Answer:
ab + bc + ca = 40
Step-by-step explanation:
Using the expansion identity
(a + b + c)² = a² + b² + c² + 2(ab + bc + ca) , that is
9² = 1 + 2(ab + bc + ca)
81 = 1 + 2(ab + bc + ca) ← subtract 1 from both sides
80 = 2(ab + bc + ca) ← divide both sides by 2
40 = ab + bc + ca
The proof that the diagram is a square is that; D: slopes are perpendicular where the sides meet
<h3>How to Prove a quadrilateral is a Square?</h3>
We know that a square is a quadrilateral that has 4 sides. Now, the 4 sides of a square are all equal and at right angles.
Since all sides of the square are equal, then it means that 2 consecutive sides must be perpendicular to each other. Thus, this means that the slope of 2 consecutive sides must be perpendicular to each other.
Read more about Square proof at; brainly.com/question/4471785
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Answer:
1. True
2. False
3. False
Step-by-step explanation:
1. In parallelograms, opposite sides are congruent. Therefore EV=16
2. In parallelograms, adjacent angles add up to 180°, so measure of angle V = 100°
3. Opposite angles are equal so measure of angle L = 95°
4. Diagonals of parallelograms bisect each other. DE=10
5. Same rule as #4. LV=18
If Sheila started with 8 yards of fabric and used 2 1/4 yards, she will have the difference of these two values remaining. Subtract 2 1/4 from 8.
Convert the mixed fraction to an improper fraction. (Multiply its denominator by the whole number and replace the numerator with this new number.)
2 1/4 = 9/4
We now have:
8/1 - 9/4
Multiply 8/1 by 4/4 to get common denominators.
8/1 × 4/4 = 32/4
Now subtract.
32/4 - 9/4 = 23/4 = 5.75
Alternatively, we could have converted the fraction 2 1/4 to decimal form and subtracted it from 8.
2 1/4 = 2.25
8 - 2.25 = 5.75
Answer:
Sheila has 5.75 yards of fabric left.