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3 years ago

Let f(x) = 3x+5 and g(x) = x^2. Find g(x)/f(x) and state its domain

Mathematics

2 answers:

lianna [129]3 years ago

7 0

Answer:

1/x-2; domain is the set of all real numbers except 2

Step-by-step explanation:

rodikova [14]3 years ago

3 0

Answer:

All real x except x = -5/3.

Step-by-step explanation:

g(x) / f(x)

= x^2/ (3x + 5)

We can't have a zero denominator so the domain is

All real x except x = -5/3.

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8) The height of a building h varies directly as the length and inversely as the width, if h = 25m when l = 10m and w = 5m, find

shtirl [24]

Let h,l, and w represent the height, length, and width of the building respectively

Then

$\begin{gathered} h\text{ = }\frac{kl}{w} \\ \text{where k is the constant of proportionality} \end{gathered}$ $\begin{gathered} \Rightarrow k=\frac{hw}{l} \\ \Rightarrow k=\frac{25\times5}{10}=12.5 \end{gathered}$ $\Rightarrow h=\frac{12.5l}{w}$

The new value of h = 50m, but l remains the same.

That is l = 10m

Therefore

$\begin{gathered} \frac{50}{1}=\frac{12.5\times10}{w} \\ \Rightarrow\frac{50}{1}=\frac{125}{w} \\ \text{Cross multiplying, we have} \\ 50w\text{ = 125} \\ \Rightarrow\text{ w=}\frac{125}{50}=2.5 \end{gathered}$

Hence, the width is 2.5m

8 0

1 year ago

How do you break this down percent proportion showing work withIs/of=%/100

bixtya [17]

20% of 56

Let the number be x

Solving

$\begin{gathered} \frac{x}{56}=\frac{20}{100} \\ \Rightarrow x=11.2 \end{gathered}$

The answer is 11.2.

6 0

1 year ago

The difference between the product of four and a number and six

Olin [163]

Answer- 4x-6
explain- i got it right

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3 years ago

state the domain, the range, and the intervals on which function is increasing, decreasing, or constant in interval notation

erma4kov [3.2K]

Answer:

domain (-∞, ∞)
range (-∞, 4]
increasing (-∞, 0)
decreasing (0, ∞)
constant (only at x=0, not on any interval)

Step-by-step explanation:

The graph is of the equation y = -x^2 +4. It is a polynomial of even degree, so has a domain of all real numbers: (-∞, ∞).

The vertical extent of the graph includes y=4 and all numbers less than that:

range: (-∞, 4]

The graph is increasing to the left of its vertex at x=0, decreasing to the right.

increasing (-∞, 0); decreasing (0, ∞)

There is no interval on which the function is constant. It has a horizontal tangent at x=0, but a single point does not constitute an interval.

8 0

3 years ago

How can I get help with linear equations with fractions? I dont remember how to solve

xz_007 [3.2K]

Answer:

to find the missing number, compare both sides of the equation. If the variable terms are the same and the constant terms are different, then the equation has no solutions.

Step-by-step explanation:

to find the missing number, compare both sides of the equation. If the variable terms are the same and the constant terms are different, then the equation has no solutions.

3 0

3 years ago