An exterior angle is formed by one side of the triangle, and a side EXTENDED outside the triangle. Two angles are like that, ∠4 and ∠2.
Angle 3 is NOT an exterior angle because it is made up of two extended sides. It does not use one of the sides of the triangle.
Lets x = # of hours Melania works at <span>office clerk
and y = </span># of hours Melania works as a <span>cashier
x + y = 38 so x = 38 - y
13x + 9.25y = 434
substitute </span> x = 38 - y into 13x + 9.25y = 434
13x + 9.25y = 434
13(38 - y) + 9.25y = 434
494 - 13y + 9.25y = 434
-3.75y = -60
y = 16
x = 38 - y so x = 38 - 16 = 22
answer
Melania works at office clerk = 22 hours
Melania works as a cashier = 16 hours
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To Prove: ΔEFI ~ Δ GFH
Proof:
When two triangles are similar, their corresponding sides are Proportional and their corresponding interior angles are equal.
Two Triangles can be proven similar by following Similarity Criterion.
1. AA
2.SSS
3.SAS
→∠EFI=∠GFH-------[Vertically Opposite angles]
The Other statement which is needed to prove that triangles EFI and GFH are similar is
Option C:→ ∠E ≅ ∠G
So, Two triangles ΔEFI and Δ GFH are Similar by Angle-Angle(AA) Criterion.
Solutions
Factor <span>3x</span>²<span><span>−2x−8</span><span>
</span></span>1. Multiply 3 by -8, which is -24.
2. Ask: Which two numbers add up to -2 and multiply to -24?
3. Answer: 4 and -6
4. Rewrite <span>−2x </span>as the sum of <span>4x </span>and <span>−6x</span>:

<span>
</span><span>Factor out common terms in the first two terms, then in the last two terms
</span>
Factor out the common term <span>3x+4
</span>
Solve for <span>x
</span>1. Ask: When will <span>(3x+4)(x−2) </span>equal zero?
2. Answer: When <span>3x+4=0 </span>or <span>x−2=0.</span>
3. Solve each of the 2 equations above:
x = −<span>4 / 3</span>,<span>2</span>