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3 years ago

Write an equation of a line parallel to y=10x+6 and going through point (2,-4)

Mathematics

1 answer:

nadya68 [22]3 years ago

7 0

Answer:

Y= 10x-24 would be parralel to y=10x+6

Step-by-step explanation:

well a parralel line has to have the same slope and a different y-intercept.

To find the y-intercept the x has to be exactly 0.

So we have (2,-4)

The slope is 10/1 which is 10y and 1 x which in an ordered park would be Add 1 x and add 10 y. But we’re trying to get x to be 0 to find the y-intercept.

So subtract 1 x and subtract 10y

2-1=1

-4-10=-14

(1, -14)

1-1=0

-14-10=-24

(0, -24)

THe y-intercept is -24 and w have the slope since its the same thing So

y=10x-24 is the equation

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3 years ago

The fish population of Lake Collins is decreasing at a rate of 5% per year. In 2004 there were about 1,350 fish. Write an expone

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Answer:

Part 1) The exponential function is equal to $y=1,350(0.95)^{x}$

Part 2) The population in 2010 was $992\ fish$

Step-by-step explanation:

Part 1) Write an exponential decay function that models this situation

we know that

In this problem we have a exponential function of the form

$y=a(b)^{x}$

where

y ----> the fish population of Lake Collins since 2004

x ----> the time in years

a is the initial value

b is the base

we have

$a=1,350\ fish$

$b=(100\%-5\%)=95\%=0.95$

substitute

$y=1,350(0.95)^{x}$ ----> exponential function that represent this scenario

Part 2) Find the population in 2010

we have

$y=1,350(0.95)^{x}$

For $x=(2010-2004)=6\ years$

substitute

$y=1,350(0.95)^{6}=992\ fish$

7 0

3 years ago

What are the coordinates of the point (1, –6) after a counter clockwise rotation of 90° about the origin?

IgorLugansk [536]

(-6 ,-1) is the correct answer

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3 years ago

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Now there is a square city of unknown size with a gate at the center of each side. There is a tree 20 b from the north gate. Tha

Brums [2.3K]

Answer:

The length of each side of the city is 250b

Step-by-step explanation:

Given

$a = 20$ --- tree distance from north gate

$b =14$ --- movement from south gate

$c = 1775$ --- movement in west direction from (b)

See attachment for illustration

Required

Find x

To do this, we have:

$\triangle ADE \sim \triangle ACB$ --- similar triangles

So, we have the following equivalent ratios

$AE:DE = AB:CB$

Where:

$AE = 20\\ DE = x/2 \\ AB = 20 + x + 14 \\ CB = 1775$

Substitute these in the above equation

$20:x/2 = 20 + x + 14: 1775$

$20:x/2 = x + 34: 1775$

Express as fraction

$\frac{20}{x/2} = \frac{x + 34}{1775}$

$\frac{40}{x} = \frac{x + 34}{1775}$

Cross multiply

$x *(x + 34) = 1775 * 40$

Open bracket

$x^2 + 34x = 71000$

Rewrite as:

$x^2 + 34x - 71000 = 0$

Expand

$x^2 + 284x -250x - 71000 = 0$

Factorize

$x(x + 284) -250(x + 284)= 0$

Factor out x + 284

$(x - 250)(x + 284)= 0$

Split

$x - 250 = 0 \ or\ x + 284= 0$

Solve for x

$x = 250 \ or\ x =- 284$

x can't be negative;

So:

$x = 250$

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3 years ago

Use the explicit

Leno4ka [110]

Answer:913

Step-by-step explanation:

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3 years ago

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