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3 years ago

Distribute. 8(3x + 9)

Mathematics

2 answers:

Alexandra [31]3 years ago

5 0

The answer would be 24x+72 because 3x times 8 is 24x and and 9 times 8 is 72.

FinnZ [79.3K]3 years ago

4 0

Answer:

24x+72

Step-by-step explanation:

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Need help fast!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

earnstyle [38]

Use the subusitution method for r

g(4)=25-3(4)

g(4)= 25-12

g(4)= 13

Answer is g(4)= 13

8 0

3 years ago

Read 2 more answers

Bradley bought 2 cakes for his class Valentines's party. There are 23 students in his class. How much cake will each student rec

Cloud [144]

So 2 divded into 23 parts =2/23 which is simplest form

so each person will recieve 2/23 of a cake

4 0

3 years ago

A bag of apples weighs 7 7/8 pounds and a full bag costs $10.88. By weight 1/18 of the apples are rotten . What is the cost of t

ioda

Try Analysing The Information Like This, Step by Step;

1. We know that a full bag of 7 7/8 pounds and is $10.88.
2. Now we subtract the bad apples 7 7/8-1/18= a (now we have no bad apples).
3. Part 'a' answer will give you a no. in pounds.
4. Part 'b' - we have to find out $10.88/7 7/8 - 1/18 / 2 to give you the answer.

I hope this helps, sorry I couldn't really help you :)

7 0

3 years ago

Read 2 more answers

Help with num 1 please.

KengaRu [80]

Answer:

(i) $\displaystyle y' = (6x - 1)ln(2x + 1) + \frac{2x(3x - 1)}{2x + 1}$

(ii) $\displaystyle y' = \frac{2x}{ln(x)} - \frac{x^2 + 2}{x(lnx)^2}$

(iii) $\displaystyle y' = \frac{e^x[xln(2x) + 1]}{x}$

General Formulas and Concepts:

Calculus

Differentiation

Derivatives
Derivative Notation

Derivative Property [Multiplied Constant]: $\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)$

Derivative Property [Addition/Subtraction]: $\displaystyle \frac{d}{dx}[f(x) + g(x)] = \frac{d}{dx}[f(x)] + \frac{d}{dx}[g(x)]$

Basic Power Rule:

f(x) = cxⁿ
f’(x) = c·nxⁿ⁻¹

Derivative Rule [Product Rule]: $\displaystyle \frac{d}{dx} [f(x)g(x)]=f'(x)g(x) + g'(x)f(x)$

Derivative Rule [Quotient Rule]: $\displaystyle \frac{d}{dx} [\frac{f(x)}{g(x)} ]=\frac{g(x)f'(x)-g'(x)f(x)}{g^2(x)}$

Derivative Rule [Chain Rule]: $\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)$

Exponential Differentiation

Logarithmic Differentiation

Step-by-step explanation:

(i)

Step 1: Define

Identify

$\displaystyle y = (3x^2 - x)ln(2x + 1)$

Step 2: Differentiate

Product Rule: $\displaystyle y' = (3x^2 - x)'ln(2x + 1) + (3x^2 - x)[ln(2x + 1)]'$
Basic Power Rule/Logarithmic Differentiation [Chain Rule]: $\displaystyle y' = (6x - 1)ln(2x + 1) + (3x^2 - x)\frac{1}{2x + 1}(2x + 1)'$
Basic Power Rule: $\displaystyle y' = (6x - 1)ln(2x + 1) + (3x^2 - x)\frac{2}{2x + 1}$
Simplify [Factor]: $\displaystyle y' = (6x - 1)ln(2x + 1) + \frac{2x(3x - 1)}{2x + 1}$

(ii)

Step 1: Define

Identify

$\displaystyle y = \frac{x^2 + 2}{lnx}$

Step 2: Differentiate

Quotient Rule: $\displaystyle y' = \frac{(x^2 + 2)'lnx - (x^2 + 2)(lnx)'}{(lnx)^2}$
Basic Power Rule/Logarithmic Differentiation: $\displaystyle y' = \frac{2xlnx - (x^2 + 2)\frac{1}{x}}{(lnx)^2}$
Rewrite: $\displaystyle y' = \frac{2xlnx}{(lnx)^2} - \frac{(x^2 + 2)\frac{1}{x}}{(lnx)^2}$
Simplify: $\displaystyle y' = \frac{2x}{ln(x)} - \frac{x^2 + 2}{x(lnx)^2}$

(iii)

Step 1: Define

Identify

$\displaystyle y = e^xln(2x)$

Step 2: Differentiate

Product Rule: $\displaystyle y' = (e^x)'ln(2x) + e^x[ln(2x)]'$
Exponential Differentiation/Logarithmic Differentiation [Chain Rule]: $\displaystyle y' = e^xln(2x) + e^x(\frac{1}{2x})(2x)'$
Basic Power Rule: $\displaystyle y' = e^xln(2x) + e^x(\frac{1}{2x})2$
Simplify: $\displaystyle y' = e^xln(2x) + \frac{e^x}{x}$
Rewrite: $\displaystyle y' = \frac{xe^xln(2x) + e^x}{x}$
Factor: $\displaystyle y' = \frac{e^x[xln(2x) + 1]}{x}$