Answer:
center of x²+2x+y²+4y=20:(-1,-2),r=5
Step-by-step explanation:
look at the attachment above ☝️
Answer:
10 carbs in snack bars
14 carbs in milk
Step-by-step explanation:
Glasses of Milk = m
Snack Bars = s
I am going to make this a system of equations:
2m + 3s = 58
4m + 2s = 76
I am going to simplify one of them for a s:
4m + 2s = 76
2s = 76 - 4m
s = 38 - 2m
I am going to insert this into the other equation:
2m + 3s = 58
2m + 3(38 - 2m) = 58
2m + 114 - 6m = 58
(-4)m + 114 = 58
(-4)m = -56
m = 14 calories
I am going to plug this m into one of the equations (doesn't matter which):
2(14) + 3s = 58
28 + 3s = 58
3s = 30
s = 10
You can plug these values back into each of the equations to make sure they work.
Hope it helps! UvU
ANSWER:
60°
EXPLAINATION:
= 2r + θ/360°× 2 x 227 x 21
64 = 2 x 21 + θ/360° x 2 x 22/7 x 21
64 = 42 + θ/360° x 44 x 3
64 - 42 = θ/360° x 11 x 3
22 = 33θ/90
θ=22×30/11
= 60°
Answer:
In the year 2010, the population of the city was 175,000
Step-by-step explanation:
If we rewrote this as a linear expression in standard form (it is linear, btw), it would look like this:
The rate of change, the slope of this line, is 11/2. If the year 2010 is our time zero (in other words, we start the clock at that year), then 0 time has gone by in the year 2010. In the year 2011, t = 1 (one year goes by from 2010 to 2011); in the year 2012, t = 2 (two years have gone by from 2010 to 2012), etc. If we plug in a 0 for t we get that y = 175,000. That is our y-intercept, which also serves to give us the starting amount of something time-related when NO time has gone by.
Answer:
z - 2*x - 1.5*y = 0 maximize
subject to:
3*x + 5*y ≤ 800
8*x + 3*y ≤ 1200
x, y > 0
Step-by-step explanation:
Formulation:
Kane Manufacturing produce x units of model A (fireplace grates)
and y units of model B
quantity Iron cast lbs labor (min) Profit $
Model A x 3 8 2
Model B y 5 3 1.50
We have 800 lbs of iron cast and 1200 min of labor available
We need to find out how many units x and units y per day to maximiza profit
First constraint Iron cast lbs 800 lbs
3*x + 5*y ≤ 800 3*x + 5*y + s₁ = 800
Second constraint labor 1200 min available
8*x + 3*y ≤ 1200 8*x + 3*y + s₂ = 1200
Objective function
z = 2*x + 1.5*y to maximize z - 2*x - 1.5*y = 0
x > 0 y > 0
The first table is ( to apply simplex method )
z x y s₁ s₂ Cte
1 -2 -1.5 0 0 0
0 3 5 1 0 800
0 8 3 0 1 1200
