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2 years ago

What is the equation of the line through the origin and (2,5)?

Mathematics

1 answer:

Anni [7]2 years ago

4 0

Answer:

Step-by-step explanation:

We can just use the slope equation here.

$m=\frac{y2-y1}{x2-x1}$

The two given points are (0,0) and (2,5)

$m=\frac{5-0}{2-0}=\frac{5}{2}$

Since the line intersects the y-axis at the origin, the y-intercept is 0.

So, our slope-intercept equation is $y=\frac{5}{2}x$ .

Hope this helps!

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An investment banker deposited $50,000 in an account earning a nominal 6% per year compounded continuously. How much was in the

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The amount in the account at the end of three years will be $59,861.

Step-by-step explanation:

The formula to compute the amount at the end of t years, compounded continuously is:

$A=P\times e^{t\times i}$

Here,

A = Amount at the end

P = Principal amount

i = interest rate

t = number of years.

It is provided that:

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Compute the amount in the account at the end of three years as follows:

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3 years ago

This equation represents an exponential function that passes through the point (2, 80).

miss Akunina [59]

we know that

If the point belongs to the graph, then the point must satisfy the equation

we will proceed to verify each case

case A.) $f(x)=4(x^{5})$

The point is $(2,80)$

Verify if the point satisfy the equation

For $x=2$ find the value of y in the equation and compare with the y-coordinate of the point

$f(2)=4(2^{5})$

$f(2)=128$

$128\neq 80$

therefore

the equation $f(x)=4(x^{5})$ not passes through the point $(2,80)$

case B.) $f(x)=5(x^{4})$

The point is $(2,80)$

Verify if the point satisfy the equation

For $x=2$ find the value of y in the equation and compare with the y-coordinate of the point

$f(2)=5(2^{4})$

$f(2)=80$

$80=80$

therefore

the equation $f(x)=5(x^{4})$ passes through the point $(2,80)$

case C.) $f(x)=4(5^{x})$

The point is $(2,80)$

Verify if the point satisfy the equation

For $x=2$ find the value of y in the equation and compare with the y-coordinate of the point

$f(2)=4(5^{2})$

$f(2)=100$

$100\neq 80$

therefore

the equation $f(x)=4(5^{x})$ not passes through the point $(2,80)$

case D.) $f(x)=5(4^{x})$

The point is $(2,80)$

Verify if the point satisfy the equation

For $x=2$ find the value of y in the equation and compare with the y-coordinate of the point

$f(2)=5(4^{2})$

$f(2)=80$

$80=80$

therefore

the equation $f(x)=5(4^{x})$ passes through the point $(2,80)$

therefore

the answer is

$f(x)=5(x^{4})$

$f(x)=5(4^{x})$

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