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Dominik [7]
3 years ago
6

Here is a central angle that measures 1.5 radians. Select all true statements. Question 1 options: A) The area of the whole circ

le is 1.5 times the area of the slice. B) The radius is 1.5 times longer than the length of the arc defined by the angle. C) The ratio of radius to arc length is 1.5. D) The length of the arc defined by the angle is 1.5 times longer than the radius. E) The ratio of arc length to radius is 1.5. F) The circumference of the whole circle is 1.5 times the length of the arc formed by the angle.
Mathematics
1 answer:
KATRIN_1 [288]3 years ago
8 0

Answer:

  D, E

Step-by-step explanation:

The applicable formula is ...

  s = rθ

so, for θ = 1.5, the arc length is 1.5 times the radius. The true statements are ...

  D) The length of the arc defined by the angle is 1.5 times longer than the radius.

  E) The ratio of arc length to radius is 1.5.

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The height of a triangle is 5 m less than its base. The area of the triangle is 42 m².
SCORPION-xisa [38]
A = (1/2) b * h
h = b - 5
42 = (1/2) * b * (b - 5)
42 = (1/2) * b^2 - 5b
multiply both sides by 2 to clear the fraction (1/2)
2(42) = 2(1/2) *b^2 - 5b
84 = b^2 -5b
Since this is a quadratic equation, subtract 84 from both sides so that it is set = to zero.
b^2 - 5b - 84 = 0
Now factor.
(b - 12)(b + 5) = 0
b - 12 = 0; b = 12
b + 5 = 0; b = -5
You can't have a negative length so the answer is 12m
To check the answer:
A = (1/2) * 12* 7
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3 years ago
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irakobra [83]

Answer:

The length of side AC is 5 units.

The areas of triangle ABC is 10 square units.

Step-by-step explanation:

From point A (1,3) to point C (1,-2) is 5 units

To check this:

3 - (-2) = 3 + 2 =5

We're subtracting since the point went down (from positive 3 to negative 2)

Now for the area:

Area formula for a triangle: \frac{1}{2}bh = \frac{1}{2}⋅b⋅h

We already found the height (length) : 5

The base is from point C (1,-2) to point B (5,-2), which is 4 units

To check this:

5 - 1 = 4

Now that we have found the base and height, Let's solve:

\frac{1}{2}⋅4⋅5 = \frac{1}{2}⋅20 = 10

Our area is 10 square units.

Hope that helps :)

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