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insens350 [35]

Answer:

Question 4: $y=\displaystyle -\frac{4}{5}x$

Question 5: $y=-5x-3$

Step-by-step explanation:

Hi there!

Linear equations are typically organized in slope-intercept form: $y=mx+b$ where m is the slope of the line and b is the y-intercept (the y-coordinate of the point where the line crosses the y-axis).

Question 4

1) Determine the slope (m)

$\displaystyle m=\frac{y_2-y_1}{x_2-x_1}$ where two points that pass through the line are $(x_1,y_1)$ and $(x_2,y_2)$

In the graph, two easy-to-identify points on the line are (-5,4) and (5,-4). Plug these into the equation:

$\displaystyle m=\frac{-4-4}{5-(-5)}\\\\\displaystyle m=\frac{-4-4}{5+5}\\\\\displaystyle m=\frac{-8}{10}\\\\\displaystyle m=-\frac{4}{5}$

Therefore, the slope of the line is $\displaystyle -\frac{4}{5}$ . Plug this into $y=mx+b$ as the slope (m):

$y=\displaystyle -\frac{4}{5}x+b$

2) Determine the y-intercept (b)

On the graph, we can see that the line crosses the y-axis when y is 0. Therefore, the y-intercept (b) is 0. Plug this into $y=\displaystyle -\frac{4}{5}x+b$ :

$y=\displaystyle -\frac{4}{5}x+0\\\\y=\displaystyle -\frac{4}{5}x$

Question 5

1) Determine the slope (m)

$\displaystyle m=\frac{y_2-y_1}{x_2-x_1}$

Two easy-to-identify points are (-1,2) and (0,-3). Plug these into the equation:

$\displaystyle m=\frac{-3-2}{0-(-1)}\\\\\displaystyle m=\frac{-3-2}{0+1}\\\\\displaystyle m=\frac{-5}{1}\\\\m=-5$

Therefore, the slope is -5. Plug this into $y=mx+b$ :

$y=-5x+b$

2) Determine the y-intercept (b)

On the graph, we can see that the line crosses the y-axis at the point (0,-3). The y-coordinate of this point is -3. Therefore, the y-intercept (b) is -3. Plug this into $y=-5x+b$ :

$y=-5x+(-3)\\y=-5x-3$

I hope this helps!

8 0

3 years ago

Write and equation of the translated or rotated graph in general form (picture below)

WINSTONCH [101]

Answer:

The answer is hyperbola; (x')² - (y')² - 16 = 0 ⇒ answer (a)

Step-by-step explanation:

* At first lets talk about the general form of the conic equation

- Ax² + Bxy + Cy² + Dx + Ey + F = 0

∵ B² - 4AC < 0 , if a conic exists, it will be either a circle or an ellipse.

∵ B² - 4AC = 0 , if a conic exists, it will be a parabola.

∵ B² - 4AC > 0 , if a conic exists, it will be a hyperbola.

* Now we will study our equation:

xy = -8

∵ A = 0 , B = 1 , C = 0

∴ B² - 4 AC = (1)² - 4(0)(0) = 1 > 0

∴ B² - 4AC > 0

∴ The graph is hyperbola

* The equation xy = -8

∵ We have term xy that means we rotated the graph about

the origin by angle Ф

∵ Ф = π/4

∴ We rotated the x-axis and the y-axis by angle π/4

* That means the point (x' , y') it was point (x , y)

- Where x' = xcosФ - ysinФ and y' = xsinФ + ycosФ

∴ x' = xcos(π/4) - ysin(π/4) , y' = xsin(π/4) + ycos(π/4)

∴ x' = x/√2 - y/√2 = (x - y)/√2

∴ y' = x/√2 + y/√2 = (x + y)/√2

* Lets substitute x' and y' in the 1st answer

∵ (x')² - (y')² - 16 = 0

∴ $(\frac{x-y}{\sqrt{2}})^{2}-(\frac{x+y}{\sqrt{2}})^{2}=$

( $\frac{x^{2}-2xy+y^{2}}{2})-(\frac{x^{2}+2xy+y^{2}}{2})-16=0$

* Lets open the bracket

∴ $\frac{x^{2}-2xy+y^{2}-x^{2}-2xy-y^{2}}{2}-16=0$

* Lets add the like terms

∴ $\frac{-4xy}{2}-16=0$

* Simplify the fraction

∴ -2xy - 16 = 0

* Divide the equation by -2

∴ xy + 8 = 0

∴ xy = -8 ⇒ our equation

∴ Answer (a) is our answer

∴ The answer is hyperbola; (x')² - (y')² - 16 = 0

* Look at the graph:

- The black is the equation (x')² - (y')² - 16 = 0

- The purple is the equation xy = -8

- The red line is x'

- The blue line is y'

6 0

3 years ago

Read 2 more answers

A drug is eliminated from the body through urine. Suppose that for a dose of 10 milligrams, the amount A(t) remaining in the bod

adell [148]

Answer: a - 4.512 hours

b - 1.94 hours

Step-by-step explanation:

Given,

a) A(t) = 10 (0.7)^t

To determine when 2mg is left in the body

We would have,

A(t) = 2, therefore

2 = 10(0.7)^t

0.7^t =2÷10

0.7^t = 0.2

Take the log of both sides,

Log (0.7)^t = log 0.2

t log 0.7 = log 0.2

t = log 0.2/ 0.7

t = 4.512 hours

Thus it will take 4.512 hours for 2mg to be left in the body.

b) Half life

Let A(t) = 1/2 A(0)

Thus,

1/2 A(0) = A(0)0.7^t

Divide both sides by A(0)

1/2 = 0.7^t

0.7^t = 0.5

Take log of both sides

Log 0.7^t = log 0.5

t log 0.7 = log 0.5

t = log 0.5/log 0.7

t = 1.94 hours

Therefore, the half life of the drug is 1.94 hours

6 0

3 years ago

the perimeter of a rectangle is 48 in. if the length is twice the width, what is the length of the rectangle?

konstantin123 [22]

16. hope that helps. :)

6 0

4 years ago

HELP ASAP

suter [353]

That sounds horrible

6 0

3 years ago