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3 years ago

Which of the following statements is true?

Mathematics

1 answer:

emmainna [20.7K]3 years ago

4 0

Given:

A figure of a circle.

To find:

The correct statement for the given figure.

Solution:

According to the tangent secant theorem, if two tangents or two secants are drawn to the circle from an exterior point, then the measure of angle between the tangents or secants is:

$\text{Exterior angle}=\dfrac{1}{2}(\text{Difference between intercepted arcs})$

$\text{Exterior angle}=\dfrac{1}{2}(\text{Larger arc - smaller arc})$

In the given figure, the exterior angle is 32 degrees, larger arc is QAI and smaller arc is QI.

$32^\circ=\dfrac{1}{2}(m(arcQAI)-m(arcQI))$

Therefore, the correct option is C.

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a dog searching for a bone walks 3.5 m southeast, then 8.2 m at an angle 30 degrees north of east. Find the magnitude of the dog

lianna [129]

Answer:

Step 1: Firstly, we draw both of the axes.

Step 2: We then draw a vector of length 3.5 m (theoretical) along the (-x) axis.

Step 3: Next, we draw a vector of length 8.2 m from the endpoint towards to top, at an angle of 60° from that point (N.B: 90-30, since it is required to make a 30°∠ with the current vertical; eventually the triangle being formed will be 90° minus the 30°.) Most importantly, the 8.2 m vector should be drawn in such a way so that it is higher than the starting point of the 3.5 m vector. )

Step 4: Lastly, we draw a 15 m vector from the endpoint of the 8.2 m vector, running above the original vector, and to the left. This one should be drawn on the left side, and must be situated far enough.

∴ Triangle 1 () is of angles 30°, 60° and 90°;

On solving for the vertical side (the slope similar to the 3.5 vector), we get

(8.2/2) m = 4.1 m

Next, we solve for the opposite side via 4.1 × √3= 7.1 m

Moving on to Triangle 2 (),

top side = (15 - 7.1) m = 7.9 m

similarly, right side = (4.1 - 3.5) m = 0.6 m

∴ last side = resultant displacement:

⇒ + (0.6)² = 7.9 m

and, direction of displacement = arcTan(y/x)

= arcTan(0.6/7.9)

= 4.3° north of west

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7 0

4 years ago

What is the equation of the line that passes through the point (-2,0) and has a<br> slope of -2?

WARRIOR [948]

Answer:

y=-2x-4

Step-by-step explanation:

y-y1=m(x-x1)

y-0=-2(x-(-2))

y-0=-2(x+2)

y=-2x-4+0

y=-2x-4

6 0

3 years ago

The coach of the track and field team is putting together groups of runners to run relays. Each group will need to run a race th

andrew11 [14]

Answer:

16 runner

Step-by-step explanation:

It is given that,

Each group will need to run a race that is 1/2 of a mile long. Each runner has to run 1/8 of a mile in the race.

Let there are x no of runners. ATQ,

$\dfrac{1}{8}x=\dfrac{1}{2}\\\\x=\dfrac{(1/2)}{(1/8)}\\\\x=16$

So, there are 16 runner that are needed for each relay race group.

4 0

3 years ago

Read 2 more answers

A sample of n = 16 scores is selected from a population with LaTeX: \muμ = 80 with LaTeX: \sigmaσ = 20. On average, how much err

bagirrra123 [75]

Answer:

Step-by-step explanation:

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