Envision Math Answers

Introduction to envision math answers:

Envision math deals with solving problems in certain topics such as numeration, addition, subtraction, multiplication, division, fractions and decimals, equivalent fractions, expressions and equations. Basically envision math deals with solving arithmetic problems with answers. The step by step solution for envisions math is given below. Here we are going to discuss some of the arithmetic problems and solving expressions. Envision math problems and answers are discussed below.

Example Problems to Envision Math Answers:

Example: 1

Solve: 44 -2x + 2 = 100

Solution:

Given: 44 -2x + 2 = 100

Step 1:

44 + 2 -2x = 100

46 - 2x = 100

Step 2:

46 - 2x - 46 = 100 - 46 (Subtract 46)

-2x = 54

Step 3:

`(-2)/(-2)` x = `54/(-2)`(Divide by -2)

x = -27

Answer: x = -27

Example: 2

Expand binomial: (x + 9)3

Solution:

Given binomial: (x + 9)3

Step 1:

Binomial theorem:

(x + y)n = xn + n xn-1 y + `(n(n-1))/(2!)` xn-2 y2  + `(n(n-1)(n-2))/(3!)`  xn-3 y3  + ... + yn

y = 9, n =3:

(x + 9)3 = x3 + 3 x3-1 9 + `(3(3-1))/(2!)` x3-2 92  + `(3(3-1)(3-2))/(3!)`  x3-3 93

= x3 + 27 x2 + `(3(2))/(2)` x1 (81)  + `(3(2)(1))/(6)`  x0 (729)

= x3 + 27 x2 + 243  x + 729

Answer: (x + 9)3 = x3 + 27 x2 + 243  x + 729

Practice Problems to Envision Math Answers:

Example: 3

Solve: log8 50

Solution:

Given: log8 50

Step 1:

Change of base theorem is,

logp r = `(log_qr)/(log_qp)`

Here,

p, q, r - positive numbers

p, q ? 1

Step 2:

log8 50 = `(log_(10)50 )/(log_(10)8)`

Step 2:

log10 50 = 1.6990

Step 3:

log10 8 = 0.9031

Step 4:

`(log_(10)50 )/(log_(10)8)` = `1.6990/0.9031`

= 1.8812

Answer: log8 50 = 1.8812

Example: 4

Solve: 4 - 2x > 50

Solution:

Given: 4 - 2x > 50

Step 1:

4 - 2x - 4 > 50 - 4 (Subtract 4)

-2x > 46

Step 2:

`(-2)/(-2)` a > `46/(-2)`(Divide by -2)

a < -23 (Multiplication of an inequality by a negative number changes the symbol)

To check:

x = -22:

4 - 2(-22) > 50

4 + 44 > 50

48 > 50 (False)

x = -25:

4 - 2(-25) > 50

4 + 50 > 50

54 > 50 (True)

Answer: a < -23