Answer: a) 3 and -3 b) 4 and 2
c) 3.5 and 2.5 d) 5.5 and 0.5 e) This is due to the difference in the coefficient of (x-3)² and the value at the right side of each equation.
Step-by-step explanation:
a) 3x²-9 = 0
3x² = 0+9
3x² = 9
Dividing both sides by 3
x² = 9/3
x² = 3
x = √3
x = +3 and -3
b) (x-3)² = 1
Taking square root of both sides to remove the square,
√(x-3)² = √1
x-3 = √1
x-3 = 1 and x-3 = -1 (note that √1 is +1 and -1)
x = 4 and x = 2
c) 4(x-3)² = 1
Dividing both sides by 4 we have;
(x-3)² = 1/4
Taking the square root of both sides to eliminate the square.
√(x-3)² = √1/4
x-3 = √1/4
x-3 = +1/2 and x-3 = -1/2
x = 1/2+3 and x = -1/2+3
x = 3.5 and 2.5
d) 2(x-3)² = 12
Dividing both sides by 2 we have;
(x-3)² = 12/2
Taking the square root of both sides to eliminate the square.
√(x-3)² = √12/2
x-3 = √6
x-3 = 2.5 and x-3 = -2.5
x = 2.5+3 and x = -2.5+3
x = 5.5 and 0.5
e) The answers to questions 1 to 4 has different solutions due to the different value of the coefficient of (x-3)² and also the value at the right hand side of the equations also differs, hence, the reason for the difference in their answers.
The only thing I can see that you can do with this is to move the 2 up to make it an exponent on the 5: log(base 7) = 5^2. Is that what you mean?
Answer:
-10 4/64, -.3125, 1/16, 10 51/80, 10 45/48
Step-by-step explanation:
negatives, the larger the number the smaller it is, opposite for positives. 10 45/48 is closer to 11 than 10 51/80
Let assume x be the sale price
A clothing store advertises that it is having a 25% off sale.
The sale price with 25% discount is f(x) = sale price - 25% of sale price
f(x)= x - 0.25x = 0.75x
For one day only, the store advertises and additional savings of 10%.
The sale price with 10% discount is g(x) = sale price - 10% of sale price
g(x)= x - 0.10x = 0.90x
Use composition function
g(f(x)) = g( 0.75x) = 0.90(0.75x) = 0.675x
That is 0.675/100 = 67.5%
The total percent discount = 100% - 67.5% = 32.5%
what would be the sale price of a $40 sweater?
Here sale price x= 40
So we plug in 40 for x
g(f(40)) = g( 0.75(40)) = 0.90(0.75(40)) = 0.675(40) = 27
The sale price of sweater = $27
