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seraphim [82]
3 years ago
14

The length of a rectangle is 7 cm than 6 times its width. It's area is 10 square centimeters. Find the dimensions

Mathematics
1 answer:
ad-work [718]3 years ago
7 0
So legnth is 7 more than 6 times width
l=7+6w
area=10 cm^2

lw=area

subsitute
7+6w for l
(7+6w)(w)=10
7w+6w^2=10
subtract 10 from both sides
6w^2+7w-10=0
factor
multiply 6 and -10
get -60
now find what 2 numbers multiply to get -60 and add to get 7
the answe ris -5 and 12
split up 7w into that
6w^2+7w-10=0
6w^2+12w-5w-10=0
group
(6w^2+12w)+(-5w-10)=0
undistribute factors
(6w)(w+2)+(-5)(w+2)=0
reverse distribute (ab+ac=a(b+c)
(w+2)((6w)+(-5))=0
(w+2)(6w-5)=0
set each to zero
w+2=0
subtract 2
w=-2
false, legnths cannot be negative

6w-5=0
add 5
6w=5
divide both sides by 6
w=5/6
subsitute
l=7+6w
l=7+6(5/6)
l=7+5
l=12


legnth=12 cm
width=5/6 cm

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3 years ago
An isosceles triangle has two sides of equal length, a, and a base, b. The perimeter of the triangle is 15.7 inches, so the equa
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⇒a+a+b=15.7

⇒2a+b=15.7

⇒b=15.7-2a

Also, we know that he sum of the lengths of any two sides of a triangle must be greater than the length of the third side that means,

⇒a+a>b

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8 0
3 years ago
Read 2 more answers
Drag a statement or reason to each box to complete this proof.
mars1129 [50]

     Statements                                                  Reason

1. -6(x-4)= 42                                        Given

2. \frac{-6(x-4)}{-6} = \frac{42}{-6}       Division property of equality

" Division property of equality states that if we divide both sides of an equation by the same nonzero number, the equation remains equal".

3. x-4 = -7                                            Simplifying

4. x-4+4 = -7+4                                  Addition property of equality

"Addition property of equality states that if the same number is added to both sides of an equation, then the equality is still true".

5. x = -3                                               Simplifying

Therefore, the solution to the equation -6(x-4)= 42 is x = -3.

6 0
3 years ago
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