Insert six rational number between 3/5 and 2/3
1 answer:
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Answer:
Step-by-step explanation:
1. Let the number be x
x^2 + 4x = 21
x^2 + 4x - 21 = 0
Solve the quadratic equation using factorization method
x^2 - 3x + 7x - 21 = 0
x(x - 3) + 7(x - 3) = 0
(x - 3)(x+7) = 0
x - 3 = 0 x + 7 = 0
x = 3 x = -7
The number is either 3 or -7
2. Same solution as number 1
3. Let
Width = x
Length = 2x - 3
Area of the rectangle = 9 square ft
Area of a rectangle = length × width
9 = (2x - 3) (x)
9 = 2x^2 - 3x
2x^2 - 3x - 9 = 0
Solve using quadratic formula
a = 2
b = -3
c = -9
x = -b +or- √b^2 - 4ac / 2a
= -(-3) +or- √(-3)^2 - 4(2)(-9) / 2(2)
= 3 +or- √ 9 - (-72) / 4
= 3 +or- √9 + 72 / 4
= 3 +or- √81 / 4
= 3 +or- 9 / 4
x = (3 + 9)/4 or (3 - 9) / 4
= 12 / 4 or -6 / 4
x = 3 or -3/2
Width can not be a negative value
So,
Width = x = 3 ft
Length = 2x - 3
= 2(3) - 3
= 6 - 3
= 3ft
2.if the sum of the square of the number and 4 time that number is 21 the what is the number?
3. the length of the rectangle is 3 less than twice the width. if the area is 9 square ft, the length and width of the rectangle.
4.given the figure below. find the area of the shaded part of the rectangle if the area of the big but angle is 6 times the area of the unshaded rectangle
Unshaded area
Length = 2x
Width = x
Shaded area
Length = (2x+3)
Width = (x+3)
Area of the shaded area = 6 × the unshaded area
(2x) (x) = 6(2x + 3)(x+3)
2x^2 = 6(2x^2 + 6x + 3x + 9)
2x^2 = 12x^2 + 36x + 9x + 54
2x^2 = 12x^2 + 45x + 54
12x^2 + 45x + 54 - 2x^2 = 0
10x^2 + 45x + 54 = 0
Answer:
Polynomial expression that represents the area of blanket:
If :
Step-by-step explanation:
The area of the rectangle can be calculated with the formula:
Being l the lenght of the rectangle and w the width of the rectangle.
In this case, the lenght and the width are represented with:
Substitute them into :
Then:
Use Distributive property (Remember the Product of powers property: ):
Add like terms:
(Simplied form)
Evaluate :
