Write two functions f(x) and g(x) for which [f∘g](x)

Which best describes the function represented by the table?

trasher [3.6K]

Answer:

Option B is correct.

direct variation; k = 5/2

Step-by-step explanation:

The Direct variation says:

$y \propto x$

then the equation is of the form: $y = kx$ ......[1] where k is the constant of variation.

From the given table:

Consider x = -2 and y = -5

Substitute these in [1] to solve for k;

$-5 = -2k$

or

5 = 2k

Divide both sides by 2 we get;

$k = \frac{5}{2}$

⇒ the equation becomes: $y = \frac{5}{2}x$

Check:

Take x = 4 and y = 10;

$y = \frac{5}{2}x$

$10 = \frac{5}{2} \times 4$

$10 = 5 \times 2$

10 = 10 True

Therefore, the direct variation ; $k = \frac{5}{2}$ best describe the function represented by the table

8 0

4 years ago

F(n) = 45 • (4/5) ^n-1

tatiyna

Evaluate answer is 9 • 4 ^n-1

7 0

3 years ago

Please help !!! I can’t solve this The teacher doesn’t teach well

Scorpion4ik [409]

So here are 4 rules when it comes to exponents:

When you raise a power to a power, you really just multiply the exponents: $(x^m)^n=x^{m*n}$
When you multiply 2 exponents of the same base, you add the exponents together: $x^m*x^n=x^{m+n}$
When you divide 2 exponents of the same base, you subtract the exponents: $\frac{x^m}{x^n}=x^{m-n}$
To convert a negative exponent into a positive one, flip it to its reciprocal: $x^{-m}=\frac{1}{x^m}\\ \frac{1}{x^{-m}}=\frac{x^{m}}{1}=x^m$

Part A:

$\frac{2x^3y^3}{4y^2}=\frac{1}{2}x^{3-0}y^{3-2}=\frac{1}{2}x^3y$

Part B:

$(\frac{x^{-8}}{y^{11}})^{-2}=\frac{x^{-8*-2}}{y^{11*-2}}=\frac{x^{16}}{y^{-22}}=\frac{x^{16}y^{22}}{1}=x^{16}y^{22}$

Part C:

$\frac{(2x^3)(x^4)^2}{8x^{11}}=\frac{(2x^3)(x^{4*2})}{8x^{11}}=\frac{(2x^3)(x^8)}{8x^{11}}=\frac{2x^{3+8}}{8x^{11}}=\frac{2x^{11}}{8x^{11}}=\frac{1}{4}x^{11-11}=\frac{1}{4}x^0=\frac{1}{4}$

5 0

3 years ago

one of the fastest recorded speeds of a turtle while swimming is 9m/s. Approximately, what is this speed in kilometers per hour?

Alex73 [517]

$32.4\frac{km}{h}$

This problem can be solved by using unit conversion. The trutle swimming at $9\frac{m}{s}$ , to calculate its speed in $\frac{km}{h}$ :

We have to convert meter to kilometer, and second to hour as follow:

$9\frac{m}{s}*\frac{1km}{1000m}*\frac{3600s}{1h}\\9*\frac{3600km}{1000h}\\32.4\frac{km}{h}$

4 0

3 years ago

Tom spends 30% of his monthly budget on rent. His total monthly budget is $3,000. How much does Tom spend on rent?

WINSTONCH [101]

The simplest way to do this is (in my opinion; but it is not the only way) to find then answer is to find 10% of his budget and multiply by three. Since he has a budget of $3000, 10% is $300. Multiply it by three to get $900, how much he spends on rent.

6 0

3 years ago

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