You can put this solution on YOUR website!
Well, if you can walk 35 miles an hour......then 10 minutes.
You have to know the speed of the person walking.
www.algebrahouse.com

You can put this solution on YOUR website!
- (z + 89)
= - z - 89 {distributed the negative sign through the parentheses}
www.algebrahouse.com

You can put this solution on YOUR website!
6s - 2t = 10
s - 5t = 14
-------------
5s + 3t = - 4 {subtracted the two equations}
www.algebrahouse.com

You can put this solution on YOUR website!
"Pizzazz Publications is having some books printed. The printer charges $800 plus $5 per book. How many books can be printed for $4000?"
x = number of books
800 + 5x = 4000 {charges 800 plus 5 per book equals 4000}
5x = 3200 {subtracted 800 from both sides}
x = 640 {divided both sides by 5}

640 books can be printed
www.algebrahouse.com

You can put this solution on YOUR website!
"Two scooters travel from the same point in the same direction, leaving at the same time. The faster scooter travels at twice the speed of the slower scooter. After three seconds, the faster scooter has traveled 6 feet more than the slower scooter. What is the speed of each scooter?

Distance = rate x time
D = rt

slower scooter
r = r
t = 3 {after 3 seconds}
D = 3r {distance = rate x time}

faster scooter
r = 2r {twice the slower scooter}
t = 3 {after 3 seconds}
D = 6r {distance = rate x time}

After 3 seconds the faster scooter was 6 feet in front of slower scooter:
3r + 6 = 6r {slower scooter distance plus 6 = faster scooter distance}
6 = 3r {subtracted 3r from both sides}
r = 2 {divided both sides by 3}
2r = 4 {substituted 2, in for r, into 2r}

slower scooter's speed is 2
faster scooter's speed is 4
www.algebrahouse.com

You can put this solution on YOUR website!
-36uv
-------
117uv

- 4
---- {reduced 36 and 117...9 goes into both, also cancelled uv on top and bottom}
13
www.algebrahouse.com

You can put this solution on YOUR website!
8 wrong out of 43
means
35 right out of 43

35
---- ≈ .814 {divided}
43

≈ 81.4% {changed decimal to percent by moving decimal point right two places}
www.algebrahouse.com

You can put this solution on YOUR website!
(3x² - 5x + 5) + (-x² + 2x - 7)
= 3x² - 5x + 5 - x² + 2x - 7 {took out parentheses}
= 2x² - 3x - 2 {combined like terms}
www.algebrahouse.com

You can put this solution on YOUR website!
"If a number is triple and then decrease by 82, the result is the sum of
six times the number and forty-four. Find the number."

x = the number

3x - 82 = 6x + 44 {number is tripled and decreased by 82 equals the sum of six times number and 44}
-82 = 3x + 44 {subtracted 3x from both sides}
-126 = 3x {subtracted 44 from both sides}
x = -42 {divided both sides by 3}

the number is - 42
www.algebrahouse.com

You can put this solution on YOUR website!
"Alma traveled 324 miles to vist her grandmother. Kevin traveled 5 times as far to see his uncle. About how many miles did kevin travel"

Alma traveled 324 miles
Kevin trabeled 5 times that

324
x 5
----
1620 miles {multiplied}
www.algebrahouse.com

You can put this solution on YOUR website!
"The area of a rectangular wall in a classroom is 165 square feet. Its length
is 4 feet longer than its width. Find the width of the wall of the
classroom."


x = width
x + 4 = length {the length is 4 longer than the width}

Area of a rectangle = width x length

x(x + 4) = 165 {area of a rectangle is width x length}
x² + 4x = 165 {used distributive property}
x² + 4x - 165 = 0 {subtracted 165 from both sides}
(x + 15)(x - 11) = 0 {factored into two binomials}
x + 15 = 0 or x - 11 = 0 {set each factor equal to 0}
x = -15 or x = 11 {subtracted 15 and added 11}
x = 11 {width of a rectangle cannot be negative}

width = 11 ft
www.algebrahouse.com

You can put this solution on YOUR website!
"Serena's father is twenty-six years older than serena. In ten years, the sum of the ages will be eighty. What are their present ages?"

x = Serena's age now
x + 26 = father's age now

x + 10 = Serena's age in 10 years
x + 36 = father's age in 10 years {added 10 on to each one}

x + 10 + x + 36 = 80 {in ten years the sum of the ages will be 80}
2x + 46 = 80 {combined like terms}
2x = 34 {subtracted 46 from both sides}
x = 17 {divided both sides by 2}
x + 26 = 43 {substituted 17, in for x, into x + 26}

Serena is 17
her father is 43
www.algebrahouse.com

You can put this solution on YOUR website!
"Of the 294 million people in the United States, 26% are smokers. How many are smokers?"

26% of 294
= 294 x (.26) {changed 26% to a decimal and multiplied by 294}
= 76.44 {multiplied}
Approximately 76 are smokers.
www.algebrahouse.com

You can put this solution on YOUR website!
eighteen is what percent of 60?

18
---
60

= .3 {divided}
= 30% {changed decimal to percent by moving decimal point right two places}
www.algebrahouse.com

You can put this solution on YOUR website!
"the sum of two consecutive odd numbers is 20. find the numbers."

x = 1st odd integer
x + 2 = 2nd odd integer

x + x + 2 = 20 {the sum of the two is 20}
2x + 2 = 20 {combined like terms}
2x = 18 {subtracted 2 from both sides}
x = 9 {divided both sides by 2}
x + 2 = 11 {substituted 9, in for x, into x + 2}

9 and 11 are the two consecutive odd integers
www.algebrahouse.com

You can put this solution on YOUR website!
"marks dad is 3 times as old as mark . The sum of their ages is 48 , how old is mark?"

x = Mark's age
3x = Mark's dad's age {Mark's dad is 3 times Mark}

x + 3x = 48 {sum of ages is 48}
4x = 48 {combined like terms}
x = 12 {divided both sides by 4}

Mark is 12
www.algebrahouse.com

You can put this solution on YOUR website!
If you had 4 goats - 1 goat .....how many goats would you have?

4g - g
= 3g {combined like terms}
www.algebrahouse.com

You can put this solution on YOUR website!
"Which values of b will make the expression x^2 + bx+400 a perfect square trinomial?"
a. -80,80 b.-40,40 c.-100,100 d.-20,20


B. is the answer

x² + 40x + 400
= (x + 20)(x + 20) {when factored}
or (x - 20)(x - 20)
www.algebrahouse.com

You can put this solution on YOUR website!
Reduce the rational expression to lowest terms. If it is already in lowest terms, enter the expression in the answer box. Also, specify any restrictions on the variable.

-8
-------
4x - 20

-8
-------- {factored 4 out of bottom}
4(x - 5)

-2
------- {cancelled -8 and 4}
x - 5

Restrictions on variable would be those that make the denominator equal to 0.
Variable restriction: x cannot be equal to 5 {that would make denominator 0}
www.algebrahouse.com

You can put this solution on YOUR website!
3
= 3/1 {wrote 3 as a fraction}
www.algebrahouse.com

You can put this solution on YOUR website!
36 ÷ (-6)
= -6 {dividing a positive by a negative equals a negative}
www.algebrahouse.com

You can put this solution on YOUR website!
Volume of a cube is (one edge)³

V = s³ {s is the edge or side of a cube}
V = (3cm)³ {substituted 3 in for s}
V = 27 cm³ {cubed the 3}
www.algebrahouse.com

You can put this solution on YOUR website!
Even integers increase by two each time

x = 1st even integer
x + 2 = 2nd even integer
x + 4 = 3rd even integer
x + 6 = 4th even integer
x + 8 = 5th even integer

x + x + 2 + x + 4 + x + 6 + x + 8 {added all even integers}
= 5x + 20 {combined like terms}
www.algebrahouse.com

You can put this solution on YOUR website!
4 books in 1 box

4 x 5

= 20 books in 5 boxes {multiplied}
www.algebrahouse.com

You can put this solution on YOUR website!
3x² - 22x + 40
= 3x² - 12x - 10x + 40 {factoring by grouping, split -22x into -12x and -10x}
= 3x(x - 4) - 10(x - 4) {factored 3x out of 1st two terms and -10 out of last two}
= (3x - 10)(x - 4) {factored x - 4 out of the two terms}
www.algebrahouse.com

You can put this solution on YOUR website!
6 x 7 2/5

= 6/1 x 37/5 {changed to improper fractions}
= 222/5 {multiplied, horizontally, through numerators and denominators}
= 44 2/5 {changed to mixed number}
www.algebrahouse.com

You can put this solution on YOUR website!
(6x^7 - 6)(x^9 - 1)
= 6x^7(x^9) + 6x^7(-1) - 6(x^9) - 6(-1) {used foil method}
= 6x^16 - 6x^7 - 6x^9 + 6 {multiplied through, adding exponents when multiplying}
= 6x^16 - 6x^9 - 6x^7 + 6 {combined like terms}
www.algebrahouse.com

You can put this solution on YOUR website!
"Max is 5 years old than Paul. Next year, Max will be twice as old as Paul. How old are they now? Show equation and check."

x = Paul's age now
x + 5 = Max's age now

x + 1 = Paul's age next year
x + 6 = Max's age next year

x + 6 = 2(x + 1) {next year, Max will be twice as old as Paul}
x + 6 = 2x + 1 {used distributive property}
6 = x + 1 {subtracted x from both sides}
x = 5 {subtracted 1 from both sides}
x + 5 = 10 {substituted 5, in for x, into x + 5}

Paul is 5 now
Max is 10 now
www.algebrahouse.com

You can put this solution on YOUR website!
4x + 3
---------------
20x² + 23x + 6

4x + 3
----------------- {factored bottom into two binomials}
(4x + 3)(5x + 2)

1
------ {cancelled 4x + 3 on top and bottom}
5x + 2

Restrictions on x, would be those that would make the denominator equal to 0.

5x + 2 = 0 {set denominator equal to 0}
5x = -2 {subtracted 2 from both sides}
x = -2/5 {divided both sides by 5}
Therefore x cannot be -2/5
www.algebrahouse.com

You can put this solution on YOUR website!
a^4 - 7a^2 + 10
= (a^2 - 5)(a^2 - 2) {factored into two binomials}
www.algebrahouse.com

You can put this solution on YOUR website!
"One number is 2 more than 5 times another. Their product is 39. Find the numbers."

x = one number
5x + 2 = other number

x(5x + 2) = 39 {their product is 39}
5x^2 + 2x = 39 {used distributive property}
5x^2 + 2x - 39 = 0 {subtracted 39 from both sides}
(5x - 13)(x + 3) = 0 {factored into two binomials}
5x - 13 = 0 or x + 3 = 0 {set each factor equal to 0}
5x = 13 or x = -3 {added 13 and subtracted 3, respectively}
x = 13/5 or x = -3 {divided first equation by 5}
5x + 2 = 15 or 5x + 2 = -13 {substituted 13/5 and -3, in for x}


The numbers are:
13/5 and 15
and
-3 and -13

www.algebrahouse.com