Answer:
The system of inequalities that represents this situation will be:
![f + s < 10](https://tex.z-dn.net/?f=f%20%2B%20s%20%3C%2010)
![f - s > 3](https://tex.z-dn.net/?f=f%20-%20s%20%3E%203)
Step-by-step explanation:
- Let 'f' represent the first number
- Let 's' represent the second number.
Given that the sum of the two numbers is less than 10. As 'less than' can be represented by '<'.
- so the inequality would be: f + s < 10
Given that If we subtract the second number from the first, the difference is greater than 3. As 'greater than' can be represented by '>'.
- so the inequality would be: f-s > 3
Thus, the system of inequalities that represents this situation will be:
![f + s < 10](https://tex.z-dn.net/?f=f%20%2B%20s%20%3C%2010)
![f - s > 3](https://tex.z-dn.net/?f=f%20-%20s%20%3E%203)
I believe the answer is 24 if not im sorry
Answer:
![A=1,720.16\ units^2](https://tex.z-dn.net/?f=A%3D1%2C720.16%5C%20units%5E2)
Step-by-step explanation:
we know that
The area of the trapezoid is equal to
![A=\frac{1}{2}(DC+AB)DE](https://tex.z-dn.net/?f=A%3D%5Cfrac%7B1%7D%7B2%7D%28DC%2BAB%29DE)
step 1
Find the measure of angle DAE
m∠ADC+m∠DAE=180° -----> by consecutive interior angles
we have
m∠ADC = 134°
substitute
134°+m∠DAE=180°
m∠DAE=180°-134°=46°
step 2
In the right triangle ADE
Find the length side AE
cos(∠DAE)=AE/AD
![AE=cos(46\°)(40)\\AE=27.79\ units](https://tex.z-dn.net/?f=AE%3Dcos%2846%5C%C2%B0%29%2840%29%5C%5CAE%3D27.79%5C%20units)
step 3
In the right triangle ADE
Find the length side DE
sin(∠DAE)=DE/AD
![DE=sin(46\°)(40)\\DE=28.77\ units](https://tex.z-dn.net/?f=DE%3Dsin%2846%5C%C2%B0%29%2840%29%5C%5CDE%3D28.77%5C%20units)
step 4
Find the area of ABCD
![A=\frac{1}{2}(DC+AB)DE](https://tex.z-dn.net/?f=A%3D%5Cfrac%7B1%7D%7B2%7D%28DC%2BAB%29DE)
we have
![DC=32\ units\\AB=DC+2(AE)=32+2(27.79)=87.58\ units\\DE=28.77\ units](https://tex.z-dn.net/?f=DC%3D32%5C%20units%5C%5CAB%3DDC%2B2%28AE%29%3D32%2B2%2827.79%29%3D87.58%5C%20units%5C%5CDE%3D28.77%5C%20units)
substitute
![A=\frac{1}{2}(32+87.58)28.77](https://tex.z-dn.net/?f=A%3D%5Cfrac%7B1%7D%7B2%7D%2832%2B87.58%2928.77)
![A=1,720.16\ units^2](https://tex.z-dn.net/?f=A%3D1%2C720.16%5C%20units%5E2)
Tax=2.5+6+1=9.5
deluxe=38.75x1.095=42.43125
fc atlas=41.10x1.095=45.0045
total purchase price=87.43576
rounded=87.44