1. six less than a square of a number is equal to 5 times the number.find the number

Question

i need help in my homework i got more questions

2.the square of a positive number is 12 more than 4 times the number.find the number

3.the product of 2 consecutive integers is 56.find the integers.

4.find 3 consecutive integers such that the product of the second integer and the third integer is 20

5. The perimeter of a rectangle is 20in and its area is 16 square inches find the dimensions of the rectangle.

6.Tamara has two sisters one of the sisters is 7 yrs older than tamara the other sister is 3yrs younger than tamara. the product of her sisters ages is 24. how old is tamara?

Answer 1

1.  x²-6=5x

x²-5x-6=0

(x-6)(x+1)=0

x=6,x=-1

 

2.  x²=12+4x

x²-4x-12=0

(x-6)(x+2)=0

x=6,x=-2

 

3. x(x+1)=56

x²+x=56

x²+x-56=0

(x+8)(x-7)=0

x=-8,x=7

 

4.  (x+1)(x+2)=20

x²+3x+2=20

x²+3x-18=0

(x+6)(x-3)=0

x=-6,x=3

x=3 only then 4, then 5 when you plug in x into (x+1)(x+2)

 

 

5.  2l+2w=20, l*w=16

solve for l and minus 2w on both sides and get 2l=-2w+20 then divide by 2 and get l =-w+10

substitute the expression for l in the second equation and get (-w+10)*w=16

-w²+10w=16

0=w²-10w+16

0=(w-8)(w-2)

w=8, w = 2

both solutions work plug back in and length will equal 2 and 8

 

6. Sister #1 = T+7, Sister #2=T-3

(T+7)(T-3)=24

T²-3T+7T-21=24

T²+4T-45=0

(T+9)(T-5)=0

T=-9, T=5. 

Tamara can't be -9 years old so she is 5.