Factor 12x^3-9x^2-4x-3

6. There are 90 seats in the school auditorium. The school had a sold out show of their play last weekend, and made $315. The co

Olegator [25]

Answer:

90

Step-by-step explanation:

4 0

3 years ago

Z= -12i + 11 what are the real imaginary parts of z

Sergio039 [100]

Let's solve for i.

z=−12i+11

Step 1: Flip the equation.

−12i+11=z

Step 2: Add -11 to both sides.

−12i+11+−11=z+−11

−12i=z−11

Step 3: Divide both sides by -12.

−12i−12=z−11−12

i=−112z+1112

Answer:

i=−112z+1112

5 0

4 years ago

Ratios, Rates, and Circles Solve each problem. Show your work. Sierra has a pet Burmese python. It has grown too large for its e

saw5 [17]

Answer:

144in

Step-by-step explanation:

METHOD 1:

18 - 36

x - 48

36x = 18 * 48

36x = 864

x = 24

ALTERNATIVE METHOD:

18:36 (breadth:length)

1:2

When the length is 48in, the breadth is half the length, hence, the breadth is 24in.

Final Solution:

So, when the base is 48in, the width is 24in.

Since we have the two values

P = 2(l+b)

= 2(48+24)

= 2 * 72

= 144in

Feel free to mark this as brainliest! :D

8 0

3 years ago

Integrating sums of functions

Andrei [34K]

Answer:

(a) -12

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Equality Properties

Multiplication Property of Equality
Division Property of Equality
Addition Property of Equality
Subtraction Property of Equality

Calculus

Integrals

Integration Rule [Reverse Power Rule]: $\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C$

Integration Property [Swapping Limits]: $\displaystyle \int\limits^b_a {f(x)} \, dx = -\int\limits^a_b {f(x)} \, dx$

Integration Property [Multiplied Constant]: $\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx$

Integration Property [Addition/Subtraction]: $\displaystyle \int {[f(x) \pm g(x)]} \, dx = \int {f(x)} \, dx \pm \int {g(x)} \, dx$

Integration Property [Splitting Integral]: $\displaystyle \int\limits^c_a {f(x)} \, dx = \int\limits^b_a {f(x)} \, dx + \int\limits^c_b {f(x)} \, dx$

Integration Rule [Fundamental Theorem of Calculus 1]: $\displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)$

Step-by-step explanation:

Step 1: Define

$\displaystyle \int\limits^6_4 {f(x)} \, dx = 5$

$\displaystyle \int\limits^4_{10} {f(x)} \, dx = 8$

$\displaystyle \int\limits^{10}_6 {[4f(x) + 10]} \, dx$

Step 2: Solve Pt. 1

[Integral] Rewrite [Integration Property - Addition]: $\displaystyle \int\limits^{10}_6 {[4f(x) + 10]} \, dx = \int\limits^{10}_6 {4f(x)} \, dx + \int\limits^{10}_6 {10} \, dx$
[Integral] Rewrite [Integration Property - Multiplied Constant]: $\displaystyle \int\limits^{10}_6 {[4f(x) + 10]} \, dx = 4\int\limits^{10}_6 {f(x)} \, dx + 10\int\limits^{10}_6 {} \, dx$

Step 3: Redefine

Manipulate the given integral values.

[Integrals] Combine [Integration Property - Splitting Integral]: $\displaystyle \int\limits^6_4 {f(x)} \, dx + \int\limits^4_{10} {f(x)} \, dx = \int\limits^6_{10} {f(x)} \, dx$
[Integral] Rewrite: $\displaystyle \int\limits^6_{10} {f(x)} \, dx = \int\limits^6_4 {f(x)} \, dx + \int\limits^4_{10} {f(x)} \, dx$
[Integral] Substitute in integrals: $\displaystyle \int\limits^6_{10} {f(x)} \, dx = 5 + 8$
[Integral] Add: $\displaystyle \int\limits^6_{10} {f(x)} \, dx = 13$
[Integral] Rewrite [Integration Property - Swapping Limits]: $\displaystyle -\int\limits^{10}_6 {f(x)} \, dx = 13$
[Integral] [Division Property of Equality] Isolate integral: $\displaystyle \int\limits^{10}_6 {f(x)} \, dx = -13$

Step 4: Solve Pt. 2

[Integral] Substitute in integral: $\displaystyle \int\limits^{10}_6 {[4f(x) + 10]} \, dx = 4(-13) + 10\int\limits^{10}_6 {} \, dx$
[Integral] Integrate [Integration Rule - Reverse Power Rule]: $\displaystyle \int\limits^{10}_6 {[4f(x) + 10]} \, dx = 4(-13) + 10(x) \bigg| \limits^{10}_6$
[Integral] Evaluate [Integration Rule - FTC 1]: $\displaystyle \int\limits^{10}_6 {[4f(x) + 10]} \, dx = 4(-13) + 10(10 - 6)$
[Integral] (Parenthesis) Subtract: $\displaystyle \int\limits^{10}_6 {[4f(x) + 10]} \, dx = 4(-13) + 10(4)$
[Integral] Multiply: $\displaystyle \int\limits^{10}_6 {[4f(x) + 10]} \, dx = -52 + 40$
[Integral] Add: $\displaystyle \int\limits^{10}_6 {[4f(x) + 10]} \, dx = -12$