Answer:
B
Step-by-step explanation:
Step 1: Add 2 to both sides.
x−2+2>3+2
x>5
Answer: the diagonal is 10 units
Step-by-step explanation:
The rectangle has 2 parallel and equal sides. Each of the 4 angles in a rectangle is 90°. Therefore, the diagonal of the rectangle divides it into 2 equal right angle triangles and the diagonal represents the hypotenuse of both right triangles.
To determine the length of the diagonal of the rectangle, d, , we would apply Pythagoras theorem which is expressed as
Hypotenuse² = opposite side² + adjacent side²
Therefore
d² = 5² + (5√3)²
d² = 25 + 25×3 = 100
d = √100
d = 10 units
Answer:
Step-by-step explanation:
Answer:
Q1: No solutions
Q2: x=2, y=-2
Q3: x=1, y=4
Step-by-step explanation:
Q1: Found out 0y = 18 which is impossible therefore no solution.
Q2:
In the first equation: ![2x - 4y = 12](https://tex.z-dn.net/?f=2x%20-%204y%20%3D%2012)
Let's express x in terms of y by changing the subject. Follow my steps.
![2x = 12+4y](https://tex.z-dn.net/?f=2x%20%3D%2012%2B4y)
![x = \frac{12+4y}{2}](https://tex.z-dn.net/?f=x%20%3D%20%5Cfrac%7B12%2B4y%7D%7B2%7D)
Now let's put the x above into the second equation: ![-14x-4y=-20](https://tex.z-dn.net/?f=-14x-4y%3D-20)
It becomes:
. Follow my steps.
![-7(12+4y)=-20+4y](https://tex.z-dn.net/?f=-7%2812%2B4y%29%3D-20%2B4y)
![-84-28y=-20+4y](https://tex.z-dn.net/?f=-84-28y%3D-20%2B4y)
![-32y=64](https://tex.z-dn.net/?f=-32y%3D64)
![y=-2](https://tex.z-dn.net/?f=y%3D-2)
Put y = -2 into the first equation:
![2x-4(-2)=12](https://tex.z-dn.net/?f=2x-4%28-2%29%3D12)
![2x+8=12](https://tex.z-dn.net/?f=2x%2B8%3D12)
![2x=12-8](https://tex.z-dn.net/?f=2x%3D12-8)
![2x=4](https://tex.z-dn.net/?f=2x%3D4)
![x=2](https://tex.z-dn.net/?f=x%3D2)
Q3:
Multiply the first equation by 3 and the second equation by 7, so that both are 21x.
1st equation:
![3(7x-3y)=3(-5)](https://tex.z-dn.net/?f=3%287x-3y%29%3D3%28-5%29)
![21x-9y=-15](https://tex.z-dn.net/?f=21x-9y%3D-15)
2nd equation:
![7(3x+2y) = 7(11)](https://tex.z-dn.net/?f=7%283x%2B2y%29%20%3D%207%2811%29)
![21x+14y = 77](https://tex.z-dn.net/?f=21x%2B14y%20%3D%2077)
We can now substract the 2nd equation with the 1st equation so that both 21x cancels out and only the variable y remains.
![21x-9y-(21x+14y)=-15-77](https://tex.z-dn.net/?f=21x-9y-%2821x%2B14y%29%3D-15-77)
![21x-9y-21x-14y=-92](https://tex.z-dn.net/?f=21x-9y-21x-14y%3D-92)
![-23y=-92](https://tex.z-dn.net/?f=-23y%3D-92)
![y=4](https://tex.z-dn.net/?f=y%3D4)
Put y = 4 into the second equation to find x.
![3x+2(4)=11](https://tex.z-dn.net/?f=3x%2B2%284%29%3D11)
![3x+8=11](https://tex.z-dn.net/?f=3x%2B8%3D11)
![3x=11-8](https://tex.z-dn.net/?f=3x%3D11-8)
![3x = 3](https://tex.z-dn.net/?f=3x%20%3D%203)
![x=1](https://tex.z-dn.net/?f=x%3D1)
Answer:
length = 17 ft and width = 12 ft
Step-by-step explanation:
The rug is rectangular .
Let
width = a
length = a + 5
Area of the rug = a × (a + 5) = a² + 5a
The rug is always placed 2 ft from the wall. The illustration describes a rectangle place into another. The space between the rug and the wall is 100 ft².
The living room
length = a + 5 + 2 + 2= a + 9
width = a + 2 + 2 = a + 4
area = (a + 9)(a + 4) = a² + 4a + 9a + 36 = a² + 13a + 36
a² + 13a + 36 - (a² + 5a) = 100
a² + 13a + 36 - a² - 5a = 100
8a + 36 = 100
8a = 100 - 36
8a = 64
a = 64/8
a = 8
Dimension of the living room
length = a + 9
length = 8 + 9 = 17 ft
width = a + 4
width = 8 + 4 = 12 ft
length = 17 ft and width = 12 ft