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let x = positive odd integer and x + 2 be the next positive odd integer.
we get
x^2 + (x+2)^2 = 202
foiling the left and combining like terms, we get
2x^2 + 4x + 4 = 202
and then
2x^2 + 4x - 198 = 0
divide by 2 to get
x^2 + 2x - 99 = 0
factor to get
(x+11)(x-9) = 0
solving for x, we get
x = -11 and x = 9
we get (-11,-9) OR (9,11)

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P(speak foreign language) = .20
P(NOT speak foreign language) = .80
(a) What is the probability that none can transact business in a foreign language?
answer: we want zero "YES" and 10 "NO" so,
nCr*(no)^10*(yes)^0
or
10c0*.8^10*.2^0 ~ .1074
--
(b) That at least two can?
answer: This means that 0 or 1 cannot. It is easier to do this in negation.
1 - p(0 not) + p(1 not) = 1 - 10c0(.8)^0*(.2)^10 + 10c1*(.8)^1*(.2)^9 ~ .99999
--
(c) That all 10 can?
answer; we want all 10 yes, so,
10c10*(.2)^10 ~ 1.02 x 10^-7
(d) Sketch the probability distribution and discuss its appearance.
The sketch should be a normal curve with cum sum = 1.

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If a line has no slope then it can be expressed as 1/0 or in general as a/0, where a not = 0.
A perpendicular slope is the negative reciprocal.
So, 1/0 turns into -0/1 = 0,
or in general a/0 turns into -0/a = 0.

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For every 1 increase in y, we increase x by 4.
unit rate of change of y with respect to x = rise information over run information.

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Your original equation was:

suppose * = 2. then we have a quadratic of the form

which can easily be solved using the quadratic formula as

which is simplified as

From here you have one of two ways to go.
(1) if you have never been shown imaginary numbers, then say no solution.
(2) If you have been shown imaginary numbers, then say
,

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If you mean
, then
simplify as
.
multiplying both sides by 8^x, we get

in this case, there is no x value which is true.
--
If you mean

simplifies as
.
Multiply both sides by 8 to get

In this case, there is no x value which is true.
--
If you mean

then rewrite the right side as

the 4 can be expressed as 2^2, so we get

cancel the base 2's to get

solve for x to get

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Let x be an angle.
180-x is the supplement.
90 - x is the compliment.
So, we get

By distributive prperty, we get

combining like terms on the right we get

and simplifying we get


The supplement of 66 is 114. Half of 114 is 57.
So answer is 57.

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step 1 - solve the equation for y. That is already done and given as
(i)
step 2 - find the slope of (i) and we get m = 3.
step 3 find perpendicular slope. m = 3, so perpendicular means flip and change sign. Perp m = -1/3.
step 4 - using new slope and (6,-2) we put that information into
to get



step 5 - write the answer as

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step 1 - divide 4.2 by .2 to get

step 2 - subtract 21y from both sides to get

step 3 - divide by -20 to get

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step 1 - distribute the negative through to get

step 2 - combine like terms on the left to get

step 3 - subtract 40n from both sides to get

step 4 - divide to get

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This is a RTD problem. Here is the table based on given information:
airplane . . . . . . . . .rate . . . . . . . . .time . . . . . . . . .distance
A . . . . . . . . . . .. . . .360 . . . . . . . . .3 . . . . .. . . . . .. . 1080
B . . . . . . . . . . . . . . .R . . . . . . . . . . .3 . . . . . . .. . . . .. . 3R
totals . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 1950
The distance of A + distance of B = total distance. So,
1080 + 3R = 1950
3R = 870
R = 290 km/h

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Lets start with slope intercept form as

we know m = 5 and b = -5, so we get
(i)
standard form requires 2 things
(1) no decimals
(2) X and Y stuff on the same side and the # by itself.
From (i) subtract 5x to get
(ii)
This is standard form.

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This is a trick question. If one cannot be a quarter, the other one CAN be a quarter. So, we have dime and then quarter.

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Notice there is no decimal. IF you don't see one, it is all the way to the right. We want a number expressed in the following form:

where 0 < a < 10 and b is an integer.
step 1 - move the decimal left 3 jumps to get
5.580
step 2 - ask yourself how many jumps and in which direction?
# jumps = 3
direction = left
OUr answer is:
5.580 x 10^3

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x^4 - 5x^3 - 54x^2 - 80x - 32 = 0
step 1 - set up P, N, i
P are the number of sign changes you see when (x) is placed into the equation. We get P = 1.
N are the number of sign changes you see when (-x) is placed into the equation. We get N = 3.
Now 1 + 3 = 4.
P . . . 1 . . . . 1
N . . . 3 . . . . 1
i . . . .0 . . . . .2
Notice that i = 0 or 2. Imaginary numbers always travel in conjugate pairs.
Now on to rational zeros. or P/Q
P = +-(1, 2, 4, 8, 16, 32)
Q = +-(1)
We can find that x = -4 and x = -1 give us 2 zeros.
By synthetic division, using x = -4, we get
(x^3-9x^2-18x-8)
and this divided by x = -1 gets us
(x^2-10x-8)
setting this = 0 and solving gets us

or

or simplified as

SO our four answers are:
x = -4, x = -1, x = 5 +-sqrt(33)

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This is an rtd problem with currents. Here is a table based on the given information:
plane . . . . . .rate . . . . . . . . . . . time . . . . .distance
against . . . .r-c=1050 . . . . . . . .3.5 . . . . . . 3675
with . . . . . .r+c . . . . . . . . .. . . .. 3 . . .. . . . .3675
we know
(i) r-c = 1050.
solve with for r+c, we get
(ii) r+c = 1225
adding (i) and (ii) together, we get
(iii) 2r = 2275
r = 1137.5
c then is 87.5 Kph

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OUr expression is:

step 1 - factor each part separately:
x^2-x = x(x-1)
x^2 + 3x + 2 = (x+2)(x+1)
x^2+ 2x = x(x+2)
x^2-1 = (x+1)(x-1)
we get
/
step 2-Multiply the top fraction by the reciprocal of the bottom fraction to get
*
step 3 - cancel where possible to get

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Suppose you are given 2 coordinates: A (x1,y1) and B (x2,y2). We can find the slope with the dollowing equation:

--
EX: A(1,4) B (-3,9)
using the slope formula we get
= 5/-4
so
m = -5/4

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step 1 - find the common denominator. It is 28.
step 2 - multiply every number by 28 to get

and then

step 3 - combine like terms on the left to get

add 190 to both sides to get


c= 18.1818....
--
checking, we get


3.3116 - 2.9545 ~ .357054 ; 5/14 = .3571428

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(a) the values of n are: -1, 0, 1, 2, and 3. We can't use -2 because it is not =.
(b) 3x + 2 ≤ 4
step 1 - subtract 2 to get
3x <=2
step 2 - divide by 3 to get
x<= 2/3
If you want the set of integers then
(- 00, 0]

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we have
1,1,1,1,1
1,1,1,2
1,1,2,1
1,2,1,1
2,1,1,1
1,2,2
2,1,2
2,2,1
so, it appears we have 8 ways

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this is the same as

now (x+2)(x-2) = x^2-4, so we get

squaring this gets us

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Part of 26! are the numbers: 5, 10, 15, 20, and 25.
5*1 = 5
5*2 = 10
5*3 = 15
5*4 = 20
5*5 = 25
factor out the 5's from the left and we have
5(1*2*3*4*5)
or 5*120.
So, k = 120

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Let's call the bulls eye - circle 1 including circle #1, there are 10 concentric circles.
radius of circle 1 = 6.1
radius of circle 2 = 12.2 or 6.1 * 2.
and so on.
A) hit the bulls eye
P(bulls eye) = pi*6.1^2 = 37.21pi cm^2
B) Land somewhere in the outmost four circles.
P(outer 4 circles) = p(whole target - inner 6 circles) = pi*R^2 - pi*r^2 = pi*61^2 -pi*36.6^2.
The 36.6 is the radius of the first 6 circles or 6.1 * 6.
This gives us 2381.44pi cm^2
C) Land within the fifth ring in from the outer edge.
P(5th ring) = p(5th ring - p(4th ring). We want only the fifth ring so all other inner rings must be subtracted out. We get pi*R^2 - pi*r^2 = pi*30.5^2 -pi*24.4^2 = 334.89pi cm^2

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The length of a rectangle is x + 4
The width of a rectangle is x - 1
The perimeter is 46 cm
--
We can use th perimter formula as:
(i)
replacing x + 4 for L, x - 1 for W, and 46 for P, we get
(ii)
we solve for x as
(iii)
(iv)
(v)
(vi)
Now, the length = 14, and the width is 9.
--
Using the Pythagorean theorem:

we get



the diagonal, c, ~ 16.64

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Simplify
(i)
turn everything into sin and cos as
(ii)
simplify the denominator to get
(iii)
Notice cos^2x + sin^2 x = 1. Multiply by the reciprocal to get
(iv)
and simply
(v)

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We have 1 formula:
(i) A = L x W
step 1 - replace A = 5 and W = 10 to get
(ii) 5 = 10L
step 2 - divide by 10 to get
(iii) 1/2 = L
Length = 1/2 in.

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I assume it is isosceles. We can use Pythagorean theorem
a^2 + b^2 = c^2
and then
3^3 + 4^2 = c^2
9 + 16 = c^2
25 = c^2
5 = c.
The perimeter is 3 + 4 + 5 + 5 = 17 m.

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Yes, since PI is irrational, a rational / irrational is irrational.

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A= 1/2h (a+b) for b.
step 1 - multiply both sides by 2 to get

step 2 - divide by h to get

subtract a to get

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To solve this via algebraic means may get messy, but the answer is rather simple:
n = 4sqrt(5)