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Please see my earlier solution of this problem...the answer is
36rad(2)

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See my earlier solution to this one...the answer is
36rad(2)

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If it is a rectangular yard, the area of it is found by
A = l x w (that is, length times width)
A = 9 x 5 = 45 square yards

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If you mean to simplify 6rad(72), I can show you...
The idea is to separate (that is, factor) the radicand (the 72) into the largest perfect square within 72 and what's left.
Since 72 = 36 x 2, we have this:
6rad(72) =
6rad(36)rad(2)
But rad(36) = 6
So the final answer is found by
6rad(36)rad(2) =
(6)(6)rad(2) =
36rad(2)

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This one is not easy to show here, but we can do it by the reduction-by-minors technique:
(-1) times the rows and columns not including the -1 MINUS
(0) times the rows and columns not including the 0 PLUS
(1) times the rows and columns not including the 1
so we get
(-1)(-5 - 3) - 0 + 1(2 - 0) =
8 - 0 + 2 =
10

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Here we substitute the given values for x and y into the expression
3x - 7y
to get
3(-2) - 7(-3) =
-6 - (-21) =
-6 + 21 =
15

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We need to apply the order of operations, PEMDAS, when doing problems such as this:
-2 - 4 + 7 + 3(-4) + 17 =
Thus multiplying comes before adding and subtracting, and we get
-2 - 4 + 7 - 12 + 17 =
Then we add and subtract left to right as we find them...yielding
6 as our answer

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From -3[-4+1] / (-9), we need to combine what's in the parentheses first, giving us
(-3)(-3) / (-9) =
9 / -9 =
-1

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Since you know both lines go thru (1, 4), you can plug x = 1 and y = 4 in both and get
a + 4b = 13 and
a - 4b = -3
Now add equations and get
2a = 10 and
a = 5
You can also subtract equations and get
8b = 16
b = 2

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Not too much you can do here, but from
5x/x^2-9 + 2/x+4 we can combine fractions and get
[5x(x + 4) + 2(x^2 - 9)] / [(x + 4)(x - 3)(x + 3)] =
[5x^2 + 20x + 2x^2 - 18] / [(x + 4)(x - 3)(x + 3)] =
(7x^2 + 20x - 18) / [(x + 4)(x - 3)(x + 3)]

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8.38 x 10^7 feet - 5.84 x 10^7 feet =
2.54 x 10^7 feet
Leave the powers of ten alone and merely subtract the decimals. Of course you have to be sure that your answer is in proper scientific notation, which it is...

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Yes. The question asks, "What number divided by 7 gives you 500?"
In algebra we show that as
x/7 = 500
We then multiply both sides by seven and get
x = 3500

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Please see my earlier solution of this problem.
It turns out that these two lines are parallel, thus no solution exists, and the system is said to be inconsistent.

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Sometimes you solve an equation and get two answers. By plugging them in to the original equation to check, you discover one (or both) do not work. That is an example of an extraneous root. Very common in rational expressions/equations, and equations containing radicals.

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Well, you should arrive at the same solution. The algebraic method is more precise because trying to estimate exact solutions from a written diagram can be difficult...for example, you may think the solution from your graph is (2, 3) but it may actually be (2 1/8, 2 15/16)...tis hard to tell sometimes...especially with handwritten graphs and thick pencil lines...

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Okay if a = b + 3(4 - c) when b = 5 and c = 2, we can find a by plugging in values for b and c...so we have
a = b + 3(4 - c) = 5 + 3(4 - 2) = 5 + 3(2) = 5 + 6 = 11

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Well for no solution to exist, the lines that govern them would need to be parallel and the shaded half-planes would have to be in opposite directions so that there is no overlapping of shaded areas. They could even represent the same line as long as they are both dotted and are shaded oppositely. For a system of inequalities to have a solution in the first quadrant, both (or all) shaded half-planes must intersect somewhere in the first quadrant.

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Okay...starting from
6(rad(24x^5)) / 18x
Let us pull the perfect squares out of the 24x^5 and we get
6(rad(24x^5)) / 18x =
6(rad(4x^4))(rad(6x)) / 18x =
6(2x^2)(rad(6x)) / 18x =
(12x^2)(rad(6x)) / 18x
Now do some cancelling...
2x(rad(6x)) / 3

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If 75% of the students had taken 8 courses, 25% had not. Of these remaining 25%, 60% of them (or 60% of 25% = 15%) had taken 6 or 7 courses. Thus 90% (75% + 15%) of the students had taken 6, 7 or 8 courses.
Thus only 10% had taken less than 6 courses.
When working with percents, it is often easier to work with hundreds...in this case you could imagine there are 100 students and do the problem in real numbers instead of percentages.

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Please see my earlier solution...
y = -0.6

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From 1.3y + 4.4 = 0.8y + 4.1
we subtract 0.8y from both sides and get
0.5y + 4.4 = 4.1
Now subtract 4.4 from both sides and get
0.5y = -0.3
Now divide both sides by 0.5 and get
y = -0.6

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Okay, let's see...
1) 3^x = 729 I got 6 ====> CORRECT
2) 6^x - 28 = -8 I got 10/3 ====> not correct. First add 28 to both sides...
6^x = 20
Now take the log of both sides and solve for x...
ln 6^x = ln 20
x = ln 20 / ln 6 and
x = 1.672
3) 4ln 3x =15 I got 14.17 ====> CORRECT. Here divide by four, then exponentiate and solve and we get
ln 3x = 15/4
3x = e^(15/4)
x = e^(15/4) / 3
x = 14.17

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Please see my earlier solution...47/126

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1/3 ÷ (-4/7)(-1/6) + (-1/18) =
1/3 + 4/42 + (-1/18) We need a lowest common denominator...here it's 126...so
1/3 + 4/42 + (-1/18) = 42/126 + 12/126 - 7/126 =
47/126

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Let us evaluate
(x^2 + xy - y^2) / (x + y) when x = 6 and y = -2
The technique is to merely to plug in 6 for every x and -2 for every y...we get
(36 + (-12) - 4) / (6 - 2)=
20 / 4 =
5

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From
x - 2 y = 2
2x + 3y = 11
Solve for x in the first and substitute into the second:
x = 2y + 2
2(2y + 2) + 3y = 11
4y + 4 + 3y = 11
7y + 4 = 11
7y = 7
y = 1
Then since x = 2y + 2, we have
x = 2(1) + 2
x = 4
Our solution is (4, 1)

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After you factor everything, then invert the denominator, and then cancel where you can the answer boils down to
x^2 / (x + 9)

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Yes, it is correct.

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Well this is a bit difficult to show you without a diagram and graph, but here goes...
Since we are cutting a length x out of both ends of both the length and the width, the dimensions of the base of the box will be (6 - 2x) by (4 - 2x). It will have a height of x. Therefore the function for the volume is
V(x) = x(6 - 2x)(4 - 2x) = 4x^3 - 20x^2 + 24x
I can't show you the graph but you know x must be less than two.
To find the maximum volume, we take the derivative of V(x) and set it equal to zero...
dV/dx = 12x^2 - 40x + 24 = 0
Now solve for x
Use the quadratic formula to get
x = (5 ± rad(7)) / 3
But only one root works (as mentioned above), so the answer here is
x = (5 - rad(7)) / 3 or about .785 feet

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From
2a = 3b - 13
b = 2a + 7
let us take the given value for b in the second equation and substitute it into the first equation, like this
2a = 3(2a + 7) - 13
2a = 6a + 21 - 13
2a = 6a + 8
-4a = 8
a = -2
Now using b = 2a + 7 we have
b = 2(-2) + 7
b = -4 + 7 = 3
So our solution is (-2, 3) and is a consistent system.

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We can summarize what we have in two equations:
3M + 2W + (1/2)C = 100 (this is the bushels equation)
M + W + C = 100 (this is the number of people equation)
Since we have three unknowns but just two equations, there should be a number of solutions avalable.
One way to find some of them is to eliminate one variable by linear combination.
I multiplied the top equation by two and subtracted the bottom equation...
6M + 4W + C = 200
M + W + C = 100
yielding
5M + 3W = 100
so that any combination that satisfies this equation solves the problem...for example, eight men and twenty women (leaving 72 children) works...or 14 men, 10 women and 76 children...