In the given figure, line m is parallel to line n, and line a is parallel to line b.

erik [133]

Answer:

6 < x < 23.206

Step-by-step explanation:

To properly answer this question, we need to make the assumption that angle DAC is non-negative and that angle BCA is acute.

The maximum value of the angle DAC can be shown to occur when points B, C, and D are on a circle centered at A*. When that is the case, the sine of half of angle DAC is equal to 16/22 times the sine of half of angle BAC. That is, ...

(2x -12)/2 = arcsin(16/22×sin(24°))

x ≈ 23.206°

Of course, the minimum value of angle DAC is 0°, so the minimum value of x is ...

2x -12 = 0

x -6 = 0 . . . . . divide by 2

x = 6 . . . . . . . add 6

Then the range of values of x will be ...

6 < x < 23.206

_____

* One way to do this is to make use of the law of cosines:

22² = AB² + AC² -2·AB·AC·cos(48°)

16² = AD² + AC² -2·AD·AC·cos(2x-12)

The trick is to maximize x while satisfying the constraints that all of the lengths are positive. This will happen when AB=AC=AD, in which case the equations be come ...

22² = 2·AB²·(1-cos(48°))

16² = 2·AB²·(1 -cos(2x-12))

The value of AB drops out of the ratio of these equations, and the result for x is as above.

4 0

2 years ago

Read 2 more answers

What is the simplified version for these 4 ?

VladimirAG [237]

1. -3x + -6
2. -3x + 9
3. 2x - 6
4. -2x + 6

here u go

3 0

3 years ago

Scott and Letitia are brother and sister. After dinner, they have to do the dishes, with one washing and the other drying. They

ehidna [41]

Answer:

The probability that Scott will wash is 2.5

Step-by-step explanation:

Given

Let the events be: P = Purple and G = Green

$P = 2$

$G = 3$

Required

The probability of Scott washing the dishes

If Scott washes the dishes, then it means he picks two spoons of the same color handle.

So, we have to calculate the probability of picking the same handle. i.e.

$P(Same) = P(G_1\ and\ G_2) + P(P_1\ and\ P_2)$

This gives:

$P(G_1\ and\ G_2) = P(G_1) * P(G_2)$

$P(G_1\ and\ G_2) = \frac{n(G)}{Total} * \frac{n(G)-1}{Total - 1}$

$P(G_1\ and\ G_2) = \frac{3}{5} * \frac{3-1}{5- 1}$

$P(G_1\ and\ G_2) = \frac{3}{5} * \frac{2}{4}$

$P(G_1\ and\ G_2) = \frac{3}{10}$

$P(P_1\ and\ P_2) = P(P_1) * P(P_2)$

$P(P_1\ and\ P_2) = \frac{n(P)}{Total} * \frac{n(P)-1}{Total - 1}$

$P(P_1\ and\ P_2) = \frac{2}{5} * \frac{2-1}{5- 1}$

$P(P_1\ and\ P_2) = \frac{2}{5} * \frac{1}{4}$

$P(P_1\ and\ P_2) = \frac{1}{10}$

<em>Note that: 1 is subtracted because it is a probability without replacement</em>

So, we have:

$P(Same) = P(G_1\ and\ G_2) + P(P_1\ and\ P_2)$

$P(Same) = \frac{3}{10} + \frac{1}{10}$

$P(Same) = \frac{3+1}{10}$

$P(Same) = \frac{4}{10}$

$P(Same) = \frac{2}{5}$

8 0

3 years ago

21. What numbers come next in this pattern? 3 5 7 9

Ray Of Light [21]

Answer:

11, 13, 15,

Step-by-step explanation:

have a great day :D

lol i answered ur last question also

8 0

3 years ago

Read 2 more answers

Samantha glued stickers on a sheet with an area of 1260 square sentimeters in 1/6 of an hour what is the speed, in square centim

kondor19780726 [428]

All you have to do here is to find the unit rate for
"<span>an area of 1260 square sentimeters in 1/6 of an hour:"

1260 sq. cm.
------------------- = (1260)(6) sq cm per hour = 7560 sq cm per hour (answer)
(1/6) hr</span>

4 0

3 years ago