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3 years ago

(0,1),(2,5),(3,7) in an equation

Mathematics

1 answer:

12345 [234]3 years ago

7 0

The equation that gives the coordinates (0,1), (2,5), (3,7) is y =2x + 1.

Step-by-step explanation:

Step 1; We need to determine the equation relating the x to the f(x) values from the given coordinates. y is the dependent value whereas x is the independent value i.e. y's value depends on x's value.

Step 2; If we multiply the x value with 2 and add the resulting answer with 1 we get the y value.

y = 2x + 1 is the equation that relates the values in the table.

Step 3; Now we substitute the values in the equation to see if it's correct.

For x = 0, y = 2(0) + 1 = 0 + 1 = 1,

For x = 2, y = 2(2) + 1 = 4 + 1 = 5,

For x = 3, y = 2(3) + 1 = 6 + 1 = 7.

So the equation that gives the coordinates (0,1), (2,5), (3,7) is y =2x + 1.

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Which statement best describes f(x)= -2 √x-7 +1 –6 is in the domain of f(x) but not in the range of f(x). –6 is not in the domai

Archy [21]

Answer:

B. -6 does not belong to the domain but belongs to the range of f(x).

Step-by-step explanation:

We have the function, $f(x)=-2\sqrt{x-7}+1$ .

So, the domain of the function is obtained when $x-7\geq 0$ i.e. $x\geq 7$

That is, the domain is {x | x≥ 7}.

Now as we have,

$x\geq 7$ → $x-7\geq 0$ → $\sqrt{x-7} \geq 0$ → $-2\sqrt{x-7} \leq 0$ → $-2\sqrt{x-7}+1 \leq 1$ .

That is, $f(x)\leq 1$

Thus, the range of the function f(x) is {y | y≤ 1}.

Thus, we can see that,

-6 does not belong to the domain but belongs to the range of f(x).

5 0

4 years ago

Find a solution x = x(t) of the equation x′ + 2x = t2 + 4t + 7 in the form of a quadratic function of t, that is, of the form x(

Temka [501]

The particular quadratic solution to the ODE is found as follows:

$x=at^2+bt+c$
$x'=2at+b$

$(2at+b)+2(at^2+bt+c)=t^2+4t+7$
$2at^2+(2a+2b)t+(b+2c)=t^2+4t+7$

$\begin{cases}2a=1\\2(a+b)=4\\b+2c=7\end{cases}\implies a=\dfrac12,b=\dfrac32,c=\dfrac{11}4$

Note that there's also the fundamental solution to account for, which is obtained from the characteristic equation for the ODE:

$x'+2x=0\implies r+2=0\implies r=-2$

so that $x_c=Ce^{-2t}$ is a characteristic solution to the ODE, and the general solution would be

$x=Ce^{-2t}+\dfrac{t^2}2+\dfrac{3t}2+\dfrac{11}4$

4 0

4 years ago

List x1, x2, x3, x4 where xi is the midpoint endpoint of the five equal intervals used to estimate the area under the curve of f

Amanda [17]

Answer:

$\bf x_1 = 2\\x_2 = 4\\x_3=6\\x_4=8$

Step-by-step explanation:

The given interval : x = 0 to x = 10

Length of interval = 10 - 0

= 10

$\text{Now, each }x_i \text{ is midpoint and endpoint of the five equal intervals}$

⇒ Number of equal intervals = 5

$\textbf{Length of each interval = }\frac{10}{5}$

$\textbf{Therefore, }\bf x_1 = 0 + 2 = 2\\x_2 = 2 +2 =4\\x_3=4+2=6\\x_4=6+2=8$

3 0

3 years ago

What is the equation in standard form?

xeze [42]

Come on you know this! Don’t give up

7 0

3 years ago

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Dima020 [189]

Answer:

The binomial theorem allows you to write out the expansion of your polynomial immediately. (I feel like this is good enough)

Step-by-step explanation:

<em>It also allows you to answer such questions as:</em> "What is the coefficient of x20 in (1+x)100?" Its generalization to non-integer exponents allows you to get the expansion of (1−x)−1/2. There are all sorts of reasons.

3 0

3 years ago