The methods of solving quadratic equations

Answers

Answer 1

         There are three main ways of solving quadratic equations. The quadratic formula, factoring, and completing the square.

[1] using the quadratic formula

     When the equation is in the form of ax² + bx + c = 0.

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

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[2] factoring

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[3] completing the square

     To start out with completing the square, make sure your constant is isolated on one side. The equation will be as ax² + bx = -c

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Related Questions

In which table does yvary directly with x?

Answers

The table in which y varies directly with x is table C.

What is direct variation?

When a variable varies directly with another variable, it means that as one variable increases, the other variable also increases.

The equation that is used to represent direct variation is:

y = kx

Where y is the constant of proportionality

In table c, k is equal to 26

26 x 2 = 54 26 x 3 = 78

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Volume of a cube with a side length of 18.8m

Answers

Answer:

[tex]6644.672~ m^3[/tex]

Step-by-step explanation:

[tex]\text{Volume} = (18.8)^3~ m^3 = 6644.672~ m^3[/tex]

PLEASE HELP!!!!!!!!!! I'll NAME BRAINLIEST!!!!!!
Classify the expression by the number of terms.
5y^2-8+6y^4

Answers

Answer:

5x2-2x+1 The highest exponent is the 2 so this is a 2nd degree trinomial.

Step-by-step explanation: Also pls answer by question

Given that tan^2 theta=3/8,what is the value of sec theta?

Answers

Answer:

Sqrt (11/8)

Step-by-step explanation:

Sec^2 - Tan^2 = 1

- Tan^2 = 1 - Sec^2

Tan^2 = -1 + Sec^2

Tan^2 = 3/8

3/8 = -1 + Sec^2 Theta

1 + 3/8 = Sec ^2 Theta

11/8 = Sec^2 Theta

Sqrt ( 11/8) = Sec of theta

-- Gage Millar, Algebra 1/2 Tutor (Pending Pre-Calc Tutor)

Please help we’re stuck

Answers

Answer:

Divide 12 by -6

please help! acellus
find the missing side of this right triangle.
30
3
x
x= [?]

Answers

Answer:

The number that belongs in the green box is equal to 909.

General Formulas and Concepts:
Algebra I

Equality Properties

Multiplication Property of EqualityDivision Property of EqualityAddition Property of EqualitySubtraction Property of Equality

Trigonometry

[Right Triangles Only] Pythagorean Theorem:
[tex]\displaystyle a^2 + b^2 = c^2[/tex]

a is a legb is another legc is the hypotenuse

Step-by-step explanation:

Step 1: Define

Identify given variables.

a = 30

b = 3

c = x

Step 2: Find x

Let's solve for the general equation that allows us to find the hypotenuse:

[Pythagorean Theorem] Square root both sides [Equality Property]:
[tex]\displaystyle \begin{aligned}a^2 + b^2 = c^2 \rightarrow c = \sqrt{a^2 + b^2}\end{aligned}[/tex]

Now that we have the formula to solve for the hypotenuse, let's figure out what x is equal to:

[Equation] Substitute in variables:
[tex]\displaystyle \begin{aligned}c & = \sqrt{a^2 + b^2} \\x & = \sqrt{30^2 + 3^2}\end{aligned}[/tex]Evaluate:
[tex]\displaystyle \begin{aligned}c & = \sqrt{a^2 + b^2} \\x & = \sqrt{30^2 + 3^2} \\& = \boxed{ \sqrt{909} } \\\end{aligned}[/tex]

∴ the hypotenuse length x is equal to √909 and the number under the square root, our answer, is equal to 909.

___

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Topic: Trigonometry

Multiply:
(x+y)by (x+y)
a+b by a^2-b^2
(a+5) by (a^2-2a-3)
(a^2-ab+b^3) by (a+b)​

Answers

Answer:

Multiply:

[tex](x+y)by (x+y)[/tex]

[tex] : \implies(x + y)(x + y)[/tex]

[tex] : \implies \: x(x + y) + y(x + y)[/tex]

[tex] : \implies {x}^{2} + xy + xy + {y}^{2} [/tex]

[tex] : \implies{x}^{2} + 2xy + {y}^{2} [/tex]

Multiply:

[tex]a+b \: by \: a^2-b^2[/tex]

[tex]: \implies( {a}^{2} + {b}^{2} ) \times (a + b)[/tex]

[tex]: \implies \: {a}^{2} (a + b) - {b}^{2} (a + b)[/tex]

[tex]: \implies \: {a}^{3} + {a}^{2} b - {ab}^{2} - {b}^{3} [/tex]

Multiply:

[tex](a+5) by (a^2-2a-3)[/tex]

[tex]: \implies{(a + 5) \times ( {a}^{2} - 2a - 3) }[/tex]

[tex]: \implies \: a({a}^{2} - 2a - 3) + 5( {a}^{2} - 2a - 3)[/tex]

[tex]: \implies(a \times {a}^{2} - a \times 2a - a \times 3) + (5 \times {a}^{2} - 5 \times 2a - 5 \times 3)[/tex]

[tex]: \implies{a}^{3} - {2a}^{2} - 3a + 5 {a}^{2} - 10a - 15 [/tex]

[tex]: \implies{ {a}^{3} + {3a}^{2} - 13a - 15}[/tex]

Multiply:

[tex](a^2-ab+b^3) by (a+b)[/tex]

[tex]: \implies{(a + b) \times ( {a}^{2} - ab + {b}^{3} )}[/tex]

[tex]: \implies \: a( {a}^{2} - ab + {b}^{3}) + b( {a}^{2} - ab + {b}^{3} ) [/tex]

[tex]: \implies {a}^{3} - {a}^{2} b + a {b}^{3} + {a^2b} - {ab}^{2} + {b}^{4} [/tex]

[tex]: \implies{ {a}^{3}+ab^3 - ab^2+ {b}^{4} }[/tex]

Step-by-step explanation:

[tex] \blue{ \frak{Seolle_{aph.rodite}}}[/tex]

Donovan is paying for gym classes. Each type of class has its own weekly fee. He signed up for x weeks of yoga classes and y
weeks of kickboxing classes. He paid a total of $136. The equation below describes the relationship between the number of weeks
of yoga classes and the number of weeks of kickboxing classes Donovan signed up for.
8x + 12y
-
136
The ordered pair (5,8) is a solution of the equation. What does the solution (5.8)

Answers

Considering the given function, the ordered pair (5,8) means that the signed up for 5 weeks of yoga classes and 8 weeks of kickboxing classes.

What does the function represent?


The function that represents the relationship between the number x of yoga classes that Donovan signs up for and the number y of kickboxing classes is given by:

8x + 12y = 136.

Hence the ordered pair (5,8) means that the signed up for 5 weeks of yoga classes and 8 weeks of kickboxing classes.

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x² + 10x + 3 = -21?!?!!?!?!!!?

Answers

Answer:

-6,-4

Step-by-step explanation:

if you have to evaluate its 4

and there is 2 solutions

An auto weighing 2,000 pounds is on a street inclined at 10° with the horizontal. Find the force necessary to prevent the car from rolling down the hill. (Round your answer to the nearest whole number.)

347 pounds
14,397 pounds
2,462 pounds

Answers

Force (F) = WSin(angle)

F = 2000×Sin(10)

Therefore, F = 347lb.

what is a variable in mathematics?

Answers

Answer:

variable, In algebra, a symbol (usually a letter) standing in for an unknown numerical value in an equation. Commonly used variables include x and y (real-number unknowns), z (complex-number unknowns), t (time), r (radius), and s (arc length).

Answer:

variable, In algebra, a symbol (usually a letter) standing in for an unknown numerical value in an equation. Commonly used variables include x and y (real-number unknowns), z (complex-number unknowns), t (time), r (radius), and s (arc length).

Step-by-step explanation:

In Maths, a variable is an alphabet or term that represents an unknown number or unknown value or unknown quantity. The variables are specially used in the case of algebraic expression or algebra. For example, x+9=4 is a linear equation where x is a variable, where 9 and 4 are constants.

find the slope of the lined graph

Answers

Answer:

1

Step-by-step explanation:

The points go rise:1 up:1 so the slope is 1.

Answer:

hey!! we can taIk here

Step-by-step explanation:


A bowl contains 28 black, 21 red, 23 blue, and 10 green balls
A ball is drawn at random. P (blue).

Answers

Answer:

P (blue) = 23 / 82

Step-by-step explanation:

There are 23 blue out of 82 (28 + 21 + 23 + 10 = 82) balls

or,

23 / 82

So, the probability of a blue ball being chosen is  23/82  

(or a 28% chance [rounded])

willams bought piece of woods that is 3 feet long.he cuts it in to two pieces.one piece is 14 in long how long is the other piece

Answers

Answer:

22 inches

Step-by-step explanation:

3 feet = 36 inches

36-14=22

The other half is 22 inches long

Suppose a nuclear power plant disaster occurs. How could GDP be a "false beacon" in this case?

Answers

If there was a nuclear plant disaster, then GDP would be a false beacon because it would account for government spending but not for the pollution caused.

Why would GDP be a false beacon?

Two of the components of GDP are government spending and private investment.

If there is a nuclear plant disaster, either the government will spend a lot to clean it up, or a private company will depending on if the plant is public or private.

GDP would therefore increase.

This would be a false beacon however, because this increase would not take into account the nuclear pollution that would have occurred that would negatively impact future production.

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What are the domain and range of g(x)= √x-3?

A. D: [3, ∞) and R: [0, ∞)
B. D: [–3, ∞) and R: [0, ∞)
C. D: (–3, ∞) and R: (–∞, 0)
D. D: (3, ∞) and R: (–∞, 0)

Answers

Answer:

I guess, A is the wanted answer, but

A and D together are the really correct answer.

Step-by-step explanation:

if I understand this correctly, then

g(x) = sqrt(x - 3)

the domain of a function is the definition of all valid x (input) values.

the range of a function is the definition of all valid y (result) values.

well, the content (the arguments) of a square root cannot be negative (at least not while dealing with real numbers).

so, the answer options B and D are automatically out, because the domain contains values that would make the arguments of the square root negative.

I guess your teacher wants to focus only on the positive results of the square root, so A is the correct number.

BUT formally, without designated restrictions, a square root has always 2 solutions : a positive and a negative one.

because (-x)² = (x)² = x².

so, I would have to say that the really correct answer is

A + D, because the range contains both, the positive and the negative numbers.

need help with this graphing question please

Answers

Step-by-step explanation:

12 . The x-intercept is where a line crosses the x-axis, and the y-intercept is the point where the line crosses the y-axis. Thinking about intercepts helps us graph linear equations..

Which represents the solution(s) of this system of equations?

(4, 4)
(–4, –12)
(4, 4) and (–4, 12)
(–4, 4) and (4, 12)

Answers

The solution to the given system of equation is (4, 4)

Factorizing quadratic functions

From the solved steps, the final quadratic functions is given as;

x^2 - 8x + 16 = 0

Factorize to have;

x^2 - 4x - 4x + 16 = 0

x(x-4)-4(x-4) = 0
(x-4)(x-4) = 0

x = 4 and 4

Hence the solution to the given system of equation is (4, 4)

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A group of kids just finished trick-or-treating. The number of pieces of candy collected by each of the 5 kids is listed below.
31,33,36,41,34
Find the standard deviation of the data set. Round your answer to the nearest hundredth.

Answers

The standard deviation is about 3.81
To find standard deviation on calculator hit stat, 1, enter in each number, hit stat again, the hit the arrow to go to calc, then 1, and enter until it shows you the stats. The icon that says Sx is standard deviation for the data set you entered.

If you help me you get a lot of points

Answers

Answer:

Step-by-step explanation:

#a

pattern 0 will include 4 reds in square

Because it's independent of pattern no

#b

Figure 1 has 4+4=8

Figure 2=4+8+2=14

Figure 3=4+12+3=19

The pattern n rule is

n²+3n+4

So for 13th n

13²+3(13)+4169+39+4212squares

#c

attached

y=x²+3x+4

#d

Already given in c

12. Find the solution to the system of equations by
using
substitution.
y = -2x + 13
4x + 8y = 20
A)(-7,-1)
B)(4,5
C)(7,-1)
D)(-3,7)

Answers

Answer: C) x = 7, y = -1

Step-by-Step Explanation:

=> y = -2x + 13 (Eq. 1)
=> 4x + 8y = 20 (Eq. 2)

Substitute value of ‘y’ from Eq. 1 in 2 :-

4x + 8y = 20
4x + 8(-2x + 13) = 20
4x + -16x + 104 = 20
-12x + 104 = 20
-12x = 20 - 104
-12x = -84
12x = 84
x = 84/12
=> x = 7

Substitute value of ‘x’ in Eq. 1 :-

y = -2x + 13
y = -2(7) + 13
y = -14 + 13
=> y = -1

Therefore, x = 7, y = -1 which can be written in an ordered pair as (7,-1).


Solve the following radical equation.
√2x-3 =2

Answers

Answer:

First, we have to add 3 to both sides.
[tex]\sqrt{2x} - 3 + 3 = 2 + 3[/tex]

Then we simplify the equation,
[tex]\sqrt{2x} = 5[/tex]

Divide both sides of the equation by [tex]\sqrt{2}[/tex]
[tex]\frac{\sqrt{2x} }{\sqrt{2}} = \frac{5}{\sqrt{2}}[/tex]

Finally, simplify.
[tex]x = \frac{5\sqrt{2}}{2}[/tex]

Therefore, our answer is [tex]x = \frac{5\sqrt{2}}{2}[/tex]

3.5

Step-by-step explanation:

square means 1/2.so,1/2(2x-3)=(2)^2

then square cancel by square. 2x-3=4

2x=4+3, 2x=7then divided by 2.

x=3,5

A box has candies in it: are taffy, are peppermint, and are caramel. (Each candy falls into only one of these categories.) Brian wants to select two candies to eat for dessert. The first candy will be selected at random, and then the second candy will be selected at random from the remaining candies. What is the probability that the first candy selected is taffy and the second candy is caramel?
Do not round your intermediate computations. Round your final answer to three decimal places.

Answers

Probability that the first candy selected is taffy and the second candy is caramel is 0.144.

The data missing in the question is

A box has 18 candies in it: 3 are peppermint, 4 are caramel, and 11 are taffy.

What is Probability ?

Probability can be defined as the study of likelihood of an event to happen.

It has a range of 0 to 1.

Probability is the ratio of the expected outcomes / total coutcome.

Total outcomes = 18

The probability that the first candy is taffy is 11/18

Now as there is no replacement , the total outcomes can be 17

The probability that the second candy is caramel is 4/17

Probability that the first candy selected is taffy and the second candy is caramel =  (11/18)(4/17)

= 0.144

Therefore the Probability is 0.144

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EASY POINTS
What is the slope-intercept equation of this line?

Answers

Answer:

B

Step-by-step explanation:

The y-intercept is 8

The slope is -2x

Therefore the slope-intercept is y = -2x + 8

If the population is highly skewed, the sample size needed for the central limit theorem to apply usually has to be ______ that when the population is not highly skewed a. different from b. the same as c. larger than d. smaller than​

Answers

Answer:

2

Step-by-step explanation:

the same as...

(2) is the answer

If the population is highly skewed, the sample size needed for the central limit theorem to apply usually has to be the same as that when the population is not highly skewed.

What is the central limit theorem?

The central limit theorem states in probability theory that, in many instances, when independent random variables are added together, their correctly normalized sum tends toward a normal distribution, even if the original variables are not normally distributed.

If the population is highly skewed, the sample size needed for the central limit theorem to apply usually has to be the same as that when the population is not highly skewed.

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WHAT IS THIS HELP




if u put a bad answer i'll report

Answers

Answer:

C

Step-by-step explanation:

Two negatives cancel out and turn into a positive.

In the expression 11 - ( -3 5/8 ) there are two negative signs. If the parenthesis are removed, the two negative signs cancel out and turn into a positive and we are left with 11 +3 5/8

So the answer is C

A gardener has 75 clients, 45% of whom are businesses. Find the number of business clients.

Answers

Answer:

33,75 clients(huh?)

Step-by-step explanation:

75 / 100 = 0,75(1% of all clients)

0,75 * 45 = 33,75(number of business clients)

3375 is not the number of clients the other guy who answered is lying

Compare 3.5 • 10^4 to standard form

Answers

Answer:

35,000

Step-by-step explanation:

^4 means 4 zeros

10^4 = 10,000

3.5 times 10,000 =

35,000

17.
select the correct answer
what is the equation of the problem shown with its focus on this graph?
Options are in photo!

Answers

Answer:

B

Step-by-step explanation:

0.00002165 in scientific notation.

Answers

Answer:

2.165 × 10⁻⁵

Step-by-step explanation:

Move the decimal -5 places to the right. For every scientific notation, 10 is the default number you are multiplying the decimal by. The exponent is the number of places you moved the decimal point. The exponent is positive when moving left, negative when moving right.

Hope it helps!

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