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Question 752354: What two numbers multiplied together equal -75 and added equal -10
Answer by josgarithmetic(1538)

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Assign some variables and formulate your equations.

x and y are the numbers.
xy=-75

and

.
Solve either equation for one variable and substitute the expression into the other equation. Solve this resulting equation. Now, solve for the other still unknown variable.

Question 752217: Find m: 2x/m + 3a/x = 5/c
Answer by stanbon(57387)

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Find m: 2x/m + 3a/x = 5/c
-----
2x/m = (5/c)-(3a/x)
---
2x/m = (5x-3ac)/(xc)
---
m/(2x) = (xc)/(5x-3ac)
---
m = (2x^2c)/(5x-3ac)
============================
Cheers,
Stan H.
================

Question 752137: Solve each equation by factoring.
2p2+128=-32p

Answer by lenny460(775)

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Solve each equation by factoring.
2p2+128=-32p
I will assume 2p2 is 2p^2
Add 32p to each side of the equation.
2p^2 + 128 + 32p = -32p + 32p
Combine like terms:
-32p + 32p = 0
Therefore:
2p^2 + 128 + 32p = 0
Rearrange the above equation.
2p^2 + 32p + 128 = 0
Divide each term by 2
p^2 + 16p + 64 = 0
Factor the trinomial:
(p + 8)^2
Therefore:
(p + 8)(p + 8) = 0
Answer:
p = -8

Lennox Obuong
Algebra Tutor
Nairobi, Kenya
Email: obuong3@aol.com

Question 752106: Factor polynomial completely:
First problem: x^6-x^3
Second problem: 5a(a-3)-7(a-3)
Answer by lenny460(775)

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Factor polynomial completely:
First problem: x^6-x^3
Second problem: 5a(a-3)-7(a-3)

x^6 - x^3

Answer:
x^3(x - 1)(x^2 + x + 1)

Lennox Obuong
Algebra Tutor
Nairobi, Kenya
Email: obuong3@aol.com

Question 752153:
Answer by lenny460(775)

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Question 752110: Solve equation:
First problem: 4g^2-32g=0
Second problem: 3m^2=-6m
Answer by nerdybill(6962)

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First problem:
4g^2-32g=0
factor out common factor of 4g:
(4g)(g-8)=0
setting each term to zero:
g = {0, 8}
.
Second problem:
3m^2=-6m
3m^2+6m = 0
factor out common factor of 3m:
(3m)(m+2) = 0
setting each term to zero:
m = {0, -2}

Question 752093: If a person cuts a piece of wood measuring 3 1/8 inches into 2 pieces. How long is each piece?
Answer by rfer(12670)

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(25/8)/2=
25*1/2=1 9/16

Question 752098: Solve: u^3+6u^2=4u+24

Answer by JoeTaxpayer(138)

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u^3+6u^2=4u+24
u^3+6u^2-4u-24=0
((u^2)(u+6))-((4)(u+6)=0
(u^2-4)(u+6)=0
u=-2,u=2 or u=-6

Question 752096: What is 9t^4+30t^3+25t^2
Answer by JoeTaxpayer(138)

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9t^4+30t^3+25t^2 first, factor out a t^2
t^2(9t^2+30t+25) next factor as -
t^2 (3t+5)^2
if it's zeros you want, t=-5/3 and t=0

Question 752070:
Answer by tommyt3rd(606)

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Question 751833: Simplify: -2^-2
Answer by tommyt3rd(606)

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%0D%0A+-2%5E-2=-1%2F2%5E2=-1%2F4%0D%0A

Question 752039: A card is drawn from a deck of cards and replaced. A second card is then drawn from the deck. Are these events independent or not independent?
Answer by solver91311(16897)

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Does the outcome of the second trial depend on the outcome of the first trial? Does the probability that you will draw a specific card on the second draw change depending on what was drawn on the first card, given that the first card is replaced in the deck before making the second draw?

John

Egw to Beta kai to Sigma
My calculator said it, I believe it, that settles it

The Out Campaign: Scarlet Letter of Atheism

Question 752015: -4c(-9c^2+5c+8)
Foil
Answer by tommyt3rd(606)

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If by FOIL you mean distribute then...

-4c(-9c^2+5c+8)=

-4c(-9c^2)+(-4c)5c+(-4c)8=

36c^3-20c^2-32c

:)

Question 751980:
Answer by tommyt3rd(606)

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Question 751858: 3 ( log 5 - log 3 ) - ( log 5 - 2 log 6 ) = 2 - log n , find n.

Answer by nerdybill(6962)

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3 ( log 5 - log 3 ) - ( log 5 - 2 log 6 ) = 2 - log n , find n.
.
3 ( log 5 - log 3 ) - ( log 5 - 2 log 6 ) = 2 - log n
3log 5 - 3log 3 - ( log 5 - 2 log 6 ) = 2 - log n
log 5^3 - log 3^3 - ( log 5 - 2 log 6 ) = 2 - log n
log 125 - log 27 - ( log 5 - 2 log 6 ) = 2 - log n
log 125 - log 27 - ( log 5 - log 6^2 ) = 2 - log n
log 125 - log 27 - ( log 5 - log 36 ) = 2 - log n
log 125 - log 27 - log 5 + log 36 = 2 - log n
log 125/27 - log 5 + log 36 = 2 - log n
log 125/(27*5) + log 36 = 2 - log n
log (125*36)/(27*5) = 2 - log n
log (125*36)/(27*5) = 2 - log n
log (125*36)/(27*5) - 2 = -log n
-[log (125*36)/(27*5) - 2] = log n
10^(-[log (125*36)/(27*5) - 2]) = n
10^(-[log (4500)/(27*5) - 2]) = n
10^(-[log 900/27 - 2]) = n
10^(-[log 100/3 - 2]) = n
10^(-[1.52287874528 - 2]) = n
10^(0.4771212547196624372950) = n
3 = n

Question 751886: If the odds of winning the lotto are 1 in 195,000,000 what are the odds if I buy 360 tickets?
Answer by MathLover1(6638)

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The odds are therefore halved to

(

).
I buy one ticket at first - a chance. is 1%2F195000000=+0.000000005128205

%.
I then buy 360

tickets to increase my chances - a chance is 360%2F195000000+=+0.0000084615

Question 751857: What's 5×5?
Answer by Cromlix(353)

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5 x 5 = 25

Question 751859: 3 ( log 5 - log 3 ) - ( log 5 - 2 log 6 ) = 2 - log n , find n.

Answer by dkppathak(43)

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3 ( log 5 - log 3 ) - ( log 5 - 2 log 6 ) = 2 - log n , find n.
3log 5/3 -lg5/36 + log n =2
log 125/27 -log 5/36 +log n =log100
log 125x36/5x27 +log n =log100
log 100/3 +log n =log100
log100n/3=log100
100n/3=100
n=100x3/100 =3
ANSWER N = 3

Question 751810: Write the repeating decimal as a fraction: 0.3535
Answer by rfer(12670)

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3535/10000=707/2000

Question 751686:
Answer by tommyt3rd(606)

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Question 751698: 6^4-96
Answer by tommyt3rd(606)

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6^4-96=1296-96=1200

:)

Question 751691:
Answer by tommyt3rd(606)

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Question 751610: A box contains 4 red cubes, 3 blue cubes, 2 green cubes, and 1 yellow cube. You pick two cubes at random, replacing after you pick. Find P(red, then yellow). What's the answer?
Answer by stanbon(57387)

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A box contains 4 red cubes, 3 blue cubes, 2 green cubes, and 1 yellow cube. You pick two cubes at random, replacing after you pick. Find P(red, then yellow). What's the answer?
----
Because of replacement the selections are independent.
-----
P(red, then yellow) = (4/10)(1/10) = 4/100
---------------------------
Cheers,
Stan H.
======================

Question 751549: a man rode a bike fot 12 miles and then hiked an addiyional 8 miles. the time of the trip was 5 hrs. if his rate when rifing the bike was 10 miles per hr fastr than his walking rate what was each rate?
Answer by josmiceli(9697)

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Let +s+

= his speed in mi/hr walking
+s+%2B+10+

= his speed in mi/hr riding the bike
Let +t+

= his time in hrs spent walking
+5+-+t+

= his time in hrs spent riding bike
-----------------
Equation when riding bike:
(1) +12+=+%28+s+%2B+10+%29%2A%28+5+-+t+%29+

Equation when walking:
(2) +8+=+s%2At+

--------------
(1) +12+=+5s+%2B+50+-+s%2At+-+10t+

(1)

(1)

and
(2)

(2)

Substitute this into (1)
(1) +s%2A%28+5+-+8%2Fs+%29+=+10%2A%288%2Fs%29+-+38+

(1)

Multiply both sides by +s+

(1)

(1)

(1)

complete the square
(1) +s%5E2+%2B+6s+%2B+%286%2F2%29%5E2+=+16+%2B+%286%2F2%29%5E2+

(1)

(1)

(1)

(1)

and

His speed in mi/hr walking is 2 mi/hr
His speed in mi/hr riding the bike is 12 mi/hr
check:
(2) +8+=+s%2At+

(2)

(2)

hrs
and
(1) +12+=+%28+s+%2B+10+%29%2A%28+5+-+t+%29+

(1)

(1)

(1)

(1)

(1)

(1)

hrs
OK

Question 751566: Write an equation in point-slope form and slope intercept form:
Slope= -1, passing thru (-1/2, -2)
Answer by Cromlix(353)

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y - b = m(x - a)
y + 2 = -1(x + 1/2)
y = -x - 1/2 - 2
y = -x - 5/2
or
2y = -2x -5

Question 751570: I need help
Answer by lynnlo(4164)

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Question 751482: find telephone no of friend?
1. number is six digit?
a.first digit is smallest prime no.?
b.second digit is twice of first digit?
c.third digit is sum of first digit and second digit?
d.fourth digit is repetition of third digit?
e.fifth digit is half of fourth digit?
f.diference of sixth digit and second digit is equal to fifth digit?
so tell what is my friend sixth digit number??????

Answer by stanbon(57387)

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find telephone no of friend?
1. number is six digit?------
a.first digit is smallest prime no.?::: 2
---------------------------------------------
b.second digit is twice of first digit?::4
c.third digit is sum of first digit and second digit?::6
-------------------------------
d.fourth digit is repetition of third digit?:::6
----------------------------------------------
e.fifth digit is half of fourth digit?:::3
--------------------------------------
f.difference of sixth digit and second digit is equal to fifth digit?
5th = 6th-4
So, 5th could be 1 or 2 or 3 or 4 or 5
-------------------------------------------
so tell what is my friend sixth digit number??????
So, 6th could be 5 or 6 or 7 or 8 or 9
===================
Cheers,
Stan H.

Question 751338:
Answer by lenny460(775)

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Question 751336:
Answer by lenny460(775)

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Question 751408: A parabola shaped tunnel is 10m high at the centre and spans 18m wide at the base. A 7.5 m high vehicle needs to use the tunnel;, what is the maximum width of the vehicle that can fit through the tunnel?
I need to draw a diagram to represent the tunnel on a coordinate number plane , and find the equation of the parabola. using algebra and coordinate geometry to determinate the maximum width of the truck
I try to solve this problem many times but my results seems to be wrong, please help me I'm so stuck
Ally
Answer by jim_thompson5910(28598)

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The parabola is upside down and has the vertex at (0,10). Notice how this is the highest point.

The two roots are (-9,0) and (9,0). The horizontal distance between these two points is exactly 18 m. Basically how I found these two points is that I divided the distance of 18 m in half to get 9 m, then you walk 9 m in each direction to land on (-9,0) and (9,0)

So we have the three points: (0,10), (-9,0) and (9,0)

The first point is the vertex. The first point is also the y-intercept.

The next two points are the x-intercepts or roots.

Let's use the roots to find the equation

x = -9 or x = 9

x+9 = 0 or x-9 = 0

k(x+9)(x-9) = 0 ... for some fixed number k (we don't know it yet, but we'll find it soon)

k(x^2 - 81) = 0

The equation so far is y = k(x^2 - 81)

Since the y-intercept is (0,10), we can plug in x = 0 and y = 10 to find k

y = k(x^2 - 81)

10 = k(0^2 - 81)

10 = k(0 - 81)

10 = k(-81)

10 = -81k

-81k = 10

k = 10/(-81)

k = -10/81

So the equation that models the tunnel is y+=+-expr%2810%2F81%29%28x%5E2-81%29

which distributes to y+=+-expr%2810%2F81%29%28x%5E2%29-expr%2810%2F81%29%28-81%29

and that simplifies to y+=+-expr%2810%2F81%29%28x%5E2%29%2B10

So the equation in standard form is y+=+-expr%2810%2F81%29x%5E2%2B10

Now we're told that the truck is 7.5 m, so this means that the height y is 7.5, so we can plug in y = 7.5 and solve for x to find the clearance

y+=+-expr%2810%2F81%29x%5E2%2B10

So when

, the height is exactly 7.5 m, which means that the truck's width must be less than 2*4.5 = 9 feet across so it can fit in the tunnel.

Question 751301: -20x=-300
Answer by jim_thompson5910(28598)

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-20x=-300

x=-300/(-20)

x = 15

Question 751320: 7x^6y^4 + (x^3y^2)^2
Answer by stanbon(57387)

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7x^6y^4 + (x^3y^2)^2
------
7x^6y^4 + x^6y^4
----
= 8x^6y^4
================
cheers,
Stan H.
================

Question 751311:
Answer by tommyt3rd(606)

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Question 751292: I am stuck on elimination by substitution. The variable has to be "naked" or alone, but both x and y have numbers before the variables.
Answer by josgarithmetic(1538)

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Ax%2BBy=C+

A process to eliminate terms of y.
E%28Ax%2BBy=C%29

Note each entire equation is being multiplied.
AEx%2BBEy=E%2AC

We may sometimes apply commutative property of multiplication,
AEx%2BBEy=CE

Subtract one equation from the other equation:
AEx%2BBEy-BDx-BEy=CE-BF

And this is how we have the term, "elimination method".

In this general case, symbolically giving
AEx-BDx=CE-BF

, or

, and then division by the coefficient expression on x,
highlight%28x=%28CE-BF%29%2F%28AE-BD%29%29

Question 751286:
Answer by tommyt3rd(606)

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Question 751263: Y= -x2 + 4x + 16
Answer by tommyt3rd(606)

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Question 751133: What is an algebra

Answer by Edwin McCravy(8909)

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From wikipedia:

In mathematics, an algebra over a field is a vector space equipped with a
bilinear product. An algebra such that the product is associative and has an
identity is therefore a ring that is also a vector space, and thus equipped
with a field of scalars. Such an algebra is called here a unital associative
algebra for clarity, because there are also nonassociative algebras.

In other words, an algebra over a field is a set together with operations of
multiplication, addition, and scalar multiplication by elements of the
underlying field, that satisfy the axioms implied by "vector space"
and "bilinear".[1]

One may generalize this notion by replacing the field of scalars by a
commutative ring, and thus defining an algebra over a ring.

Because of the ubiquity of associative algebras, and because many textbooks
teach more associative algebra than nonassociative algebra, it is common for
authors to use the term algebra to mean associative algebra. However, this does
not diminish the importance of nonassociative algebras, and there are texts
that give both structures and names equal priority.

Wikipedia

Question 751222: 3x^2+5x=42

Answer by jim_thompson5910(28598)

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3x^2+5x=42

3x^2+5x-42 = 0

Use the quadratic formula to solve for x

x+=+%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F%282a%29