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3 years ago

Help with these please.

Mathematics

1 answer:

zepelin [54]3 years ago

7 0

For numbers 15-17, we need to remember that two of a triangle's angles are always acute and the third angle will allow us to classify the triangle based on its angles. now that we know this, let's look at #15. the first two angles listed are acute, and the third is an obtuse angle, therefore it is an obtuse triangle. on #16 we have three acute angles, so it is an acute triangle. #17 has two acute angles and a right angle so it is a right triangle.
on numbers 21-23, we need to know that a triangle with all congruent sides is called equilateral, a triangle with two equal sides is isosceles, and a triangle with no equal sides is called scalene. #21 shows two equal sides so it is an isosceles triangle. #22 has three equal sides so it is an equilateral triangle. #23 has no equal sides so it is scalene. hope this helped! :)

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3 years ago

Help!! algebra two!! c-h :)

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Answer:

c. (2x + 3y)² = (2x)² + 2(2x)(3y) + (3y)²

d. (w - 1)(1 + w + w²) =  w³ - 1

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f. (2x + 5y)(2x - 5y) = 4x² - 25y²

g. (2²¹ - 1)(2²¹ + 1) = 2⁴² - 1

h. [(x - y) - 3][(x - y) + 3] = (x - y)² - 9

Step-by-step explanation:

c. Although this expression, when squared, is really 4x² + 12xy + 9y², they just splitted it up into several more terms. In this last blank should be a 9y², but instead, they took the square root of the term, which is 3y, and set the square outside of the parentheses.

*I bet that was what made it confusing, but have no fear. The mathematics tutor is here.

d. This is similar to the Quadratic Equation [y = Ax² + Bx + C] where you can, what I like to call... FOIL it, however, you have an extended amount of terms. Although you still have to FOIL it, it is just a unique procedure. This time, you have to one-by-one, take each term in the first set of parentheses [-1 and w] and multiply them by the second all three terms in the second set of parentheses.

e. This is a piece of cake because we know BOTH square roots of 16 and we are multiplying what are called conjugates.

f. Again, we are multiplying conjugates, so we just multiply the first and last two terms in each set of parentheses.

g. Again, we are multiplying conjugates EXCEPT now, we have exponents in each set of parentheses. Whenever you multiply terms, you add the exponents and your base remains the same, which is what you see in the above answer.

h. For the final exercise, we are multiplying conjugates again, and we obviously can see what fills that blank because there are TWO IDENTICAL EXPRESSIONS that are being multiplied, which in this case are being "squared", and that expression is x - y. It appears twice, so that is a giveaway.

If you are ever in need of assistance, do not hesitate to let me know by subscribing to my You-Tube channel [USERNAME: MATHEMATICS WIZARD], and as always, I am joyous to assist anyone at any time.

**Conjugates are IDENTICAL expressions with OPPOSITE operation symbols. Whenever you multiply conjugates, just add the first and last two terms in both sets of parentheses because when you FOIL, the midst term will ALWAYS result in zero.

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Answer:

Step-by-step explanation:

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