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2 years ago

F(x) = x2 -2x & g(x) = 12-8x. Find f(2) - g(3)

Mathematics

1 answer:

Marianna [84]2 years ago

3 0

<h3>Answer: 24</h3>

=========================================

Work Shown:

f(x) = x^2 - 2x

f(2) = 2^2 - 2*2 ... replace every x with 2

f(2) = 4 - 4

f(2) = 0

----------------------------

g(x) = 12-8x

g(3) = 12-8*3 ... replace every x with 3

g(3) = 12-24

g(3) = -24

----------------------------

Subtract the results of the previous two sections

f(2) - g(3) = 0 - (-24)

f(2) - g(3) = 0 + 24

f(2) - g(3) = 24

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Read 2 more answers

What are the potential solutions of log4x+log4(x+6)=2?

lions [1.4K]

The potential solutions of $log_4x+log_4(x+6)=2$ are 2 and -8.

<h3>Properties of Logarithms</h3>

From the properties of logarithms, you can rewrite logarithmic expressions.

The main properties are:

Product Rule for Logarithms - $log_{b}(a*c)=log_{b}a+log_{b}c$
Quotient Rule for Logarithms - $log_{b}(\frac{a}{c} )=log_{b}a-log_{b}c$
Power Rule for Logarithms - $log_{b}(a^c)=c*log_{b}a$

The exercise asks the potential solutions for $log_4x+log_4(x+6)=2$ . In this expression you can apply the Product Rule for Logarithms.

$log_4x+log_4(x+6)=2\\ \\ x*(x+6)=4^2\\ \\ x^2+6x=16\\ \\ x^2+6x-16=0$

Now you should solve the quadratic equation.

Δ= $b^2-4ac=36-4*1*(-16)=36+64=100$ . Thus, x will be $x_{1,\:2}=\frac{-6\pm \:\sqrt{100} }{2\cdot \:1}=\frac{-6\pm \:10}{2}$ . Then:

$x_1=\frac{-6+10}{2}=\frac{4}{2} =2\\ \\ \:x_2=\frac{-6-10}{2}=\frac{-16}{2} =-8$

The potential solutions are 2 and -8.

Read more about the properties of logarithms here:

brainly.com/question/14868849

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2 years ago

The equation h=-16t^2+58t+3 models the height of a baseball t seconds after it has been hit.

Nata [24]

At 40 seconds I got 23,277 feet so yes it was ever 60 feet

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3 years ago

In the school library, 28% of the books are non-fiction. If there are 1.224 fiction books in

denis-greek [22]

Answer:

1700 books

Step-by-step explanation:

We are given;

% of non-fiction books in the library as 28%
Number of fiction books in the library as 1,224 books

We are required to determine the total number of books.

First we determine the percentage of non-fiction books

We need to know that;

% of fiction books + % of non-fiction books = 100%

Therefore;

% of non-fiction books = 100 % - 28 %

= 72%

Second we determine the total number of books

We know that;

Total number of books = 100%

But;

72% = 1,224 books

Therefore;

Total number of books = (1,224 × 100%) ÷ 72%

= 1700 books

Hence, the library has a total number of 1700 books

7 0

2 years ago