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2 years ago

-4x+3<9 help please and show your answer

Mathematics

1 answer:

vladimir1956 [14]2 years ago

8 0

Answer:

X =1,5

Step-by-step explanation:

==>-4x+3<9

==>-4x<9-3

==>-4x<6.

==> $x = \frac{6}{4}$

==>x =1.5

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3 years ago

Solving Inequalities Independent Practice

Gelneren [198K]

Answer:

X< 9

Step-by-step explanation:

1/3x-6<-3 is correct.

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3 years ago

Condense the following logs into a single log:

mamaluj [8]

QUESTION 1

The given logarithm is

$8\log_g(x)+5\log_g(y)$

We apply the power rule of logarithms; $n\log_a(m)=\log_(m^n)$

$=\log_g(x^8)+\log_g(y^5)$

We now apply the product rule of logarithm;

$\log_a(m)+\log_a(n)=\log_a(mn)$

$=\log_g(x^8y^5)$

QUESTION 2

The given logarithm is

$8\log_5(x)+\frac{3}{4}\log_5(y)-5\log_5(z)$

We apply the power rule of logarithm to get;

$=\log_5(x^8)+\log_5(y^{\frac{3}{4}})-\log_5(z^5)$

We apply the product to obtain;

$=\log_5(x^8\times y^{\frac{3}{4}})-\log_5(z^5)$

We apply the quotient rule; $\log_a(m)-\log_a(n)=\log_a(\frac{m}{n} )$

$=\log_5(\frac{x^8\times y^{\frac{3}{4}}}{z^5})$

$=\log_5(\frac{x^8 \sqrt[4]{y^3} }{z^5})$

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3 years ago

What is addition and subtraction

choli [55]

$\huge\text{Hey there!}$

$\huge\textsf{What is addition \& subtraction?}$

$\huge\textbf{What is addition?}$

$\bullet\large\textbf{ Well, \underline{addition} simply means when you're ADDING}\\\large\textbf{2 or more numbers from each other to get the result of}\\\large\textbf{a number.}$

$\huge\textbf{Random notes}$

$\star\large\textbf{ Usually, you start working with addition when you're in}\\\large\textbf{pre-kindergarten (pre-k also known as head-start)}\\\\\star\large\textbf{ When, you're adding you are going upward.}\\\\\star\large\textbf{ Addition sometimes come after you learn how to count}\\\large\textbf{the basic numbers and so forth because adding never}\\\large\textbf{ends if you really think about.}$

$\huge\textbf{Example:}$

$\heartsuit\large\textbf{ 2 \boxed{\bf +} 5 = 7}\\\\\\\heartsuit\large\textbf{ You got the result of 7 because you started at 2 \& went}\\\larg\textbf{up 5 spaces to your right on your number and you landed}\\\large\textbf{on 7.}$

$\huge\textbf{What is subtraction?}$

$\bullet\large\textbf{ Well, subtraction simply means you're taking away. Often}\\\large\textbf{people call it take aways.}$

$\huge\textbf{Random notes:}$

$\star\large\textbf{ Usually, you start working with subtraction when you're}\\\large\textbf{in pre-kindergarten (pre-k also known as headstart)}\\\\\star\large\textbf{When you're subtracting you are doing downward.}\\\\\star\large\textbf{You focus more on subtraction when you're counting}\\\large\textbf{backwards.}$

$\huge\textbf{Example:}$

$\heartsuit\large\textbf{ 7 \boxed{\bf -} 5 = 2 }\\\\\\\heartsuit\large\textbf{ 7 \boxed{\bf -} 2 = 5}\\\\\\\heartsuit\large\textbf{ For equation \#1. you begin at 7 and go BACK 5 spaces}\\\large\textbf{and you should have landed on 2.}\\\\\\\heartsuit\large\textbf{ For equation \#2. you begin at 7 \& go BACK 2 spaces}\\\large\textbf{and you should have landed on 5.}$

$\huge\textsf{KEEP IN MIND:}$

$\circ\large\textsf{ Addition OPPOSITE is subtraction \& subtraction OPPOSITE is}\\\large\textsf{addition.}$

$\huge\text{Good luck on your assignment \& enjoy your day!}$

~ $\frak{Amphitirite1040:)}$

4 0

1 year ago

Read 2 more answers

Find a point on the curve x^3+y^3=11xy other than the origin at which the tangent line is horizontal.

attashe74 [19]

Compute the derivative dy/dx using the power, product, and chain rules. Given

x³ + y³ = 11xy

differentiate both sides with respect to x to get

3x² + 3y² dy/dx = 11y + 11x dy/dx

Solve for dy/dx :

(3y² - 11x) dy/dx = 11y - 3x²

dy/dx = (11y - 3x²)/(3y² - 11x)

The tangent line to the curve is horizontal when the slope dy/dx = 0; this happens when

11y - 3x² = 0

y = 3/11 x²

(provided that 3y² - 11x ≠ 0)

Substitute y into into the original equation:

x³ + (3/11 x²)³ = 11x (3/11 x²)

x³ + (3/11)³ x⁶ = 3x³

(3/11)³ x⁶ - 2x³ = 0

x³ ((3/11)³ x³ - 2) = 0

One (actually three) of the solutions is x = 0, which corresponds to the origin (0,0). This leaves us with

(3/11)³ x³ - 2 = 0

(3/11 x)³ - 2 = 0

(3/11 x)³ = 2

3/11 x = ³√2

x = (11•³√2)/3

Solving for y gives

y = 3/11 x²

y = 3/11 ((11•³√2)/3)²

y = (11•³√4)/3

So the only other point where the tangent line is horizontal is ((11•³√2)/3, (11•³√4)/3).

3 0

2 years ago