Lara G.

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SAT

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Question:

What are the best strategies for studying for the SAT?

Lara G.

Answer:

Different people learn in different ways, so find what works best for you. But here are my favorite tips. First of all, start early! It's a lot more manageable to study for 10 minutes a day than it is to try to learn everything the week before. Take at least one full practice test before you sit for the real one. It helps you get a sense of the timing for each section, and it can also help you narrow your studying by determining which sections you need to work on. Get a study guide, and use it. There are many different options out there, and they're all a little different. I recommend going to a bookstore or checking them out from a library to figure out which book you like best. Learning test-taking strategies is equally as important as learning the material. Spend some time learning the best way to approach the questions and how to eliminate answers, and you'll increase your chances of getting the questions correct. Don't panic! If nothing else, you'll learn from the experience, and you can always take the test again.

Biology

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Question:

In pea plants, purple flowers are dominant over white flowers. Two plants, both heterozygous for the gene that controls flower color, are crossed. What percentage of their offspring will have purple flowers?

Lara G.

Answer:

To answer this question, we will have to determine all possible allele combinations for the offspring of the two plants. Since both plants are heterozygous, they both have one dominant and one recessive allele. We will write this as Pp, where P is the dominant (purple) allele, and p is the recessive (white) allele. To visualize this problem, we will set up a Punnett square. P p P PP Pp p Pp pp Out of the 4 possible combinations, 3 have the purple phenotype and 1 has the white phenotype. Therefore, approximately 3/4 (75%) of the offspring will be purple, and about 1/4 (25%) of the offspring will be white.

Algebra

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Question:

Find all values of b and c so that the quadratic function $$ f(x) = x^2 + bx + c $$ has a graph that is tangent to the $$x$$-axis and a $$y$$-intercept at $$(0, 9)$$.

Lara G.

Answer:

First off, we can use the information given to find $$c$$. We are given a point that we know is on the graph, which is $$(0, 9)$$. Plugging this into the quadratic function gives us $$9 = (0)^2 + b(0) + c$$, which simplifies to $$9 = c$$. The second thing we know is that $$a = 1$$. Since $$ a $$ is positive, the parabola opens upwards. We are therefore looking for a minimum point of the function. The minimum value of $$x$$ will be at $$x = \frac{-b}{2a} $$. Since we know $$a = 1$$, we can write this as $$x = \frac{-b}{2} $$. If we plug this into the original equation, we get $$ y = (\frac{-b}{2})^2 + b(\frac{-b}{2}) + 9 $$. Expanding this gives us $$ y = \frac{b^2}{4} - \frac{b^2}{2} + 9 $$. Since we know that the minimum point occurs on the $$x$$-axis, we can infer that $$y=0$$. Plugging this into our equation and solving for $$b$$ gives us $$b^2=13$$. Therefore, $$ b=\pm\sqrt {13} $$. Therefore, the two possible points at which the parabola is tangent to the $$x$$-axis are $$(\sqrt{13},0)$$ and $$(-\sqrt{13},0)$$. Our solution is $$b = \sqrt{13}$$ or $$-\sqrt{13}$$ and $$c=9$$.

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