Answer:
17.8 meters
Step-by-step explanation:
Given:
before expansion railroad rail= 4 km
expansion= 16 cm
railroad makes an isosceles triangle at the center of the rail when it expands
The base of the triangle=4 km
As 1km=100,000 cm
thus 16 cm= 16/100,000 km
each side of this triangle= (4 + 16/100,000) / 2 = 4.0001 / 2 = 2.00008 km
One half of the isosceles triangle makes a right triangle with one of the side =4 / 2 = 2 km
and the hypotenuse = 2.00008 km
Using Pythagoras theorem to find the third side of this right angles triangle:
c^2=a^2+b^2
2.00008^2= 2^2 + b^2
2.00008^2 - 2^2=b^2
b=0.0178 km
b= 17.8 m
hence, approximately 17.8 meters would the center of the rail rise above the ground!
<span><u><em>The correct answers are:</em></u>
A, B and C.
<u><em>Explanation</em></u><span><u><em>: </em></u>
<u>A parallelogram</u> is a quadrilateral with both pairs of opposite sides parallel.
<u>A rectangle</u> is a parallelogram with all right angles, so yes, every rectangle is a parallelogram.
<u>A square</u> is a parallelogram with all right angles and all congruent sides; since it is a parallelogram with all right angles, every square is a rectangle.
<u>A rhombus</u> is a parallelogram with all congruent sides.
Since a square is a parallelogram with all congruent sides, then every square is a rhombus.
<u>A </u><u>trapezoid</u> is a quadrilateral with one pair of parallel sides. Since a rhombus is a parallelogram, with 2 pairs of parallel sides, rhombus are not trapezoids.</span></span>
27. To find this one, you would need to use the Pythagorean theorem, making the answers B and D.
28. Make a mark with your pencil. Set the compass so it has a point on each end of line ab. Now set the side of the compass without the pencil on the mark you already made and mark it. Use the straight edge to make the marks into a line. Now set the compass to the size of line cd. Set the non pencil side on one of the point of your line you just made. Make a mark. Now erase the part of the line that is the length of cd so it is ab-cd.
29. (4,3) I look at the distance between the x coordinates and add it to the end that is the middle and do the same for the y.
30. Put either side of the compass on the ends of the line. put the non pencil side on point x. Make a decent sized arc with the compass. Pick however many spots you needed and mark them. Use the straight edge to connect these points to point x. Repeat for all the points. Erase the arc.
Hope this helped. Let me know if you need any more help!
Step-by-step explanation:
The answer is D.
<span><span>(<span>6−d</span>)</span><span>(<span><span><span>d^2</span>−5</span>+<span>3d</span></span>)</span></span><span>=<span><span>(<span>6+<span>−d</span></span>)</span><span>(<span><span><span>d^2</span>+<span>−5</span></span>+<span>3d</span></span>)</span></span></span><span>=<span><span><span><span><span><span><span>(6)</span><span>(<span>d^2</span>)</span></span>+<span><span>(6)</span><span>(<span>−5</span>)</span></span></span>+<span><span>(6)</span><span>(<span>3d</span>)</span></span></span>+<span><span>(<span>−d</span>)</span><span>(<span>d^2</span>)</span></span></span>+<span><span>(<span>−d</span>)</span><span>(<span>−5</span>)</span></span></span>+<span><span>(<span>−d</span>)</span><span>(<span>3d</span>)</span></span></span></span><span>=<span><span><span><span><span><span>6<span>d^2</span></span>−30</span>+<span>18d</span></span>−<span>d^3</span></span>+<span>5d</span></span>−<span>3<span>d^2</span></span></span></span><span>
=<span><span><span><span> −<span>d3^</span></span>+<span>3<span>d^2</span></span></span>+<span>23d</span></span>−<span>30</span></span></span>
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