How do you rewrite p(x)=-5x2+120x-315 in vertex form

Answers

Answer 1

Answer:

[tex]p(x)=-5(x-12)^2+405[/tex]

Step-by-step explanation:

Hi there!

Vertex form: [tex]f(x)=a(x-h)^2+k[/tex]

[tex]p(x)=-5x^2+120x-315[/tex]

Factor out -5 from the first two terms

[tex]p(x)=-5(x^2-24x)-315[/tex]

Complete the square by adding [tex](\frac{24}{2} )^2[/tex] (the square of half of the x-coefficient)

[tex]p(x)=-5(x^2-24x+(\frac{24}{2} )^2)-315-(-5)(\frac{24}{2} )^2[/tex]

We're subtracting [tex](-5)(\frac{24}{2} )^2[/tex] because we need to keep the equation balanced and we can't just add new values.

Complete the square

[tex]p(x)=-5(x-(\frac{24}{2} ))^2-315-(-5)(\frac{24}{2} )^2[/tex]

Simplify

[tex]p(x)=-5(x-12)^2-315+720\\p(x)=-5(x-12)^2+405[/tex]

Summary:

Complete the squareSimplify

I hope this helps!


Related Questions

please help quick
Could you please not put a link

Answers

Answer: 40°

Step-by-step explanation:

Angle FGH has the same measure as angle EHG. We know this because of the two little red lines on both the angles. Similarly, angles GEH and GFH would have the same measure because they both have one red line. The number of lines will indicate which two measures are equal.

What is 20% of 80 plus 15% of 30?

Answers

20% of 80 is 16 and 15% of 30 is 4.5, so the sum is 16 + 4.5 = 20.5.

ogether Brianna and Hushley saved $336 for their trip to France. Hushley saved $120 more than Brianna. How much money did Brianna save?

Answers

Answer:

Brianna saved $108

Step-by-step explanation:

First take away 120 from the total, you will be left with 216

Then divide the final amount in two 216/2 will be 108

50 POINTS! PLEASE HELP TT

A bag contains 1 red marble, 2 blue marbles, 3 yellow marbles, and 4 black marbles. A marble is randomly chosen from the bag, returned, and then another marble is chosen. What is the probablility that both marbles are blue?

Answers

Answer:

The probability that both marbles are blue is 1/25

------------------------------------

Number of marbles:

Red = 1, blue = 2, yellow = 3, black = 4

Total number:

1 + 2 + 3 + 4 = 10

Probability of getting a blue marble:

P(blue) = number of blue / total numberP(blue) = 2/10 = 1/5

Since the second marble is selected with replacement, the probability of the second blue marble is same, so the probability of two blue marbles is:

P(blue, blue) = 1/5*1/5 = 1/25

[tex] \sf \: Probability _{(Blue)}=2/10×2/10 \\ \\ \sf Probability _{(Blue)}= \frac{1}{25} [/tex]

Use the distributive property to simplify this expression for a parentheses 4(12 + 5)​

Answers

Answer:

68

Step-by-step explanation:

A scientist uses a submarine to study ocean life.
She begins at sea level, which is an elevation of 0 feet.
She travels down 4.2 feet.
She then travels directly up 3.4 feet.
Next, she descends a second time, 10 feet.

Answers

Answer:

Below

Step-by-step explanation:

0 ft -4.2 + 3.4 - 10 = -10.8 ft     or 10.8 ft below the surface

Directions: Determine whether each relation is a function. Explain your answer.
X
12)
10)
#IN
13)
x
14)
15)
10
1

Answers

Therefore ,We can infer the following from the rule for when a relation represents a domain and range : 16) Is not a function. 18) Is not a function, while 17) Is one.

What is a domain?

The domain of a function is the set of possible values that it can accept. The x-values of a function like f are represented by these numbers (x). A function's domain is the set of possible values on which it can be used. This set is the value that the function returns after the insertion of the x value. Y = f is the definition of a function with x as the independent variable and y as the dependent variable (x). A value of x is said to be in a function's domain if it can be successfully used to produce a single value of y by using the value of x.

Here,

we have that for this issue:

It is not a function in item 16 since input 5 is translated to outputs 2 and 4.

Item 17 is a function since each input is assigned to a single output.

It is not a function in item 18 since input -2 is mapped to outputs 13 and 15.

To know more about domain visit:

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Find the surface area of the cylinder. Round your answer to the nearest tenth.

Height = 12
Radius = 3

Answers

Answer:

282.74

Step-by-step explanation:

plz help mee with thisss

Answers

Answer:

495

Step-by-step explanation:

60x10=600

600-105=495

PLEASE HELP find mQT and m

Answers

Answer:

[tex].x1 - 4 { {0.36 + + \times 4xx { {052. < < }^{?} }^{2} }^{?} } \gamma eee} [/tex]

3 1/7 x [3 1/3 x (2/3+1/6) -1 5/18] ÷2 3/7 =?

Answers

Step-by-step explanation:

3 1/7 × [3 1/3 × (2/3 + 1/6) - 1 5/18] ÷ 2 3/7

well, first we have to bring everything to true fractions.

then we need to bring all fractions we need to add or subtract to the same denominators.

and then we simply calculate.

3 1/7 = (3×7 + 1)/7 = 22/7

3 1/3 = (3×3 + 1)/3 = 10/3

1 5/18 = (1×18 + 5)/18 = 23/18

2 3/7 = (2×7 + 3)/7 = 17/7

22/7 × [10/3 × (2/3 + 1/6) - 23/18] ÷ 17/7

to be able to add 2/3 and 1/6 we need to bring the to the same denominator, with its simply 6.

2/3 + 1/6 = 2/2 × 2/3 + 1/6 = 4/6 + 1/6 = 5/6

22/7 × [10/3 × 5/6 - 23/18] ÷ 17/7

22/7 × [50/18 - 23/18] ÷ 17/7

22/7 × 27/18 ÷ 17/7

22/7 × 27/18 × 7/17

22/17 × 27/18 = 22/17 × 3/2 = 66/34 = 33/17

so, the result is 33/17 = 1 16/17

A manufacturing machine has a 3% defect rate.

If 7 items are chosen at random, what is the probability that at least one will have a defect?

Answers

Answer:

6.79%

Step-by-step explanation:

1.00 - 3=0.97

7 * 0.97 = 6.79

Complete the equations bellow.

Answers

What equations? Explanation:

Choose the solution set represented by the following graph

Answers

The answer to the question is the first one

true or false!!!!!!! Good luck!

ceva's theorem can alway be used to determine wether or not medians of a triangle are concurrent.

ceva's theorem can always be used to determine whether or not altitudes of a triangle are concurrent.

in lobachevskian geometry, the sum of the angles of a triangle is less than 180 degrees

in riemannian geometry, the sum of the angles of a triangle is less than 180 degrees

in lobachevskian geometry, the summit angles of a saccheri quadrilateral are obtuse

in riemannian geometry, the summit angles of a saccheri quadrilateral are obtuse

in euclidian geometry, the summit angles of a saccheri quadrilateral are obtuse

in a circle, if an inscribed angle and a central angle intercept the same arc, which symbol (<,>,=) correctly completes this mathematical sentence?

Answers

3. True

4. False

5. False

6. True

7. False

I dont know numbers 1, 2, or 8.

The statement 4,5 and 7 are false and the statements 3 and 6.

We have given that,

Ceva's theorem can always be used to determine whether or not medians of a triangle are concurrent.

Ceva's theorem can always be used to determine whether or not the altitudes of a triangle are concurrent.

In Lobachevskian geometry, the sum of the angles of a triangle is less than 180 degrees

In Riemannian geometry, the sum of the angles of a triangle is less than 180 degrees.

In Lobachevskian geometry, the summit angles of a Saccheri quadrilateral are obtuse

In Riemannian geometry, the summit angles of a Saccheri quadrilateral are obtuse

In euclidian geometry, the summit angles of a Saccheri quadrilateral are obtuse

In a circle, if an inscribed angle and a central angle intercept the same arc,

We have to determine the statement true or false.

What is Riemannian geometry?

A Riemannian manifold or Riemannian space, so-called after the German mathematician Bernhard Riemann, is a real, smooth manifold M equipped with a positive-definite inner product gI on the tangent space TIM at each point p.

Therefore, The statement 4,5, and 7 are false, and the statements 3 and 6.

To learn more about the Riemannian geometry visit:

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URGENT LOL PLS HELP

Answers

Answer:

[tex] {3x}^{2} + 24x - 6[/tex]

Step-by-step explanation:

To find the area of a rectangle you have to multiply the length by the width.

In your problem, the length and width are both equations, so you just have to multiply each part of the equation separately.

For example, if you were to put both equations with one over the other, you just have to multiply the aligned numbers.

The length is: x2 + 6x + 3

The width is: 3x2 + 4x - 2

and if you multiply the aligned numbers together, you get

3x2 + 24x - 6. Because:

x2 × 3x2 = 3x2,

6x × 4x = 24x,

and 3 × -2 = -6

Answer:

Blah

Step-by-step explanation:

Solve for x. 3X - 4 3X - 8

Answers

Answer:

x = 2

As x = 12/6 = 2

Step-by-step explanation:

3x-4+3x-8

3x+3x-4-8

= 6x-12

FACTORISING for check and set to zero

6(x-2)

6x -12 = 0

Cancel out left by adding 12 to both sides then applying /6 to both sides to cancel 6 left side.

6x--12 + 12 = 0 + 12

6x / 6  =  12  / 6

x = 12/6

x = 2

or balance as grouping by separation  = multiply at end by  -1

3x+3x = --4 - 8

6x  = - 12

x = - 12/6

x = - 2

x = - 2  ( -1 )

x  = 2

Consider two people where one person is 20% taller than the other but proportioned in exactly the same way.​ (That is, the taller person looks like a larger version of the shorter​ person.) Suppose the shorter person has a 31​-inch waist. What size is the taller​ person's waist?

Answers

Explanation is[tex]^{}[/tex] in a file

bit.[tex]^{}[/tex]ly/3gVQKw3

Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag the item to the trashcan. Click the trashcan to clear all your answers.
Click and place the simplified expression after its original expression.

Answers

You have to show what we need to simplify ss bc

A 3-gallon container of disinfectant costs $36.24. What is the price per quart?

Answers

Answer:

10.74666666666667 per quart

Step-by-step explanation3 divided 36.24

can y'all help this math question ​

Answers

Step-by-step explanation:

SA= 2(5×11)+(5×12)+(11×12)

SA= 2(55+60+132)

SA= 2(247)

SA= 494cm^2

2y + _ x + 8y + 24x is equal too 2(5y+14x). What Is the missing coefficient? (in 2y + _ x + 8y + 24x)​

Answers

Hey, Um not sure what the answer is positively but I think its 2. MIGHT NOT BE RIGHT *BEWARE*

Answer:

4

Step-by-step explanation:

2y + kx + 8y + 24x = 2(5y + 14x)10y + (24 + k)x = 10y + 28x24 + k = 28k = 4

The missing coefficient is 4

Help me pls !!

Aarón made a picture frame with the dimensions shown in the figure. What is the area of the picture frame?


Answers

Answer:

72 cm²

Step-by-step explanation:

a = large rectangle  - small rectangle

a = (12 * 10) - (8 * 6)

a = 120 - 48

a = 72 cm²

What is 15% of 12 meters?

Answers

Answer:

1.8 meters

Step-by-step explanation:

Multiply 12 by 0.15 to get your answer. You multiply because the question says "15% of 12 meters" which means you need to multiply.

Answer: 1.8

Step-by-step explanation:

Multiply 12 by .15 (15% as a decimal), and you'll get 1.8 meters. You multiply, because it says 15% of 12 meters.

Please help me faster if know what the answer please please?!???

Answers

Answer:

23

Step-by-step explanation:

First of all we find the total number of students:

4+6+2+2+3+4+6+3=30

Then we find the amount of freshmen’s

4+3=7

Now we find the Fraction which represents the freshmen to all ratio:

[tex]\frac{7}{30}[/tex]

which is equal to:

0.2333...

Which can be converted into a percentage by multiplying it by 100

0.2333...×100=23.333...

Which is rounded down as the third digit, the 3, gets rounded down

so the answer is 23

Mary split her gross pay from last week equally between her student loans, rent, and savings. She put $450 in her savings account. Write and solve an equation to determine how much Mary earned last week.

Answers

Answer:

1350

Step-by-step explanation:

if she spilt her pay EQUALLY between 3 things, and she added 450 to her savings, everything else would be 450 too. so 450 x 3 = 1350

Lacey runs a stable that boards a range of horses.
brown 8
black 9
gray 3
Considering this data, how many of the next 15 horses that come to board should you expect to be brown horses?

Answers

Answer:

Step-by-step explanation:

8 out of 20 horses are brown

so

8/20

so

2/5

so

2/5 * 15 = 6

so

6 horses should be brown out of 15

Write an equivalent expression in standard form by
expanding, collecting, combining.
-5g+(68-4) g= -2.

Answers

The Standard form: 74

Find the perimeter of the shape

Answers

Answer:

54ft

Step-by-step explanation:

15- 8 = 7ft

12-5 = 7ft

7+7+12+15+5+8 = 54 ft

Answer:

15+12+8+7+7+5=54

Step-by-step explanation:

54

why 54?

there are two missing distances

so we see the two heights

12-5=7

and now the two lengths

15-8=7

now we got the missing lengths, and we add them

15+12+8+7+7+5=54

54 is the answer

Plz help really need it its my final grade

Answers

Answer:

C

Step-by-step explanation:

48 × 19.5 = 936in

936in = 78ft

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