The number 18 can be written as the sum of 9 consecutive integers.What's the product of these integers?

which when solved leads to x=-2
so our product is

Evaluate the expression sin 270 degrees

sin 270 degrees is the same as sin (-90)= -sin90 = -1

what part of .072 is .06

it is 
 
which is 60/72 which when reduced becomes 5/6

when making a phone call using a calling card a call lasting 6 minutes cost $1.60. a call lasting 13 minutes cost $3.00. Y=cost and X=minutes. Write a linear equation. predict how much a 25 minute call cost?

so using the first pair (6,1.6)

we'll write:

Y-1.6=0.2(X-6)

so a 25 minute call will cost...

$5.40

find the value of x log3 x = 4

Your Answer:

the inverse to

 is 

so we raise both sides of the equation to 3


 

what is the vertex: y = -x^2 - 4x - 3

Your Answer:

has a=-1, b=-4, c=-3
We can use the vertex formula:



and substitute to get y:




so our vertex is v(-2,1)

Use the Rational Zero Test to list all possible rational zeros of f. f(x)=x^3-4x^2-4x+16

since the leading coefficient is 1, we only look at the constant terms factors
16:
1, -1, 2, -2, 4, -4, 8, -8, 16, -16
in fact toe actual zeros are -2, 2, and 4

How can you graph in a simple way?

simple way...?
Simple is a subjective word, but the most basic way is to just choose some values of one of the variable and compute values of other variables. Then plot the resulting points. The art/skill of choosing good values can be developed with practice. As with any mathematics the key to success is practice.

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What is the equation of a line that has a slope of 7/9 and contains the point (0,6) ?

using point-slope equation:
y-6=7/9 (x-0)

Factorize m^4+m^2+1

Factoring isn't easy, until you get good at it. One useful technique is to introduce terms that add to 0 as follows:




now we can write...

rearranging and grouping leads to

there are 75 students there is 15 more girls than boys .How many girls and boys are there?

1) G+B=75
2) G-B=15
subtracting equations...
2G=90
G=45
so that B=30

How long will it take $2900 being invested at 7% compounded quarterly to double? Use A=P(1+r/n)^nt.

Doubling time does not depend upon amount invested because A=2P and so P divides out of the equation. There is a formula, but the computation is really not that bad:

simplify, take any log of both sides, and...
t=9.99 years (about 10 years)

Solve: |4x+7|+5>4

|4x+7|+5-5>4-5

|4x+7|>-1
which is true for all real numbers

Solve: -12<|-3x|+1

This is true for any real number because the right side of the inequality is always positive

find the exact value of tan75

which is...

3+|6x-1| < 14

|6x-1| < 11
-11 < 6x-1 < 11
-11+1 < 6x < 11+1
-10/6 < x < 2
-5/3 < x < 2

Write an absolute value equation or inequality representing all real numbers x at least 3 from 7

so we want:

x < 7-3 or x > 7+3
which means:
|x-7| > 3

What is 0.154545454545454(repeating decimal) as a fraction? And How do you rewrite repeating decimals as a fraction?

n=0.154545454545454...
10n=1.5454545454545...
1000n=154.545454545...
1000n-10n=153
990n=153
9*110n=9*17
n=17/110

Solve: |x+7|+15>12

|x+7|+15 > 12
|x+7|+15 > 12-15
|x+7| > -3
which is true for all real numbers because an absolute value expression is always greater than any negative number.

how do I write in inequality form : all real numbers at most 6 units from 0 ?

|x-6| < 0

Solve: 7-4|x+7|>-5

7-4|x+7|>-5
-4|x+7| > -5-7
|x+7| < -12/(-4)
-3 < x+7 < 3
-10 < x < -4

A number n is no more than 7 units way from 5. Write an absolute-value inequality to show the range of possible values for n.

so that

|2r - 1| = 1/4. The answer was 3/8 and 5/8. We could figure out the 5/8 but how do you get 3/8?

it means:
2r-1=1/4
or
2r-1=-1/4 which leads to
2r=-1/4+1
2r=3/4
r=3/8

Find an equation of the line through the given points. Write the equation in standard form. Through (-1,1) and (1, -13).

m=(-13-1)/(1-(-1))=-14/2=-7
y-1=-7(x-(-1))
y-1=-7x-7
7x+y=-6

Martha is 1 year older than twice his sisters age. The difference of their ages is 8. Find their present ages.

1) M=2S+1
2) M-S=8
setting the equations up to solve...
M-2S=1
-M+S=-8

-S=-7
S=7
M=2(7)+1=15 

Simplify (21x^5w^3)/(9x^2w^10)

Find the reciprocal of the rational expression. (y^2 - 3y + 2)/ (y^2 - 4)

The length of a rectangle is 5 inches more than the width. The perimeter is 38 inches. Find the length and width.

1) l=w+5
2) 2(l+w)=38
from 2)
l+w=19

so that
w+5+w=19
2w=14
w=7

l=7+5=12

Solve the inequality. Express the final answer in interval notation. -5(2x-3)≤-2(x+7)

we'll move the term with the greatest absolute value so that we can avoid dividing by a negative number:









rewriting so that the variable is on the left...

Solvbe: 1/5 + 1/x = 1/8

moving terms...



common denominator...






taking reciprocal...

What is the nearest number to 10000 which is divisible by 2,3,4,5,6,7,8,9,11?

Your Answer:

we'll get 2,3,4,6 from 8 and 9, so we'll need a 5, a 7, an8, a 9 and an 11:
11*9*8*7*5=27720

Find the value of x Right triangle with the sides x, 2x+4, 2x+6

sides: x, 2x+4=2(x+2), 2x+6=2(x+3) 
so we write: 

 
 
 

 
 
 
 
which gives us x=-2 or x=10 
but x>0 

so only x=10 works :) 

Fractions

If somebody could please help me on a college algebra problem. I need to simplify this problem : 5/6*(2/3-1/6)+7/18 I started out by reducting it to (4/6 - 1/6) 5/6*3/6+7/8 than somehow got 15/6+7/8 but than i got stuck. So could somebody please help me and show me how to do this? That'd be great. Thank you! :)

:)