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Expand: Use FOIL.
Combine like-terms.

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Profound!
Andromeda is light-years from earth.
The speed of light is: km/sec.
One light-year is (secs) X (km/sec) = km.
The distance to Andromeda is:
(ligh-years) X (km/light-year) = km or
km.

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You can use the formula: d = rt where d = distance, r = rate (speed), and t = time.
For the trip to the store , the rate (speed) is 4.5 mph so we can write:
1)
For the return trip at 3 mph, we can write:
2)
Now since the distance to the store is the same as the return distance, you can write:
and, since the total time for the trip was 1 hour, then:
Now we can rewrite this as: and substitute it for the in equation 2) after setting equation 1) equal to equation 2).
Substitute
Simplify and solve for
Add to both sides.
Divide both sides by 7.5
hours.
So it took Noel 0.4 hours or 24 minutes to walk to the store.
To find the distance to the store (), substitute into either equation 1) or equation 2) and solve for the distance.
Substitute

miles.
Noel walked 1.8 miles to the store.

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Let x = the high temperature, then:
Add 15 to both sides.

The high temperature was 9 degrees C.

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The area of the base of the box can be found by multiplying the sides of the base. The sides of the base are equal to the length of the sides of the original rectangular piece of tin less two times the length of the corner pieces (2x). So the area of the base of the box can be expressed as:
Performing the indicated multiplication, we get:
...and this, we are told = 315 sq.cm., so we set these two things equal to get:
Now you subtract 315 from both sides of this equation.
You can solve this quadratic equation using the quadratic formula:
where: a = 4, b = -84, and c = 117, so making the approriate substitutions, we get:



or
or
Now as you can see, if x = 19.5, this would not make any sense because that would mean the cut-out would be larger than the side of the original rectangle! So discard that solution and take the x = 1.5 cm.

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If (2a+b= 80) and (2b+a = 76) then a =?
2a+b = 80 Rewrite this as b = 80-2a and substitute into the 2nd equation.
2b+a = 76
2(80-2a)+a = 76 Simplify.
160-4a+a = 76
160-3a = 76 Subtract 160 from both sides.
-3a = -84 Divide both sides by -3.

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The probability of drawing a marble that is odd or green (an inclusive event)is expressed by:
P(odd or green) = P(odd) + P(green) - P(odd and green) and this can be written as:
P(odd or green) = P(odd) + P(green) - P(odd)*P(green)
P(odd or green) = 5/10 + 5/10 - (5/10)*(5/10) = 1-(25/100) = 1-(1/4) = 3/4
So the probability of drawing a marble that is odd or green is 3/4 or 75%

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You are correct on the excluded value of x = 3 because that's the value of x that would make the denominator zero and this, of course, is a no-no in math.
Now to simplify:
Factor from the numerator and factor from the denominator.
Cancel the indicated factors.
Reduce the fraction to...

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Factor by grouping:
Group as shown, and remember to change the sign (+ to -) in the last term:
Factor the m in the second group.
Now factor the (1-n)
...and you're done!

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You can't really "solve" an expression such as you have here but you certainly can "simplify" it, so we'll show how that's done.
3{[7(x-2)+4]-[2(2x-5)+6]} The different parentheses don't have any particular meaning and are used only as a grouping symbol. To simplify this expression, start on the inner parentheses (), then go on to the curly brackets {}, then to the square brackets [].
3{[7(x-2)+4]-[2(2x-5)+6]} Apply the "distributive property" on 7(x-2) = 7x-14 and 2(2x-5)=4x-10, to get:
3{[7x-14+4]-[4x-10+6]} Now simplify the quantities inside the square brackets []
3{[7x-10]-[4x-4]} Now you can combine the insides of the two square brackets and, of course, remember to change the sign of the second group.
3{7x-10-4x+4} Combine like-terms inside the curly brackets {}.
3{3x-6} Finally, apply the distributive property to get:
9x-18 as the answer.

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Let the height of the glass = h. Using the sine function: Sin(a) = h/c where a = 60 degrees and c is the hypotenuse.



cm
The glass is 17 cm. tall.

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Write the equation of variation:
where d = distance in feet and t = time in seconds. k = the constant of variation. To find the value of k, substiute d = 64 ft. and t = 2 secs.

Divide both sides by 4.

The equation is now:
Substitute t = 10 secs.


feet.

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a) Decreased...Increased.
b) Subtracted...Added.
c) Less than...More than.
d) Minus...Plus.
e) Added to...Subtracted from.
f) More than...Less than.

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Invert the second divisor and multiply:
Factor where possible:
Cancel as indicated:
Cancel an x:
=

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Yes it is!
To see this, put the equation into the "slope-intercept" form: y = mx+b where m = slope and b = y-intercept.
subtract 2x from both sides of the equation.
compare this with:

and
The slope is -2 and the y-intercept is 4.

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Solve the system of equations:
1)
2)
Substitute equation 1) for the 2y in equation 2).
2a) Simplify and solve for x by comining the x's.
2a) Subtract 6 from both sides of the equation.
2a) Divide both sides by -2.
2a) Now substitute this value of x into either one of the original equations to find y. Let's use equation 1).
Substitute x = 4.

Divide both sides by 2.

The solution is: (4, 5) which is the intersection point of the two lines represented by the two linear equation.

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You really should use parentheses to clearly describe the problem!
Is it: or or
Evaluate:
if and



or

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Solve for x:
First subtract from both sides.
Now add 10 to both sides.
Next, subtract x from both sides to leave the by itself.
Now square both sides.
Subtract 9x from both sides.
Factor the trinomial.
Apply the zero product rule.
or so...
or But notice that while x = 4 is a valid root, x = 25 is an "extraneous" root introduced during the process by squaring, so x=25 does not work.

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Let x = the smaller even integer and x+2 = the next consecutive even integer.
2(x+2)-x = 10 "...the smaller integer subtracted from twice the larger integer gives a difference of 10."
2x+4-x = 10
x+4 = 10
x = 6 and x+2 = 8
The two consecutive even integers are 6 and 8.

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Solve for f:
Multiply both sides by -2, and don't forget to reverse the inequality symbol.

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Let B = the number of boys and G = the number of girls.
B+G = 26 "The number of students is 26"
The girls drew triangles, each of which has three sides, so the total number of sides from the triangles is: 3*G
The boys drew rectangles each of which has four sides, so the total number of sides from the rectangles is: 4*B
Now you can write two equations as follows:
1) B+G = 26 Rewrite this as: B = 26-G and substitute for B in equation 2).
2) 4*B+3*G = 92 which is the total number of sides.
4(26-G)+3*G = 92 Simplify and solve for G.
104-4G+3G = 92 Subtract 104 from both sides.
-G = -12 Divide through by -1 to make positive.
G = 12
To find the number of boys (B):
B = 26-G
B = 26-12
B = 14
So the number of boys is 14 and the number of girls is 12
Check:
B+G = 26
14+12 = 26
26 = 26 OK!
4*B+3*G = 92
4*14+3*12 = 92
56+36 = 92
92 = 92 OK!

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You would use logarithms to solve this kind of problem.
Take the log of both sides.
Apply the power rule to the left side.
Now divide both sides by
Evaluate using your calculator.

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You can temporarily chang variables to facilitate solving problems like this:
You can rearrange this as:

Let's substitute to give us:
Factor this:
from which:
or Replacing the variable: we get:
or so...
If Raise each side to the third power.
but so...
Add 5 to both sides.
and...
Cube both sides.

Add 5 to both sides.

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Your problem statement seems to have some anomalies in it!
The standard formula for the height (as a function of time) of an object propelled upwards from an initial height of with an initial velocity of is given by:
where g (the constant of acceleration due to gravity) is 32 ft/sec^2, so your formula should look like:

Your formula also shows two different varaibles. t and x.
So, back to the problem but starting with the correct formul, (the d in your problem will work just as well as the h(t)) we have:
First, we'll find the time, t, at which the height, d, is at its maximum. The graph of the quadradtic equation that we have here is a parabola that opens downward (signified by the negative first term) so its maximum will occur at the vertex of the parabola, and this is given by:
where a = -16 and b = 64, so...
}

secs.
To find the maximum height, we substitute the time, t=2secs into the original equation and solve for d.



feet.
The rock will reach a maximum height of 192 feet.

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Factor:
Factor the trinomial on the right side.

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It would help you if you were to draw a diagram of the situation in which the right triangle's height represents the height of the roller coaster (105 ft.) and the triangle's base represents the roller coaster's distance from the start of the hill to the top of the hill (200ft.).
To answer the question "How far do you actually travel on the roller coaster's track?", you need to find the length of the hypotenuse of the right triangle. This can be done using the Pythagorean theorem: where c is the hypotenuse and a and b are the lengths of the other two legs. So...
Substitute a = 200ft. and b = 105ft.


Take the square root of both sides of the equation.
Using your calculator, you get...
Rounding to the nearest foot, you get...
c = 226 feet as the distance actually traveled on the roller coaster's track.

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Let x = the amount Walt invested at 7%, so the remainder ($12000-x) was invested at 9%.
The interest earned on these two amounts can be expressed as:
(7%)(x) + (9%)($12000-x) and the sum of these two amounts is given as $970.00
Now you can write the equation that will allow you to so;ve for x, the amount invested at 7%.
First, change the percentages to their decimal equivalents:
(7% = 0.07) and (9% = 0.09)
Simplifying this, you'll get:
Combine the x-terms.
Subtract 1080 from both sides of the equation.
Finally, divide both sides by -0.02

$5,500.00 was invested at 7% while $12000-$5500 = $6,500.00 was invested at 9%

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Solve for x:
Square both sides of the equation.
Subtract 3 from both sides.
Finally, divide both sides by 2.

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Convert the improper fractions to mixed numbers:
1) Perform the indicated division (The numerator (28) divided by the denominator (4)).

2) Perform the indicated division.
+ or 3 1/3
3) Perform the indicated division.

4) Perform the indicated division.
+ or 3 11/13

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Convert to equivalent fractions:
1) Multiply both sides by 16.
Simplify the left side.
Cancel as indicated.
, so...

2) Multiply both sides by 48.
Simplify the left side.
Cancel as indicated.
so...

3) Multiply both sides by 30.
Simplify the left side.
Cancel as indicated.
so...

4) Multiply both sides by 64.
Simplify the left side.
Cancel as indicated.
so...

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Verify that and for:
for
First, you'll need to find
Start with the given function:
Substitute for
Now exchange x and y.
Next, solve this for y. Multiply both sides by
Expand the left side.
Subtract xy from both sides.
Factor the y from the right side.
Divide both sides by
Now replace the with

Now you are in a position to find:
Substitute recalling that
Notice that where there is an x on the left side, it's replaced with on the right side. Now we'll simplify the right side.
Invert and multiply.


Do you think you can manage to show that ?