What is the correct answer??? Help me please!!!

Mathematics

1 answer:

BlackZzzverrR [31]3 years ago

4 0

Image 1: a) the combined area of mat and photo is: $(8+2w)(10+2w)=224$

b) factors are : $4(w-3)(w+12)=0$

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

$(8+2w)(10+2w)=224$

So, the combined area of mat and photo is: $(8+2w)(10+2w)=224$

Part B:

Now finding factors:

$(8+2w)(10+2w)=224$

$Multiplying:\\80+16w+20w+4w^2=224\\4w^2+36w+80-224=0\\4w^2+36w-144=0\\Taking\,\,4\,\,common:\\4(w^2+9w-36)=0\\Factorize:\\4(w^2+12w-3w-36)=0\\4(w(w+12)-3(w+12))=0\\4(w-3)(w+12)=0$

So, factors are : $4(w-3)(w+12)=0$

Image 2:

We need to find factors of $y=6x^2-5x-25$

Factorizing:

$y=6x^2-5x-25$

$6x^2-5x-25=0\\6x^2+10x-15x-25=0\\2x(3x+5)-5(3x+5)=0\\(2x-5)(3x+5)=0\\2x-5=0\,\,and\,\,3x+5=0\\2x=5\,\,and\,\,3x=-5\\x=\frac{5}{2}\,\,and\,\,3x=\frac{-5}{3}$

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:

$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

Putting values:

$w=\frac{-(-10)\pm\sqrt{(-10)^2-4(3)(-9)}}{2(3)}\\w=\frac{10\pm\sqrt{100+108}}{6}\\w=\frac{10\pm\sqrt{208}}{6}\\w=\frac{10\pm14.4}{6}\\w=\frac{10+14.4}{6}\,\,and\,\,w=\frac{10-14.4}{6}\\w=4.0\,\,and\,\,w=-0.7$