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algol [13]
3 years ago
15

I'm stuck on b.please help me!!!!​

Mathematics
1 answer:
Sloan [31]3 years ago
5 0

The area under the speed curve tells you how much distance the vehicle covers.

The distance for first 30 s corresponds to the area of a rectangle with height <em>k</em> m/s and length 30 s, or

(<em>k</em> m/s) (30 s) = 30<em>k</em> m

The distance for the last 20 s corresponds to the area of triangle with height <em>k</em> m/s and length 20 s, or

1/2 (<em>k</em> m/s) (20 s) = 10<em>k</em> m

If the total distance traveled was 1.7 km = 1700 m, then

30<em>k</em> + 10<em>k</em> = 1700

40<em>k</em> = 1700

<em>k</em> = 42.5

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In triangle abc, the perimeter is 36, and ab=ac. line ad is perpendicular to bc at the point d, and triangle abd's perimeter is
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Let x=ab=ac, and y=bc, and z=ad.

Since the perimeter of the triangle abc is 36, you have:

Perimeter of abc = 36
ab + ac + bc = 36
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(eq. 1) 2x + y = 36

The triangle is isosceles (it has two sides with equal length: ab and ac). The line perpendicular to the third side (bc) from the opposite vertex (a), divides that third side into two equal halves: the point d is the middle point of bc. This is a property of isosceles triangles, which is easily shown by similarity.

Hence, we have that bd = dc = bc/2 = y/2 (remember we called bc = y).

The perimeter of the triangle abd is 30:

Permiter of abd = 30
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(eq. 2) 2x + y + 2z = 60

So, we have two equations on x, y and z:

(eq.1) 2x + y = 36
(eq.2) 2x + y + 2z = 60

Substitute 2x + y by 36 from (eq.1) in (eq.2):

(eq.2') 36 + 2z = 60

And solve for z:

36 + 2z = 60 => 2z = 60 - 36 => 2z = 24 => z = 12

The measure of ad is 12.

If you prefer a less algebraic reasoning:

- The perimeter of abd is half the perimeter of abc plus the length of ad (since you have "cut" the triangle abc in two halves to obtain the triangle abd).

- Then, ad is the difference between the perimeter of abd and half the perimeter of abc:

ad = 30 - (36/2) = 30 - 18 = 12
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Step-by-step explanation:

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Answer:

B) identity property of addition.

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Given:

The statement given is:

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