This one can besolved using system of equations. From the first statement we can assume that
length = 2 * width. The area of rectange equals product of it's width and length. By knowing that and following to the second statement we get the second equation:
(3 * width) * (length - 5) = width * length + 4. Let's mark the
width as
x and the
length as
y and write down our equations system:
![\begin{cases} y=2x \\ 3x\cdot (y-5)=xy+4 \end{cases}](https://tex.z-dn.net/?f=%5Cbegin%7Bcases%7D%20y%3D2x%20%5C%5C%203x%5Ccdot%20%28y-5%29%3Dxy%2B4%20%5Cend%7Bcases%7D)
Using substituion method, lets replace every
y with
2x within second equation and solve it:
![3x\cdot (2x-5)=x\cdot2x+4](https://tex.z-dn.net/?f=3x%5Ccdot%20%282x-5%29%3Dx%5Ccdot2x%2B4)
![6x^2-15x=2x^2+4](https://tex.z-dn.net/?f=6x%5E2-15x%3D2x%5E2%2B4)
![6x^2-15x-2x^2-4=0](https://tex.z-dn.net/?f=6x%5E2-15x-2x%5E2-4%3D0)
![4x^2-15x-4=0](https://tex.z-dn.net/?f=4x%5E2-15x-4%3D0)
Now lets find the discriminant in order to solve this quadratic equation:
![D=b^2-4ac=15^2-4\cdot4\cdot(-4)=225+64=289](https://tex.z-dn.net/?f=D%3Db%5E2-4ac%3D15%5E2-4%5Ccdot4%5Ccdot%28-4%29%3D225%2B64%3D289)
![x_{1}=\frac{-b+\sqrt{D}}{2a}=\frac{15+\sqrt{289}}{2\cdot4}=\frac{15+17}{8}=\frac{32}{8}=4](https://tex.z-dn.net/?f=x_%7B1%7D%3D%5Cfrac%7B-b%2B%5Csqrt%7BD%7D%7D%7B2a%7D%3D%5Cfrac%7B15%2B%5Csqrt%7B289%7D%7D%7B2%5Ccdot4%7D%3D%5Cfrac%7B15%2B17%7D%7B8%7D%3D%5Cfrac%7B32%7D%7B8%7D%3D4)
![x_{2}=\frac{-b-\sqrt{D}}{2a}=\frac{15-\sqrt{289}}{2\cdot4}=\frac{15-17}{8}=\frac{-2}{8}=-0.25](https://tex.z-dn.net/?f=x_%7B2%7D%3D%5Cfrac%7B-b-%5Csqrt%7BD%7D%7D%7B2a%7D%3D%5Cfrac%7B15-%5Csqrt%7B289%7D%7D%7B2%5Ccdot4%7D%3D%5Cfrac%7B15-17%7D%7B8%7D%3D%5Cfrac%7B-2%7D%7B8%7D%3D-0.25)
The second root is negative, so we ignore it as
x represents width which can't be negative.
Now, using found root, let's find
y value from the first equation:
![y=2x=2\cdot4=8](https://tex.z-dn.net/?f=y%3D2x%3D2%5Ccdot4%3D8)
So,
the width is equal 4 (and the length is equal 8).
Answer:
Siham ran for 305 minutes
Step-by-step explanation:
Let
Siham Ran for time = X
Siham Ran for time = X-60
According to given condition
X + (X-60) = 670
X + X - 60 = 670
2X = 670-60
2X = 610
X = 610/2
X = 305
So Siham ran for 305 minutes only
Answer:
Soup B has more sodium per cup.
Step-by-step explanation:
If we're doing sodium per cup, then we have to divide 5 by 12, and 8 by 13.
5÷12=~0.4 grams
8÷13=~0.6 grams
0.6>0.4
So B has more sodium per cup.
Answer:
y=97
Step-by-step explanation:
1st do 42+55=97 to find
2nd do 180-97=83 to find z so z=83
3rd do then do 180-83=97 sense y and z are supplementary
so therefore the answer is y=97
If brainiest is earned its greatly appreciated