PLEASE HELP the vertex form of the equation of a parabola is y = (x - 3)2 + 36. what is the standard form of the equation?

Answer:

9108

Step-by-step explanation:

23^3+(-12)^3+(-11)^3                              remove parentheses

= 23^3-12^3-11^3                                  group difference of two cubes

= (23-12)(23^2+23*12+12^2) + 11^3      factor difference of two cubes

= 11 (23^2+23*12+12^2-11^2)                factor ou 11

= 11(23(23+12) + (12+11)(12-11))              apply difference of two squares

= 11 (23*35+23*1)                                  factor out 23

= 11(23*(35+1))                                       simplify

= 11*23*36                                             convert 11*23 into difference of 2 squares                                                                    

= (17^2-6^2)*6^2                                   expand parentheses

= 102^2-36^2                                       evaluate squares

= 10404 - 1296                                     subtraction

= 9108

(no calculator required)

Answer: D. The quadratic function has two distinct real zeros.

There are no complex roots as a quadratic's roots are maxed out at 2. The fundamental theorem of algebra says that if you have an nth degree polynomial, then the max number of real roots is n.

This quadratic's roots are distinct because the two x intercepts are in different places. Each x intercept is a root.

Answer:

coordinates of point g is ( -6, 14)

Step-by-step explanation:

The coordinates of the point which divides the point (x1,y1) and (x2,y2) in m:n ratio is given by (nx1+mx2)/(m+n), (ny1+my2)/(m+n).

___________________________________________

given point

F(-1, -1) to H(-8, 20)

ratio : 5:2

the coordinates of point g is

(2*-1+5*-8)/(5+2), (2*-1+5*20)/(5+2)

=> (-2 -40/7 , -2+100/7)

=> (-42/7, 98/7)

=>( -6, 14)

Thus ,  coordinates of point g is ( -6, 14)

Answer:

34 feet

Step-by-step explanation:

let length of ladder be x

[tex] \ \sin(34) = \frac{17}{x} [/tex]

[tex]x \sin(34) = 17[/tex]

[tex]x = \frac{17}{ \sin(34) } [/tex]

x = 32.131083564

Answer:

67.63 oz

Step-by-step explanation:

1 liter = 33.814 oz

2 litres = 2 x 33.814 oz = 67.628 oz

Answer:

Step-by-step explanation:

A=a(r)^t

a=1

time=2.5 hours=25/10 ×60=150 minutes

10t=150

t=150/10=15

[tex]A=1(2)^{15}=32,768[/tex]

Answer:

4 of the berries will be shaded

Step-by-step explanation:

The model that shows that 4 out of 10 strawberries were eaten is attached.

We have, 4 out of 10 strawberries were eaten in a fruit tray.

Refer to the image attached. This model shows that the 4 out of 10 strawberries were eaten.

Therefore, the model that shows that 4 out of 10 strawberries were eaten is attached.

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a = 18°

we have opposite angles =>

=> 6a + 11 = 2a + 83

6a - 2a = 83 - 11

4a = 72

a = 72 : 4

a = 18°

Answer:

The equation for S which gives the score he needs to earn on the 6th test to average exactly 85 points for all 6 tests is;

S + 429 = 85 × 6

Step-by-step explanation:

The parameters given are;

The scores earned by Mele on the first five test in Economics II are;

75, 70, 92, 95, and 97 points

The total test points = 429 points

Therefore, the score, S, Mele needs to earn on the 6th test for him to get an average of exactly 85 points for the 6 tests is found as follows;

From the definition of average, μ = (Sum of data values)/(Number of data)

Sum of data values = S + 429

The number of data = 5 test + 6th test =  6

μ = 85 = (S + 429)/6

Therefore;

S + 429 = 85 × 6

Therefore, the equation for S which gives the score he needs to earn on the 6th test to average exactly 85 points for all 6 tests is S + 429 = 85 × 6.

Answer:

two complex solutions

Step-by-step explanation:

2x^2 + 4x+4

Factor out 2

2( x^2+2x+2)

Using the discriminant on the inner term

b^2 -4ac  where a=1  b=2  c=2

2^2 -4 (1) (2)

4 - 8

-4

Since the  discriminant  is negative, we will have 2 complex solutions

Answer:

  2 complex solutions

Step-by-step explanation:

Given the standard form quadratic ...

  ax^2 +bx +c

The expression b^2-4ac is called the "discriminant." Its value can be used to predict the type of solutions. Here, we have ...

  a=2, b=4, c=4

so the discriminant is ...

  d = b^2 -4ac = 4^2 -4(2)(4) = -16

Because the discriminant is negative, we can predict there are 2 complex solutions.

__

The graph has no x-intercepts, confirming there are 2 complex solutions.

Answer:

y = 6x -27

Step-by-step explanation:

y-3=6(x-5)

Distribute

y-3 = 6x-30

Add 3 to each side

y-3+3 = 6x-30+3

y = 6x -27

This is in slope intercept form  y=mx+b where m is the slope and b is the y intercept

Hey there! I'm happy to help!

Slope intercept form is y=mx+b. So, the first thing we want to do is isolate y on side of the equation.

y-3=6(x-5)

We use distributive property to undo parentheses.

y=3=6x-30

We add 3 to both sides.

y=6x-27

Now, this in slope intercept form.

Have a wonderful day! :D

Answer:

16/7

Step-by-step explanation:

16k / 7k

Divide the numbers

16/7  

Divide the variables

k/k = 1

16/7

Answer:

[tex]\huge\boxed{Option \ C}[/tex]

Step-by-step explanation:

∠CAD is the central angle and ∠CBD is the inscribed/circumference angle which means that

∠CAD = 2(∠CBD)

So, If ∠CBD = 55° then ∠CAD = 110°

[tex](6x - 5) + (4x^2- 3x + 4)=\\6x-5+4x^2-3x+4=\\4x^2+3x-1[/tex]

Answer:

x = 33

Step 1:

First, let's add the values together from both parentheses.

2x + x = 3x

1 + (-10) = -9

Now we are left with:

3x - 9 = 90.

Step 2:

Add 9 on the left side to cancel out the 9. Add it to the right side.

3x = 99

Finally, divide both sides by 3 to get our answer.

3x / 3 = x

99 / 3 = 33

x = 33

Answer:

2/5

Step-by-step explanation:

First for the sum:

3/5 + 1/5 i + 4/5 - 2/5 i = 7/5 - 1/5 i

Now for the difference

9/5 - 1/5 i - (7/5 - 1/5 i)

= 9/5 - 1/5 i - 7/5 + 1/5 i

= 2/5 , which is the answer :)

The answer is  2/5.

To find the fraction bar in the box.

A fraction is a part of a whole. In arithmetic, the number is expressed as a quotient, in which the numerator is divided by the denominator. In a simple fraction, both are integers. A complex fraction has a fraction in the numerator or denominator. In a proper fraction, the numerator is less than the denominator.

Given that:

First for the sum:

3/5 + 1/5 i + 4/5 - 2/5 i = 7/5 - 1/5 i

Now substract the sum,

9/5 - 1/5 i - (7/5 - 1/5 i)

= 9/5 - 1/5 i - 7/5 + 1/5 i

= 2/5

So, the answer is  2/5.

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Answer:

a = 1

Step-by-step explanation:

Given that both ax³ + 3x² - 3 and 2x³ - 5x + a have the same remainder when divided by x - 4.

x - 4 = 0

x = 4

When ax³ + 3x² - 3 is divided by x - 4, the remainder is gotten by substituting x = 4:

a(4)³+3(4)²-3 = 64a + 48 - 3 = 64a + 45

The remainder is 64a³ + 45

For 2x³ - 5x + a we find the remainder by substituting x = 4:

2(4)³ - 5(4) + a = 128 - 20 + a = 108 + a

Since they both have the same remainder, therefore:

64a + 45 = 108 + a

64a - a = 108 - 45

63a = 63

a = 1

Answer:

[tex]6b[/tex]

Step-by-step explanation:

We know that the distance formula is [tex]\sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}[/tex]. We already have the x values, which are [tex]5a[/tex] and [tex]-a[/tex], subtracting [tex]-a[/tex] from 5a gets us [tex]6a[/tex].

Same concept for the y values, let's subtract the first y value from the second.

The second y value is [tex]b[/tex], while the first is [tex]-5b[/tex]

[tex]b - (-5b) = b + 5b = 6b[/tex]

Hope this helped!

Answer:

6b is your answer!

Step-by-step explanation:

I wish ALL ACELLUS USERS LUCK

Answer:

5040

Step-by-step explanation:

All the possible Numbers that can be placed in the last for places =0,1,2,3,4,5,6,7,8,9

If all the digits  have be different , then

= 10 x 9 x 8 x 7

= 90 x 56

=  5040   are total no. of 4-digit numbers can be made using those 4 digits.

Find the circumference of the wheel:

Circumference = PI x Diameter = 3.14 x 15 = 47.1 inches.

Every revolution the tire travels 47.1 inches.

1 mile = 5,280 feet, so 2 miles = 5280 x 2 = 10,560 feet.

1 foot = 12 inches.

2 miles = 10,560 feet x 12 = 126,720 inches.

Revolutions = total distance /  distance per revolution:

Revolutions = 126,720 / 47.1 = 2,690.45 revolutions ( round answer as needed.)

Answer:

Hope it helps U can still ask me if u have confusions

Answer:

  60+16√30 cm² ≈ 147.64 cm²

Step-by-step explanation:

You can figure the height of the object from ...

  V = Bh

  120 cm^3 = (30 cm^2)h

  4 cm = h . . . . . divide by 30 cm^2

However, this is insufficient to tell you the surface area.

__

If you assume that the base is square, then its side length is

  A = s^2

  s = √A = √(30 cm^2) = (√30) cm

The lateral surface area can then be found from the perimeter of the base and the height

  LA = Ph = (4√30 cm)(4 cm) = 16√30 cm^2

The total surface area will be the sum of this lateral area and the area of the two bases:

 total area = 16√30 cm^2 +2·30 cm^2

 total area = (60 +16√30) cm^2 ≈ 147.64 cm^2

__

For any other shape, the total area will be larger. It can be arbitrarily large, unless limits are put on the dimensions of the object.

[tex]\left(\dfrac{1}{1+2i}+\dfrac{3}{1-i}\right)\left(\dfrac{3-2i}{1+3i}\right)=\\\\\left(\dfrac{1-2i}{(1+2i)(1-2i)}+\dfrac{3(1+i)}{(1-i)(1+i)}\right)\left(\dfrac{(3-2i)(1-3i)}{(1+3i)(1-3i)}\right)=\\\\\left(\dfrac{1-2i}{1+4}+\dfrac{3+3i}{1+1}\right)\left(\dfrac{3-9i-2i-6}{1+9}\right)=\\\\\left(\dfrac{1-2i}{5}+\dfrac{3+3i}{2}\right)\left(\dfrac{-3-11i}{10}\right)=\\\\\left(\dfrac{2(1-2i)}{10}+\dfrac{5(3+3i)}{10}\right)\left(\dfrac{-3-11i}{10}\right)=[/tex]

[tex]\dfrac{2-4i+15+15i}{10}\cdot\dfrac{-3-11i}{10}=\\\\\dfrac{17+11i}{10}\cdot\dfrac{-3-11i}{10}=\\\\\dfrac{-51-187i-33i+121}{100}=\\\\\dfrac{70-220i}{100}=\\\\\dfrac{70}{100}-\dfrac{220i}{100}=\\\\\boxed{\dfrac{7}{10}-\dfrac{11}{5}i}[/tex]

Answer:

Jada drank less water than Elina.

Step-by-step explanation:

Water drunk by Elina = 3 liters

Jada drank the water [tex]\frac{3}{4}[/tex] times as much as water as Elina.

Therefore, water drunk by Jada = [tex]\frac{3}{4}\times 3[/tex]

                                                     = [tex]\frac{9}{4}[/tex]

                                                     = 2.25 liters

Lin drank water twice as much as Jada.

Therefore, Lin drank the amount of water = 2 × 2.25

                                                                   = 4.5 liters

Since Jada drank 2.25 liters of water and Elina drank 3 liters

Therefore, Jada drank less water than Elina.

Answer:

34.7

Step-by-step explanation:

First Step: Multiply.

3 × 10 = 30

4 × 1 = 4

7 × 1/10 = 7/10

Second step: Add.

30 + 4 + 7/10= 347/10

Final step: Make it a decimal.

347 ÷ 10 = 34.7

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      Hi my lil bunny!

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[tex]3\times 10+4\times 1+7\times 1/10[/tex]

[tex]= \frac{347}{10}[/tex] (Decimal: 34.7)

Step by Step Explanation.

[tex](3) (10) + (4) (1) + \frac{(7)(1)}{10} \\= 30 + (4) (1) + \frac{(7)(1)}{10} \\= 34 + \frac{(7)(1)}{10} \\= 34 + \frac{7}{10} \\= \frac{347}{10}[/tex]

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If this helped you, could you maybe give brainliest..?

❀*May*❀

Answer:

1/22

Step-by-step explanation:

Simplify it.

It becomes 3/22-1/11

Change the denominator to 22 becasue that is the LCM.  

It becomes 3/22-2/22 which is 1/22. :)

Answer:

4%

Step-by-step explanation:

There are ₁₃C₃ ways to choose 3 diamonds from 13.

There are ₃₉C₁ ways to choose 1 non-diamond from 39.

There are ₅₂C₄ ways to choose 4 cards from 52.

Therefore, the probability is:

₁₃C₃ ₃₉C₁ / ₅₂C₄

= 286 × 39 / 270,725

≈ 0.04

The approximate probability that exactly three of the cards are diamonds is 4%.

Probability refers to a possibility that deals with the occurrence of random events.

The probability of all the events occurring need to be 1.

We are given that standard deck of 52 playing cards contains 13 cards in each of four suits: hearts, diamonds, clubs, and spades.

Since we can see that there are ₁₃C₃ ways to choose 3 diamonds from 13.

₃₉C₁ ways to choose 1 non-diamond from 39.

₅₂C₄ ways to choose 4 cards from 52.

Therefore, the probability is:

₁₃C₃ ₃₉C₁ / ₅₂C₄

= 286 × 39 / 270,725

≈ 0.04

Therefore, the answer could be 4 percent.

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Answer:

e=-2

Step-by-step explanation:

9e-7e=-11+7

2e=-4

e=-2

Answer:

-8

Step-by-step explanation:

2(-2) +3(-2) +2

-4 -6 +2

-10 +2

-8