Write 5x^2 - 10x + 4 in vertex form.

5(x - 1)² - 1

Step-by-step explanation:

Given

5x² - 10x + 4

Using the method of completing the square

The coefficient of the x² term must be 1 , so factor out 5 from the first 2 terms

= 5(x² - 2x) + 4

add/ subtract ( half the coefficient of the x- term )² to x² - 2x

= 5(x² + 2(- 1)x + 1 - 1 ) + 4

= 5(x - 1)² - 5 + 4

= 5(x - 1)² - 1 ← in vertex form

3< x< 5

step-by-step explanation:

|x - 4| < 1

there are two solutions, one positive and one negative.   remember to flip the inequality when taking the negative solution

x-4 < 1       x-4 > -1

add 4 to each side

x-4+4 < 1+4       x-4+4 > -1+4

x< 5                 x> 3

3< x< 5

3

step-by-step explanation:

in standard form:

a= dictionaries

b= maps

you have to buy 3 dictionaries, so put a 3 next to the a (dictionaries) so that you can multiply them by each other.

a3+b= 60 (the amount of money you have)

we already know the cost of a=15 so replace a with $15

($15 x 3)+b=60

multiply 15 and 3 to get $45 and replace it with $45

45+b=60

and then replace b with 15 to get the total:

45+15=60

that means you have $15 left after buying 3 dictionaries.

15 divided by the cost of a map ($5) equals 3.

so you can buy 3 maps.

sorry if it was confusing!