How many 1-inch cubes do you need to create a cube with an edge length of 5 inches?

it took Dean's family 3 hours to drive 195 miles on Friday. Then they drove at the same speed for 5 on saturday. how far did Dea

inn [45]

Hey!

Dean's family has been traveling on the same speed for two days, so to find how far you will need to travel you will need to find how far they are traveling in one hour..

To find this you will need to set up a proportion...

3/195 = 1/x

Solve this proportion by cross multiplying and then dividing..

195 * 1 = 195/3 = 65

This tells you that they are traveling 65 miles per hour. Now with this you will simply have to multiply 65 by 5 to tell you how far they would be traveling in 5 hours with the given speed...

65 * 5 = 325

Your answer of 325 miles tells you how far they traveled.

Hope it Helped!

~A

6 0

3 years ago

Help find zeros for 9 and 10

Bingel [31]

x4-10x2+9=0 Four solutions were found : x = 3 x = -3 x = 1 x = -1

Step by step solution :Step 1 :Skip Ad
Equation at the end of step 1 : ((x4) - (2•5x2)) + 9 = 0 Step 2 :Trying to factor by splitting the middle term

2.1 Factoring x4-10x2+9

The first term is, x4 its coefficient is 1 .
The middle term is, -10x2 its coefficient is -10 .
The last term, "the constant", is +9 

Step-1 : Multiply the coefficient of the first term by the constant 1 • 9 = 9

Step-2 : Find two factors of 9 whose sum equals the coefficient of the middle term, which is -10 .

-9 + -1 = -10 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -9 and -1
 x4 - 9x2 - 1x2 - 9

Step-4 : Add up the first 2 terms, pulling out like factors :
 x2 • (x2-9)
 Add up the last 2 terms, pulling out common factors :
 1 • (x2-9)
Step-5 : Add up the four terms of step 4 :
 (x2-1) • (x2-9)
 Which is the desired factorization

Trying to factor as a Difference of Squares :

2.2 Factoring: x2-1

Theory : A difference of two perfect squares, A2 - B2 can be factored into (A+B) • (A-B)

Proof : (A+B) • (A-B) =
 A2 - AB + BA - B2 =
 A2 - AB + AB - B2 =
 A2 - B2

Note : AB = BA is the commutative property of multiplication.

Note : - AB + AB equals zero and is therefore eliminated from the expression.

Check : 1 is the square of 1
Check : x2 is the square of x1 

Factorization is : (x + 1) • (x - 1)

Trying to factor as a Difference of Squares :

2.3 Factoring: x2 - 9

Check : 9 is the square of 3
Check : x2 is the square of x1 

Factorization is : (x + 3) • (x - 3)

Equation at the end of step 2 : (x + 1) • (x - 1) • (x + 3) • (x - 3) = 0 Step 3 :Theory - Roots of a product :

3.1 A product of several terms equals zero.

When a product of two or more terms equals zero, then at least one of the terms must be zero.

We shall now solve each term = 0 separately

In other words, we are going to solve as many equations as there are terms in the product

Any solution of term = 0 solves product = 0 as well.