Image 1: a) the combined area of mat and photo is: ![(8+2w)(10+2w)=224](https://tex.z-dn.net/?f=%288%2B2w%29%2810%2B2w%29%3D224)
b) factors are : ![4(w-3)(w+12)=0](https://tex.z-dn.net/?f=4%28w-3%29%28w%2B12%29%3D0)
Image 2: Option A is correct
Image 3: Width = 4 feet and Length = 2 feet
Step-by-step explanation:
Image 1:
Part A:
The combined are of mat and photo is 224
The length is: 8+2w
The width is: 10+2w
So, Area = length * width
![(8+2w)(10+2w)=224](https://tex.z-dn.net/?f=%288%2B2w%29%2810%2B2w%29%3D224)
So, the combined area of mat and photo is: ![(8+2w)(10+2w)=224](https://tex.z-dn.net/?f=%288%2B2w%29%2810%2B2w%29%3D224)
Part B:
Now finding factors:
![(8+2w)(10+2w)=224](https://tex.z-dn.net/?f=%288%2B2w%29%2810%2B2w%29%3D224)
![Multiplying:\\80+16w+20w+4w^2=224\\4w^2+36w+80-224=0\\4w^2+36w-144=0\\Taking\,\,4\,\,common:\\4(w^2+9w-36)=0\\Factorize:\\4(w^2+12w-3w-36)=0\\4(w(w+12)-3(w+12))=0\\4(w-3)(w+12)=0](https://tex.z-dn.net/?f=Multiplying%3A%5C%5C80%2B16w%2B20w%2B4w%5E2%3D224%5C%5C4w%5E2%2B36w%2B80-224%3D0%5C%5C4w%5E2%2B36w-144%3D0%5C%5CTaking%5C%2C%5C%2C4%5C%2C%5C%2Ccommon%3A%5C%5C4%28w%5E2%2B9w-36%29%3D0%5C%5CFactorize%3A%5C%5C4%28w%5E2%2B12w-3w-36%29%3D0%5C%5C4%28w%28w%2B12%29-3%28w%2B12%29%29%3D0%5C%5C4%28w-3%29%28w%2B12%29%3D0)
So, factors are : ![4(w-3)(w+12)=0](https://tex.z-dn.net/?f=4%28w-3%29%28w%2B12%29%3D0)
Image 2:
We need to find factors of ![y=6x^2-5x-25](https://tex.z-dn.net/?f=y%3D6x%5E2-5x-25)
Factorizing:
![y=6x^2-5x-25](https://tex.z-dn.net/?f=y%3D6x%5E2-5x-25)
![6x^2-5x-25=0\\6x^2+10x-15x-25=0\\2x(3x+5)-5(3x+5)=0\\(2x-5)(3x+5)=0\\2x-5=0\,\,and\,\,3x+5=0\\2x=5\,\,and\,\,3x=-5\\x=\frac{5}{2}\,\,and\,\,3x=\frac{-5}{3}](https://tex.z-dn.net/?f=6x%5E2-5x-25%3D0%5C%5C6x%5E2%2B10x-15x-25%3D0%5C%5C2x%283x%2B5%29-5%283x%2B5%29%3D0%5C%5C%282x-5%29%283x%2B5%29%3D0%5C%5C2x-5%3D0%5C%2C%5C%2Cand%5C%2C%5C%2C3x%2B5%3D0%5C%5C2x%3D5%5C%2C%5C%2Cand%5C%2C%5C%2C3x%3D-5%5C%5Cx%3D%5Cfrac%7B5%7D%7B2%7D%5C%2C%5C%2Cand%5C%2C%5C%2C3x%3D%5Cfrac%7B-5%7D%7B3%7D)
So, Option A is correct
Image 3:
Let width = w
then length = 3w-10
Area = 8
We need to find length and width
The formula used is:
Area = length * Width
9=(3w-10)*w
9=3w^2-10w
3w^2-10w-9=0
Using quadratic formula to find value of w:
![x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B-b%5Cpm%5Csqrt%7Bb%5E2-4ac%7D%7D%7B2a%7D)
Putting values:
![w=\frac{-(-10)\pm\sqrt{(-10)^2-4(3)(-9)}}{2(3)}\\w=\frac{10\pm\sqrt{100+108}}{6}\\w=\frac{10\pm\sqrt{208}}{6}\\w=\frac{10\pm14.4}{6}\\w=\frac{10+14.4}{6}\,\,and\,\,w=\frac{10-14.4}{6}\\w=4.0\,\,and\,\,w=-0.7](https://tex.z-dn.net/?f=w%3D%5Cfrac%7B-%28-10%29%5Cpm%5Csqrt%7B%28-10%29%5E2-4%283%29%28-9%29%7D%7D%7B2%283%29%7D%5C%5Cw%3D%5Cfrac%7B10%5Cpm%5Csqrt%7B100%2B108%7D%7D%7B6%7D%5C%5Cw%3D%5Cfrac%7B10%5Cpm%5Csqrt%7B208%7D%7D%7B6%7D%5C%5Cw%3D%5Cfrac%7B10%5Cpm14.4%7D%7B6%7D%5C%5Cw%3D%5Cfrac%7B10%2B14.4%7D%7B6%7D%5C%2C%5C%2Cand%5C%2C%5C%2Cw%3D%5Cfrac%7B10-14.4%7D%7B6%7D%5C%5Cw%3D4.0%5C%2C%5C%2Cand%5C%2C%5C%2Cw%3D-0.7)
Since width of rectangle is always positive, so: w = 4
Length= 3w-10 = 3(4)-10 =12-10 = 2
So, Width = 4 feet and Length = 2 feet
Keywords: Area of Rectangle, Quadratic Equations
Learn more about Quadratic Equations at:
#learnwithBrainly
ANSWER IS NO SOLUTION OR NO REAL NUMBER
300x .02= 6
6x10=60
Therefore the answer is $360
To model the scenario, the following will be the numerical coefficients for the variables: 0.05 for nickels (5 cents), 0.10 for dime (10 cents) and 0.25 for quaters (25 cents). Thus the model/equation is, $1.87 = 0.25q + 0.10d + 0.05n + 60.
Answer:
one fifth
Step-by-step explanation:
divide 2 by 2 and get 1. divide 10 by 2 and get 5.