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Again, let n be the number.
You can write, from the description:
Add 2n to both sides.
Divide both sides by 5.

The number is: 7.
Check:
= 21 And this is 3(7)

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Let n be the number you are looking for.
From the description, you can write:
Let's clear the fractions by multiplying through by the common denominator of 40.

Add 30 to both sides.
Divide both sides by 16.
= 4 1/16
The number is: 4 1/16 That's 4 and 1/16
Check:
= 7/8

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We'll let S be Ms. Santos' present age and V be Ms. Valdez's present age.
At present:
1) S + V = 50 The sum of their ages is 50.
19 years from now:
2) S + 19 = 2V In 19 years, Ms. Santos will be twice Ms. Valdez present age.
Rewrite equation 1) as:
V = 50 - S Multiply both sides by 2 because you want to get 2V.
2V = 2(50 - S) = 100 - 2S Now substitute this for the 2V in equation 2).
2) S + 19 = 100 - 2S Solve this for S. Add 2S to both sides.
3S + 19 = 100 Subtract 19 from both sides.
3S = 81 Finally, divide both sides by 3.
S = 27
Ms. Santos' present age is 27 years
V = 50 - S
V = 50 - 27
v = 23
Ms. Valdez's present age is 23 years.

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Remember! Kilo = 1,000
So, 1 kilogram = 1,000 grams or 1 gm = 1/1,000 Kg
(7,800g )/(1,000g/Kg) = 7.8 Kg
Similarly for liters.
1 Kiloliter = 1,000 liters or 1 liter = 1/1,000 Kl.
240 Kl = 240 Kl (1,000 l/Kl) = 240,000 liters

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I'm presuming that you have to "simplify" the given expressions.
Simplify:
Apply the "distibutive property" (Check your math book if you are not familiar with this.)
First do:
Multiply the 7 and (-3) to get -21, then m times n = mn, finally, -21 times mn = -21mn
Repeat this for the second term:
Multiply 3 times (-4) to get -12, then m times n = mn, finally, -12 timed mn = -12mn. You will now have and when you add these two negative quantities you will get -33mn.

Second problem is handled in exactly the same way.
Multiply 10 by 12 to get 120, then m times n = mn, finally, 120 times mn = 120mn

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There is really nothing to solve here!
You have an algebraic expression and, unless you are given the values for x and y, you cannot evaluate it.
To "solve" this, it would have to be an "equation" in which the "expression" you have is equal (=) to something. But, no equals, no equation.
The only thing that you can do is to "simplify" this expression by applying the "distributive property".
Is this what you wanted?
Simplify:
Apply the distributive property.

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While a diagram is useful for many siuations, in this case, all you really needed to say was...Find the circumference of a circle with a diameter of 4 inches.
By the way, all circles are round!
The circumference of a circle is given by the formula: where D is the length of the diameter (4 inches) (the straight line through the center and terminting on the edges of the circle) and approximately.



The circumference of the circle is 12.56 inches.

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The simple way to graph y = x-1 is to generate at least two points, put those on your graph paper and draw a straight line through them.
Here's how you geneate the required points:
Use your equation, y = x-1 and choose an integer for x, say x=2, and substitute this into your equation to find the corresponding value of y.
y = 2 - 1
y = 1
So your first point has coordinates of (2, 1) Now repeat this operation with a different value of x, say x = 5.
y = 5 - 1
y = 4
Your second point has coordinates (5, 4)
Now mark these two locations on your graph paper. Starting at the origin of your graph (where the x-axis crosses the y-axis), go to the right 2 squares (x=2) then up 1 square (y=1) and mark your first point.
For the second point, again, start at the origin and go right 5 squares (x=5) and then up 4 squares (y=4) and mark your second point.
Using a straight-edge, draw a line joining these two points.
You have now graphed the equation: y = x - 1.
Compare your graph with the graph of y = x - 1 shown below.

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After changing the percentages to decimals, you can set up your equation as follows: x = number of grams of the 35% Ni alloy. (35% = 0.35, 65% = 0.65, 41% = 0.41)
Simplify and solve for x.

Subtract 13 from both sides.
Divide both sides by -0.3

16 grams of 35% Ni alloy are required.

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Try this!
720 = 2 * 360
360 = 2 * 180
180 = 2 * 90
90 = 2 * 45
45 = 3 * 15
15 = 3 * 5
5 = 5 * 1
So 720 = 2*2*2*2*3*3*5 Notice that all the factors are prime numbers.
You can also write this as:

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You can do this! Translate right from the description.
The sum of a number (add to n) and 8. That's n + 8

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Here's the rule:
In , x is the base and n is the exponent.
In your problem:
, (-2) is the base and 5 is the exponent.

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Ok, since you have been asked for an "expression", there wouldn'tbe any = signs any because "expressions" don't have = signs.
Let's write an expression for the area of a circle:
But you need it in terms of c, the circumference.
Let's write an equation for c:
Now, solve this for :
and, after squaring, substitute this into the expression for the area:
Now simplify:
This is an expression for the area of a circle in terms of the circumference, c.

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You can do this problem with algebra. The key is remembering that parallel lines have identical slopes and perpendicular lines have slopes that are the negative reciprocal of each other.
First, find the slope of the line passing through the given points (-1, -1) and (3, 2). You know the formula.



The slope of the line passing through the given points is m = 3/4
The slope of a parallel line is also m = 3/4
The slope of a perpendicular line is -4/3

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Well, you got a good start on this. Let's take it step-by-step.

At this point I would change completely to scientific notation.
Now, I would make the exponents positive by moving them up (or down, as the case may be).
Simplify.



m/sec.

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Ok, here we go!
First change percentages to decimals:
30% = 0.3
80% = 0.8
50% = 0.5
Now you can set up the equation in which x is the number of Kg. of 80% Cu alloy needed.
Simplify and solve for x.
Subtract 0.5x from both sides.
Subtract 6 from both sides.
Now divide both sides by 0.3

13.33... Kg of 80% copper alloy are needed.

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You can start with the equation:
Add (k + m) to both sides.
Now subtract 25 from both sides.

What are the possiblities for k and m?
k = 0 & m = 5 or
k = 1 & m = 4 or
k = 2 & m = 3 or
k = 3 & m = 2 or
k = 4 & m = 1 or
k = 5 & m = 0

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Well, you had the right idea.
Add 35n (not just 35 as have shown) to both sides.
Now divide both sides by 42.
Not -7 as you have shown.

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Let P be the price the good truck.
The low end of the range would be:
($12,000 + (0.08)($12,000) + $84.00)
($12,000)(1.08) + $84.00 = $12,960 + $84.00 = $13,044.00
The high end of the range would be:
($15,000)(1.08) + $84.00 = $16,200 + $84.00 = $16,284.00
This can be writen:
$13,044.00 <= P <= $16,284.000 Including tax & license. (<= means less than or equal to)

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Try this:

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You started out ok by finding the distance of the two riders from the starting point after two hours of travel. But, since these two are not traveling in a straight line, you cannot simply subtract their distances.
What you need to do is to draw a diagram showing one rider going north for 24 miles and the second rider going west for 10 miles. This forms the two legs of a right triangle. Their distance apart at this time is represented by the length of the hypotenuse of this right triangle, so you can use the Pythagorean theorem to calculate this length because you already know the lengths of the two legs.
c is the length of the hypotenuse or their distance apart after two hours of riding.


Take the square root of both sides.


They are 26 miles apart after two hours of riding.

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First, I don't see any need to convert Km to feet. Ok to convert 2 minutes to 120 seconds.
For the primary wave:


For the secondary wave:


But, d1 = d2, so:
Simplify and solve for t1.
Subtract 5t1 from both sides.
Divide both sides by 75.
seconds. Substitute this into and solve for d1.

Km.
Check:



Km.

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Let x = the original number of jelly beans in the jar before the pilfering began.
After Michael has pinched his third, the number left is:

After Tanya's sampling, the number left is:
=
Finally, after Brian has helped himself to one third, there are 40 jelly beans remaining:

Multiply both sides by 27.
Divide both sides by 8.
There were 135 jelly beans in the jar before the crime.
Check:
= 90
= 60
= 40

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Rearrange the equation as follows:

Add 10 to both sides.

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I can why you are having so much trouble finding x, I can't see it anywhere either.
But the good news is, you got the right answer for m, congratulations, you did everything right and m = 1/2
Here's the check:
Substitute m = 1/2
Simplify.

OK.

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This is another version of the legend of King Shiram of India who wanted to reward his grand vizier Sissa Ben Dahir for inventing and presenting to him the game of chess. The clever vizier wanted a grain of wheat on the first square of the chessboard, two grains on the second square, four on the next, and so, doubling the number on each successive square until all of the 64 squares of the chessboard were covered.
Well, this works out to be: grains of wheat (or rice, in your problem).
= 18,446,744,073,709,551,615 grains of rice.
The volume of rice? How do you tell? 5,000,000 grains of rice in a bushel?
Around 400 billion bushels of rice!

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Add the fractions on the right. Common denominator is xy.
Invert both sides.

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Multiply the numbers:(-12)(-1/2)(-2) = -12
Now, add the exponents since the base (c) is the same in all of the factors.
=
Finally you get:

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Simplify: 2 1/3(4/3 - 2/5(3/4 + 3/7)) Start at the innermost parentheses. The common denominator is 28.
2 1/3(4/3 - 2/5(21/28 + 12/28))
2 1/3(4/3 - 2/5(33/28)) Now do the distributive property on the inside parentheses.
2 1/3(4/3 - 66/140) Now subtract the fractions inside the parentheses. The common denominator is 420.
2 1/3(560/420 - 198/420)
2 /13(362/420) Change 2 1/3 to 7/3 and multiply.
7/3(362/420}
2534/1260 Simplify.
1277/630

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Using the distance formuls:
where: d = distance (10 miles), r = speed (rate) and t = time.
Downstream trip:

mph
Upstream trip:

mph
Let x = speed of canoe and y = rate of the current.
Downstream:

Upstream:
Rewrite as: and substitute into the above.
Simplify and solve for y.
Subtract 2.5 from both sides.
Divide both sides by 2.
mph is the rate of the current.

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The volume of a regular pyramid is found by multiplying the area of the base by the height of the pyramid and dividing by 3. B = area of base.
You are given the height (31') but I'm having trouble figuring out what you mean by..."the sides are 21' apart"
If you know the length of each side of the hexagonal base, you can find its area. Also, if you know the length of the apothem of the hexagonal base, you can find the area.
Let's assume that the length of each side of the hexagonal base is 21'.
The area of a regular polygon, in terms of the length of the sides, is given by:
Where: n = number of sides (6) and s = length of side (21')



Now multiply this by the height and divide by 3 to find the volume

Cubic feet.