Answer:
y < -3 and
2x - 3y ≥ -15
Step-by-step explanation:
y < -3
Take any two points on the bold line
(0 , -5) and (-3 , -7)
Now find the slope for this line and then the equation of the line
Slope = ![\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\\](https://tex.z-dn.net/?f=%5Cfrac%7By_%7B2%7D-y_%7B1%7D%7D%7Bx_%7B2%7D-x_%7B1%7D%7D%5C%5C)
![= \frac{-7-[-5]}{-3-0}\\\\=\frac{-7+5}{-3}\\\\=\frac{-2}{-3}\\\\= \frac{2}{3}\\](https://tex.z-dn.net/?f=%3D%20%5Cfrac%7B-7-%5B-5%5D%7D%7B-3-0%7D%5C%5C%5C%5C%3D%5Cfrac%7B-7%2B5%7D%7B-3%7D%5C%5C%5C%5C%3D%5Cfrac%7B-2%7D%7B-3%7D%5C%5C%5C%5C%3D%20%5Cfrac%7B2%7D%7B3%7D%5C%5C)
Slope, point equation,
y - y1 = m(x -x1)
![y - [-5)=\frac{2}{3}(x-0)\\\\y +5 = \frac{2}{3}x\\\\3*y + 5*3 = \frac{2}{3}x*3\\\\3y + 15 =2x\\\\2x - 3y = -15\\](https://tex.z-dn.net/?f=y%20-%20%5B-5%29%3D%5Cfrac%7B2%7D%7B3%7D%28x-0%29%5C%5C%5C%5Cy%20%2B5%20%3D%20%5Cfrac%7B2%7D%7B3%7Dx%5C%5C%5C%5C3%2Ay%20%2B%205%2A3%20%3D%20%5Cfrac%7B2%7D%7B3%7Dx%2A3%5C%5C%5C%5C3y%20%2B%20%2015%20%3D2x%5C%5C%5C%5C2x%20-%203y%20%3D%20-15%5C%5C)
Take any point from the shaded region and plugin the LHS of the equation.
(-6 , -5)
LHS = 2x - 3y
= 2*(-6) -3*(-5)
= -12 + 15
= 3 which is ≥ -15
2x - 3y ≥ -15
Answer:
1095
Step-by-step explanation:
There is a common difference between consecutive terms , that is
7 - (- 10) = 24 - 7 = 17
This indicates the sequence is arithmetic with n th term
= a₁ + (n - 1)d
where a₁ is the first term and d the common difference
Here a₁ = - 10 and d = 17 , thus
= - 10 + (65 × 17) = - 10 + 1105 = 1095
Answer:
Step-by-step explanation:
Use the slope formula here along with the fact that the slope is equal to 1:
and
and cross multiply to get x - 4 = -7 so
x = -3
Answer:
2 isnt the domain
Step-by-step explanation: