Answer: The radius is 11.5 meters (to the nearest tenth)
Step-by-step explanation: The circle with center H has an arc TX that measures 24 meters, and also the angle subtended by YX equals 120°.
The length of an arc is given b the formula;
Length of arc = (∅/360) x 2πr
Where the length of the arc is 24 and ∅ is 120, the formula becomes;
24 = (120/360) x 2(3.14) r
24 = (1/3) x 6.28 r
By cross multiplication we now have,
(24 x 3)/6.28 = r
72/6.28 = r
11.4649 = r
r ≈ 11.5
Therefore, the radius is approximately 11.5 meters
The right answer for the question that is being asked and shown above is that: "D. all real numbers less than or equal to 0." This is the statement that <span>best describes the range of the function f(x) = 2/3(6)x after it has been reflected over the x-axis</span>
The first step is to assign the decimal number to a variable.
For the repeating fraction 0.111_1, this would look like
.. x = 0.111_1 . . . . . . . . . . where we use an underscore to identify the following digit(s) as repeating
The next step is to multiply that value by 10 to a power equal to the number of repeating digits. If there is one repeating digit (as here), then you want (10^1)x = 10x.
.. 10x = 1.111_1
The third step is to subtract x from this.
.. 10x -x = 1.111_1 -0.111_1 = 1
.. 9x = 1
And the final step is to divide by the coefficient of x.
.. x = 1/9 . . . . . . this is the value of the repeating decimal fraction.
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Here's one that's a little more complicated. It is done the same way.
.. x = 3.254545_45
.. 100x = 325.454545_45
.. 100x -x = 99x = 322.2
.. x = 322.2/99 = 3222/990 = 179/55
X /11.2 = 5.4 / 6.3 = 6/7
x = (6 * 11.2) / 7 = 9.6 answer
Answer:
Step-by-step explanation:
QM is the angle bisector of ∠LMP
∠LMQ = ∠QMP
QM is the angle bisector of ∠PQL
∠PQM = ∠MQL
MQ = QM as common
By ASA, triangle MQP ≅ MQL
LM = PM and LQ = PQ as they are same side of congruent triangles
Triangle LPQ and LPM are isosceles
By angle bisector theorem, LP is perpendicular to MQ
By properties of rhombus, the two diagonals are perpendicular proves that LMPQ is a rhombus.
LM ≅ PQ
