Use the equation 124 times 15 =1,860 and what you know about fractions, decimals.

Factor x3 + x2 + x + 1 by grouping. What is the resulting expression? (x2)(x + 1) (x2 + 1)(x) (x2 + 1)(x + 1) (x3 + 1)(x + 1)

yanalaym [24]

Answer : $(x^2 + 1)( x + 1)$

Factor $x^3 + x^2 + x + 1$ by grouping

We group first two terms and last two terms

$(x^3 + x^2)+( x + 1)$

Now we take out GCF from each group

GCF of $(x^3 + x^2)$ is x^2

GCF of $+( x + 1)$ is 1

$(x^3 + x^2) +( x + 1)$

$x^2(x + 1) +1( x + 1)$

Now we factor out x+1 that is in common

$(x^2 + 1)( x + 1)$

6 0

4 years ago

Read 2 more answers

To offset college expenses, at the beginning of your freshman year you obtain a nonsubsidized student loan for $15,000. Interest

soldier1979 [14.2K]

Answer:

15000(1.003425)^12t ;

4.11%

4.188%

Step-by-step explanation:

Given that:

Loan amount = principal = $15000

Interest rate, r = 4.11% = 0.0411

n = number of times compounded per period, monthly = 12 (number of months in a year)

Total amount, F owed, after t years in college ;

F(t) = P(1 + r/n)^nt

F(t) = 15000(1 + 0.0411/12)^12t

F(t) = 15000(1.003425)^12t

2.) The annual percentage rate is the interest rate without compounding = 4.11%

3.)

The APY

APY = (1 + APR/n)^n - 1

APY = (1 + 0.0411/12)^12 - 1

APY = (1.003425)^12 - 1

APY = 1.04188 - 1

APY = 0.04188

APY = 0.04188 * 100% = 4.188%

7 0

3 years ago

The volume of a rectangular prism is 2x^3 - 6x^2 + 8x , and the volume of a cube is 27x^3. What is the total volume of the prism

AleksAgata [21]

Answer:

$\displaystyle V_{P + C} = 29x^3 - 6x^2 + 8x$

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Algebra I

Terms/Coefficients

Step-by-step explanation:

Step 1: Define

Identify.

$\displaystyle V_P = 2x^3 - 6x^2 + 8x$

$\displaystyle V_C = 27x^3$

Step 2: Find Combined Volume

[Set up] Add: $\displaystyle V_P + V_C = V_{P + C}$
Substitute in variables: $\displaystyle V_{P + C} = 27x^3 + 2x^3 - 6x^2 + 8x$
Combine like terms: $\displaystyle V_{P + C} = 29x^3 - 6x^2 + 8x$

8 0

3 years ago

The formula for an arithmetic series is shown below, where n = 1, 2, 3 ...

lisov135 [29]

Answer:

4th term = 28

5th term = 37

6th term = 45

Step-by-step explanation:

f(n + 1) = f(n) + 8

f(1) = 5

f(1 + 1) = f(1) + 8 = 5+8 = 13

f(2) = 13

f(2 + 1) = f(2) + 8 = 13+8 = 21

Thus, series is 5, 13, 21......

In arithmetic series

Nth term is given by

n th term = a + (n-1)d

where a is the first term

and d is the common difference.

common difference d = nth term - (n-1)th term

For this series

a = 5

lets take nth term as 2nd term and 1st term as (n-1)th term

d = 13-5 = 8

n th term = a + (n-1)d

using the formula for nth term

4th term = 5 + (4-1)8 = 29

5th term = 5 + (5-1) 8= 37

6th term = 5+ (6-1)8 = 45

Thus, 4th term = 28

5th term = 37

6th term = 45

Note this, problem can be solved using f(n + 1) = f(n) + 8 by putting n = 3,4,5 as well but for learning concept of arithmetic series, i have used above process. Hope it helps.

5 0

3 years ago

Given ZW=20. Answer the questions please.

djyliett [7]

a) Corresponding angles of similar figures are congruent, so $\angle B \cong \boxed{\angle Z}$

b) Scale factor = (image)/(preimage). Since we are looking for ABCD to WZYX, this means that WZYX is the image and ABCD is the preimage. Thus, the scale factor is $\frac{25}{10}=\boxed{5/2}$

c) Since the scale factor is 5/2,

$\frac{20}{t}=\frac{5}[2}\\\\40=5t\\ \\ t=\boxed{8}$

8 0

2 years ago