Simplifying entire surds 4√48

Which set of ordered pairs represents a function?

jasenka [17]

Answer:

The final set of ordered pairs represents a function.

Step-by-step explanation:

Each X value corresponds to exactly one y- value. Essentially, none of the x values are the same in the final set.

8 0

2 years ago

Kent has paid a total of $589 For internet service. Each month of service cost $19. How many months, m, of internet service has

max2010maxim [7]

Answer:

31 months

Step-by-step explanation:

8 0

2 years ago

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Rewrite the statement in mathematical notation. (Let y be the distance from the top of the ladder to the floor, x be the distanc

In-s [12.5K]

Answer:

$\frac{dy}{dt}=\frac{6y}{x}\text{ ft per sec}$

Step-by-step explanation:

Let L be the length of the ladder,

Given,

x = the distance from the base of the ladder to the wall, and t be time.

y = distance from the base of the ladder to the wall,

So, by the Pythagoras theorem,

$L^2 = y^2 + x^2$

$\implies L = \sqrt{y^2 + x^2}$ ,

Differentiating with respect to time (t),

$\frac{dL}{dt}=\frac{d}{dt}(\sqrt{x^2 + y^2})$

$=\frac{1}{2\sqrt{x^2 + y^2}}\frac{d}{dt}(x^2 + y^2)$

$=\frac{1}{2\sqrt{x^2 + y^2}}(2x\frac{dx}{dt}+2y\frac{dy}{dt})$

$=\frac{1}{\sqrt{x^2 +y^2}}(x\frac{dx}{dt}+y\frac{dy}{dt})$

Here,

$\frac{dy}{dt}=-6\text{ ft per sec}$

Also, $\frac{dL}{dt} = 0$ ( Ladder length = constant ),

$\implies \frac{1}{\sqrt{x^2 +y^2}}(x(-6)+y\frac{dy}{dt})=0$

$-6x + y\frac{dy}{dt}=0$

$y\frac{dy}{dt}=6x$

$\implies \frac{dy}{dt}=\frac{6y}{x}\text{ ft per sec}$

Which is the required notation.

8 0

3 years ago

Greg goes fishing every day for a week. On the first day he catches seven fish and each

Oliga [24]

so first day and so on

7, 10, 13,....

as you can see it's an arithmetic progression

so sum for nth term= n/2 { 2a + (n-1) d}

it's the sum of the 7th term

so

7/2 { 7 ×2 + ( 7-1) 3}

7/2 × 32

7× 16

112 fishes

6 0

3 years ago

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A complete graph of the polynomial function f is provided. Use your knowledge of the domain, range, behavior at each x intercept

Papessa [141]

The graph represents a polynomial graph, and the equation of the polynomial graph is f(x) = -(x + 5)³(x - 2)²

<h3>How to determine the equation?</h3>

From the graph, we have the following observations:

The graph has a turning point at x = 2
The graph changes the factor of its direction at x = -5

This means that the graph has a multiplicity of 2 at x = 2 and a multiplicity of 3 at x = -5

So, we have:

f(x) = a(x + 5)³(x - 2)²

The curve is inverted,

This means that a < 0

Assume a = -1.

Then, we have:

f(x) = -(x + 5)³(x - 2)²

Hence, the equation of the polynomial graph is f(x) = -(x + 5)³(x - 2)²