Which of the following relations is a function?

Y=x^2-6x+3 help write the vertex form of the equation

Artist 52 [7]

Answer:

$y=(x-3)^2-6$

Step-by-step explanation:

$y=x^2-6x+3$

This is written in the standard form of a quadratic function:

$y=ax^2+bx+c$

where:

ax² → quadratic term
bx → linear term
c → constant

You need to convert this to vertex form:

$y=a(x-h)^2+k$

where:

(h,k) → vertex

To find the vertex form, you need to find the vertex. For this, use the equation for axis of symmetry, since this line passes through the vertex:

$x=-\frac{b}{2a}$

Using your original equation, identify the a, b, and c terms:

$a=1\\\\b=-6\\\\c=3$

Insert the known values into the equation:

$x=-\frac{(-6)}{2(1)}$

Simplify. Two negatives make a positive:

$x=\frac{6}{2} =3$

X is equal to 3 (3,y). Insert the value of x into the standard form equation and solve for y:

$y=3^2-6(3)+3$

Simplify using PEMDAS:

$y=9-18+3\\\\y=-9+3\\\\y=-6$

The value of y is -6 (3,-6). Insert these values into the vertex form:

$(3_{h},-6_{k})\\\\y=a(x-3)^2+(-6)$

Insert the value of a and simplify:

$y=(x-3)^2-6$

:Done

6 0

3 years ago

If an intravenous solution containing 123 mg of a drug substance in each 250-mL bottle is to be administered at the rate of 200

12345 [234]

Answer:

24.39mL of the solution would be given per hour.

Step-by-step explanation:

This problem can be solved by direct rule of three, in which there are a direct relationship between the measures, which means that the rule of three is a cross multiplication.

The first step to solve this problem is to see how many mg of the solution is administered per hour.

Each minute, 200 ug are administered. 1mg has 1000ug, so

1mg - 1000 ug

xmg - 200 ug

$1000x = 200$

$x = \frac{200}{1000}$

$x = 0.2mg$

In each minute, 0.2 mg are administered. Each hour has 60 minutes. How many mg are administered in 60 minutes?

1 minute - 0.2 mg

60 minutes - x mg

$x = 60*0.2$

$x = 12mg$

In an hour, 12 mg of the drug is administered. In 250 mL, there is 123 mg of the drug. How many ml are there in 12 mg of the drug.

123mg - 250mL

12 mg - xmL

$123x = 250*12$

$x = \frac{250*12}{123}$

$x = 24.39$ mL

24.39mL of the solution would be given per hour.

7 0

3 years ago

A rectangular swimming pool measures 40 ft by 60 ft and is surrounded by a path of uniform width around the four edges. The peri

Alex_Xolod [135]

Answer:

6ft

Step-by-step explanation:

Lets x = the width of the path the surrounding path will add 2x to the pool dimension,therefore over all dimesion: (2x+40) by (2x+60) the overall perimeter (2x + 40) + 2(2x+60) = 248 Simplify divide by 2, result (2x+40) +(2x+60) = 124

 Combine like terms 2x + 2x +40 +60 =124 

4x + 100 = 124 

4x=124 = 100

4x=24

x=24/4

x= 6ft is the width of the path

check this by finding the perimeter with these values; 2x = 12 ft 

2 ( 12 + 40 ) + 2( 12 +60 ) 

2( 52 + 2(72)

104 + 144 = 248; confirms our solution of x= 6 ft

5 0

3 years ago

What is the value of x in the equation x – y = 30, when y = 15?

wariber [46]

The answer is equal to a

8 0

3 years ago

Read 2 more answers

First come first served brainiest *easy*

tigry1 [53]

Answer:

15

Step-by-step explanation:

3 0

3 years ago

Read 2 more answers