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Tanzania [10]
3 years ago
10

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

Mathematics
1 answer:
kotegsom [21]3 years ago
8 0

Answer:

c. (2x + 3y)² = (2x)² + 2(2x)(3y) + (<u>3y</u>)²

d. (w - 1)(1 + w + w²) = <u> </u><u>w³</u> - 1

e. a² - 16 = (a + <u>4</u>)(a - <u>4</u>)

f. (2x + 5y)(2x - 5y) = <u>4x²</u> - <u>25y²</u>

g. (2²¹ - 1)(2²¹ + 1) = <u>2⁴²</u> - 1

h. [(x - y) - 3][(x - y) + 3] = (<u>x - y</u>)² - 9

Step-by-step explanation:

c. Although this expression, when squared, is really <em>4x</em><em>²</em><em> </em><em>+</em><em> </em><em>12xy</em><em> </em><em>+</em><em> </em><em>9y</em><em>²,</em><em> </em>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 <em>3y,</em><em> </em>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 [<em>y</em><em> </em><em>=</em><em> </em><em>Ax</em><em>²</em><em> </em><em>+</em><em> </em><em>Bx</em><em> </em><em>+</em><em> </em><em>C</em>] 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 <em>x</em><em> </em><em>-</em><em> </em><em>y</em><em>.</em><em> </em>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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A new car depreciates as soon as you drive it out of the parking lot. A certain car depreciates to half its original value in 4
Alexandra [31]

Answer:

Original price of car = $20,000

Step-by-step explanation:

Let the original price of the car be 'x' dollars.

Given:

Here, the depreciation of the car is occuring exponentially as the value depreciates to half in every four years.

Worth of car after 8 years = $5000

Value after depreciation in 4 years = Half of original value = \frac{x}{2}

So, value of car after depreciation in another 4 years = Half of the value after 4 years = \frac{1}{2}(\frac{x}{2})=\frac{x}{4}

Therefore, final depreciated value after 8 years is \frac{x}{4}.

But, as per question, final depreciated value is $5000. Thus,

\frac{x}{4}=5000\\x=5000\times 4\\x=20000

Therefore, the original price of the car was $20,000.

3 0
3 years ago
Help please, Which expression does not belong? Explain your reasoning.
ZanzabumX [31]

Answer:

My best answer is option number 4.

Step-by-step explanation:

Because the first 3 answers follow a specific pattern in addition and division, i.e. they only go up to 4 different numbers, whereas with the 4th option, that changes. Not only that, but if you look closely, the 4th option adds 6 to itself 5 times, that's the same as 6x5, which equals 30, so if you divide 30 by 5, its almost pointless seeing as how you already know it's gonna get you 6.

4 0
3 years ago
What is the volume of a cylinder with a height of 13 yards and a diameter of 5 yards?
Anton [14]

Volume of cylinder = πr^2 × h

= π × (5/2)^2 × 13

= 255.25 yd^3

4 0
1 year ago
What is the volume of a cube whose edges each have a measure of 1.5 cm?
inysia [295]
Using the cube formula for volume I got V=3.38cm^3
7 0
3 years ago
Read 2 more answers
1 2/5m-3/5(2/3m+1) How do you solve this problem
igor_vitrenko [27]

Step-by-step explanation:

I am not sure what you mean by "solve".

I assume you mean simplify the expression.

and then it is very tricky to find the true original expression the way you typed it.

I think you meant

1 2/(5m) - 3/(5(2/(3m + 1)))

1 = 5m/5m

1 2/(5m) = (5m+2)/5m

3/(5(2/(3m + 1))) = 3/(10/(3m + 1)) = 3/1 / (10/(3m + 1))

when dividing by a fraction, it is the same as multiplying with the upside-down fraction

so, this is the same as

3/1 × (3m + 1)/10 = (3(3m + 1)) / (10×1) = (9m + 3)/10

this would give us in total

(5m + 2)/5m - (9m + 3)/10

to do the subtraction we need to bring both fractions to the save denominator (lower part).

it seems to me the easiest one would be 10m.

so,

2×(5m + 2)/10m - m×(9m + 3)/10m =

= (10m + 4)/10m - (9m² + 3m)/10m =

= (10m + 4 - 9m² - 3m)/10m = (-9m² + 7m + 4)/10m

if we want to transform this back to a sum of fractions :

4/10m - (9m² - 7m)/10m = 2/5m - (9m - 7)/10

5 0
2 years ago
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