Let's say you had a cake that is cut into 5 equal slices. Then someone eats 2 of those slices. They ate 2/5 of the cake.
Now let's say you have another cake that you cut into 10 equal slices. If someone eats 4 of those ten, then they have eaten 4/10 = 2/5 of the cake.
Check out the diagram below to see a visual of how 4/10 and 2/5 are equivalent fractions.
Going from 2/5 to 4/10 has us multiply top and bottom by 2.
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Similarly, 1/2 = 5/10 after multiplying top and bottom by 10
The original expression 2/5 + 1/2 turns into 4/10 + 5/10
Then you add the numerators to get 4+5 = 9, placing that over the common denominator of 10
<h3>Answer: 9/10</h3>
F(x) = 2x² - 8x - 10.
This is a parabola open upward (since a>0) with an axis of symmetry = -b/2a:
a) axis of symmetry: x = -(-8)/(2*2) = 8/4 = 2. Then x = 2, which is the x component of the vertex
b) for x = 2, f(x) = f(2) = - 18 (component of y of the vertex)
c) VERTEX(2, - 18)
d) DISCRIMINENT: b² - 4.a.c = 64 - 4*2*(-10) = 144
Answer: see proof below
<u>Step-by-step explanation:</u>
Use the Double Angle Identity: sin 2Ф = 2sinФ · cosФ
Use the Sum/Difference Identities:
sin(α + β) = sinα · cosβ + cosα · sinβ
cos(α - β) = cosα · cosβ + sinα · sinβ
Use the Unit circle to evaluate: sin45 = cos45 = √2/2
Use the Double Angle Identities: sin2Ф = 2sinФ · cosФ
Use the Pythagorean Identity: cos²Ф + sin²Ф = 1
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<u>Proof LHS → RHS</u>
LHS: 2sin(45 + 2A) · cos(45 - 2A)
Sum/Difference: 2 (sin45·cos2A + cos45·sin2A) (cos45·cos2A + sin45·sin2A)
Unit Circle: 2[(√2/2)cos2A + (√2/2)sin2A][(√2/2)cos2A +(√2/2)·sin2A)]
Expand: 2[(1/2)cos²2A + cos2A·sin2A + (1/2)sin²2A]
Distribute: cos²2A + 2cos2A·sin2A + sin²2A
Pythagorean Identity: 1 + 2cos2A·sin2A
Double Angle: 1 + sin4A
LHS = RHS: 1 + sin4A = 1 + sin4A 
Answer:
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Answer:
With an enlargement the scale factor would be greater than zero. With a reduction the scale factor would be a fraction or maybe even a decimal.
