how to know which way to solve a quadratic equation

Answers

Answer 1

Answer:

  Practice -- lots of it

Step-by-step explanation:

I usually choose a solution method that I believe will find the desired answer for me in the least number of simple steps. What constitutes a "simple" step depends on a number of things:

the given information and/or the given form of the equationfamiliarity with all of the different solution processesfamiliarity with arithmetic facts (multiplication tables, squares)familiarity with quadratic forms: difference of squares, perfect square binomials, product of binomials, vertex formavailability of a graphing calculatorwhether an approximation will serve the purpose.

__

I often choose a graphing calculator as my first approach to solving a quadratic. It easily shows the roots, and can show the vertex. (Sometimes, scaling the graph is required, so I actually prefer to use a touch-screen for the purpose. It is easier to "pinch" than to type in possible graph limits by trial and error.) The answer is generally provided to 3 or 4 significant figures, which is usually enough to tell if the solution is rational or irrational.

The easiest way to describe an integer (or rational) solution to someone else (on Brainly, for example) is usually to show the factoring of the quadratic. Finding the roots with a graphing calculator significantly aids the factoring process. (It is much easier to "find" the solution if you know the solution before you start looking.)

__

As we said at the beginning, the answer to your question is "practice." Many curricula try to offer opportunities to practice. I find most of these pretty annoying. What I suggest is that you find your own internal motivation to practice solving different kinds of quadratics in several different ways. That is, solve the same quadratic by ...

using the formulacompleting the squarefactoringgraphing (with a graphing calculator)scaling and/or translation and/or transformation*

It might take you a couple of hours of work to learn the best way to solve an equation in under 5 minutes.

In this process, you will discover what you need to know to choose a method that works nicely for you. I believe you will find that total familiarity with arithmetic facts (sums, products, squares) and operations on all the different ways to represent numbers (integer, decimal, fraction, percent, scientific notation) will help you significantly.

_____

* Additional comment

Some "area" problems give you the difference of dimensions (length and width), and ask you to find the dimensions that give a specific area. This can be solved by (x)(x -d) = A. If you don't immediately recognize factors of A that differ by d, then you might have to resort to the quadratic formula to solve this.

Another approach is to let the variable represent the average dimension. Then the equation becomes (x -d/2)(x +d/2) = A, which is a "difference of squares" form that is much more easily solved. The solution for x is √(A +(d/2)²), and all you have to do is add and subtract d/2 from that solution to find the dimensions. This is an example of what I mean by transforming the problem.


Related Questions

To make 8 dozen cookies, you must use 2 eggs. How many eggs are needed to make 40 dozen cookies? Use a proportion to solve.

Answers

Answer:

10 eggs for 40 dozens

Step-by-step explanation:

40÷8=5

5*2=10

Answer:For 40 dozen cookies, 10 eggs are required.Step-by-step explanation:

Our created proportion is 8:2::40:x

=> 8x = 80=> x = 10Conclusion:

Therefore, for 40 dozen cookies, 10 eggs are required.

Hoped this helped.

[tex]BrainiacUser1357[/tex]

What is 2/3 – (-2/3)

Answers

Answer:

2/3 - (-2/3)

=0.66 - (-0.66)

=0.66+0.66

= 1.32

Find the inverse function. f(x) = (x + 1​

Answers

Answer:

( x + 1 ) ^ 3

Step-by-step explanation:

f(x) = 3√x - 1

replace x with y

x = 3√y - 1

solve for y,

x = 3√y - 1

x^3 + 3x^2 + 3x + 1 = (x+1)^3

HOPE THIS HELPS :)

A) by AA similarity
B) by sas similarity
C)Not enough information
D) by sss similarity




Please see the photo



Please don't answer randomly because if you answer randomly you are gonna lose points

Answers

Answer: b

Step-by-step explanation:

Answer: It's yes and (D) SSS because all the angles are side side side and all have the same angles but one's smaller while the other is bigger but that doesn't change anything. :)

Step-by-step explanation:

h(8) = -2(8)^2 + 4(8)- 7

Answers

Answer:

h = - 103/8

Step-by-step explanation:

1) Re-order terms so constants are on the left

8h = = -2(8)²+4(8)-7

2) Evaluate the exponent

8h = -2·64+4(8)-7

3) Multiply the numbers

8h = -128+4(8)-7

4) Multiply the numbers

8h = -128+32-7

5) Add the numbers

8h = -103

6) Divide both sides of the equation by the same term

8h/8 = -103/8

7) Simplify

- Cancel terms that are in both the numerator and denominator

h = -103/8

X
-9
-5
-1
3
Y
- 2
0
2
4
What is the slope of the line?

Answers

ok done. Thank to me :>

I tried to make sense of this and it doesn’t make sense. Can someone please help?

Answers

Answer:

85 because if you do the math

Work out length AC.

10 cm
Not drawn
accurately

120
7 cm

Answers

Step-by-step explanation:

Well. Let's call α the 120° angle, and β its supplementary angle (80°). Let's draw also the height of the triangle. We'll call it CH. We know, from goniometric relations, that BC * sinβ = CH and BC * cosβ = BH. We just apply the pythagorean theorem so we get: AC = [tex]\sqrt{(AB+BH)^2+CH^2}.[/tex] By inserting all the values you'll get the result.

i need answer please I got a them wrong ​

Answers

Answer:

See image

Step-by-step explanation:

I'm guessing a little bit, bc although you attached an image, it doesn't say what you are trying to prove, nor what you are given. Usually that is provided for a proof.

But we can see that the parallel segments are marked, so we'll call that the given information. Then there are actually two pairs of corresponding angles that are congruent by the Corresponding Angles postulate. But we only need one pair. Then Angle A is congruent to itself by Reflexive Property. Finally what we have proven is that the two triangles ABC and ART are similar by AA

is this a function

Find the domain and range

Answers

Answer:

Yes

Domain: 1, -1, 0, -3, 3

Range: 1, -1, 6

Step-by-step explanation:

The domain is in the left oval, the range is in the right oval. To find if its a function you have to make sure the domain (left side) doesn't "cheat". One number in the domain cant have more than one number in the range (right side), BUT (for future reference) the range can cheat. As shown, the right side numbers 1 and 6 have two different arrow pointed at them. As long as the domain doesnt "cheat" it is a function

What addition statement does this show?



A. 5.2 + 6.4 = –11.6
B. –5.2 + 6.4 = –11.6
C. 5.2 + (–6.4) = –11.6
D. –5.2 + (–6.4) = –11.6

Answers

Answer:

D. –5.2 + (–6.4) = –11.6

Step-by-step explanation:

First, you can eliminate A and C because 5.2 is positive. Since the red arrow is pointing left, it indicates that the number (-5.2) is negative.

Then, you look at the second arrow, the green one. It is pointing left, so it would be -6.4.

I hope this helps :)

Suppose two bicyclists start at the same location.
The first bicyclist rides due north and the other rides
due west. Find the speed that each bicyclist rode in
miles per hour if they are 8V2 miles apart after riding
for 2 hours at the same speed

Answers

Answer:

  4 mi/h

Step-by-step explanation:

The distance between the cyclists is the hypotenuse of an isosceles right triangle. The hypotenuse is √2 times the length of the legs in such a triangle, so each cyclist must have ridden 8 miles in 2 hours.

Their speed is (8 mi)/(2 h) = 4 mi/h.

_____

Additional comment

Consider an isosceles right triangle with leg lengths 1. Then the Pythagorean theorem tells us the length of the hypotenuse is ...

  c² = a² +b² . . . square of hypotenuse is sum of squares of legs

  c² = 1² +1² . . . . both legs are 1 in our example triangle

  c² = 2

  c = √2

That is, the hypotenuse is √2 times the leg length.

R, P, Q act on the base AB, BC, CA triangles ABC in alphabetical order, respectively. Show that P sec A + Q sec B + R sec C = 0, if the fluid of this power system passes through the center of the triangle.​

Answers

Answer:

(i) In △ABD and △ACD,

AB=AC ....(since △ABC is isosceles)

AD=AD ....(common side)

BD=DC ....(since △BDC is isosceles)

ΔABD≅ΔACD .....SSS test of congruence,

∴∠BAD=∠CAD i.e. ∠BAP=∠PAC .....[c.a.c.t]......(i)

(ii) In △ABP and △ACP,

AB=AC ...(since △ABC is isosceles)

AP=AP ...(common side)

∠BAP=∠PAC ....from (i)

△ABP≅△ACP .... SAS test of congruence

∴BP=PC ...[c.s.c.t].....(ii)

∠APB=∠APC ....c.a.c.t.

(iii) Since △ABD≅△ACD

∠BAD=∠CAD ....from (i)

So, AD bisects ∠A

i.e. AP bisects∠A.....(iii)

In △BDP and △CDP,

DP=DP ...common side

BP=PC ...from (ii)

BD=CD ...(since △BDC is isosceles)

△BDP≅△CDP ....SSS test of congruence

∴∠BDP=∠CDP ....c.a.c.t.

∴ DP bisects∠D

So, AP bisects ∠D ....(iv)

From (iii) and (iv),

AP bisects ∠A as well as ∠D.

(iv) We know that

∠APB+∠APC=180

....(angles in linear pair)

Also, ∠APB=∠APC ...from (ii)

∴∠APB=∠APC=

2

180

=90

BP=PC and ∠APB=∠APC=90

Hence, AP is perpendicular bisector of

Step-by-step explanation:

HOPE ITS HELP YOU

can anyone plz help me with this math problem

Answers

the answer to the question is f=1

NEED HELPPP ASAAPPPPPPP

Answers

Answer:

me too

Step-by-step explanation:

Help I give brainly
The acute angles of a right triangle measure (48 - x) and (3x – 10). What is the value of x?

Answers

Answer:

[tex]\huge\boxed{\sf x = 26}[/tex]

Step-by-step explanation:

The acute angles of a right-angled triangle other than the right angle always add up to 90 degrees.

So, we get:

(48 - x) + (3x - 10) = 90

48 - x + 3x - 10 = 90

-x + 3x - 10 + 48 = 90

2x + 38 = 90

2x = 90 - 38

2x = 52

Divide both sides by 2

x = 52 / 2

x = 26

[tex]\rule[225]{225}{2}[/tex]

Hope this helped!

~AH1807

Answer:

Step-by-step explanation:

x=26

The acute angles of a right-angled triangle other than the right angle always add up to 90 degrees.

So, we get:

(48 - x) + (3x - 10) = 90

48 - x + 3x - 10 = 90

-x + 3x - 10 + 48 = 90

2x + 38 = 90

2x = 90 - 38

2x = 52

Divide both sides by 2

x = 52 / 2

x = 26

Hope this helped!


I really need help!!

Answers

Answer:

Red: y=4

Green: x=-1

Yellow: x=6

Blue: x=-2

Step-by-step explanation:

The lines are all passing through the Axis, so there is no slope for each line.

scores on a test have a mean of 66 and Q3 is 80. The scores have a distribution that is approximately normal. Find the standard deviation. Round your answer to the nearest tenth.
A) 10.5
B) 20.9
C) 9.4
D) 18.7

Answers

The correct answer is B

someone help pls pls

Answers

Answer:

3.636 hour. dividing 200miles /55m/h =3.636h

Answer:

3 hours 38 minutes is what calculators online say

Step-by-step explanation:

You should put both answers that were given to you. The answer on top seemed to do it the mathematical way youre suppose to. Maybe the teacher will take both answers i don’t know

Which inequality is graphed below

Answers

The answer would be C

1/2x divided by 3=6 what is x

Answers

Answer:

x = 36

Step-by-step explanation:

1/2x ÷ 3 = 6=> 1/2x × 1/3 = 6=> 6 x 1/6x = 6 x 6=> x = 36

Conclusion:

Therefore, the answer is 'x = 36'.

Hoped this helped.

[tex]BrainiacUser1357[/tex]

Would someone help me out?
A)56.6
B)58.4
C)53.5

Answers

Answer:

it is c

Step-by-step explanation:

5x-15y=-20, 5x-4y=-9 systems of equations (elimination)

Answers

Answer:

(- 1, 1 )

Step-by-step explanation:

5x - 15y = - 20 → (1)

5x - 4y = - 9 → (2)

Multiplying (2) by - 1 and adding to (1) will eliminate the x- term

- 5x + 4y = 9 → (3)

Add (1) and (3) term by term to eliminate x

0 - 11y = - 11

- 11y = - 11 ( divide both sides by - 11 )

y = 1

Substitute y = 1 into either of the 2 equations and solve for x

Substituting into (1)

5x - 15(1) = - 20

5x - 15 = - 20 ( add 15 to both sides )

5x = - 5 ( divide both sides by 5 )

x = - 1

solution is (- 1, 1 )

Rsound answer to two decimal places

80.75757575757575757575​

Answers

Answer:

[tex]80. \bar{75}[/tex]

9 13 / 16 + 10 3 / 8 =

Answers

It equals 20 3/16, or 20.1875

2.4x-9.1x+12.5= -39.44
Solve for x

Answers

Answer:

x= 2597/335

Step-by-step explanation:

collect like terms

2.4x-9.1x= -6.7x

-39.44-12.5 = -51.94

-6.7x=-51.94

divide both sides by -6.7

x= 2597/335

can someone tell me if i did this right lol

Answers

Answer:

Your calculation is correct, but I'd answer 33.0 in.

Step-by-step explanation:

You are correct. Good job.

Answer:

I'm 96% sure its right, and those are pretty good odds ^^

The table displays the amount of money Stephen has in his piggy bank.

Stephen’s Piggy Bank
Types of Coins Amount ($)
Quarters 7.50
Dimes 6.00
Nickels 5.50
Pennies 3.00

Which answer choices accurately approximate a comparison between the value of the dimes in the piggy bank and the total value of Stephen’s coins?
Select all the correct answers.


Answer choices:
6%
3/11
6/22
60%
27%
3/5

Answers

Answer:

The answer is 27%, 6/22, and 3/11.

Pls mark brainliest. :D

how to turn 18/48 into the power of 10 please tell the answer as soon as possible, it's for my semester

Answers

1. You can do this 18/48x18/48x18/48x 18/48 and so on. X is not a variable
2. You can write down a power or in text you use a carrot or a ^ and write 18/48^10

The function after synthetic division f(x) = 4x3 + 3x2 − 16x − 12

Answers

Answer:

[tex]\huge\purple{\overline{\quad\quad\quad\quad\quad\quad\quad\quad\quad \ \ \ }}[/tex]

»ANSWER«

(1) Write properties of function:

x intercept/zero:

[tex] x_{1} = \frac{3}{4} [/tex]

y intercept:

[tex]y = - 12[/tex]

domain:

[tex]( - \infty \: \infty )[/tex]

type of function: cubic fraction

standard form:

[tex]f(x) = 4 {x}^{3} - 3 {x}^{2} + 16x - 12[/tex]

factorize form:

[tex]f(x) = (4x - 3)( {x}^{2} + 4)[/tex]

even/odd/neither: neither

bounce/cross x axis:

[tex]x = \frac{3}{4} \: across[/tex]

increasing interval:

[tex]( - \infty \: \infty )[/tex]

decreasing interval: no

number of positive real zeros: 1

number of possible turning point: 2

order/degree: 3

leading term:

[tex]4x ^{3} [/tex]

leading coefficent: 4

constant term: -12

end behavior:

[tex]as \: x \: → \infty f(x) → \infty \: as \: x → - \infty f(x) → - \infty [/tex]

#CarryOnLearning

Other Questions
Noah starts with 0 and then adds the number 5 four times. Diego starts with 1 and then multiplies by the number 5 four times. For each expression, decide whether it is equal to Noahs result, Diegos result, or neither. What's the correct entry to record a tool purchase of $500?. How is a special interest group like AARP different from an organized labor interest group? Fill in the blanks with the present tense form of the reflective verbs in parenthesis.1.Yo (afeitarse)____las maanas,2. T no (despertarse)____a tiempo3. Eduardo (alvidarse)___de hacer las compras.4. Nosotros (dusharse)___con agua caliente.5. Los estudiantes (dormirse)___durante la clase.6. Yo no (enamorarse)___fcilmente.7. T (vestirse)____rpidamente antes de salir.8. Ricardo (sentarse)____antes de tomar caf.9.Mi esposa y yo (enfermarse)___en el invierno.10. Raquel y Brbara (encontrarse)_____en la biblioteca. Which of the following describes how other body systems differ from the male and female reproductive systems? its suppolsy the hardest question in math Two systems of equations are shown: System A System B 6x + y = 2 2x 3y = 10 x y = 3 x y = 3 Which of the following statements is correct about the two systems of equations? The value of x for System B will be 4 less than the value of x for System A because the coefficient of x in the first equation of System B is 4 less than the coefficient of x in the first equation of System A. They will have the same solution because the first equations of both the systems have the same graph. They will have the same solution because the first equation of System B is obtained by adding the first equation of System A to 4 times the second equation of System A. The value of x for System A will be equal to the value of y for System B because the first equation of System B is obtained by adding 4 to the first equation of System A and the second equations are identical. what is 7.5% as a fraction 1. WHO CAN DO AFFILIATE MARKETING? Solve for x: 7 |x - 2| + 7 = -2 |x - 2| + 2 do you eat more than five times a day? *WILL GIVE BRAINLIEST FOR BEST ANSWER*Jasper won the raffle at the zoo and gets to feed the dolphins! The dolphin trainer gives Jasper a bucket of fish to divide evenly among 4 dolphins. Each dolphin gets 3 fish.Which equation can you use to find the number of fish f in the bucket before Jasper feeds the dolphins?Solve this equation for f to find the number of fish in the bucket before Jasper feeds the dolphins. fish When would a point mutation occur? It can occur before and after cell division Before the cell divides After the cell divides Before DNA replication Which of the following expressions is equal to P/17 what is false humility? being dishonest with yourself to please others being a people pleaser being honest with yourself telling part of the truth but not the whole truth what percentage of american black genes are european Given the function f(x)=|x|, if the function is shifted 0.5 units down, then shifted 3 units left, and reflected over the y-axis, what is the equation of the new function ok here PLEASE HELP ME !!!!! 7. Read this sentence from paragraph 1.But if he be a fool, he will stay and stay on until the town becomes all inall to him; until the very streets are his chums and certain buildings andcorners his best friends.What does the narrator suggest by the phrase "if he be a fool"?If the visitor foolishly leaves New York City0If the visitor behaves foolishly while visiting New York City0If the visitor falls foolishly in love with New York City0If the visitor foolishly spends too much time in the streets ofNew York City 2. Why do you _______ the trip? Because I try to find exciting things to do. A. seek B. change C. connect D. succeed