I think the correct answer from the choices listed above is option D. For the function f(x) = (x − 2)2 + 4, the <span>vertex is (2, 4), the domain is all real numbers, and the range is y ≥ 4. The domain is all x-values available for the function and the range are the y values and in this case it should be greater than or equal to 4. Hope this answers the question.</span>
<u>Given:</u>
A triangular piece is cut out of a rectangular piece of paper to make the class banner.
<u>To find:</u>
The area of the class banner.
<u>Solution:</u>
The rectangular piece of paper is 14 inches long and 
inches wide.
From the given diagram, the triangle has a base length of the same 8 inches and has a height of 
inches long.
To determine the area of the banner, we subtract the area of the triangle from the area of the rectangle.
The area of a triangle 
The area of the triangle 
square inches.
The area of a rectangle 
The area of the rectangle 
square inches.
The area of the class banner 
square inches.
So the banner has an area of 100 square inches which is the first option.
f = 2
Simplify both sides of the equation <span><span>1.25f</span>+2</span>=<span><span>−<span>2.75f</span></span>+<span>10
Add 2.75 to each side </span></span><span><span>4f</span>+2</span>=<span>10
Subtract 2 from both sides </span><span>4f</span>=<span>8
Divide each side by 4 </span>f=<span>2</span>
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</span>
Like your writing, but what exactly is it??
A. True. Summing any rational number with an irrational number leads to an irrational result. The proof is a bit lengthy so I'm leaving it out.
B. True. Adding p/q with r/s leads to (ps+qr)/(qs) which is rational. Keep in mind that q and s cannot be zero.
C. False. One counter example is sqrt(3)*sqrt(12) = sqrt(3*12) = sqrt(36) = 6. This shows the product of two irrational numbers, in this case sqrt(3) and sqrt(12), multiplying to get a rational result 6 = 6/1.
D. True. Multiplying p/q and r/s leads to (p*r)/(q*s) which is rational. Keep in mind that q and s cannot be zero.
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The final answer is choice C
