Which equation can be used to find the surface area of the cylinder?

What is the vertex form of the parabola whose standard form equation is y=5x^2-30x+49

agasfer [191]

Answer:

The vertex is (3,4)

Step-by-step explanation:

To convert a quadratic from

y = a x 2 + b x + c

form to vertex form,

y = a ( x − h ) 2 + k , you use the process of completing the square.

First, we must isolate the x

terms:

y − 49 = 5 x 2 − 30 x + 49 − 49

y − 49 = 5 x 2 − 30 x

We need a leading coefficient of 1

for completing the square, so factor out the current leading coefficient of 2.

y − 49 = 5 ( x 2 − 6 x )

Next, we need to add the correct number to both sides of the equation to create a perfect square. However, because the number will be placed inside the parenthesis on the right side we must factor it by

2

on the left side of the equation. This is the coefficient we factored out in the previous step.

y − 49 + ( 5 ⋅ ? ) = 5 ( x 2 − 6 x + ? )

<- Hint:

62 = 3 ; 3 ⋅ 3 = 9

y − 49 + ( 5 ⋅ 9 ) = 5 ( x 2 − 6 x + 9 )

y− 49 + 45 = 5 ( x 2 − 6 x + 9 )

y − 4 = 5 ( x 2 − 6 x + 9 )

Then, we need to create the square on the right hand side of the equation:

y − 4 = 5 ( x − 3 ) 2

Now, isolate the y term:

y − 4 + 4 = 5 ( x − 3 ) 2 + 4

y − 0 = 5 ( x − 3 ) 2 + 4

The vertex is:

( 3 , 4 )

7 0

3 years ago

Determine the y-intercept of the line that passes through (-5,-12) and has a slope of -5

brilliants [131]

Answer:

-37

Step-by-step explanation:

Not sure what the method is called, but you do this.

substitute the slope into slope formula

y= -5x+b

substitute the points you have for x and y

-12= -5(-5)+b

solve

-12= 25+b

-37= b

6 0

3 years ago

11/5,0.05,5,0.5,1/5 from least to greatest

anygoal [31]

0.05,1/5,0.5,11/5,5

3 0

3 years ago

NEED HELP NOW 25 POINTS WILL MARK BRAINLIEST ANSWER!!!!!

Pachacha [2.7K]

The sandwich cost 2.25 meaning that that would be our slope since the price can go higher with every sandwich you buy.. and it will be negative because you will be taking away that sum to your five dollars.. so we have y=-2.25 +5 it has plus five because it is how much you had in the first place.. so lets test it, lets say you buy 2 sandwiches. you will put 2 in for x and solve it.. -2.25(2) +5 multiply -4.5+5 and you get .5 this lets you see first how much you will spend and what will be left out

Hope i helped

4 0

3 years ago

What is 2x + 4 < 16

harina [27]

Answer:

x<6 just letting you know that / is not meant for division it means a fraction bar

Step-by-step explanation:

1. Group all constants on the right side of the inequality

2x+4<16

Subtract from both sides

(2x+4)-4<16-4

Simplify the arithmetic

2x<16-4

Simplify the arithmetic

2x<12

2. Isolate the x

2x<12

Divide both sides by 2

(2x)/2<12/2

Simplify the fraction

x<12/2

Find the greatest common factor of the numerator and denominator

x<6*2/1*2

Factor out and cancel the greatest common factor

x<6

3. Solution on a coordinate plane

Solution: x<6

Interval notation:

(-∞,6)

7 0

1 year ago