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2 years ago

The railing of a wheelchair ramp is parallel to the ramp. Find x and y in the diagram.

Mathematics

1 answer:

yKpoI14uk [10]2 years ago

5 0

Given:

The wheel chair ramp is parallel to the ramp.

To find:

The value of x and y.

Solution:

If two lines are parallel, then the alternate interior angles are congruent.

4x° + 6y° = 86° --------- (1)

Similarly,

5x° + 6y° = 94°

Subtract 5x° from both sides.

5x° + 6y° - 5x° = 94° - 5x°

6y° = 94° - 5x° --------- (2)

Substitute (2) in (1).

4x° + 94° - 5x° = 86°

94° - x° = 86°

Subract 94° on both sides.

94° - x° - 94° = 86° - 94°

- x° = 86° - 94°

- x° = -8°

Multiply by -1 on both sides, we get

x = 8

Substitute x = 8 in (2).

6y° = 94° - 5(8)°

6y° = 54°

Divide by 6 on both sides, we get

y = 6

The value of x is 8 and y is 6.

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With reference to the figure match the angles and arcs to their measures

photoshop1234 [79]

Angle BAC = (180 - 114) degrees = 66 degrees [angle on a straight line]

Angle OCA = Angle OBA = 90 degrees    [angle at the point where the tangent and the radius meet]

Thus, the measure of arc BC = (360 - 66 - 90 - 90) degrees = 114 degrees [sum of interior angles of a quadrilateral]

Angle CDE = (180 - 124) degrees = 56 degrees [angle on a straight line]

Angle OCD = Angle OED = 90 degrees    [angle at the point where the tangent and the radius meet]

Thus, the measure of arc CE = (360 - 56 - 90 - 90) degrees = 124 degrees    [sum of interior angles of a quadrilateral]

Given that the measure of arc BC is 114 degrees and the measure of arc CE is 124 degrees, thus the measure of arc BE = (360 - 114 - 124) degrees = 122 degrees [angle at a point]

Angle OBF = Angle OEF = 90 degrees    [angle at the point where the tangent and the radius meet]

Thus, angle BFE = (360 - 122 - 90 - 90) degrees = 58 degrees.

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2 years ago

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There are 1,000 golden delicious and 1,000 red delicious apples in a cooler. In a random sample of 75 of the golden delicious ap

Delvig [45]

Answer:

98% confidence interval is (-0.105 , 0.265)

Step-by-step explanation:

n1 = 75 n2 = 75

X1 = 48 X2 = 42

P1 = X1/N1 = 0.64 P2 = X2/N2 = 0.56

98% confidence interval for difference between two proportions is :

P1 - P2 <u>+</u> Z $\sqrt{P1 (1-P1)/n1 + P2 (1-P2)/n1}$

= 0.08 <u>+</u> 0.185

= (-0.105 , 0.265)

98% confidence interval is (-0.105 , 0.265)

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2 years ago

Using a 16-sided number cube, what is the probability that you will roll a multiple of 4 or an odd prime number? The number 1 is

iogann1982 [59]

<h3>Answer: 0.563 (choice C)</h3>

================================================

Explanation:

E = event space

E = set of outcomes we want to happen

E = rolling a multiple of 4 or rolling an odd prime number

E = {4,8,12,16 3,5,7,11,13}

n(E) = number of items in set E

n(E) = 9, (four multiples of 16+five ways to roll odd prime number)

-----

S = sample space

S = set of all possible outcomes (whether we want them to happen or not)

S = {1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16}

n(S) = number of items in set S

n(S) = 16

-----

P(E) = probability of event space occurring

P(E) = probability of rolling a multiple of 4 or rolling an odd prime number

P(E) = n(E)/n(S)

P(E) = 9/16

P(E) = 0.5625

P(E) = 0.563

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2 years ago

Which graph represents the equation x2 = 8y?

UNO [17]

Direction: Opens up
Vertex: (0,0)
Focus: (0,2)
Axis of Symmetry: x=0
Directrix: y=-2

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2 years ago

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An angle measuring (525n)° is in standard position. For which value of n will the terminal side fall along the negative portion

Mazyrski [523]

For n=2,

put the value 2 in the above equation we get 525*2=1050°.

1050° angle takes 2 complete revolution and then makes an angle of 330° which will fall in the negative portion of y-axis.

For n=6,

put the value 6 in the above equation we get 525*6=3150°.

3150° angle takes 8 complete revolution and then makes an angle of 270° which will fall along negative y-axis.

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2 years ago

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