1. if the sum of the square of the number and 4 time the number is 21 what is the number?
1 answer:
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
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Answer with Step-by-step explanation:
We are given that if sum of several numbers is odd
We have to prove that at least one of the number is itself odd.
Suppose, we have three numbers
a=6 , b=7,d=8
Sum of numbers=6+7+8=21=Odd number
We know that sum of two odd numbers is always an even number.
Sum of an odd number and an even number is always an odd number.
If we take even odd numbers then sum is always an even number and sum of odd odd numbers then the sum is always an odd number.
Sum of even numbers is always an even number.
Hence, there are atleast one numebr is odd then the sum of several number is odd.
Answer:
This is a percent INCREASE
The percent change is 83.33%
Step-by-step explanation:
Let us solve the question
∵ A pair of Jordans sold at retail for $180
∴ The initial price = 180
∵ Now it sells for $330 aftermarket
∴ The new price = 330
→ That means the new price is greater than the initial price
∵ The new price is greater than the initial price
∴ This is a percent INCREASE
∵ The percent of change = (amount of increase ÷ initial amount) × 100%
∵ The amount of increase = new price - initial price
∴ The amount of increase = 330 - 180 = 150
→ Substitute it in the rule of percent of increase above
∵ The percent change = × 100%
∴ The percent change = × 100%
∴ The percent change = 83.33%