Converting Units Attachment Included

Where will the lines 2x-3y=-1 and y=x-1 intersect 4,3 6,5 9,8 11,10

ivolga24 [154]

The answer is 3x-x+2=4

7 0

3 years ago

Read 2 more answers

Can someone please help me ASAP

Sonja [21]

Answer:

x^2 + 5n = 4mx

=> x^2 - 4mx + 5n = 0

D=0 (since one root then roots are equal)

b^2-4ac = 0

(-4m)^2 - 4(1)(5n) = 0

16m^2 - 20n = 0

16m^2 = 20n

8m^2 = 10n

4m^2 = 5n

hope it helps.......

7 0

3 years ago

HELP ASAP!!

elena-14-01-66 [18.8K]

Replace f(x) with y
switch x and y
solve for y
replace y with g(x)

y=1/3x+2
x=1/3y+2
x-2=1/3y
3x-6=y
g(x)=3x-6

f(g(x)) should have the same result as g(f(x)) which should be x

f(g(x))=1/3(3x-6)+2=x-2+2=x
g(f(x))=3(1/3x+2)-6=x+6-6=x

the inverse is g(x)=3x-6

8 0

3 years ago

Almost done help......

Anton [14]

Answer:

x = 1 + ( √ 10 )/ 2, or x = 1 - ( √ 10 )/ 2; Option A

Step-by-step explanation:

See steps below;

I would prefer answering this question by completing the square, rather than applying a quadratic formula;

3x^2 - 6x - 12 = 0, ⇒ Add 12 to either side,

3x^2 - 6x = 12, ⇒ Divide either side by 3,

x^2 - 2x = 4, ⇒ Write the equation in the form x^2 + 2ax + a^2 = (x + a)^2,

x^2 - 2ax + a^2 = 4 + a^2, ⇒ Solve for a

2ax = -2x,

a = - 1, ⇒ Substitute value of a,

x^2 - 2x + 1 = 4 + 1,

( x - 1 )^2 = 5, ⇒ Solve for x,

x = √5 + 1, and x = - √5 + 1,

In other words; Solution : x = 1 + ( √ 10 )/ 2, or x = 1 - ( √ 10 )/ 2; Option A

4 0

4 years ago

I need help with letters (D) and (E). My model equation from letter (C) is: P = -55/4 t+ 340.

IceJOKER [234]

Answer:

(a) The two ordered pairs are (0 , 340) and (4 , 285)

(b) The slope is m = -55/4

The slope means the rate of decreases of the owl population was 55/4

per year (P decreased by 55/4 each year)

(c) The model equation is P = -55/4 t + 340

(d) The owl population in 2022 will be 216

(e) At year 2038 will be no more owl in the park

Step-by-step explanation:

* Lets explain how to solve the problem

- The owl population in 2013 was measured to be 340

- In 2017 the owl population was measured again to be 285

- The owl population is P and the time is t where t measure the numbers

of years since 2013

(a) Let t represented by the x-coordinates of the order pairs and P

represented by the y-coordinates of the order pairs

∵ t is measured since 2013

∴ At 2013 ⇒ t = 0

∵ The population P in 2013 was 340

∴ The first order pair is (0 , 340)

∵ The time from 2013 to 2013 = 2017 - 2013 = 4 years

∴ At 2017 ⇒ t = 4

∵ The population at 2017 is 285

∴ The second order pair is (4 , 285)

* The two ordered pairs are (0 , 340) and (4 , 285)

(b) The slope of any lines whose endpoints are (x1 , y1) and (x2 , y2)

is $m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

∵ (x1 , y1) is (0 , 340) and (x2 , y2) is (4 , 285)

∴ x1 = 0 , x2 = 4 and y1 = 340 , y2 = 285

∴ $m = \frac{285-340}{4-0}=\frac{-55}{4}$

* The slope is m = -55/4

∵ The slope is negative value

∴ The relation is decreasing

* The slope means the rate of decreases of the owl population was

55/4 per year (P decreased by 55/4 each year)

(c) The linear equation form is y = mx + c, where m is the slope and c is

the value of y when x = 0

∵ The population is P and represented by y

∵ The time is t and represented by t

∴ P = mt + c , c is the initial amount of population

∵ m = -55/4

∵ The initial amount of the population is 340

∴ P = -55/4 t + 340

* The model equation is P = -55/4 t + 340

(d) Lets calculate the time from 2013 to 2022

∵ t = 2022 - 2013 = 9 years

∵ P = -55/4 t + 340

∴ P = -55/4 (9) + 340 = 216.25 ≅ 216

* The owl population in 2022 will be 216

(e) If the model is accurate , then the owl population be be zero after

t years

∵ P = -55/4 t + 340

∵ P = 0

∴ 0 = -55/4 t + 340

- Add 55/4 t to both sides

∴ 55/4 t = 340

- Multiply both sides by 4

∴ 55 t = 1360

- Divide both sides by 55

∴ t = 24.7 ≅ 25 years

- To find the year add 25 years to 2013

∵ 2013 + 25 = 2038

* At year 2038 will be no more owl in the park

8 0

3 years ago