All Answers 358514 Answers

A = (b1/2 + b2/2)h

1) A/h = b1/2 + b2/2 --> A/h - b2/2 = b1/2 --> 2A/h - 2b2/2 = b1 --> b1 = 2A/h - (b2).

2) A/h = b1/2 + b2/2 --> A/h - b1/2 = b2/2 --> 2A/h -2b1/2 = b2 --> b2 = 2A/h - (b1).

3) 2A = (b1 + b2)h --> 2A/(b1+b2) = h.

Haha, that's funny! 

Here's a ruler:

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Ohh yes, yours makes more sense Phill...was wondering how come there weren't any direct square roots for the 2nd question. 

I believe the second one is this....

5(3x+1)^¼=10     divide both sides by 5

(3x+1)^¼= 2       raise each side to the 4th power

3x + 1  = 16       subtract 1 from both sides

3x = 15              divide both sides by 3

x = 5

Sorry, not sure if it is available on the calculator here but for graphing calculators: Hit Mode --> Find seq (near fun par pol) --> Then, hit the "Y =" button --> enter your information.

sqrt6x^3 / sqrt3x = sqrt(2x^2)*sqrt(8x^2) = sqrt(16x^4) / A.

When someone requests to borrow my ruler....I always suspect that something's "a foot"

......or so......

I found one, you can stop looking!!!!

Sorry, Nataszaa, but I believe my answer to the second one was correct......we could "simplify" it further as:

4x + (4/3)x√(6)    (I actually prefer it as a single fraction, but it's arbitrary)

(I believe Aziz forgot to distribute the x over the second term)

Using dimensional analysis:

1 m^3 X ((100cm)^3 / 1m^3) X (1 mL / 1 cm^3) X (1 L / 1000 mL) = 1,000,000 / 1,000 = 1,000 L.

Those are the variables: x = number of flags, y = number of square yards, & z = total cost -->

In verbal form:

The number of square yards needed is equal to 0.6 times the number of flags required. The total cost of the material will be 2 times the square yards needed.

Aziz, what does x, z, and y stand for?

Since each flag requires 0.6 square yards of material and the material costs $2 per square yard:

Let x = number of flags & y = number of square yards needed -->

y = 0.6x

Then, let z = total cost of the material -->

z = 2y

EDIT: It should be z = 2y; I had written 1.2 before.

2+sqrtx+5=4 --> 

sqrtx = -3 --> No solution since square root of x will be positive.

5(3x+1)¼=10 -->

(3x+1)¼= 2 -->

(3x + 1) = 8 -->

3x = 7 -->

x = 7/3.

25 1/2 as in 25^(1/2) --> sqrt(25) = 5.

(sqrt9xy^2)^4 --> (sqrt9xy^2)(sqrt9xy^2)(sqrt9xy^2)(sqrt9xy^2)

(sqrt9xy^2)(sqrt9xy^2) = 9x^2y^4

Now, we can just square this term [9x^2y^4] since we have another (sqrt9xy^2)(sqrt9xy^2) -->

(9x^2y^4)(9x^2y^4) = 81x^4y^8.

An easier way is to just distribute the ^4 to each of the terms -->

(sqrt9xy^2)^4 = (sqrt9)^4*x^4*(y^2)^4 = 81x^4y^8.

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EDITED: First answer.

okay so apparently Aziz was right...

If only it were that simple; unfortunately a^x - b^x doesn't equal (a-b)^x in general!

4.466^x - 2*2.331^x + 1 = 0 has one immediately obvious solution; namely x = 0, because:

4.466⁰ - 2*2.331⁰ + 1 = 1 - 2*1 + 1 = 0.

I can't see any way of getting another (real number) solution except by a numerical method.  A straightforward, though rather inefficient way is just to rearrange the equation as shown below, guess an initial value and then iterate until the iterates converge.  It takes about 100 iterations to get 5 decimal places!

More information is needed; however, if you are looking for the total wages for a week: $9.00/hour --> 40 hours a week = 40 hours/week*($9.00/hour) = $360/week.

4.466^x -2(2.331)^x + 1 = 0

4.466^x - 4.662^x = -1 -->

-0.196^x = -1 -->

log(-0.196^x) = log(-1) -->

Properties of logs allow: x log(-0.196) = log(-1) -->

x = log(-1) / log(-0.196) = Error

However, when plugging in values such as x = 0.02 into -0.196^x = -1, we obtain a number that is close to -1, -0.9679326095185039.

9.075 X 10^-6

(5x3 + 2x2 + x - 1) - (2x3 - 3x2 + 4x)

Distribute the negative sign: 5x3 + 2x2 + x - 1 -2x3 + 3x2 - 4x -->

Combine like terms: 2x^3 + 5x^2 -3x - 1.

0.4545454545

x = 0.4545454545

x*100 = 45.45454545 -->

100x = 45.45454545

subtract x = 0.4545454545

99x = 45 --> x = 45/99 = 15/33.

(2√7)/(√3-√5)

The trick here is just to multiply by the conjugate of the denominator in both the numerator and denominator....so we have.....

[(2√7)/(√3-√5)] *[(√3+√5) / (√3+√5)] =

[2√(21) + 2√(35)] / (3-5) =

[(2)[√(21) + √(35)]] / (-2)  =

-[√(21) + √(35)]

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The next one is similar........

(4x)/(3-√6) * [ (3+√6) / (3+√6)] =

[(4x)(3+√6)]/[9 -6] =

[12x + 4x√6] / [3]

2sqrt7 / (sqrt3 - sqrt5)

(2sqrt7) / (sqrt3 - sqrt5) * [(sqrt3 + sqrt5) / (sqrt3 + sqrt5)] -->

2(sqrt(21) + sqrt(35)) / (3 - 5) -->

2(sqrt(21) + sqrt(35)) / (-2) -->

-(sqrt(21) + sqrt(35)).

4x / (3 - sqrt6)

4x / (3 - sqrt6) * [(3 + sqrt6) / (3 + sqrt6)] -->

4x(3 + sqrt6) / (9 - 6) -->

12x + 4sqrt6 / (3) -->

4x + (4/3)sqrt6.

what about the other one CPhill?