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3 years ago

Let f(x) = -6x + 3 and g(x) = 5x + 4. Find fg and state its domain.

Mathematics

1 answer:

r-ruslan [8.4K]3 years ago

7 0

Answer:

$f(g(x))=-30x-21$

The domain is all real numbers

Step-by-step explanation:

we have

$f(x)=-6x+3$

$g(x)=5x+4$

we know that

$(fog)(x)=f(g(x))$

In the function f(x) substitute the variable x by the function g(x)

$f(g(x))=-6(5x+4)+3$

$f(g(x))=-30x-24+3$

$f(g(x))=-30x-21$

This is a linear function (equation of a line)

The domain is all real numbers

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Katie wants to know how much she needs to deposit into a two year CD account in order to earn $100 in simple interest. The accou

sergey [27]

Answer:

To obtain $ 100 in simple interest with a rate of 1.5%, Katie must deposit $ 6,666.66.

Step-by-step explanation:

Given that Katie wants to know how much she needs to deposit into a two year CD account in order to earn $ 100 in simple interest, knowing that the account currently has a 1.5% interest rate, the following calculation must be performed:

X x 0.015 = 100

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X = 6,666.66

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Thus, to obtain $ 100 in simple interest with a rate of 1.5%, Katie must deposit $ 6,666.66.

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2 years ago

Which equation below represents a line with a slope of - 2/3 that passes through the point (-4.5 , 10)?

Lostsunrise [7]

Answer:

Option C

Step-by-step explanation:

If a line passes through a point, then that point is called a solution to the line's equation. Substituting the x and y values of that solution into the equation will give a true statement. So, to find out which option is correct, we can substitute the x and y values of (-4.5, 10) into each equation and see if the result is a true statement.

Let's try this with option C. To make things easier, convert -4.5 into decimal form: $-4\frac{1}{2}$ . Substitute $-4\frac{1}{2}$ for x and 10 for y in the equation, then solve:

$y = -\frac{2}{3} x+7\\\\10 = -\frac{2}{3} (-4\frac{1}{2} )+7\\10 = -\frac{2}{3} (-\frac{9}{2})+7\\10 = 3+7\\10 = 10$

10 does equal 10, so this is a true statement. Option C is the right answer.

8 0

2 years ago

A 10 2/3 inch long pipe is cut into 8 equal length pieces, how long is each piece

storchak [24]

Answer:

$\frac{4}{3}$ inches

Step-by-step explanation:

The total length of pipe is 10 2/3rd inches

It is cut into 8 equal pieces

We need to divide total length by 8 to get length of each piece. First, we have to convert mixed number (total length) to improper fraction by using formula shown below:

$a\frac{b}{c}=\frac{(a*c)+b}{c}$