All categories

2 years ago

Given a linear function y =23x+2, which two points make the line?

Mathematics

1 answer:

timurjin [86]2 years ago

8 0

Answer:

(0, 2) and (3, 4)

Step-by-step explanation:

The equation is in slope-intercept form:

y = mx +b . . . . . a line with slope m and y-intercept b

So, you know immediately that the y-intercept is (0, 2). This matches only one answer choice.

(0, 2) and (3, 4)

You might be interested in

Solve y ' ' + 4 y = 0 , y ( 0 ) = 2 , y ' ( 0 ) = 2 The resulting oscillation will have Amplitude: Period: If your solution is A

Vlad [161]

Answer:

$y(x)=sin(2x)+2cos(2x)$

Step-by-step explanation:

$y''+4y=0$

This is a homogeneous linear equation. So, assume a solution will be proportional to:

$e^{\lambda x} \\\\for\hspace{3}some\hspace{3}constant\hspace{3}\lambda$

Now, substitute $y(x)=e^{\lambda x}$ into the differential equation:

$\frac{d^2}{dx^2} (e^{\lambda x} ) +4e^{\lambda x} =0$

Using the characteristic equation:

$\lambda ^2 e^{\lambda x} + 4e^{\lambda x} =0$

Factor out $e^{\lambda x}$

$e^{\lambda x}(\lambda ^2 +4) =0$

Where:

$e^{\lambda x} \neq 0\\\\for\hspace{3}any\hspace{3}\lambda$

Therefore the zeros must come from the polynomial:

$\lambda^2+4 =0$

Solving for $\lambda$ :

$\lambda =\pm2i$

These roots give the next solutions:

$y_1(x)=c_1 e^{2ix} \\\\and\\\\y_2(x)=c_2 e^{-2ix}$

Where $c_1$ and $c_2$ are arbitrary constants. Now, the general solution is the sum of the previous solutions:

$y(x)=c_1 e^{2ix} +c_2 e^{-2ix}$

Using Euler's identity:

$e^{\alpha +i\beta} =e^{\alpha} cos(\beta)+ie^{\alpha} sin(\beta)$

$y(x)=c_1 (cos(2x)+isin(2x))+c_2(cos(2x)-isin(2x))\\\\Regroup\\\\y(x)=(c_1+c_2)cos(2x) +i(c_1-c_2)sin(2x)\\$

Redefine:

$i(c_1-c_2)=c_1\\\\c_1+c_2=c_2$

Since these are arbitrary constants

$y(x)=c_1sin(2x)+c_2cos(2x)$

Now, let's find its derivative in order to find $c_1$ and $c_2$

$y'(x)=2c_1 cos(2x)-2c_2sin(2x)$

Evaluating $y(0)=2$ :

$y(0)=2=c_1sin(0)+c_2cos(0)\\\\2=c_2$

Evaluating $y'(0)=2$ :

$y'(0)=2=2c_1cos(0)-2c_2sin(0)\\\\2=2c_1\\\\c_1=1$

Finally, the solution is given by:

$y(x)=sin(2x)+2cos(2x)$

5 0

3 years ago

N the triangle below, what is the value<br> of x?

Elenna [48]

Answer:

Step-by-step explanation:

can u help me

What is the volume of a square-based pyramid with a base length of 5 ft and a height of 24 ft?

Enter your answer in the box.

answer asap

ft³

5 0

3 years ago

Help pls i really need help !!!

bixtya [17]

Answer:

that a tough one i'm guessing its longitude and latitude why not tell your teacher!

5 0

2 years ago

Find the inverse of f(x)=4x+3

zhuklara [117]

$f(x) = 4x+3\\\\\text{Write f(x) as y = 4x+3}\\\\\text{Replace x with y,}\\\\x =4y +3\\\\\text{Solve for y:}\\\\ \implies x =4y+3\\\\\implies 4y = x-3 \\\\\implies y =\dfrac{x-3}4\\\\\implies f^{-1} (x) = \dfrac{x-3}4\\\\\text{This is the inverse of f(x)}$

4 0

2 years ago

A student answers a multiple-choice examination question that offers four possible answers. Suppose the probability that the stu

Salsk061 [2.6K]

Answer:

The value is $P(A | W) = 0.941$

Step-by-step explanation:

From the question we are told that

The probability that the student knows the answer to the question is $P(A) = 0.8$

The probability that that the student will guess is $P(G) = 0.2$

The probability that that the student get the correct answer given that the student guessed is $P(W /G) = 0.25$

Here W denotes that the student gets the correct answer

Generally it a certain fact that if the student knows the answer he would get it correctly

So the probability the the student got answer given that he knows it is

$P(W | A) = 1$

Generally from Bayes theorem we can mathematically evaluate the probability that the student knows the answer given that he got it correctly as follows

$P(A | W) = \frac{ P(A) * P(W | A )}{ P(A) * P(W | A) + P(G) * P(W| G)}$

=> $P(A | W) = \frac{ 0.8 * 1}{ 0.8 * 1+ 0.2 * 0.25}$

=> $P(A | W) = 0.941$

4 0

3 years ago