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Solve the system of equations:
1) 3x + 2y = 3
2) -5x + y = 8 Multiply equation 2) by 2 then subtract equation 1) from the result and solve for x.
2) -10y + 2y = 16
1) -(3x + 2y = 3)
-----------------
3) -13x = 13 Divide both sides by -13
x = -1 Now substitute this into equation 1) and solve for y.
1) 3(-1) + 2y = 3
-3 + 2y = 3 Add 3 to both sides.
2y = 6 Divide both sides by 2.
y = 3
Solution: (-1, 3)

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Simplify:
First, and
Now, and
Now add the two fractions, common denominator is xab.
=

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Factor:

This is as far as we can go for part 1.
Factor completely:

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First, a slope of 0 means that the line is horizontal.
The slope-intercept form of the equation is: where m is the slope and b is the y-intercept.
Since m = 0 and b = 3, just substitute these values into the general form.
or

See the graph of this line below:

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Solve for x:
Add the fractions on the left side. Common denominator is 6 X 7=42

Multiply both sides by 42.
Finally, divide both sides by 25.

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Simplify:
-6(14)-|4(-2)-3^2| = -84-|-8-9| = -84-|-17| = -84-17 = -101

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The general form of the equation for the height of an object propelled upward with an initial velocity of v from an initial height of h is , and since the depth of the canyon by which Jacob is standing is really irrelevant, your initial equation is correct. The initial height is zero feet.

Now you would like to find out at what time (t) will the ball return to its initial height of 0 ft.
Setting h(t) = 0 ft. you can write:
Solve for t by factoring -16t from both sides.
Apply the zero product principle.
Add 2 to both sides.

The ball will return to its initial height of 0 ft. in 2 seconds.
Check: Set t = 2
Solve for h.

ft.

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Simplify:
Apply the Quotient rule for logarithms: to the left side. The right side is rewritten because:
If then , so:

Multiply both sides by (x+3)
Subtract 243 from both sides.
Subtract 5x from both sides.
Divide both sides by 76.

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To find the x-intercepts, set y = 0 and solve for x.
Solve by factoring.
Apply the zero product principle.
You will have a double root.
If then, A double root.
See the graph:

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Solve for x:
Apply the product rule for logaritms: logMN = logM + logN
So:
Subtract log(8) from both sides.
Rewrite in exponential form: logx = y means b^y = x
You can do this on your calculator.

Check:

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1)
Here, you need to compare 12/20 with 10/15.
To do this, you must re-write the fractions with a common denominator.
First, it might be helpful to reduce the fraction to their simplest forms.


Now re-write each fraction with a common denominator of 15.

Ok, so we really didn't need to simplify this fraction.
Now compare: with
Kavita's performance was better in science than it was in maths
2)
The number of boys (30) plus the number of girls (20) means that there was a total of 50 pupils in the class.
The percentage of boys is is given by: [(# of boys)/(# of pupils)]*100
The percentage of boys is: %
Similarly, the percetage of girls is given by: [(# of girls/# of pupils)*100]
The percentage of girls is: %
3)
The employee saves 10% of Rs 1800. Change the percentage to its decimal equivalent: 10% = 0.1 and multiply this by 1800 to find the employee's savings.

The employee saves Rs 180
4)
Earnings per month = Rs 4750
Earnigs per year = Rs 4750 /month * 12 months /year = Rs 57000/year
Earning for 12 years = Rs 57000/year * 12 years = Rs 684000 in 12 years.
5)
The agent receives 5% of Rs 96000. Change the percent to its decimal equivalent: 5% = 0.05 and multiply this by 96000 to find the agent's fee.

The agent receives Rs 4800

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You can let V = number of videos and C = number of CDs.

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If the Dell computer takes 4 hrs to crack the password file, then it can crack 1/4 of the file in 1 hour.
If the Gateway computer takes 2(4) = 8 hrs to crack the same password file, then it can crack 1/8 of the file in 1 hour.
Working together, the two computers can crack (1/4 + 1/8 = 3/8) of the file in 1 hour.
Therefore, it would take them 8/3 hours, working together to crack the entire password file.
8/3 hours = 2 hours 40 minutes.

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Start with the formula for the perimeter of a rectangle:
where L = Length and W = Width. P is given as 108 feet, and L = 0.8W, so:
Simplify and solve for W.

Divide both sides by 3.6
feet.


feet.

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Rise over run is the definition of the slope, m, of a line. If your equation is in the slope-intercept form: , the slope is given by m and the y-intercept is given by b.
For example, let's say that you wanted to graph the line whose equation is: Remember that you need only two points to define a straight line.
The y-intercept is y=4, so mark a point on the y-axis at y=4.
The slope m is 2/3, so that's rise = 2 and run = 3 and since the sign of m is positive, the slope of the line will be leaning to the right.
Then, starting at the point y=4, go up (rise) 2 and then go right (positive) 3 and mark your second point.
Now join the two points with a straight line and you have your graph.
Here's what it should look like on the graph:

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Solve for x:
Factor 2x^2
Apply the zero product principle.
and/or
If then,
If then,
The solutions are:
x = 0 (A double root)
x = 3

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Well, hang in there "old man"! (I'm 73!)
First, let's find the solutions or roots, as they are commonly called.
First subtract 4 from both sides of the equation.
Solve this quadratic equation by factoring.
Now apply the zero product principle.
and/or
If then, and
If then,
The roots are:


So their sum is:
= -3 1/3
Your daughter is correct!

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The principal idea here is to isolate the variable to one side of the equation.
This is done by "undoing" (doing the opposite operation on) whatever has been done to the variable.
1) 18 - 3y = 5 Isolate the y-term by subtracting 18 from both sides of the equation.
-3y = 5-18
-3y = -13 Now divide both sides by -3
y = 13/3
y = 4 1/3
2) -14+9a = 38 Add 14 to both sides to isolate the a-term.
9a = 38+14
9a = 52 Now divide both sides by 9.
a = 52/9
a = 5 7/9
3) 14r+8 = 32 Subtract 8 from both sides.
14r = 24 Now divide both sides by 14.
r = 24/14
r = 1 5/7
4) 37-58b = 204 Subtract 37 from both sides.
-58b = 167 Now divide by -58.
b = -(167/58)
b = -2 51/58

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If your line is (-7, 2) ; (-7, -2) then the line is a vertical line (straight up-and-down) rather than a horizontal line (flat, side-to-side).
The equation of this line would be: x = -7 and, you are right, there is no y-intercept, only an x-intercept (x = -7), so the slope-intercept form has no meaning for such a line. Since the y-coordinate of this line can take on any value you please, the coordinate of any point on this line can be written: (-7, a), where a is any real number.
A vertical line has an undefined slope (m) and no y-intercept (b) so it cannot be represented by the slope-intercept form of the equation.
Also, the equation: y = x represents a line that is at 45 degrees to the axes and passes through the origin.
Here's the graph of y=x:

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When you are not sure of whether or not you have to divide, do a little dimensional analysis on the problem.
Your answer will be in number of hours.
The distance is in miles.
The speed is in miles/hour.
So, if you try: miles divided by miles/hour and simplify this you'll get hours because the miles will cancel.
You need to divide the distance (miles) by the speed (miles/hour) to get the time of travel(hours).
hours.

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Solve for x:
Apply the Quotient rule for logarithms to the left side.
If log a = log b, then a = b
Multiply both sides by x.
Subtract x from both sides.
Divide both sides by 10.


Check: Use your calculator or a table of logarithms to find the values of the logs.

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Solve by factoring:
Factor out 3x^2
Apply the zero product principle.
and/or
If then, x = 0
If then, and x = +5 or x = -5
The roots are:
x = 0 A double root.
x = 5
x = -5
Here's what the graph looks like.

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Solve for x:
log(x)+log(x-4)+16 = 18 Subtract 16 from both sides.
log(x)+log(x-4) = 2 Apply the product rule for logarithms:LogM+logN = log(MN)
log(x)+log(x-4) = log(x^2-4x) = 2 Rewrite in exponential form:
logx = y means so:
log(x^2-4x) = 2 means Subtract 3^2 = 9 from both sides.
Solve using the quadratic formula:

=

The roots are:

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Simplify:

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Roots are written as the denominator of a fractional exponent.

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Perhaps I'm being a little picky buy you can't "evaluate" (calculate the numerical value of) this expression without knowing the value of x. You can, however, simplify the expression by performing the indicated multiplication.
Now we have the English out of the way, let's do the math.
Simplify:

Multiply the 1st term of the first term (3x^2) in the 1st set of parenthese by every term in the 2nd set of parentheses. Then, multiply the 2nd term (-2) of the 1st set of parentheses by every term in the 2nd set of parentheses. Finally, combine like-terms and simplify where possible.
= =

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Let the length of the table top be L and its width W.
L = 5W-8
The area of a rectangle is:
Substitute L = 5W-8

But A = 48 sq.ft.
Subtract 48 from both sides.
Solve by factoring.
Apply the zero product principle.
and/or
If and Discard this solution as the width can only be positive.
If then,
The width is 4 feet.
The length, L, is 5(4)-8 = 20 - 8 = 12 feet.
Check:
A = L*W
A = 12*4
A = 48 sq.ft.

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Solve:
Multiply both sides by 15 to clear the fractions.
Combine the x terms.
Subtract 10 from both sides.
Divide both sides by -12.

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Use Heron's formula to find the area of your triangular yard.
where: S = semi-perimeter of the triangle S=190 ft) and a, b, & c are the lengths of the sides of the triangle.



square feet. Divide this by 1200 sq.ft. per bag.

You will need 6 bags of fertilizer

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Solve for x:
Add logx to both sides.
Simplify the left side. (loga+logb = log(ab))
Substitute log10 = 1
If loga = logb then a = b.
Subtract 10 from both sides.
Solve by factoring.
Apply the zero product principle.
and/or
If then,
If then,
You can check the solutions by substitution.

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Solve for x:
Factor out a 2.
Factor the parentheses.
Factor the parentheses again.
Apply the zero product principle.
and/or and/or and/or
The roots are:
x = -2
x = 2
x = -3
x = 3