Answer:
False,
(-4, -1) is not a solution of the given system of equations
Step-by-step explanation:
Given the system of equations:
.......[1]
......[2]
To determine (-4, -1) is a solution
Substitute x = -4 and y = -1 in both the equations, if they both satisfied then it is a solution.
⇒![-12-8 = 20](https://tex.z-dn.net/?f=-12-8%20%3D%2020)
⇒
False.
⇒![20-1 = 19](https://tex.z-dn.net/?f=20-1%20%3D%2019)
⇒
True.
Since, the given statement is not true
because the ordered pair (-4, -1) does not satisfy the given system of equations.
Answer:
7 coats
Step-by-step explanation:
they purchased 7 coats and 5 sweaters
Answer:
It takes 3 seconds for the diver to reach the water.
Step-by-step explanation:
The height, in feet, is given by the following equation:
![h(t) = -16t^{2} + 144](https://tex.z-dn.net/?f=h%28t%29%20%3D%20-16t%5E%7B2%7D%20%2B%20144)
How many seconds will it take for the diver to reach the water?
He reaches the water when his height is 0, that is, when h(t) = 0. So
![h(t) = -16t^{2} + 144](https://tex.z-dn.net/?f=h%28t%29%20%3D%20-16t%5E%7B2%7D%20%2B%20144)
![0 = -16t^{2} + 144](https://tex.z-dn.net/?f=0%20%3D%20-16t%5E%7B2%7D%20%2B%20144)
![16t^{2} = 144](https://tex.z-dn.net/?f=16t%5E%7B2%7D%20%3D%20144)
![t^{2} = \frac{144}{16}](https://tex.z-dn.net/?f=t%5E%7B2%7D%20%3D%20%5Cfrac%7B144%7D%7B16%7D)
![t^{2} = 9](https://tex.z-dn.net/?f=t%5E%7B2%7D%20%3D%209)
![t = \pm \sqrt{9}](https://tex.z-dn.net/?f=t%20%3D%20%5Cpm%20%5Csqrt%7B9%7D)
![t = \pm 3](https://tex.z-dn.net/?f=t%20%3D%20%5Cpm%203)
There are no negative instant of time, so just t = 3.
It takes 3 seconds for the diver to reach the water.
The value of x+y+z = 93
<u>Explanation:</u>
<u></u>
angle 1 = 18x
angle 2 = x+y
angle 3 = 30z
In rhombus, the diagonals intersect at 90°
Therefore,
angle 1 : 18x = 90
x = 90/18 = 5
angle 2: x+y = 90
5+y = 90
y = 85
angle 3: 30z = 90
z = 90/30 = 3
Value of x+y+z = 5+85+3 = 93
Thus, the value of x+y+z = 93