A toolbox contains a pile of mixed up pile of wrenches. The wrenches are all labeled with the dimension of their openings in fra
ctions of an inch.the measurements of the wrenches are 1/2 3/4 3/8 5/8 5/16 7/16 and 11/16 inches
1. You want to put the wrenches is order from smallest to largest opening just using the labeled fraction measurement.
a. Give two different methods you can use to put the fractions in order.
B. Choose a method from part 1a and show your conversions below
C. List the fraction in order from least to greatest.
2.plot the sizes of the wrenches on the number line below (in the picture) label each point with a wrench measurement
3. Explain how the number line can be used to support your answer form part 1c.
1. You want to put the wrenches is order from smallest to largest opening just using the labeled fraction measurement.
a. Give two different methods you can use to put the fractions in order.
B. Choose a method from part 1a and show your conversions below
C. List the fraction in order from least to greatest.
2.plot the sizes of the wrenches on the number line below (in the picture) label each point with a wrench measurement
3. Explain how the number line can be used to support your answer form part 1c.
2 answers:
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Hi there!
√100=10
√1=1
√36=6
10-1+6
9+6
15
Hope this helps
<h3>Given</h3>
- ΔABC
- A(-3, -1), B(0, 3), C(1, 2)
- the length of the perimeter of ΔABC to the nearest tenth
The perimeter of a triangle is the sum of the lengths of its sides. The length of each side can be found using the Pythagorean theorem. Effectively, each pair of points is treated as the end-points of the hypotenuse of a right triangle with legs parallel to the x- and y-axes. The leg lengths are the differences betweeen the x- and y- coordinates of the points.
The difference of the x-coordinates of segment AB are 0-(-3) = 3. The y-coordinate difference is 3-(-1) = 4. So, the leg lengths of the right triangle whose hypotenuse is segment AB are 3 and 4. The Pythagorean theorem tells us
... AB² = 3² +4² = 9 +16 = 25
... AB = √25 = 5
You may recognize this as the 3-4-5 triangle often introduced as one of the first ones you play with when you learn the Pythagorean theorem.
LIkewise, segment AC has coordinate differences of ...
... C - A = (1, 2) -(-3, -1) = (4, 3)
These are the same leg lengths (in the other order) as for segment AB, so its length is also 5.
Segment BC has coordinate differences ...
... C - B = (1, 2) -(0, 3) = (1, -1)
The length of the line segment is figured as the root of the sum of squares, even though one of the coordinate differences is negative. The leg lengths of the right triangle used for finding the length of BC are the absolute value of these differences, or 1 and 1. Then the length BC is
... BC = √(1² +1²) = √2 ≈ 1.4
So the perimeter of the triangle ABC is
... AB + BC + AC = 5 + 1.4 + 5 = 11.4 . . . . perimeter of ∆ABC in units
_____
Please be aware that the advice to "round each step" is <em>bad advice,</em> in general. For real-world math problems, you only round the final result. You always carry at least enough precision in the numbers to ensure that there will not be any error in the final rounding.
In this problem, the only number that is not an integer is √2, so it doesn't really matter.