Answer:
(12,-6)
Step-by-step explanation:
we have
----> inequality A
---> inequality B
we know that
If a ordered pair is a solution of the system of inequalities, then the ordered pair must satisfy both inequalities (makes true both inequalities)
<u><em>Verify each point</em></u>
Substitute the value of x and the value of y of each ordered pair in the inequality A and in the inequality B
case 1) (0,-1)
Inequality A
![-1\leq \frac{4}{3}(0)+5](https://tex.z-dn.net/?f=-1%5Cleq%20%5Cfrac%7B4%7D%7B3%7D%280%29%2B5)
----> is true
Inequality B
![-1\geq -\frac{5}{2}(0)+5](https://tex.z-dn.net/?f=-1%5Cgeq%20-%5Cfrac%7B5%7D%7B2%7D%280%29%2B5)
----> is not true
therefore
The ordered pair is not a solution of the system
case 2) (0,3)
Inequality A
![3\leq \frac{4}{3}(0)+5](https://tex.z-dn.net/?f=3%5Cleq%20%5Cfrac%7B4%7D%7B3%7D%280%29%2B5)
----> is true
Inequality B
![3\geq -\frac{5}{2}(0)+5](https://tex.z-dn.net/?f=3%5Cgeq%20-%5Cfrac%7B5%7D%7B2%7D%280%29%2B5)
----> is not true
therefore
The ordered pair is not a solution of the system
case 3) (-6,-6)
Inequality A
![-6\leq \frac{4}{3}(-6)+5](https://tex.z-dn.net/?f=-6%5Cleq%20%5Cfrac%7B4%7D%7B3%7D%28-6%29%2B5)
----> is true
Inequality B
![-6\geq -\frac{5}{2}(-6)+5](https://tex.z-dn.net/?f=-6%5Cgeq%20-%5Cfrac%7B5%7D%7B2%7D%28-6%29%2B5)
----> is not true
therefore
The ordered pair is not a solution of the system
case 4) (12,-6)
Inequality A
![-6\leq \frac{4}{3}(12)+5](https://tex.z-dn.net/?f=-6%5Cleq%20%5Cfrac%7B4%7D%7B3%7D%2812%29%2B5)
----> is true
Inequality B
![-6\geq -\frac{5}{2}(12)+5](https://tex.z-dn.net/?f=-6%5Cgeq%20-%5Cfrac%7B5%7D%7B2%7D%2812%29%2B5)
----> is true
therefore
The ordered pair is a solution of the system (makes true both inequalities)
Answer:
$1.82 per cup
Step-by-step explanation:
REMEMBER:16cups per gallon
2 x 16 = 32
58.24 divided by 32 = 1.82
Its mean and range . Even if we remove 70 the median is the same. The mean changes also as 580/7 isnt the same as 510/6 and also the range changes as it decreases by 5. Hope it helped :)
Answer:
k=3
Step-by-step explanation:
The given system of equations are
![9x+ky=24](https://tex.z-dn.net/?f=9x%2Bky%3D24)
![kx+y=8](https://tex.z-dn.net/?f=kx%2By%3D8)
We need to find the value of k if the given system of equation have infinite number of solutions.
If two equations
and
have infinite number of solutions, then
![\dfrac{a_1}{a_2}=\dfrac{b_1}{b_2}=\dfrac{c_1}{c_2}](https://tex.z-dn.net/?f=%5Cdfrac%7Ba_1%7D%7Ba_2%7D%3D%5Cdfrac%7Bb_1%7D%7Bb_2%7D%3D%5Cdfrac%7Bc_1%7D%7Bc_2%7D)
Using this we get
![\dfrac{9}{k}=\dfrac{k}{1}=\dfrac{-24}{-8}](https://tex.z-dn.net/?f=%5Cdfrac%7B9%7D%7Bk%7D%3D%5Cdfrac%7Bk%7D%7B1%7D%3D%5Cdfrac%7B-24%7D%7B-8%7D)
![\dfrac{9}{k}=\dfrac{k}{1}=3](https://tex.z-dn.net/?f=%5Cdfrac%7B9%7D%7Bk%7D%3D%5Cdfrac%7Bk%7D%7B1%7D%3D3)
![\dfrac{k}{1}=3](https://tex.z-dn.net/?f=%5Cdfrac%7Bk%7D%7B1%7D%3D3)
![k=3](https://tex.z-dn.net/?f=k%3D3)
Therefore, the value of k is 3.