

Please, find attached the image with the complete question

Answer:

\large\boxed{\large\boxed{tan(g\º )=2}}

Explanation:

The triangle ACB is a right triangle with these features:

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The <em>tangent ratio </em>on an angle in a right triangle is equal to the length of the leg opposite to the angle divided by the length of the leg adjacent to the angle.

Hence:

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