Answer:
AB = 5
BC = 12
AC = 13
Step-by-step explanation:
A rectangle is a quadrilateral and therefore, opposite sides are parallel and congruent to each other. Thus:
AB = CD = 12
AB = 12
BC = AD = 5
BC = 5
AC is a diagonal of the rectangle, use Pythagorean theorem to find it's length as follows:
AC² = AD² + CD²
Plug in the values
AC² = 5² + 12²
AC² = 169
AC = √169
AC = 13
Answer:
1.5 gallons
Step-by-step explanation:
2 x 0.75
1.5 gallons
Brainliest appreciated!
Answer:
1200 dollars
Step-by-step explanation:
x-0.16x=1008
.84x=1008
x=1200 dollars
![\frac{7x+1}{x-2} + \frac{2}{x} = \frac{-4}{ x^{2} -2x}](https://tex.z-dn.net/?f=%20%5Cfrac%7B7x%2B1%7D%7Bx-2%7D%20%2B%20%5Cfrac%7B2%7D%7Bx%7D%20%3D%20%5Cfrac%7B-4%7D%7B%20x%5E%7B2%7D%20-2x%7D%20)
is given
here ,
or,
![\frac{7x^{2} +x +2x-4 }{x(x-2)} = \frac{-4}{ x^{2} -2x}](https://tex.z-dn.net/?f=%20%5Cfrac%7B7x%5E%7B2%7D%20%2Bx%20%2B2x-4%20%7D%7Bx%28x-2%29%7D%20%3D%20%5Cfrac%7B-4%7D%7B%20x%5E%7B2%7D%20-2x%7D%20)
or,
![\frac{7 x^{2} +3x-4}{ x^{2} -2x} = \frac{-4}{ x^{2} -2x}](https://tex.z-dn.net/?f=%20%5Cfrac%7B7%20x%5E%7B2%7D%20%2B3x-4%7D%7B%20x%5E%7B2%7D%20-2x%7D%20%3D%20%5Cfrac%7B-4%7D%7B%20x%5E%7B2%7D%20-2x%7D%20)
or,7x²+3x-4=-4
or,7x²+3x=0
or,x(7x+3)=0
Either,x=0| Or,7x+3=0
|or,7x=-3
|or,x=
![\frac{-3}{7}](https://tex.z-dn.net/?f=%20%20%5Cfrac%7B-3%7D%7B7%7D%20)
So , the solution set is S={0,-
![\frac{3}{7}](https://tex.z-dn.net/?f=%20%5Cfrac%7B3%7D%7B7%7D%20)
}
For this case, we have that by definition, the volume of a rectangular prism is given by:
![V = A_ {b} * h](https://tex.z-dn.net/?f=V%20%3D%20A_%20%7Bb%7D%20%2A%20h)
Where:
It is the area of the base
h: It is the height of the prism
So:
![l = 3 \frac {1} {2} = \frac {6 + 1} {2} = \frac {7} {2} in\\w = 5 \ in\\h = 1 \frac {1} {2} = \frac {2 + 1} {2} = \frac {3} {2} in](https://tex.z-dn.net/?f=l%20%3D%203%20%5Cfrac%20%7B1%7D%20%7B2%7D%20%3D%20%5Cfrac%20%7B6%20%2B%201%7D%20%7B2%7D%20%3D%20%5Cfrac%20%7B7%7D%20%7B2%7D%20in%5C%5Cw%20%3D%205%20%5C%20in%5C%5Ch%20%3D%201%20%5Cfrac%20%7B1%7D%20%7B2%7D%20%3D%20%5Cfrac%20%7B2%20%2B%201%7D%20%7B2%7D%20%3D%20%5Cfrac%20%7B3%7D%20%7B2%7D%20in)
So, we have:
![A_ {b} = \frac {7} {2} * 5\\A_ {b} = \frac {35} {2}\\A_ {b} = 17.5 \ in ^ 2](https://tex.z-dn.net/?f=A_%20%7Bb%7D%20%3D%20%5Cfrac%20%7B7%7D%20%7B2%7D%20%2A%205%5C%5CA_%20%7Bb%7D%20%3D%20%5Cfrac%20%7B35%7D%20%7B2%7D%5C%5CA_%20%7Bb%7D%20%3D%2017.5%20%5C%20in%20%5E%202)
Thus, the volume will be:
![V = 17.5 * \frac {3} {2}\\V = 26.25 \ in ^ 3](https://tex.z-dn.net/?f=V%20%3D%2017.5%20%2A%20%5Cfrac%20%7B3%7D%20%7B2%7D%5C%5CV%20%3D%2026.25%20%5C%20in%20%5E%203)
Answer:
![V = 26.25 \ in ^ 3](https://tex.z-dn.net/?f=V%20%3D%2026.25%20%5C%20in%20%5E%203)