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30% reduce make 210
let original number is x
30 % reduce means 100-30 =70
70% of x= 210
70/100 of x= 210
x=210x100/70 = 300
new number 450 and original is 300
increased value =450-300=150
x/100 of 300 =150
x=50 %
answer 50%

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dollars

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Adam added 6 to a number and multiplied the results by NEGATIVE 3 and got 24. What is the number?
:
-3(n+6) = 24
-3n - 18 = 24
-3n = 24 + 18
-3n = 42
n has to be positive, mult both sides by -1
3n = -42
n = -42/3
n = -14
:
:
See if that works
-3(-14+6) =
-3(-8) = +24

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Use the quadratic formula to solve for 'a'









or

or

or

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find the first terms of:
......if



.....first term

......if





.....second term


......if



.....third term


......if





.....fourth term


......if





.....fifth term


{..,,,,..}

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A student must leave for campus in 10 minutes or he will be late for class.
Unfortunately, he is snowed in.
He can shovel the driveway in 16 minutes, and his brother claims to be able to do it in 14 minutes.
If they shovel together, how long will it take to clear the driveway?
Will this give enough time for the student to get to the campus?
:
Use a shared work equation, let t = time working together
Let the completed job = 1 (a cleared driveway)
:
+ = 1
multiply equation by the least common multiple of 16 and 14, that 112, results:
7t + 8t = 112
15t = 112
t = 112/15
t = 7.47 minutes, so you are right!

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2x^3-6x^2+8x/6x^2-12x
2x(x^2-3x+4)/6x(x-2)
x^2-3x+4/3(x-2)
restrictions: x≠0, x≠2 (these values would make denominator=0, so function would be undefined)

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what are the zeros of the quadratic equations
22=6x^2+13
6x^2=9
x^2=9/6=3/2
x=±√(3/2)
..
y=2x^2-11x
2x^2-11x=0
x(2x-11)=0
x=0
or
x=11/2
..
y=x^2+x-12
x^2+x-12=0
(x+4)(x-3)=0
x=-4
or
x=3

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Solved by pluggable solver: Find the equation of line going through points

hahaWe are trying to find equation of form y=ax+b, where a is slope, and b is intercept, which passes through points (x1, y1) = (0, -6) and (x2, y2) = (-2, -54). Slope a is . Intercept is found from equation , or . From that, intercept b is , or . y=(24)x + (-6) Your graph:

since you can't see second point on graph above, here is another graph:

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Completing the square x^2-2x-8=0
x^2-2x-8=0
(x^2-2x+1)-1-8=0
(x-1)^2=9
x-1=±√9
x=1±3

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....write as
....group

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x^2-2x-8=0
x^2-2x+1-1-8=0
x^2-2x+1=9
(x-1)^2=9
x-1 = -3 x-1 = 3
x=-2 x=4

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Three bells ring at the interval of 10,15 and 20 minutes respectively .
If they all ring at 11 a.m at once,what time they ring together again ?
:
Find the least common multiple of 10, 15, 20,
Prime factor
10: 2*5
15: 3*5
20: 2*2*5
then
2*2*3*5 = 60 is LCM
:
60 min from 11 is 12

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The LCM of 10, 15, and 20 is 60.
After 60 minutes, they will ring together again.
Answer: 12 noon

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We need the lowest common multiple of 10,15,and 20
10 = 2*5
15 = 3*5
20 = 2*2*5
These are the prime factorization for these numbers.
2*2*3*5 = 60 This is the lowest common multiple.
Noon is the answer.

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you have a parabola with a vertex at origin. From the graph I can see that if => and if => , then you have

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what is the answer of
(6^1/4)^2/3 = 6^(2/12) (multiply the exponents here
6^(1/6) (reduce the fraction)
:
(8/125)^-4/3,
inverting the fraction gets rid of the negative
(125/8)^(4/3)
find the cube root
(5/2)^4
Find the 4th power
625/16

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using base 2 logarithms solve the following equation
x-3
5 =32
(x-3)log2(5) = log2(32)
---------------------------
(x-3)log2(5) = 5
x-3 = 5/log2(5)
----
x = [5/log2(5)] + 3
----------------------
Cheers,
Stan H.

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A boat takes 8 hours to go 6 miles upstream and come back to the starting point. If the speed of the boat is 4 miles per hour in still water, what is the rate of the current?
-------
Upstream DATA:
time = x hrs ; distance = 6 miles ; rate = d/t = 6/x hrs
----
Downstream DATA:
time = 8-x hrs ; distance = 6 miles ; rate = d/t = 6/(8-x)
--------
Equation:
Upstream Rate Eq::: 4-c = 6/x
Downstream Rt Eq::: 4+c = 6/(8-x)
----------------
Add to solve for "x":
8 = (6/x)+(6/(8-x))
-----
8x(8-x) = 6(8-x) + 6x
-----
64x - 8x^2 = 48
---
x^2 - 8x + 48 = 0
-----
No Real Number solution.
================
Cheers,
Stan H.
================

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The monthly payment for the loan is equal to
= $

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9a squared-60ab+100bsquared
-----
9a^2 - 60ab + 100b^2
-----
= (3a-10b)^2
------------------
Cheers,
Stan H.

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In arithmetic sequence,
where = nth term, d = common difference
The first term of the sequence -15,-8,-1,6,13,... is -15 and the common difference is 7.
=
=
The 100th term is
=

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-15,-8,-1,6,13 tells us that d=7,








:)

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You can try possibilities:

The perimeter =
ft
-----------------------

ft
----------------------

ft
---------------------
It looks like 46 ft is the least she can buy

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The greatest area a fence can surround in a rectangle is in h shape of a square. Let me offer a reason why.
If one side is a tiny bit longer, the adjacent side is shorter by the same amount.
(X-Y)(X+Y)=X^2-Y^2 so the maximum area is when Y= 0.
In your case, we can't have sqr(102) as a side, so with two sides adding to 51, I'll say 25x26 are the dimensions.

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8s=16
s=16/8
s=2

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140 times (3.4 x 105)

Change 140 to scientific notation:
1.40×102

(1.40×102·(3.4×105)

Multiply the 1.40 by the 3.4, get 4.76.
Add the exponents of 10, get 2+5 or 7.

4.76×107 pounds

Edwin

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Factor show steps
75xysquare2-48x2xsquare
-----
75xy*sqrt(2) - 48x^2*sqrt(2)
-----
Common factor::::
3x*sqrt(2)
-----
Factored Form:
3x*sqrt(2)[25y - 16]
-----
Cheers,
Stan H.
========

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You can assume that this is a juice and water mixture.
Let = the cups of pure juice to be added
cups of pure juice in 5% mixture
----------------





2.222 cups of pure juice are needed
check:




OK

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Aya rode her bicycle from her house to a friend's house, averaging 16 kilometers per hour.
It turned dark before she ready to return home, so her friend drove her home at a rate of 80 kilometers per hour.
If Aya's total traveling time was 3 hours, how far away did her friend live?
:
let d = one way distance to friend's house
:
Write a time equation: time = dist/speed
:
bike time + ride time = 3 hrs
+ = 3
multiply by 80 to clear the denominators
5d + d = 80(3)
6d = 240
d = 240/6
d = 40 mi to fr house
:
:
Confirm this by finding the total of the time each way
40/16 = 2.5 hrs
40/80 = .5 hrs
----------------
total: 3 hrs

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12xy+8x-15y-10=
(12xy+8x)-(15y+10)=
4x(3y+2)-5(3y+2)=
(4x-5)(3y+2)


:)

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Identify the slope and the y-intercept of the equation:
y = - 5x + 4
----
slope = -5
y-int is 4
=================
Cheers,
Stan H.
=================

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Find x-intercept(s) by setting y=0:
y=0
-2x +(0)= 4
-2x=4
x=-2
x-intercept (-2, 0)
Find y-intercept by setting x=0:
x=0
-2(0)+y=4
y=4
y-intercept (0, 4)


:)

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The x-intercept ocurrs where
The y-intercept ocurrs where
So, you are looking for 2 points:
x-intercept: (x,0)
y-intercept: (0,y)
----------------
(x,0)




------------
(0,y)


----------
Here' the plot. It shows the intercepts at
(-2,0) and {0,4)

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Madeline bought 11 feet of ribbon for $1.32 per yard. How much did she pay for the ribbon?
-------
11 feet = 11/3 yards
----
Value = (11/3)(1.32) = $4.84
==============================
Cheers,
Stan H.
===========

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Solve for y:
6x + 3y = 24
----
Divide both sides by 3 to get:
2x + y = 8
----
Subtract 2x from both sides:
y = -2x+8
============
Cheers,
Stan H.
============

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A store buys jeans for $24 each and marks them up 30%. What os the selling price of a pair of jeans?
------
selling price = 24 + 0.3*24 = 1.30*24 = $31.20
=========================
Cheers,
Stan H.
================