A line passing through the origin intersects the point -8 -5 what is the slope of the line

Write the formula for a function d(x) that describes the distance between the point P and a point (x,y) on the line. You final a

vlabodo [156]

Answer:

d(x) = √[(x - 2)² + (3x - 1)²]

Step-by-step explanation:

The distance between two points with coordinates (x₁, y₁) and (x₂, y₂) is given as

d = √[(x₂ - x₁)² + (y₂ - y₁)²]

So, the distance between point (2,0) and a point (x,y)

d = √[(x - 2)² + (y - 0)²]

d = √[(x - 2)² + (y)²]

But the point (x,y) is on the line y = 3x - 1

We can substitute for y in the distance between points equation.

d(x) = √[(x - 2)² + (3x - 1)²]

QED!

6 0

2 years ago

Jarvis invested some money at 6% interest. Jarvis also invested $58 more than 3 times that amount at 9%. How much is invested at

DerKrebs [107]

9514 1404 393

Answer:

$3309 at 6%
$9985 at 9%

Step-by-step explanation:

Let x and y represent amounts invested at 6% and 9%, respectively.

y = 3x +58 . . . . . . . the amount invested at 9%

0.06x +0.09y = 1097.19 . . . . . . total interest earned

__

Substituting for y, we have ...

0.06x +0.09(3x +58) = 1097.19

0.33x + 5.22 = 1097.19 . . . . . . . . . simplify

0.33x = 1091.97 . . . . . . . . . . . . subtract 5.22

x = 3309 . . . . . . . . . . . . . . . . divide by 0.33

y = 3(3309) +58 = 9985

$3309 is invested at 6%; $9985 is invested at 9%.

8 0

3 years ago

Which pair of funtions is not a pair of inverse functions? please help!!

antiseptic1488 [7]

Answer:

$f(x)=\frac{x}{x+20} , g(x)=\frac{20x}{x-1}$

Step-by-step explanation:

we know that

To find the inverse of a function, exchange variables x for y and y for x. Then clear the y-variable to get the inverse function.

we will proceed to verify each case to determine the solution of the problem

case A) $f(x)=\frac{x+1}{6} , g(x)=6x-1$

Find the inverse of f(x)

Let

y=f(x)

Exchange variables x for y and y for x

$x=\frac{y+1}{6}$

Isolate the variable y

$6x=y+1$

$y=6x-1$

Let

$f^{-1}(x)=y$

$f^{-1}(x)=6x-1$

therefore

f(x) and g(x) are inverse functions

case B) $f(x)=\frac{x-4}{19} , g(x)=19x+4$

Find the inverse of f(x)

Let

y=f(x)

Exchange variables x for y and y for x

$x=\frac{y-4}{19}$

Isolate the variable y

$19x=y-4$

$y=19x+4$

Let

$f^{-1}(x)=y$

$f^{-1}(x)=19x+4$

therefore

f(x) and g(x) are inverse functions

case C) $f(x)=x^{5}, g(x)=\sqrt[5]{x}$

Find the inverse of f(x)

Let

y=f(x)

Exchange variables x for y and y for x

$x=y^{5}$

Isolate the variable y

fifth root both members

$y=\sqrt[5]{x}$

Let

$f^{-1}(x)=y$

$f^{-1}(x)=\sqrt[5]{x}$

therefore

f(x) and g(x) are inverse functions

case D) $f(x)=\frac{x}{x+20} , g(x)=\frac{20x}{x-1}$

Find the inverse of f(x)

Let

y=f(x)

Exchange variables x for y and y for x

$x=\frac{y}{y+20}$

Isolate the variable y

$x(y+20)=y$

$xy+20x=y$

$y-xy=20x$

$y(1-x)=20x$

$y=20x/(1-x)$

Let

$f^{-1}(x)=y$

$f^{-1}(x)=20x/(1-x)$

$\frac{20x}{1-x}\neq \frac{20x}{x-1}$

therefore

f(x) and g(x) is not a pair of inverse functions

7 0

2 years ago

Read 2 more answers

Which postulate proves the two triangles are congruent?

sammy [17]

Answer:

AAS

Step-by-step explanation:

because here it is given that two angle are

equal

and a side is common between both traingle

so, both traingle are congruent by

AAS

hope it helps

5 0

2 years ago

What is 25% of 40? Show Work please

goldenfox [79]

25% = 1/4

1/4(40)

Divide 40 by 4 to remove the 1/4

10

25% of 40 is 10.

7 0

3 years ago

Read 2 more answers