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3 years ago

Let / f(x)= -5x + 3 and g(x) = 6x - 2. Find f*g and its domain.

Mathematics

1 answer:

lina2011 [118]3 years ago

6 0

Answer:

The correct answer is: Option 3.

Step-by-step explanation:

To begin the problem asks to find $f$ · $g$ which can be defined as $[f*g](x)$ . Now we are given that:

$f(x)=-5x+3\\g(x)=6x-2$

So now we need to 'multiply' our two algebraic expressions as follow:

$fg(x)=(-5x+3)(6x-2)\\fg(x)=(-5x)(6x) +(-2)(-5x)+(3)(6x)+(3)(-2)\\fg(x)=-30x^2+10x+18x-6\\fg(x)=-30x^2+28x-6$ Eqn.(1)

The domain of Eqn. (1) is all real numbers of $x$ .

Which according to the given options , Option 3 is correct.

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On a number line, what is the distance between -9 and -5?

Makovka662 [10]

Answer:

The distance on a number line between -9 and -5 would be 4. This is kinda easy.

Step-by-step explanation:

4 0

3 years ago

Help, Solve for y 7=35y

Lapatulllka [165]

Answer:

0.2 = y

Step-by-step explanation: You have to isolate y

35 35

0.2 = y

RECHECK:

7 = 35y

7 = 35(0.2)

7 = 7

YES, this is a true statement.

Hope this helps you!!! :)

4 0

3 years ago

Jack bought five bracelets and one necklace

NikAS [45]

Answer:

Jack: 4 x 6 = 24

Jill: 5.4 x 10 = 54

Step-by-step explanation:

Jack:

5 + 1 = 6

24 ÷ 6 = 4

4 = $4 per item

Jill:

6 + 4 = 10

54 ÷ 10 = 5.4

5.4 = $5.4

B: 11

N: 5

Hope this helps!

6 0

3 years ago

Find the sum of the geometric series 512+256+ . . .+4

mario62 [17]

$\bf 512~~,~~\stackrel{512\cdot \frac{1}{2}}{256}~~,~~...4$

so, as you can see above, the common ratio r = 1/2, now, what term is +4 anyway?

$\bf n^{th}\textit{ term of a geometric sequence}\\\\a_n=a_1\cdot r^{n-1}\qquad \begin{cases}n=n^{th}\ term\\a_1=\textit{first term's value}\\r=\textit{common ratio}\\----------\\r=\frac{1}{2}\\a_1=512\\a_n=+4\end{cases}$

$\bf 4=512\left( \cfrac{1}{2} \right)^{n-1}\implies \cfrac{4}{512}=\left( \cfrac{1}{2} \right)^{n-1}\\\\\\\cfrac{1}{128}=\left( \cfrac{1}{2} \right)^{n-1}\implies \cfrac{1}{2^7}=\left( \cfrac{1}{2} \right)^{n-1}\implies 2^{-7}=\left( 2^{-1}\right)^{n-1}\\\\\\(2^{-1})^7=(2^{-1})^{n-1}\implies 7=n-1\implies \boxed{8=n}$

so is the 8th term, then, let's find the Sum of the first 8 terms.

$\bf \qquad \qquad \textit{sum of a finite geometric sequence}\\\\S_n=\sum\limits_{i=1}^{n}\ a_1\cdot r^{i-1}\implies S_n=a_1\left( \cfrac{1-r^n}{1-r} \right)\quad \begin{cases}n=n^{th}\ term\\a_1=\textit{first term's value}\\r=\textit{common ratio}\\----------\\r=\frac{1}{2}\\a_1=512\\n=8\end{cases}$

$\bf S_8=512\left[ \cfrac{1-\left( \frac{1}{2} \right)^8}{1-\frac{1}{2}} \right]\implies S_8=512\left(\cfrac{1-\frac{1}{256}}{\frac{1}{2}} \right)\implies S_8=512\left(\cfrac{\frac{255}{256}}{\frac{1}{2}} \right)\\\\\\S_8=512\cdot \cfrac{255}{128}\implies S_8=1020$

7 0

4 years ago

What is the answer in simplest form?

Arte-miy333 [17]

Answer:

P(Selecting a student aged 12)= (13/27)

Step-by-step explanation:

first find the value of (e), by getting the value of (b). check no.2.

8 0

2 years ago