Find the solution to 2/3x = -24

What is the slope and y intercept of the line y= 4x -12-2x?

aleksandr82 [10.1K]

Simplifies to y=2x-12. slope intercept form is y=MX+b where m is slope and b is intercept do slope 4 and y intercept is -12

6 0

3 years ago

Read 2 more answers

Roberta is thinking about joining the food co-op store. If she pays $10.00 to join, she will get 10% off on all the groceries sh

IceJOKER [234]

$100 worth of groceries.

8 0

3 years ago

The diagonals of a quadrilateral QRST intersect at P(-1,3). QRST has vertices at Q(3,6) and R(-4,5). What must be the coordinate

erica [24]

S = (-5,0)

T = (2,1)

Step-by-step explanation:

Step 1 :

Given

Q = (3,6) and R = (-4,5). P = (-1,3)

Let S be (a,b) and T be (c,d)

The diagonals of a parallelogram bisect each other. so in order to ensure that QRST is a parallelogram, P must be the mid point of the diagonals QS and RT.

Step 2 :

P is the midpoint of QS

So we have (3+a) ÷ 2 = -1 and (6 + b) ÷ 2 = 3

=> 3 + a = -2 and 6 + b = 6

=> a = -5 and b =0

So S should be (-5,0)

Step 3 :

P is the midpoint of RT

So we have (-4+c) ÷ 2 = -1 and (5 + d) ÷ 2 = 3

=> -4+ c = -2 and 5 + d = 6

=> c = 2 and d =1

So T should be (2,1)

Step 4 :

Answer :

S = (-5,0)

T = (2,1)

6 0

3 years ago

Kryptonite is a material found on the planet Krypton and has various effects, most importantly on Superman. The most common type

Rashid [163]

Answer:

The maximum amount of red kryptonite present is 33.27 g after 4.93 hours.

Step-by-step explanation:

dy/dt = y(1/t - k)

separating the variables, we have

dy/y = (1/t - k)dt

dy/y = dt/t - kdt

integrating both sides, we have

∫dy/y = ∫dt/t - ∫kdt

㏑y = ㏑t - kt + C

㏑y - ㏑t = -kt + C

㏑(y/t) = -kt + C

taking exponents of both sides, we have

$\frac{y}{t} = e^{-kt + C} \\\frac{y}{t} = e^{-kt}e^{C} \\\frac{y}{t} = Ae^{-kt} (A = e^{C})\\y = Ate^{-kt}$

when t = 1 hour, y = 15 grams. So,

$y = Ate^{-kt}\\15 = A(1)e^{-kX1}\\15 = Ae^{-k}$ (1)

when t = 3 hours, y = 30 grams. So,

$y = Ate^{-kt}\\30 = A(3)e^{-kX3}\\30 = 3Ae^{-3k}$ (2)

dividing (2) by (1), we have

$\frac{30}{15} = \frac{3Ae^{-3k}}{Ae^{-k}} \\2 = 3e^{-2k}\\\frac{2}{3} = e^{-2k}$

taking natural logarithm of both sides, we have

-2k = ㏑(2/3)

-2k = -0.4055

k = -0.4055/-2

k = 0.203

From (1)

$A = 15e^{k} \\A = 15e^{0.203} \\A = 15 X 1.225\\A = 18.36$

Substituting A and k into y, we have

$y = 18.36te^{-0.203t}$

The maximum value of y is obtained when dy/dt = 0

dy/dt = y(1/t - k) = 0

y(1/t - k) = 0

Since y ≠ 0, (1/t - k) = 0.

So, 1/t = k

t = 1/k

So, the maximum value of y is obtained when t = 1/k = 1/0.203 = 4.93 hours

$y = 18.36(1/0.203)e^{-0.203t}\\y = \frac{18.36}{0.203}e^{-0.203X1/0.203}\\y = 90.44e^{-1}\\y = 90.44 X 0.3679\\y = 33.27 g$

<u>So the maximum amount of red kryptonite present is 33.27 g after 4.93 hours.</u>

3 0

3 years ago

You are offered a 30--day trial period at your dream job. However, the owner of the company is a little unusual so the pay optio

S_A_V [24]

Answer:

The question is not complete but from the flow of thought, the question seems to be about what your choice will be between option 1 and option 2.

The correct answer is

option 2

Step-by-step explanation:

The question is asking you to choose an option that pays more after 30 days. In other to determine the more beneficial option, we will compare both options and select the one that pays more. This is done as follows:

option 1: $60,000 per day, after 30 days =

60,000 × 30 = $1,800,000

option 2 = $5,368,709.12 after 30 days

From the total amounts after 30 days of the two options listed above, option 2 is higher than option 1 by $3,568,709. Therefore, option 2 is a better choice.

4 0

3 years ago