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Let x and Y be the numbers. From the given information, we get
(i)
(ii)
step 1 - solve for X in (i) to get
(iii)
step 2 - substitute (iii) into (ii) to get
(iv)
expand (iv) to get
(v)
set = 0 to get
(vi)
divide by -1 and factor to get
(vii)
solve to get
Y = 2, Y = -8. We have two answers in x,y form as
(-8,2) and (2,-8)

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We have a combination problem. We want 3 face up , but also we want the rest, 49, face down, so we can say
52c3 = 22100

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We are given
(i)
standard form requires two things
(1) no fractions
(2) x and y on the same side
--
step 1 - multiply (i) by 3 to get
(ii)
step 2 - subtract 2x to get

at this point some teacher require positive x's, sop we could write

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We start with
(i)
This is similar to
(ii)
matching up the 2 we get
slope = m = 5.
--
If we were to graph this, it would be a line.
vertical intercept = do you mean x-intercept?
horizontal intercept = do you mean y-intercept?
--
X-intercept is when y = 0. If y = 0, then



--
Y-intercept is when x = 0. If x = 0, then

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This question is modeled after the I = prt question. IN this case however, we have two investments. So we can write
I = prt + prt
based on the given information, we get
(i)
simplifying (i) , we get
(ii)
and then
(iii)
subtracting, we get
(iv)
and dividing, we get
x = $11,777.78 @ 15%
and
27000 - x = $15,222.22 @ 9%.

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here is the question:

step 1 - start from inner most ( )
5-4 = 1, so we get

step 2 - multiply 2x1 to get

step 3 - subtract to get

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Notice there is no decimal - it is invisible all the way to the right of the number.
We want a number of the form a*10^b, where 0 So,
step 1 - from the given number move the decimal 7 jumps left.
step 2 - since we started with a number bigger than 10, the exponent must be positive.
step 3 - the answer is then
1.799 x 10^7

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The original problem is given as:

step 1 - multiply by the reciprocal gets us

step 2 - factor to get

step 3 - cancel to get

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Let length = L and width = W.
from the given information, we get
L = 4W + 2
P = 2L + 2W
34 > 2(4W+2) + 2W
34 > 10W + 4
30 > 10W
3 > W
The maximum width is 2.
If W = 2
L = 10
P = 24 < 34
--
If W = 3
L = 14
P = 34 this is NOT LESS than 34.

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I would suggest turning all fractions into improper then multiply.
76 and 2/3 = 230/3
44 and 1/4 = 177/4
1 and 3/8 = 11/8
--

reduced becomes

which is
4664 + 11/16 cubic inches

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Here is the original question
(i)
I notice you have two variables here. ALso M is next to the n on the keyboard, so it could be one variable. We have four options. Hopefully one of these will answer your question.
--
option 1 - solve (i) for m

subtract 4 from both sides to get

divide by 3 to get

--
option 2 - solve (i) for n

subtract 19 from both sides to get

divide by -2 to get

--
option 3 - m=n solve (i) for m

subtract 4 from both sides to get

add 2m to both sides to get

divide by 5 to get

--
option 4 - m=n solve (i) for n

subtract 4 from both sides to get

add 2n to both sides to get

divide by 5 to get

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This is a mixture problem. Be careful here, as pure acid = 100% acid and water = 0% acid. As a matter of fact any time they give you water it is automatically 0 in the % column. WE have the following table based on given information:
liquid . . . . . . . . . .% . . . . . . . . . . .L . . . . . . . . .%xL
acid . . . . . .. . . . . 100 . . . . . . . . . x . . . . . . . . .100x
water . . . . .. . . . . 0 . . . . . . . . . .. 40-x . . . .. . . . 0
mix . . . . .. . . . . . 35 . . . . . . . . . .40 . . . . . .. .. . 1400
From the third column, we get
100x = 1400
x = 14.
So we have
14 Liters of pure acid
26 liters of pure water

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Here is the original problem:
(i)
look carefully, we really have this
(ii) -
which is the difference of two squares.
Factoring (ii), we get
-
factoring as a difference of two squares, we get

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We are given the following:
x - y + 2z = -2
5x + z = 0
x + 2y+z = 4
--
in row echelon form, we have:
1 . . . . . (-1) . . . . . . .2 . . . . . . .(-2)
5 . . . . . .0 . . . . . . . .1 . . . . . . .0
1 . . . . . . 2 . . . . . . . 1 . . . . . .. 4
We need to get a diagonal matrix so take row 2 - 5 row 1 -> row 2; row 3 - row 1 -> row 3
--
1 . . . . . (-1) . . . . . . .2 . . . . . . .(-2)
0 . . . .. . 5 . . . . . . . .(-9) . . .. . . 10
0 . . . .. . 3 . . . . . .. . . -1 . . . . . . . 6
(1/5) row 2 -> row 2
--
1 . . . . . (-1) . . . . . . .2 . . . . . . .(-2)
0 . . . . . . 1 . . . . . . . .(-9/5) . . 2
0 . . . . . . 1 . . . . . . . .3 . . . . . . . 6
row 1 + row 2 -> row 1; row 3 - row 2 -> row 3
--
1 . . . . . . 0. . . . . . . .(1/5) . . . . 0
0 . . . . . . 1 . . . . . . . .(-9/5) . . . 2
0 . . . . . . 0 . . . . . . . .(22/5) . . . .0
(5/24) row 3 -> row 3
--
1 . . . . . . 0. . . . . . . .(1/5) . . . . 0
0 . . . . . . 1 . . . . . . . .(-9/5) . . . 2
0 . . . . . . 0 . . . . . . . .1 . . . . . . . 0
So,
z = 0
y = 2
x = 0
{0, 2, 0}

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This is: rate x time = distance. The rate = 500 and the distance = 10,500. we can use this formula to find the time as:

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If you graph these out, you may notice that there are no right angles. This means we can use one of three formulas:
(1) Hero's formula - approximate
To use this we need the 3 distances. They are: sqrt(255), sqrt(61), sqrt(261)
The semi perimeter, s, is about 12.79
A = sqrt(s*(s-a)(s-b)(s-c))
A = 50.5
(2) matrices
Lets use matricies. If we apply matrices, we get 50.5
--
(3) 1/2absinC
This requires trig calculations, which I don't know you have seen.
--
So the area is 50.5.

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We stat with

step 1 - reverse the x and y to get

step 2 - solve for the new y to get


separating our common denominator, we get

So, the answer is y= 1/4x-1/2

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Solving for y, we can get the slope

subtract x to get

divide by 2 to get

The slope intercept form is

matching these two equations, we see that
slope = m = (-1/2)

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Here we have a 3x3 system.
Let the cables be A, B, and C.
(i) 3A + 1B + 2C = 95
(ii) 3A + 2B + 1C = 100
(iii) 2A + 1B + 2C = 80
--
Lets eliminate the B's. Take (ii) - 2*(i) to get
(iv) -3A -3C = -90
lets eliminate the B's. take (ii) - 2*(iii) to get
(v) -1A -3C = -60
--
To eliminate C's, take (v) - (iv) to get
(vi) 2A = 30 so
A = 15 cables
C = 15 cables
B = 20 cables

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The x-intercept is when we let y = 0, and solve for x. We get
(i)
x = -3
The y-intercept is when we let x = 0, and solve for y. We get:
(ii)
y = 3
Now, we can graph these and create a line.

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We need the formula:
(i)
from the given information, we have
(ii)
so,
(iii)
dividing, we get
(iv)

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Let x be an angle.
Complementary angles add to 90. So,
x = 5(90-x)
x = 450 - 5x
6x = 450
x = 75

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Let x be an angle.
Complimentary angles add to 90 degrees, so
x = 3(90-x)+10
x = 270 - 3x + 10
4x = 280
x = 70.

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The formula for slope is

we are given

matching the equations up, we get
slope = m = -10.

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step 1 - distributive property on the left to get
(i)
step 2 - simplify to get
(ii)
step 3 - solve for x to get
(iii)
checking, we get
2(2*2-1) = 2*2^2+5*2-12
2(3) = 16+10-12
6 = 6

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step 1 - distributive property on the left and foil on the right to get
(i)
(ii)
simplifies to
(iii)
This is no solution

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This you really can't solve. You can simplify or graph.
(i)
--
Now 4x = 2x + 2x, so we get
(ii)
we have an identity:
sin(A+B) = sinA cosB + sinB cosA
or in our case
(iii)
But these are the same, so we can write
(Iv)
--
Now 2x = x + x, so we get
(v)
we have an identity:
sin(A+B) = sinA cosB + sinB cosA
or in our case
(vi)
But these are the same, so we can write
(vii)
From (iv) and (vii), we get

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Here is the original question:

step 1 - factor the second polynomial to get

step 2 - set each pat = 0 and solve:
x-1 = 0
x = 1
x + 4 = 0
x = -4
x + 6 = 0
x = -6
we have three answers
{-6, -4, 1}

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The answer is [C]. We owe 100 and eventually pay the loan down to zero.

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Step 1 write y = kx and find k using known x and y information.
y = kx
20 = 3k
k = 20/3
step 2 - rewrite the equation with your new K value as
y = (20/3)x
step 3 find x when y = 8
8 = (20/3)x
24/20 = x
x = 6/5

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There appear to be 13 ways. Here they are in {p,n,d,q} form:
{p,n,d,q}
{0,0,0,1}
(0,1,2,0}
{5,0,2,0}
{0,3,1,0}
{5,2,1,0}
{10,1,1,0}
{15,0,1,0}
{0,5,0,0}
{5,4,0,0}
{10,3,0,0}
{15,2,0,0}
{20,1,0,0}
{25,0,0,0}