Answer:
√8 ==> 2 units, 2 units
√7 ==> √5 units, √2 units
√5 ==> 1 unit, 2 units
3 ==> >2 units, √5 units
Step-by-step explanation:
To determine which pair of legs that matches a hypotenuse length to create a right triangle, recall the Pythagorean theorem, which holds that, for a right angle triangle, the square of the hypotenuse (c²) = the sum of the square of each leg length (a² + b²)
Using c² = a² + b², let's find the hypotenuse length for each given pairs of leg.
=>√5 units, √2 units
c² = (√5)² + (√2)²
c² = 5 + 2 = 7
c = √7
The hypothenuse length that matches √5 units, √2 units is √7
=>√3 units, 4 units
c² = (√3)² + (4)²
c² = 3 + 16 = 19
c = √19
This given pair of legs doesn't match any given hypotenuse length
=>2 units, √5 units
c² = (2)² + (√5)²
c² = 4 + 5 = 9
c = √9 = 3
legs 2 units, and √5 units matche hypotenuse length of 3
=>2 units, 2 units
c² = 2² + 2² = 4 + 4
c² = 8
c = √8
Legs 2 units, and 2 units matche hypotenuse length of √8
=> 1 unit, 2 units
c² = 1² + 2² = 1 + 4
c² = 5
c = √5
Leg lengths, 1 unit and 2 units match the hypotenuse length, √5
Answer:$32
Step-by-step explanation: So if the double pack of CD's is 20 dollars and that $4 less than 3/4 of the triple pack, then $20 + $4 = $24, then to find how much 1/4 of the cost is we divide 24 by 3, getting $8. Finally we multiple $8 by 4 to get $32, so the cost for a triple pack is $32.
Answer:
110 cm^2
Step-by-step explanation:
The first thing that you need to do is find the area of triangle AFE. The area of a triangle is always base*height/2. So in this case, that would be 10*6 divided by 2, which is 30 cm. Next, you will need to know the area of triangle ECB. Using that same formula, you will get 8*10/2, which is 40 cm. Finally, you will need to find the area of the whole rectangle. The area of a rectangle is always the length times the width. In this case, you would have 10*18, which is 180 cm. To get your final answer, you need to subtract the areas of the unshaded area from the whole area. That would be 180-(30+40), which is 110 cm. I hope this helped!
Answer:
Use the angle copy procedure to copy the angles to the ends of c.
Step-by-step explanation:
An angle is copied with a straightedge two settings of a compass.
- Set the compass to an arbitrary radius. An appropriate choice is a radius that is half or more of the length of the shortest ray of the angles you want to copy.
- Put the point of the compass at the vertex of an angle you want to copy. Using that same radius, draw arcs through both rays of the angle. Do this for all the angles you want to copy.
- Put the point of the compass at the place where you want the vertex of the copied angle. Here, that is either (both) end points of segment c. (You might want to label the ends of segment c as "A" and "B" so you know which angle you're copying where.) Using the same radius as before, draw an arc through the segment and through the space where you expect the ray from the copied angle to lie.
- For one of the source angles, set the compass radius to the distance between the points where the first arc crosses the angle's rays. Then, put the point of the compass at the place on the segment c where the corresponding arc crosses. Use the compass to mark a point on that arc the same distance as on the source angle. Draw a line from the vertex through the point you just marked. That line will make the same angle with c as the original angle.
- Repeat step 4 for the other angle you want to copy, at the other end of segment c. In general, the compass setting will be different (unless all the angles have the same measure).
The place where the rays from the copied angles cross is the third vertex (vertex C) of the triangle you're constructing.
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<em>Comments on the attached diagram</em>
In the attached diagram, "step 1" is to place the target vertex. You already have that as one end of segment C. The arcs numbered 2 and 3 in the diagram are the arcs resulting from executing steps 2 and 3 above. (They have arbitrary radius "r", which is the same everywhere.) You will have two sets, because you are copying two angles.
The arcs numbered 4 and 5 in the diagram have radius ST, the distance you set in step 4 above. That distance is used as the radius of arc 5, so the length VW will be the same as the length ST. The straightedge is used to draw a line through B and W, completing the copy of the angle.
C, E, and F have 50 50 chance