A portion of the Quadratic Formula proof is shown. Fill in the missing reason. A: Multiply the fractions together on the right side of the equation? B: Subtract 4ac on the right side of the equation? C: Add 4ac to both sides of the equation? D: Add the fractions together on the right side of the equation?

A Portion Of The Quadratic Formula Proof Is Shown. Fill In The Missing Reason. A: Multiply The Fractions

Answers

Answer 1

Answer:

Combine numerators over the common denominator to make one term

Step-by-step explanation:

Answer 2

Answer:

D: Add the fractions together on the right side of the equation

Step-by-step explanation:

Let's finish this proof:

Add the fractions together on the right side of the equation

[tex]$x^2+\frac{b}{a} x+\left(\frac{b}{2a} \right)^2=\frac{b^2-4ac}{4a^2} $[/tex]

[tex]\text{Consider the discriminant as }\Delta[/tex]

[tex]\Delta=b^2-4ac[/tex]

Once we got a trinomial here, just put in factored form:

[tex]$\left(x+\frac{b}{2a}\right)^2=\frac{\Delta}{4a^2} $[/tex]

[tex]$x+\frac{b}{2a}=\pm\frac{\Delta}{4a^2} $[/tex]

[tex]$x+\frac{b}{2a}=\pm \sqrt{\frac{\Delta}{4a^2} } $[/tex]

[tex]$x=-\frac{b}{2a}\pm \sqrt{\frac{\Delta}{4a^2} } $[/tex]

[tex]$x=-\frac{b}{2a}\pm \frac{ \sqrt{\Delta} }{2a} $[/tex]

[tex]$x= \frac {-b\pm \sqrt{\Delta}}{2a} $[/tex]

[tex]$x= \frac {-b\pm \sqrt{b^2-4ac}}{2a} $[/tex]


Related Questions

Find the value of p.

Answers

Answer:

[tex]\huge\boxed{p = 3}[/tex]

Step-by-step explanation:

7p + 7 = 37 - 3p (They both are equal)

7p + 3p = 37-7

10p = 30

Dividing both sides by 10

p = 3

Answer:

p=3

Step-by-step explanation:

7p+7=37-3p

7p[+3p]+7=37-3p[+3p]

10p+7=37

10p+7[-7]=37[-7]

10p=30

10p/10=30/10

p=3

I hope this helps!

Triangle L J K is shown. Angle J L K is a right angle. The length of the hypotenuse is 15 inches and the length of the side adjacent to the right angle is 10 inches. The angle between the 2 sides is x. Which equation can be used to find the measure of angle LJK? sin(x) = Ten-fifteenths sin(x) = Fifteen-tenths cos(x) = Ten-fifteenths cos(x) = Fifteen-tenths

Answers

Answer:

  cos(x) = Ten-fifteenths

Step-by-step explanation:

The mnemonic SOH CAH TOA reminds you that the relation between the adjacent side and the hypotenuse is ...

  Cos = Adjacent/Hypotenuse

  cos(x) = 10/15

Answer:

c

Step-by-step explanation:

A prisoner is trapped in a cell containing 3 doors. The first door leads to a tunnelthat returns him to his cell after 2 days’ travel. The second leads to a tunnel thatreturns him to his cell after 4 day’s travel. The third door leads to freedom after 1day of travel. If it is assumed that the prisoner will always select doors 1,2,and 3with respective probabilities 0.5,0.3, and 0.2, what is the expected number of daysuntil the prisoner reaches freedom?

Answers

Answer:

2 days

Step-by-step explanation:

Expected number of days until prisoner reaches freedom=E(x)=?

E(x)=x*p(x)

Where x is the number of days and p(x) is the probability associated with them.

X    1    2    3

P(x) 0.5 0.3 0.2

E(x)=1*0.5+2*0.3+3*0.2

E(x)=0.5+0.6+0.6

E(x)=1.7.

Thus, the expected number of days until prisoner reaches freedom are 2 days.

(10 PTS) How do I solve for this? Please show work

Answers

Answer:

4

Step-by-step explanation:

8 ^ 2/3

Rewriting 8 as 2^3

( 2^3) ^ 2/3

We know that a^ b^c = a^ (b*c)

2 ^ ( 3 * 2/3)

2 ^ 2

4

Multiply. √6x⋅√15xy⋅√20 Please answer as quickly as possible

Answers

Answer:

[tex]30x\sqrt{2y}[/tex]

Step-by-step explanation:

First, multiply sqrt.(6x) by sqrt.(15xy)

That equals sqrt.[tex]\sqrt{90x^{2}y } *\sqrt{20}[/tex]

then, rewrite [tex]90x^{2} y[/tex] as (3x)^2 * (10y)

you have [tex]\sqrt{(3x)^{2} *(10y)} *\sqrt{20}[/tex]

Next, pull the terms from out under the radical, to get:

[tex]3x\sqrt{10y} *\sqrt{20}[/tex]

Now rewrite 20 as 2^2 * 5

You get [tex]3x\sqrt{10y} *(2\sqrt{5} )[/tex]

Multiply everything together to get: [tex]6x\sqrt{50y}[/tex]

Now rewrite 50 y as 5^2 * 2y

You end up with [tex]6x\sqrt{5^{2}*(2y)}[/tex]

Then, pull out the terms from under the radical.  You get:

[tex]6x(5\sqrt{2y})[/tex]

Finally, multiply the 5 and 6 together to get: [tex]30x\sqrt{2y}[/tex]

Answer:

[tex]\boxed{30\sqrt{2} x^2 y}[/tex]

Step-by-step explanation:

[tex]\sqrt{6} *x*\sqrt{15} * x*y*\sqrt{20}[/tex]

[tex]\sf Multiply[/tex]

[tex]\sqrt{6}\sqrt{15}\sqrt{20}*x*x*y[/tex]

[tex]\sqrt{6*15*20}*x^2 *y[/tex]

[tex]\sqrt{1800}x^2y[/tex]

[tex]\sf Simplify[/tex]

[tex]\sqrt{900} \sqrt{2} x^2y[/tex]

[tex]30\sqrt{2} x^2 y[/tex]

The sum of the digits of a two digit number is 10 when the dishes are reversed the number increases by 18 find the original number

Answers

Answer:

Step-by-step explanation:

Hello, we can write this number ab where a and b are integer betwen 0 and 9.

For instance, 54, a = 5, b = 4

And then, we can say ab = 10 * a + b.

For instance, 54  = 50 + 4 = 5*10 + 4.

The sum of the digits of a two digit number is 10.

a +  b = 10

When the dishes are reversed the number increases by 18.

10b + a = 18 + 10a + b

9b = 18 + 9a

b = 2 + a

We replace in the first equation to get.

a + 2 + a = 10

2a = 10 -2 = 8

a = 4

and then, b = 6

So, the number is 46.

Thank you

4n-6 (n - 2) = -24 + 7n
O No Solutions
O All Real Numbers
O n = 4
O n = 2.9

Answers

N=4

4n-6 (n-2) = -24 + 7n

You first multiply the six with the equation in the parentheses making it:

4n-6n + 12= -24 + 7n

You then subtract 4n from -6n changing it to:

-2n + 12 = -24 + 7n after that you switch the 12 and 7n so that the equation can be

-2n -7n = -24 - 12

After that combine the numbers together:

-9n = -36

Then divide both sides by -9 making

n= 4

PLEASE HURRY!!!!! Simplify the expression. (x – 4x2 + 7) – (-5x2 + 5x – 3)

Answers

Answer:

[tex]x^{2}-4x+10[/tex]

Step-by-step explanation:

[tex](x-4x^{2}+7)-(-5x^{2}+5x-3)\\x-4x^{2}+7+5x^{2}-5x+3\\x^{2}-4x+10[/tex]

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Hi my lil bunny!

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Let's simplify step-by-step.

[tex]( x - 4x^2 + 7 ) - ( -5x^2 + 5x - 3)[/tex]

Distribute the Negative Sign:

[tex]= x - 4^2 + 7 + -1 ( -5x^2 + 5x -3) \\= x + -4x^2 + 7 + -1 ( -5x^2) + -1 (5x) + ( -1) (-3)\\= x + -4x^2 + 7+ 5x^2 + -5x + 3[/tex]

Combine Like Terms:

[tex]= x + -4x^2 + 7 + 5x^2 + -5x + 3 \\= (-4x^2 + 5x^2) + ( x + -5x) + ( 7 + 3) \\= x^2 + -4x + 10[/tex]

Answer : [tex]\boxed {x^2 -4x + 10}[/tex]

❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙

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Have a great day/night!

❀*May*❀

⚠️URGENT!!⚠️ PLEASE HELP ILL GIVE BRAINLIEST I PROMISE THE QUESTION IS ATTACHED BELOW I REALLY NEED HELP

Answers

Answer:

            m∠M = 116°               m∠N = 111°               m∠O = 64°               m∠P = 69°  

Step-by-step explanation:

A quadrilateral can be inscribed in a circle only if the sum of its opposite angles is equal to 180°, so:

7x - 15 + 3x + 15 = 180°      and      2(17y - 10) + 13y + 12 = 180°

     10x = 180°                                  34y - 20 + 13y + 12 = 180°

       x = 18°                                             47y = 188°

                                                                   y = 4°

m∠M:  2(17•4 - 10) = 2•58° = 116

m∠N:   7•18 - 15 =126 - 15 = 111

m∠O:   13•4 + 12 = 52 + 12 = 64  

m∠P:    3•18 + 15 = 54 + 15 = 69

the top of a square table is144 squared metres.what is the size of the table

Answers

Answer:

12 meters x 12 meters

Step-by-step explanation:

√144 = 12

The estimated product of 20.7 and 9.18, after rounding both factors to the nearest whole number, is . The exact product of 20.7 and 9.18 has decimal places.

Answers

Answer:

Estimated=189

Exact=190.026

Step-by-step explanation:

Estimated values

20.7 to nearest whole number= 21

9.18 to nearest whole number= 9

Product means multiplication

Estimated product of 20.7 and 9.18

=21×9

=189

Exact product of 20.7 and 9.18

=20.7 × 9.18

=190.026

It has 3 decimal places

Answer:

The estimated product of 20.7 and 9.18, after rounding both factors to the nearest whole number,

is

✔ 189

.

The exact product of 20.7 and 9.18 has

✔ 3

decimal places.

Step-by-step explanation: Hope this helps(:

Complete the square to solve 4x2 + 24x = 4.

Answers

Answer:

x = - 3 ± [tex]\sqrt{10}[/tex]

Step-by-step explanation:

Given

4x² + 24x = 4 ( divide through by 4 )

x² + 6x = 1

To complete the square

add ( half the coefficient of the x- term )² to both sides

x² + 2(3)x + 9 = 1 + 9

(x + 3)² = 10 ( take the square root of both sides )

x + 3 = ± [tex]\sqrt{10}[/tex] ( subtract 3 from both sides )

x = - 3 ± [tex]\sqrt{10}[/tex]

Answer:

X=1/8

Step-by-step explanation:

Calculate the product 4x×2 + 24x = 4

Collect like terms 8x + 24x = 4

Divide both sides of the equation by "32" 32x = 4

Solution x = 1/8

Plug in the values from the set {12, 15, 18, 19} to find the value of x. The value that holds true for the equation is . So, Jenny is years old and her mother is years old.

Answers

Answer:

Jenny´s age is 19 and her mother is 43.

Step-by-step explanation:

Given that

x + 2x + 5 = 62

where,

x = Jenny’s age

Now the following cases occured

a.  

x = 12

Now put the x value to the above equation

12 + 2(12) + 5 = 62

12 + 24 + 5 = 62

41 = 62

It is not equaled so the Jenny age is not 12

b.

x = 15

Now put the x value to the above equation

12 + 2(15) + 5 = 62

15 + 30 + 5 = 62

50 = 62

It is not equaled so the Jenny age is not 15

c.  

x = 18

Now put the x value to the above equation

18 + 2(18) + 5 = 62

18 + 36 + 5 = 62

59 = 62

It is not equaled so the Jenny age is not 12

d.

x = 19

Now put the x value to the above equation

19 + 2(19) + 5 = 62

19 + 38 + 5 = 62

62 = 62

It is equaled so the Jenny age is 19

Now the mother age is

as we know that

x + y = 62

19 + y = 62

y = 62 - 19

= 43

Also it proved that if we doubles the jenny age i.e 38 and then add 5 so the total is 43 i.e. equivalent to her mother age

What is difference between internal and external trade ​

Answers

Answer:

Trade which takes place inside a country is known as internal trade. If trade takes place with other countries of the world, it is known as external trade.

Step-by-step explanation:

Answer:Internal refers to trade within the country itself while

External refers to trade with other countries whether foreign or bordering countries

Step-by-step explanation:

''Internal'' trade-Trade within the locals of the country itself

''External'' trade-refers to ;outside of the country...trade with other countries

What the correct answer now

Answers

Answer:

527.52 m²

Step-by-step explanation:

The surface area (A) of the cone is calculated as

A = area of base + curved area

   = πr² + πrl ( r is the radius and l the slant height )

   = 3.14 × 7² + 3.14 × 7 × 17

   = 3.14 × 49 + 3.14 × 119

    = 3.14(49 + 119)

     = 3.14 × 168

      = 527.52 m²

PLEASE HELPP on THIS PICTURE FOR ONE OF MY QUESTIONS

Answers

Answer:

Linear pair postulate

Step-by-step explanation:

The Linear Pair Postulate states: "If two angles form a linear pair, then the angles are supplementary; that is, the sum of their measures is 180 degrees

A linear pair of angles is such that the sum of angles is 180 degrees.


Two angles form a
linear pair. The
measure of one
angle is three times
the measure of the
other. Find the
measure of each

Answers

Answer:

45° and 135°

Step-by-step explanation:

A linear pair of angles sum to 180°

let one angle be x , then the other is 3x ( 3 times the other ), thus

x + 3x = 180

4x = 180 ( divide both sides by 4 )

x = 45

Thus the 2 angles are

x = 45° and 3x = 3 × 45° = 135°

The measure of two angles are 135 and 45 degrees if the two angles form a linear pair. The measure of one angle is three times the measure of the other.

What is an angle?

When two lines or rays converge at the same point, the measurement between them is called a "Angle."

It is given that:

Two angles form a linear pair. The measure of one angle is three times the measure of the other.

As we know,

If two angles form a linear pair it means the angle made by the pair is 180 degrees

Let the two angles are x and y

x + y = 180

x = 3y  (one angle is three times the measure of the other)

Solving the two linear equations in two variable:

3y + y = 180

4y = 180

y = 180/4

y = 45 degrees

x = 3(45) = 135 degrees

Thus, the measure of two angles are 135 and 45 degrees if the two angles form a linear pair. The measure of one angle is three times the measure of the other.

Learn more about the angle here:

brainly.com/question/7116550

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The parent council is in charge of making lemonade for field day.They purchased 19 bags of lemon.each bag has 24 lemons.The recipe says that a gallon of lemonade will require 8 lemons.they will be able to pour 12 cups of lemonade from each gallon that they make.How many cups of lemonade will the parent council be able to serve?

Answers

Answer:

684

Step-by-step explanation:

19 x 24 = 456    

456 divided by 8 = 57

57 x 12 = 684

A plumber’s apprentice needs to cut a 54-inch length of pipe so that one piece is twice the length of the other piece. How far from the endpoint should the apprentice cut the pipe?

Answers

Answer:

18 inches

Step-by-step explanation:

To to this you would just divide 54 by 3 and you would get how far away from the endpoint which is 18 inches

Please help me answer this question. -15 - g/3 = -5.
What is g?​

Answers

Answer:

g = -30

Step-by-step explanation:

-15 - g/3 = -5

Add 15 to each side

-15+15 - g/3 = -5+15

-g/3=10

Multiply by -3 to each side

-g/3 * -3  = 10*-3

g = -30

Answer:

g= -30

Step-by-step explanation:

after writing down the problem, multiply both sides of the equation by 3 to get  -45-g= =15. then subtract 15 from both sides to get g=-30, which is your answer. hope this helps!

f(x) = x2. What is g(x)?

pls help it’s due soon!!

Answers

Answer:

A. g(x) = (2x)²

Step-by-step explanation:

From the diagram of the two functions graph f(x) is the parent function and g(x) is the transformed function. you can see that the graph of g(x) is stretched vertically compared to the graph of g(x). The Parent function has y =1 corresponding to x =1 while for the transformed function when x = 1, y = 4 the graph is vertically stretched by a factor of 4, and horizontally The Parent function has y =1 corresponding to x =1. while for the transformed function when x = 0.5, y = 1, it is stretched  horizontally by 2 (√4), i.e

This means that g(x) = 4x² = (2x)²

Tuition for one year at the University of Atlantis costs $12,000 per year. Rachel would like to attend this university and will save money each month for the next 3 years. Her parents will contribute $3,000 for her first year's tuition. How much money will Rachel need to save each month to have enough money for the first year of college at the University of Atlantis?

Answers

Answer:

250 dollars per month.

Step-by-step explanation:

We first need to subtract the amount of money her parents are giving her.

12000-3000=9000.

Since she is saving money every month for 3 years we have to multiply 3×12=36 months.

We than need to divide how much money she needs by the amount of months she has to get it.

9000÷36=250

A bag has six balls labeled a,b,c,d.e and f . One ball will be randomly picked, and its letter will be recorded as the outcome. Give the sample space describing all possible outcomes. Then give all of the outcomes for the event of choosing the letter a or c . If there is more than one element in the set, separate them with commas.

Answers

Sample space = {a,b,c,d,e,f}Event space = {a,c}

We simply list all of the letters mentioned as they are the possible outcomes. We can only pick one item from the sample space. The event space is the set of outcomes where we want to happen (picking either an 'a' or 'c').

Hey There!!

To this Question, This answer going to had A Explanation to this: Sample space--

A sample space is a set which contains the set of all the possible outcomes or results that could occur while performing an experiment.

i.e. the sample space while flipping a coin is: {H,T}

The sample space while tossing a six-sided die is: {1,2,3,4,5,6}

Here it is given that:

A bag has six balls labeled: A,B,C,D,E,F

One ball will be randomly picked, and its letter will be recorded as the outcome.

This means that the sample space is given by:

Sample space={ A,B,C,D,E,F}

Now, when the event is choosing a letter from D to F.

Then the sample space is:

Sample space= {D,E,F}

Hope It Helped!~ ♡

ItsNobody~ ☆

find y of a paralagram

Answers

Answer:

y = 15

Step-by-step explanation:

In a parallelogram, opposite sides are congruent.

5y - 20 = 2y + 25

3y = 45

y = 15

Answer:

y = 15

Step-by-step explanation:

The top and bottom sides have to be equal in length

5y-20 = 2y+25

Subtract 2y from each side

5y-2y-20 = 2y-2y+25

3y -20 = 25

Add 20 to each side

3y = 20+25

3y = 45

Divide each side by 3

3y/3 = 45/3

y = 15

Please answer this question now

Answers

Answer:

65.94 square inches

Step-by-step explanation:

Surface area of a cone=πr(r+√h^2+r^2)

π=3.14

r=diameter/2

=14/2

=7 in

h=?

h=a

To find h using Pythagoras theorem

c^2 = a^2 + b^2

14^2 = a^2 + 7^2

14^2 - 7^2= a^2

196-49=a^2

147=a^2

Square root both sides

√147=√a^2

12.12=a

a=12.12 in

Surface area of a cone=πr(r+√h^2+r^2)

=3.14(7+√12.12^2+7^2)

=3.14(7+√147+49)

=3.14(7+√196)

=3.14(7+14)

=3.14(21)

=65.94 square inches

03. O preço a ser pago por uma corrida de táxi inclui uma parcela fixa, denominada bandeirada, e uma parcela que depende da distância percorrida. Se a bandeirada custa R$ 3,20 e cada quilômetro rodado custa R$ 1,50, qual o valor de v a pagar em uma corrida de n quilômetro? * 1 ponto a) v = 1,50 + 3,20n b) v = 3,20.N c) v = 3,20.N - 1,50 d) v = 3,20 + 1,50n e) v = 1,50n

Answers

Answer: d) v = 3.20 + 1.50n.

Step-by-step explanation:

Let 'v' be the price to pay in a 'n' kilometer.

Given: The price to be paid for a taxi ride includes a fixed parcel, called a flag, and a parcel that depends on the distance traveled.

Flag costs = $ 3.20 and

Each kilometre run costs = $ 1.50

Then, the amount of 'v' to pay in a 'n' kilometer race = Flag costs +   (n)× (Each kilometre run costs )

⇒ v= 3.20 + 1.50n

Hence, the correct option is  d) v = 3.20 + 1.50n.

What is the slope of the line containing the midpoint of the segment with endpoints at (2, 4) and (0, -2) and the midpoint of the segment with endpoints at (5, 1) and (1, 5)?Express your answer in simplest form. Plzzzz help!!!!

Answers

Answer:

slope = 1

Step-by-step explanation:

midpoint of (2, 4) and (0, -2)

(2 + 0)/2 = 1 and (4 + -2)/2 = 1

(1, 1)

midpoint of (5, 1) and (1, 5)

(5 + 1)/2 = 3 and (1 + 5)/2 = 3

(3, 3)

slope = (3-1)/(3-1) = 2/2 = 1

I need help with #7 I got no clue what to do

Answers

x=3
Explanation
---------------------
12=4x
÷4 ÷4
---------------
3=x

please help me answer these in variable and constant terms 7s + 8s - 6h

Answers

Answer:

see below

Step-by-step explanation:

7s + 8s - 6h

7  8 and -6 are coefficients

s and h are variables

We can combine like terms

15s -6h

15 and -6 are coefficients and

s and h are variables

Answer:

Variable Terms:  (Alphabets)

s and h

Constant terms:   (Numbers)

No constants

Coefficient terms:  (Numbers with alphabets)

7 , 8 and -6

what is 2/3 divided by -1 1/3​

Answers

I think it is -0.5 because 2/3 is 0.66 repeated then I -1 1/3 equals - 1/3 so you just divide both and it equals -0.5
Other Questions
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