How does the minimum or maximum value of a parabola relate to the vertex of the same parabola?

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[tex]y = 2x + 3[/tex]

[tex]y = - \frac{1}{2} x - 3 \\ [/tex]

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Answer:

see explanation

Step-by-step explanation:

Parallel lines have equal slopes.

To find D and E use the midpoint formula

Given endpoints (x₁, y₁ ) and (x₂, y₂ ) then the midpoint is

( [tex]\frac{x_{1}+x_{2} }{2}[/tex], [tex]\frac{y_{1}+y_{2} }{2}[/tex] )

Here (x₁, y₁ ) = A(4, 6) and (x₂, y₂ ) = B(2, - 2) , then

D = ([tex]\frac{4+2}{2}[/tex], [tex]\frac{6-2}{2}[/tex] ) = (3, 2 ) and

let (x₁, y₁ ) = B(2, - 2[tex]\frac{-4+2}{-2-2}[/tex] ) and (x₂, y₂ ) = C(- 2, - 4 ), then

E = ( [tex]\frac{4-2}{2}[/tex], [tex]\frac{6-4}{2}[/tex] ) = (1, 1 )

Use the slope formula to find slopes of DE and BC

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = D(3, 2) and (x₂, y₂ ) = E(1, 1), then

[tex]m_{DE}[/tex] = [tex]\frac{1-2}{1-3}[/tex] = [tex]\frac{-1}{-2}[/tex] = [tex]\frac{1}{2}[/tex]

Repeat with (x₁, y₁ ) = B(2, - 2) and (x₂, y₂ ) = C(- 2, - 4), then

[tex]m_{BC}[/tex] = [tex]\frac{-4+2}{-2-2}[/tex] = [tex]\frac{-2}{-4}[/tex] = [tex]\frac{1}{2}[/tex]

Since the slopes are equal then DE and BC are parallel lines

Answer:

[tex]x=\frac{1-\sqrt{-5} }{6}\\x=\frac{1+\sqrt{-5} }{6}[/tex]

There are no real roots.

Step-by-step explanation:

[tex]6x^2-2x+1=0\\x=\frac{2-\sqrt{2^2-4*6} }{2*6} \\x=\frac{2-\sqrt{-20} }{12}\\x=\frac{1-\sqrt{-5} }{6}\\x=\frac{1+\sqrt{-5} }{6}[/tex]

Answer:

Step-by-step explanation:

Receiving Social Security Income While Working. In the year you reach full retirement age, your benefits will be reduced by $1 for every $3 you earn above $48,600 for 2020 and $50,520 for 2021. 6  Starting with the month you attain full retirement age, your benefits will no longer be reduced.

Answer:

The system of inequalities are;

q + w ≤ 20

8w + 10q ≤ 160

Step-by-step explanation:

Let the number of wigs be w and the number of quesadillas be q

Since we have a maximum of 20 packages;

then;

q + w ≤ 20

Let’s now work with the prices

price of w wings is 8 * w =$8w

price of q quesadillas is 10 * q = 10q

The maximum amount to spend is $160

Thus, the addition will be;

8w + 10q ≤ 160

Answer:

25 and 30

Step-by-step explanation:

Given the ratio of 2 numbers is 5 : 6 = 5x : 6x ( x is a multiplier ), then

5x + 6x = 55, that is

11x = 55 ( divide both sides by 11 )

x = 5

Thus

5x = 5 × 5 = 25

6x = 6 × 5 = 30

Then the 2 numbers are 25 and 30

Answer: A

Step-by-step explanation:

2x + 9 = 15

2x = 6

x = 3

2x+9 = -15

2x = -24

x = -12

Answer:

Expand  [tex]-3(9-x): -27 + 3x[/tex]

Step-by-step explanation:

[tex]-3(9-x)[/tex]

Apply the distributive law: [tex]a(b-c)=ab-ac[/tex]

[tex]a = -3, b=9, c=x[/tex]

[tex]=-3*9-(-3)x[/tex]

Apply minus - plus rules:

[tex]-(-a)=a[/tex]

[tex]= -3*9+3x[/tex]

Multiply the numbers: [tex]3 * 9 = 27[/tex]

[tex]=-27+3x[/tex]

Hope this helps! If so, may I get Brainliest and a Thanks?

Thank you, have a good one! =)

Answer:

14.2

Step-by-step explanation:

you just have to add both of the numbers shown in the question

Answer:

15

Step-by-step explanation:

its the same as the other angle on there

Answer:

15

Step-by-step explanation:

They are alternate exterior angles, meaning they are the same!!

Answer:

60

Step-by-step explanation:

Answer:

ths answrs is 40 miles pwr hour becUsd 200/5=40

Answer:The average speed  the bus was going is 40 mph

Step-by-step explanation: 200÷5=40

Can you mark me brainliest

Using the probability concept, the correct option regarding who is more likely to brush both in the morning and in the evening is:

B. Arabella. She has a 0.64 probability of brushing both times.

A probability is given by the number of desired outcomes divided by the number of total outcomes.

Considering that the events are independent, we just multiply the probabilities, hence the probability of each brushing both times is given as follows:

Hence statement B is correct, as 0.64 > 0.612.

More can be learned about probabilities at https://brainly.com/question/14398287

#SPJ1

Answer:

x=206

Step-by-step explanation:

Step-by-step explanation:

Percentage increase = (279 - 180)/180 x 100% = 55%

this is a topic on percentage. the above question requires a use of a kind of formula if you wish to explore more into this topic you can give me a follow on Instagram (learntionary) I've already posted some notes on this topic and will be doing more on others and also I'll be providing tips on some topics as well!

Answer:

55% increase

Step-by-step explanation:

First I want to say I recommend using sites like Calculator soup, and finding the option "percent increase calculator", for problems like these instead of wasting any points that you could use later on, and Secondly (happy to help), oof and third:

1) subtract the final value minus the starting value

279 - 180= 99

2) Divide that amount by the absolute value of the starting value

99 divided by 180 equals .55

3) Multiply by 100 to get percent increase

changes to 55.00 (final answer 55%)

4) If the percentage is negative, it means there was a decrease and not an increase.

Percentage Increase Formula

Answer:

2(3x+6)=18

6x+12=18

6x+12-12+18-12

6x=6

6x/6=6/6

x=1

Step-by-step explanation:

Answer:

1) B = 66.5° c = 10.9

Step-by-step explanation:

I will do question one as an example. In general, for these questions you want to use the appropriate trigonometric ratios to solve for the variables and/or apply logic using rules regarding triangles. See attached image for all solving steps.

For side c, we can use Cosine of angle A for a ratio between 10 and c. When we write out the equation, we can solve for side c. So when we write it out, we get the equation:

cos23.5 = ¹⁰⁄c

c = ¹⁰⁄cos₂₃.₅

c = 10.9044 (make sure to round to the nearest tenth, which is one decimal place)

For angle B, since they have given two angles, you can solve for B since all angles of a triangle add up to 180 degrees.

So b = 180 - (90 + 23.5) = 180 - 113.5

b = 66.5

I hope this helps you with the other 3 questions.

Answer:

Domain:(0,infinite)

Range:(5,infinite)

Step-by-step explanation:

Answer:

D = 0, 1, 2, 3, 4, 5

R = 20, 40, 80, 160

Answer:

Step-by-step explanation:

Nshsdhdhdhdjsdnddndnd

Answer:

Step-by-step explanation:

5:2

Answer:

That means it will take you 1 and 1/3 hour to go a kilometer.

Answer:

Step-by-step explanation:

[tex]0.09* \frac{1.21}{3.3}*0.00024= 0.09 * \frac{1.21*10}{3.3*10}*0.00024\\\\=0.09*\frac{12.1}{33}*0.00024\\\\= 0.09 * \frac{1.1}{3}*0.00024\\\\= 0.09 * 1.1 * 0.00008[/tex]

= 0.00000792

= 7.92 * [tex]10^{-6}[/tex]

Answer:

6x^2+10x-6=0

Step-by-step explanation:

First, you need to add all like terms:

6x^2+8x-6=-2x

Now move the -2x to the other side:

6x^2+10x-6=0

Answer:

x =(-5+√61)/6= 0.468

or:

x =(-5-√61)/6=-2.135

Step-by-step explanation:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

                    6*x^2+8*x-6-(2-2*x-2)=0  

Step by step solution :

STEP 1 :

The Equation at the end of step 1

 (((2•3x2) +  8x) -  6) -  -2x  = 0  

STEP 2 :

STEP 3 :

Pulling out like terms

3.1     Pull out like factors :

  6x2 + 10x - 6  =   2 • (3x2 + 5x - 3)  

Trying to factor by splitting the middle term

3.2     Factoring  3x2 + 5x - 3  

The first term is,  3x2  its coefficient is  3.

The middle term is,  +5x  its coefficient is  5.

The last term, "the constant", is  -3  

Step-1: Multiply the coefficient of the first term by the constant   3 • -3 = -9  

Step-2: Find two factors of  -9  whose sum equals the coefficient of the middle term, which is   5.

     -9    +    1    =    -8  

     -3    +    3    =    0  

     -1    +    9    =    8  

Observation: No two such factors can be found !!

Conclusion: Trinomial can not be factored

The Equation at the end of step 3 :

 2 • (3x2 + 5x - 3)  = 0  

STEP 4 :

Equations which are never true:

4.1      Solve :    2   =  0

This equation has no solution.

A non-zero constant never equals zero.

Parabola, Finding the Vertex:

4.2      Find the Vertex of y = 3x2+5x-3

Parabolas have the highest or lowest point called the Vertex.   Our parabola opens up and accordingly has the lowest point (AKA absolute minimum).   We know this even before plotting  "y"  because the coefficient of the first term, 3, is positive (greater than zero).  

Each parabola has a vertical line of symmetry that passes through its vertex. Because of this symmetry, the line of symmetry would, for example, pass through the midpoint of the two x-intercepts (roots or solutions) of the parabola. That is if the parabola has indeed two real solutions.  

Parabolas can model many real-life situations, such as the height above ground, of an object thrown upward, after some period of time. The vertex of the parabola can provide us with information, such as the maximum height that an object, thrown upwards, can reach. For this reason, we want to be able to find the coordinates of the vertex.  

For any parabola, Ax2+Bx+C, the x -coordinate of the vertex is given by  -B/(2A). In our case, the  x  coordinate is  -0.8333  

Plugging into the parabola formula  -0.8333  for  x  we can calculate the  y -coordinate :  

 y = 3.0 * -0.83 * -0.83 + 5.0 * -0.83 - 3.0

or   y = -5.083

Parabola, Graphing Vertex, and X-Intercepts :

Root plot for :  y = 3x2+5x-3

Axis of Symmetry (dashed)  {x}={-0.83}  

Vertex at  {x,y} = {-0.83,-5.08}  

x -Intercepts (Roots) :

Root 1 at  {x,y} = {-2.14, 0.00}  

Root 2 at  {x,y} = { 0.47, 0.00}  

Solve Quadratic Equation by Completing The Square

4.3     Solving   3x2+5x-3 = 0 by Completing The Square.

Divide both sides of the equation by  3  to have 1 as the coefficient of the first term :

  x2+(5/3)x-1 = 0

Add  1  to both side of the equation :

  x2+(5/3)x = 1

Now the clever bit: Take the coefficient of  x, which is  5/3, divide by two, giving  5/6, and finally square it giving  25/36  

Add  25/36  to both sides of the equation :

 On the right-hand side we have :

  1  +  25/36    or,  (1/1)+(25/36)  

 The common denominator of the two fractions is  36   Adding  (36/36)+(25/36)  gives  61/36  

 So adding to both sides we finally get :

  x2+(5/3)x+(25/36) = 61/36

Adding  25/36  has completed the left-hand side into a perfect square :

  x2+(5/3)x+(25/36)  =

  (x+(5/6)) • (x+(5/6))  =

 (x+(5/6))2

Things which are equal to the same thing are also equal to one another. Since

  x2+(5/3)x+(25/36) = 61/36 and

  x2+(5/3)x+(25/36) = (x+(5/6))2

then, according to the law of transitivity,

  (x+(5/6))2 = 61/36

We'll refer to this Equation as  Eq. #4.3.1  

The Square Root Principle says that When two things are equal, their square roots are equal.

Note that the square root of

  (x+(5/6))2   is

  (x+(5/6))2/2 =

 (x+(5/6))1 =

  x+(5/6)

Now, applying the Square Root Principle to  Eq. #4.3.1  we get:

  x+(5/6) = √ 61/36

Subtract  5/6  from both sides to obtain:

  x = -5/6 + √ 61/36

Since a square root has two values, one positive and the other negative

  x2 + (5/3)x - 1 = 0

  has two solutions:

 x = -5/6 + √ 61/36

  or

 x = -5/6 - √ 61/36

Note that  √ 61/36 can be written as

 √ 61  / √ 36   which is √ 61  / 6

Solve Quadratic Equation using the Quadratic Formula

4.4     Solving    3x2+5x-3 = 0 by the Quadratic Formula.

According to the Quadratic Formula,  x, the solution for   Ax2+Bx+C  = 0, where  A, B,  and  C are numbers, often called coefficients, is given by :

           - B  ±  √ B2-4AC

 x =   ————————

                     2A

 In our case,  A   =     3

                     B   =    5

                     C   =   -3

Accordingly,  B2  -  4AC   =

                    25 - (-36) =

                    61

Applying the quadratic formula :

              -5 ± √ 61

  x  =    —————

                   6

 √ 61, rounded to 4 decimal digits, is   7.8102

So now we are looking at:

          x  =  ( -5 ±  7.810 ) / 6

Two real solutions:

x =(-5+√61)/6= 0.468

or:

x =(-5-√61)/6=-2.135

HOPE THIS HELPS!

PLEASE MARK BRAINLIEST IF THIS HELPED YOU LEARN! :)

Answer: yes it has gone down 1/5th because the answer would be 27 and that is a lot lower than the other numbers.

Step-by-step explanation:

162 minus 135 = 27

Answer:

C≈402.12in

Step-by-step explanation:

The circumference of a circle is equal to pi times the diameter. The diameter is two times the radius, so the equation for the circumference of a circle using the radius is two times pi times the radius

Answer:

0.4% of the people had a mild allergic reaction.

Step-by-step explanation:

You can find the percent of the people that had a mild allergic reaction using a rule of three as you know that 9,000 people tried the new shampoo which would be the 100% and you can find the percent that represents 36 people:

9,000 → 100%

  36    →   x

x=(36*100)/9,000

x=0.4%

According to this, the answer is that 0.4% of the people had a mild allergic reaction.

Answer:

4x+5

Step-by-step explanation:

4x represents making 4 dollars per hour and 5 represent the amount of money you began with

Answer:

1) 2x

2) x represent how many candy a person have

2 is the amount of person

The total candy canbe modeled by 2x

Step-by-step explanation: