<p>1) The perimeter of the trapezoid is 34. Subtracting the known sides: 34-8-8-4-4=10. Thus the hypotenuse of each triangle is 10/2 = 5. So those are 3,4,5 right triangles. The height of the rectangle is thus 3. So the perimeter of the rectangle is 8+8+3+3=22.</p>
<p>2) If you get stuck on a problem like this you can pick a number to substitute in to all the answer choices. For example, if I let x = 2, we get:</p>
<p>(A) -6 = 2</p>
<p>So we can eliminate (A)</p>
<p>(B) -8 = 8</p>
<p>So we can eliminate (B)</p>
<p>(C) -12 = -4</p>
<p>So we can eliminate (C)</p>
<p>(D) -6 = 2</p>
<p>So we can eliminate (D) </p>
<p>(E) -10 = -10</p>
<p>So we CAN’T eliminate (E)</p>
<p>Since (E) is the only one not eliminated, (E) is the answer.</p>
<p>Notes:</p>
<p>(1) Be very careful substituting these in - lots of minus signs tend to lead to careless errors.
(2) You need to check EVERY answer choice - just because the two numbers agree doesn’t mean that that’s the correct answer. It only means you can’t eliminate it.
(3) Let me do one computation in detail for you in case you’re confused about how to do it. I’ll do choice (A):</p>
<p>f(x) = x+4
f(2) = 2+4=6
-f(2) = -6
f(-2)=-2+4=2</p>
<p>Solving the problem using actual math: The given condition says that f is an ODD function. The answer choices are all polynomials. A polynomial is an odd function if and only if all exponents are odd. Choice (E) is the only choice with all odd exponents.</p>
<p>Note that x has exponent 1, and a constant has exponent 0.</p>
<p>3) We square each part of the inequality:</p>
<p>36 < n < 100</p>
<p>99-35 = 64</p>
<p>4) -25 + -24 + … + 0 + 1 +… + 24 + 25 = 0</p>
<p>So, -25 + -24 + … + 0 + 1 +… + 24 + 25 + 26 = 26.</p>
<p>So count the integers from -25 through 26, inclusive.</p>
<p>5) You’re given that 11 7/8 < n < 12 1/8. Using choice (C) as a guide, subtract 12 from all 3 parts of the inequality to get</p>
<p>-1/8 < n-12 < 1/8.</p>
<p>This is the same as choice (C).</p>
<p>@DrSteve woow maan thx !</p>
<p>in #3 i think u meant 99-37=62 
and i have a question in #1 after subtracting the known sides from the perimeter we will have 10 as the difference…but we will also have 4 unknown sides which are the two hypotenuse and the two other sides of the rectangle so how did u know the hypotenuse?</p>
<p>if number 4 is C then i could provide a very easy way to solvie it</p>
<p>sorry but the answer of #4 is E</p>
<p>Yes - of course you are correct about #3.</p>
<p>For your question about #1. The bottom of the rectangle is not labelled, but it is the same as the top of the rectangle (because it’s a rectangle). So the missing number on the bottom is 8.</p>
<p>So the bottom base of the trapezoid is 4+8+4 = 16. Add this to the top base and you get 24. </p>
<p>Does that clarify it for you?</p>
<p>Note: The top of the rectangle is labelled as 8. Maybe you missed that.</p>
