Two solutions were found :
1. x=4
2. x= -4
Step by step solution: Step 1 :
Equation at the end of step 1 :
(((x3) + 22x2) - 16x) - 64 = 0
Equation at the end of step 1 :
(((x3) + 22x2) - 16x) - 64 = 0 :
Step 2 :
Checking for a perfect cube :
2.1 x3+4x2-16x-64 is not a perfect cube
Trying to factor by pulling out :
2.2 Factoring: x3+4x2-16x-64
Thoughtfully split the expression at hand into groups, each group having two terms :
Group 1: x3+4x2
Group 2: -16x-64
Pull out from each group separately :
Group 1: (x+4) • (x2)
Group 2: (x+4) • (-16)
-------------------
Add up the two groups :
(x+4) • (x2-16)
Which is the desired factorization
Trying to factor as a Difference of Squares :
2.3 Factoring: x2-16
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 : 16 is the square of 4
Check : x2 is the square of x1
Factorization is : (x + 4) • (x - 4)
Multiplying Exponential Expressions :
2.4 Multiply (x + 4) by (x + 4)
The rule says : To multiply exponential expressions which have the same base, add up their exponents.
In our case, the common base is (x+4) and the exponents are :
1 , as (x+4) is the same number as (x+4)1
and 1 , as (x+4) is the same number as (x+4)1
The product is therefore, (x+4)(1+1) = (x+4)2
Equation at the end of step 2 :
(x + 4)2 • (x - 4) = 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.
Solving a Single Variable Equation :
3.2 Solve : (x+4)2 = 0
(x+4) 2 represents, in effect, a product of 2 terms which is equal to zero
For the product to be zero, at least one of these terms must be zero. Since all these terms are equal to each other, it actually means : x+4 = 0
Subtract 4 from both sides of the equation :
x = -4
Solving a Single Variable Equation :
3.3 Solve : x-4 = 0
Add 4 to both sides of the equation :
x = 4
Two solutions were found :
x = 4
x = -4
(Sorry the question is too long, but I hope you understand the question)
Answer:
75 cm^2
Step-by-step explanation:
We have the lengths of two corresponding sides. The scale factor from the large triangle to the small triangle is 16/64 = 1/4. Each side of the smaller triangle is 1/4 times the length of the corresponding side of the large triangle.
For the areas, the scale factor is the square of the scale factor of the lengths. Area scale factor = 1/4^2 = 1/16.
The area of the small triangle is 1/16 the area of the large triangle.
area of small triangle = (area of large triangle) * (area scale factor)
area of small triangle = 1200 cm^2 * 1/6 = 1200 cm^2/16
area of small triangle = (1200 cm^2)/16 = 75 cm^2
im confused what is the wuestion i will aanswer still in the comments
volume of the glass:
PI x r^2 x h = 3.14 x 3^2 x 12 = 339.12 cubic cm
150 / 339.12 = 0.442 = 44.2%
Round the answer as needed.
Answer:
The answer would be A
Step-by-step explanation:
the answer is A because it shows the correct set of data