Answer:He buys 8 pounds
Step-by-step explanation:
You can either just add up the $3.25 until you get to the end-price, but that wont always work for every problem. The best way is to divide the 26 with the 3.25 in a written devision.
The first step to solving this is converting these mixed numbers into improper fractions. You would do that by multiplying the denominator by the whole number and adding the numerator to that number; this number replaces the numerator. It would look something like this:
1 8/10 --> 18/10
2 2/5 --> 12/5
Now, to subtract the second fraction from the first one, the denominators of both fractions must be the same. We can make them the same by multiplying the second fraction by 2:
12/5 * 2/2 = 24/10
Now we can set up the equation as:
18/10 - 24/10 = -6/10 --> -3/5
The answer is negative 3/5.
I hope this helps.
Answer:
PG ≅ SG (Given)
PT ≅ ST (Given)
GT = GT (Common)
∴ ∠GPT ≅ ∠GST (SSS Congruency Axiom)
Step-by-step explanation:
<u>Given</u>: PG ≅ SG and PT ≅ ST
<u>To Prove</u>: ∠GPT ≅ ∠GST
<u>Proof</u>: PG ≅ SG (Given)
PT ≅ ST (Given)
GT = GT (Common)
∴ ∠GPT ≅ ∠GST (SSS Congruency Axiom).
<u>SSS Congruency Axiom</u>: If three pairs of sides of two triangles are equal in length, then the triangles are congruent.
<u>Congruence</u>: Two sets of points are called congruent if, and only if, one can be transformed into the other by an isometry, i.e., a combination of rigid motions, namely a translation, a rotation, and a reflection. This means that either object can be repositioned and reflected (but not resized) so as to coincide precisely with the other object. Two triangles are congruent if their corresponding sides are equal in length, and their corresponding angles are equal in measure.
Answer:
B. {16, 19, 20}
Step-by-step explanation:
The <em>triangle inequality</em> requires for any sides a, b, c you must have ...
a + b > c
b + c > a
c + a > b
The net result of those requirements are ...
- the sum of the two shortest sides must be greater than the longest side
- the length of the third side lies between the difference and sum of the other two sides
__
If we look at the offered side length choices, we see ...
A: 8+11 = 19 . . . not > 19; not a triangle
B: 16+19 = 35 > 20; could be a triangle
C: 3+4 = 7 . . . not > 8; not a triangle
D: 5+5 = 10 . . . not > 11; not a triangle
The side lengths {16, 19, 20} could represent the sides of a triangle.
_____
<em>Additional comment</em>
The version of triangle inequality shown above ensures that a triangle will have non-zero area.
The alternative version of the triangle inequality uses ≥ instead of >. Triangles where a+b=c will look like a line segment--they will have zero area. Many authors disallow this case. (If it were allowed, then {8, 11, 19} would also be a "triangle.")
So first thing you need to understand is that ABC and AFE are congruent triangles. This means we can find the other angles, based on ABC:
Angle FAE = 26.56505118 degrees
Angle AEF = 63.43494882 degrees
Angles ECD and DEC are both 45 degrees
Now, we can find the angles in ACE:
AEC = 71.56505118 degrees
ECA = 71.56505118 degrees
CAE = 36.86989764 degrees
