True or False? When Liesl used the quadratic formula to solve a quadratic equation, she noticed the value of the discriminant was a perfect square. She immediately determined that she could have factored the quadratic equation she was solving.​

Answers

Answer 1

Liesl is correct, if the discriminant is a perfect square, then we can factorize the quadratic equation.

Is the statement true or false?

For a quadratic equation:

y = a*x^2 + b*x + c

The discriminant is:

D = b^2 - 4ab

Notice that for the equation:

0 = a*x^2 + b*x + c

The solutions are given by:

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

If D is a perfect square, then we know that the square root has solutions, so there are two values:

[tex]x_1 = \frac{-b + \sqrt{D}}{2a}\\\\x_2 = \frac{-b - \sqrt{D}}{2a}[/tex]

Now with these solutions, we can factorize our equation as:

[tex]y = a*(x - ( \frac{-b + \sqrt{D}}{2a}))*(x - ( \frac{-b - \sqrt{D}}{2a}))[/tex]

So Liesl is correct, if the discriminant is a perfect square, we can factorize the quadratic equation.

If you want to learn more about factorization, you can read:

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Related Questions

Solve
1/5x + 2/5x - 12 = -6.

The solution is x=

Please explain

Answers

Answer:

X = 10

Step-by-step explanation:

Multiply both sides of the equation by 5

x + 2x - 60 = -30

Collect like terms

3x - 60 = -30

Move constant to the right-hand side and change its sign

3x = -30 + 60

Calculate the sum

3x = 30

Divide both sides of the equation by 3

x = 10

Solution

x = 10

Answer: x = 10

Step-by-step explanation:

1/5x + 2/5x - 12 = -6    Add 12 to both sides

                   +12    +12

1/5x + 2/5x = 6     Combine like terms on the left side

3/5x = 6         Divide both sides by 3/5

x =  10

If you are interested in purchasing 20 year term life insurance and every $10,000 of coverage costs $1.00 per month, how much would your monthly payment be for $250,000 of coverage?

Answers

Answer:  1,200  

Step-by-step explanation:

Jessica paid $25.50 for 3.4 pounds of shrimp. How much would it cost her to buy 8 pounds?

Answers

Answer: The answer would be $60

Step-by-step explanation: You would first wanna solve for how much one pound of shrimp costs, which is $7.5 (you divide 25.50 by 3.4) Then you would want to multiply 7.5 by 8 to get how much 8 pounds of shrimp costs.

what are some ways to write 4 times x

Answers

Answer:

Some ways to write 4 times x are: 4x, 4*x

A number is chosen at random from the whole numbers
between 1 and 100, inclusive.
(a) What is the probability that the number ends in a zero?
(b) What is the probability that the number is odd?
(c) What is the probability that the number is odd or ends in
a zero?

Answers

Answer:

90 for the first oneoneoneone

Step-by-step explanation:

Plzzzzzz meeeeeeeeeeeee

Answers

Answer:

add all terms together and simplify

Step-by-step explanation:

Answer:

x= 2.1

Step-by-step explanation:

if you drive 25 miles at a rate of 50 miles per hour. how long will this take?

Answers

Answer:

30 minutes

Step-by-step explanation:

50/25 =2 x 15 = 30

Which deal is better? Pizza A is 10-inch diameter for $15 or Pizza B is a 12-inch diameter for $27? Which do you get more pizza per dollar spent?​

Answers

Answer:

the answer is pizza b

Step-by-step explanation:

first i did 15 divided by 10=1.50

then i did 27 divided by 12=2.25

then i did 1.25%of 12=0.15

then 2.25 of 12=0.27

you get more pizza per dollar with pizza b

Which expression is equivalent to

numerator: (8 × 10−4) + (6 × 10−4)

denominator: 3.5 × 102
fraction^
?

A. 4 × 10-2

B. 4 × 10-6

C. 4 × 10-8

D. 4 × 10-10

Answers

Answer:

Step-by-step explanation:

i cannot find an answer from the expression but i can guess if you didnt follow pemdas, it would be d

3.5 × 102  is 357

(8 × 10−4) + (6 × 10−4)  is 132

132/357= .369 or .37 or 0 simplified

d is 4*10-10

10-10 is 0

4*0 is 0

Please help I’m giving out likes and etc

Answers

The answer is 5

2 translates to 10 after being multiplied by 5
1 translated to 5 after being multiplied by 5

Hope this helped :)
D hope this helps!!!

ILL GIVE BRAINIEST TO WHOEVER IS CORRECT!! PLEASE HELP ASAP!! WITH WORK PLEASE!!!

Answers

Answer:

14,10

Step-by-step explanation:

8=(x+2)/2

16=x+2

x=14

4=(y-2)/2

8=y-2

y=10

Answer:

Step-by-step explanation:

can anyone help me with this one

Answers

Answer:

180+216= 396cm²

please mark brainliest♡♡

Step-by-step explanation:

First separate the shape into two rectangular

27 - 9= 18

18×10= 180cm²

9×24= 216c m²

Answer:

396 cm²

Step-by-step explanation:

Area = 10 x (27 - 9) + 24 x 9

= 10 x 18 + 24 x 9

= 20 x 9 + 24 x 9

= 44 x 9

= 396 cm²

Find the value of x. (It's an obtuse scalene triangle with two angles of 33° and 29°)

Answers

Answer:

118

Step-by-step explanation:

33+29 = 62

180 - 62 = 118

What is the value of log Subscript 0. 5 Baseline 16? –4. 00 –0. 25 1. 51 2. 41.

Answers

The value of the logarithm expression [tex]log_{0.5}(16)[/tex] evaluated is given by : Option A: -4.00

What is logarithm and some of its useful properties?

When you raise a number with an exponent, there comes a result.

Lets say you get

[tex]a^b = c[/tex]

Then, you can write 'b' in terms of 'a' and 'c' using logarithm as follows

[tex]b = log_a(c)[/tex]

Some properties of logarithm are:

[tex]\log_a(b) = \log_a(c) \implies b = c\\\\\log_a(b) + \log_a(c) = \log_a(b \times c)\\\\\log_a(b) - \log_a(c) = \log_a(\frac{b}{c})\\\\\log_a(b^c) = c \times \log_a(b)\\\\\log_b(b) = 1\\\\\log_a(b) + log_b(c) = \log_a(c)\\[/tex]

Log with base e = 2.71828... is written as [tex]\ln(x)[/tex] simply.

Log with base 10 is written as [tex]\log(x)[/tex] simply.

For this case, we have to simplify the expression [tex]log_{0.5}(16)[/tex]

Let this is equal to 'a', then:

[tex]a = \log_{0.5}(16)\\\\0.5^a = 16\\(\dfrac{1}{2})^a = 16\\\\1^a/2^a = 2^4\\\\1 = 2^4 \times 2^a\\2^0 = 2^{4+a}\\\\0 = 4 + a\\a = -4[/tex]

(we used the property that: [tex]b^0 = 1[/tex] and [tex]k^m \times k^n = k^{m+n}[/tex] )

Thus, the value of the logarithm expression [tex]log_{0.5}(16)[/tex] evaluated is given by : Option A: -4.00

Learn more about logarithm here:

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I need help you ASAP I need the answer

Answers

Answer:

[tex]\huge\boxed{<BCA = 48\°}[/tex]

Step-by-step explanation:

The measure of exterior angle is equal to the sum of the non-adjacent interior angles.

So,

∠NAB = ∠ABC + ∠BCA

105° = 57° + ∠BCA

Subtracting 57 to both sides

∠BCA = 105°-57°

∠BCA = 48°

Hope this helped!

~AnonymousHelper1807

Is ✓ 10 greater than, less than or equal to 5? Use the drop-down menus to explain your answer.
Because 10 lies between two consecutive perfect squares,
Choose.
1.110 is located between the choose...
these two numbers
of
This means that 10 is located between
Choose
.so V 10 is
Choose
5

Answers

Answer:

Step-by-step explanation:

✓9 = 3

And

✓16=4

=> ✓10 is between number 3 and 4

=> ✓10 is less than 5

Number √10 is less than 5.

Because 10 lies between two consecutive perfect squares of 3 and 4.

What is Number system?

A system of writing to express the number is called number system.

Given that;

The number is √10.

Since, Value of √10 = 3.16

Which is less than 5.

That is, 3.16 < 5

And, Value of 3² = 9

Value of 4² = 16

⇒ 3² < 10 < 4²

Hence, 10 is lies between two consecutive perfect squares 3 and 4.

Thus, Number √10 is less than 5.

Because 10 lies between two consecutive perfect squares of 3 and 4.

Learn more about the consecutive numbers visit:

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Find the area of the circle with the diameter of 16

Answers

Answer:

64 [pi]

Step-by-step explanation:

pi r²=pi (8) 2=64 pi [use the symbol]

hope this helps! :)

Answer:

803.84

Step-by-step explanation:

A=3.14r^2

A=3.14x16^2

16x16=256

256x3.14=803.84

Hope this helps : )

how do you subtract 8.43x^3 - 2.7x10^2

Answers

Answer:

Step-by-step explanation:

I tried this on a calculator but you could also do it on paper hope this helped!

Need a quick help with the point lol

Answers

Answer: Point

Step-by-step explanation: Point

Answer:

its 14 because you divide the circumfrece and then pi

Step-by-step explanation:


Please help me solve 5 and 4!

Answers

4. is A
5. i dunno sorry but 4 is A :)

35. Priscila's age is k years while Mary's age is byears. If Mary is 15 years older than b Priscila, which of the following stateinents is correct? 2k + b = 15 -K= 15 6 K-6= 15 D. 20+k=15 A. В.​

Answers

The relationship between Priscilla's and Mary's age illustrates algebraic expression

The correct representation of the statements is b - k = 15

How to determine the representation of their ages?

From the question, we have:

Priscilla = k

Mary = b

Mary = 15 years older

The third highlight above means that:

Mary = 15 + k

Substitute b for Mary

b = 15 + k

Subtract k from both sides

b - k = 15

Hence, the correct representation of the statements is b - k = 15

Read more about algebraic expression at:

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(5, 3) and (5,-9) slope:
30 POINTS

Answers

the answer is unidentified

Determine what comes next in the given pattern.

15, 10, 14, 10, 13, 10,​

Answers

Answer:

→ 12..........

I hope this will help you....

Answer: 12, 10,

Step-by-step explanation:

simplify 2 1/3 + 1 3/10 - 3 2/15



please help me quick i will mark you as brainliest and this question also gives 18 points

Answers

Answer:

7

Step-by-step explanation:

2 x 1/3 + 1 x 3/10 - 3 x 2/15

Multiplying each Side by the LCM which is 30

u will get 10 (2x1) + 3 (1x3) - 2 (3x2)

10(2) + 3(3) - 2(6)

20 + 9 -12

19 -12

7

What additional information would be sufficient, along with the given, to conclude that lmno is a parallelogram? check all that apply. ml ∥ no ml ⊥ lo lo ≅ mn ml ≅ lo mn ⊥ no

Answers

The conditions ML ║ NO and LO ≅ MN are sufficient to show that the LMNO is a parallelogram.

What is a parallelogram?

It is a polygon that has four sides. The sum of the internal angle is 360 degrees. In a parallelogram, opposite sides are parallel and equal. And its diagonals are not equal but intersect at the mid-point.

The side ML is parallel to the NO that is given as

ML ║ NO

And the side LO is equal to the side MN

LO ≅ MN

These conditions are sufficient to show that the LMNO is a parallelogram.

More about the parallelogram link is given below.

https://brainly.com/question/1563728

Answer:

ML ∥ NO, LO ≅ MN (1 and 3)

Step-by-step explanation:

edg

What is the image of (x,y) after a translation of 3 units left and 7 units down?

Answers

Answer:

[tex](x + 3, y - 7)[/tex]

Step-by-step explanation:

Given

[tex]Function = (x,y)[/tex]

Translation:

[tex]Left = 3\ units[/tex]

[tex]Down = 7\ units[/tex]

Required

Determine the image of the function

Apply the first translation

[tex]Left = 3\ units[/tex]

When function (x,y) is 3 units translated left, we add the units to the x value.

The new function becomes:

[tex](x,y) -> (x + 3, y)[/tex]

Apply the second translation

[tex]Down = 7\ units[/tex]

We subtract 7 units from the y value

[tex](x,y) -> (x + 3, y)[/tex]

becomes:

[tex](x + 3, y) ->(x + 3, y - 7)[/tex]

Hence:

The image of the function is:

[tex](x + 3, y - 7)[/tex]

The numbers 20 through 30 were written on individual cards and placed in a bag. If you take one card from the bag, what is the probability that it will not have the digit 2 on it?

Answers

Answer:

1/10

Step-by-step explanation:

20 21 22 23 24 25 26 27 28 29 30

X.   X.   X.  X.  X.  X.  X.  X.  X.  X.  V

1/10

20-29 all have a 2 in it meaning 30 is the only digit that doesnt have a 2 so 1/10 numbers

If one card taken from the bag then the probability that will not have the digit 2 on it is 1/11.

What is probability ?

Probability shows possibility to happen an event, it defines that an event will occur or not. The probability varies from 0 to 1.

Given that,

Numbers from 20 to 30 are written on individual cards.

The total numbers of cards = 11

And numbers on cards = 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30

To find the probability of cards that have not the digit 2 on it.

Since, there is only one digit 30, which does not have digit 2,

Therefore, probability = favorable outcome / total outcome

= 1 / 11

The required probability of choosing a card that will not have the digit 2 on it is 1/11.

To know more about Probability on:

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Can some one plz help me plz

Answers

1. 10 + 5x = 20

2. 5 + 10x = 20

3. 20 - 5x = 10

4. x/5 + 10 = 20

 The ratio of men to women working for a company is 8 to 5 if there are 135 woman working for the company what is the total number of employees

Answers

Answer:

351 employees

Step-by-step explanation:

5x27=135

8x27=216

135+216=351

Number 5 please I’m having trouble

Answers

Answer:

B

Step-by-step explanation:

you would just divide 37 from 8659

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