Decide whether this statement is always true, never true, or sometimes true, and explain why: In a quadratic equation of the form 0 = ax2 + bx + c, there will be two real solutions if a and c are of opposite signs

Answers

Answer 1

Answer:

Always true

Step-by-step explanation:

Here, we want to evaluate if the given statement is true

The discriminant D can be calculated using the formula;

b^2 - 4ac

if D is greater than 0, then we will have only real roots

In a case where a and c are of opposite signs;

then -4ac will always give a positive value which can be added to b^2

This positive value will ensure that D is greater than zero and hence we can have only real roots

So this assertion is always true if a and c are of opposite signs


Related Questions

Select all ratios equivalent to 7:2 ?

Answers

Answer: 14:4 , 21:6 , 28:8 , 35:10

Step-by-step explanation:

price of 1 kg sugar is rupees 104.25 find the price of 50 kg​

Answers

Answer:

5,212.5 rupees

Step-by-step explanation:

If price of 1 kg is 104.25

multiply 50 by 104.25

equals 5,212.5 rupees

Answer:

5212.50 rupees

Step-by-step explanation:

We can use a ratio

1 kg             50 kg

-----------  = ---------------

104.25            x

Using cross products

1x = 50 * 104.25

x =5212.50 rupees

How many quaters are in 4 and 3 over 4

Answers

Answer:

19

Step-by-step explanation:

If you're asking how many quarters in 4 3/4

In 1 there are 4 quarters so do 4 multiplied by the 4 quarters which is 16. In 3/4 we have 3 quarters so 16 add the 3 is 19.

Simplify the following surd expressions.
a) 5 square root of 5 - 2 square root of 5
b) 8 square root of 7 + 3 square root of 7

Answers

Answer:

A=3√5

B=11√7

Step-by-step explanation:

5√5-2√5

5-2√5

3√5

B) 8√7+3√7

8+3√7

11√7

Tantasic charges a reservation fee of 20$ and $1 per minute in a tanning bed. Bettersun charges no reservation fee but charges 2$ per minute. How many minutes will the price be the same

Answers

Answer:

The indifference point is 20 minutes

Step-by-step explanation:

Giving the following information:

Tantasic:

Reservation fee of 20$ and $1 per minute

Bettersun:

2$ per minute.

First, we need to structure both total cost formulas:

Tantasic= 20 + 1x

Bettersun= 2x

x= number of minutes

Now, we equal both formulas and isolate x:

20 + 1x = 2x

20 = 1x

20= x

The indifference point is 20 minutes

What is the solution to this system of linear equations?

x + y = 4

x − y = 6

Answers

Answer:

x=5 , y= -1

Step-by-step explanation:

You can see that one of the y's is negative while the other is positive, so you can add them together.

Now, negative 1 + positive 1 = 0, so the y's cancel out leaving only the x's.

Remember you can't add one part without adding the other so x+x = 2x, and 4+6=10. This makes the final equation 2x=10.

You can simplify that into x=5. This gives you the answer for x

Then substitute x=5 into any of the two equations (doesn't matter) I'll use the first one. So if you substitute it you get 5+y=4.

Simplified, y= -1

Therefore, x= 5 and y=-1

Answer:

(5,-1)

Step-by-step explanation:

Got it right on edge cause of the guy above me

Answer ASAP Brainliest and 22 Points!

Answers

Answer:

Step-by-step explanation:

1. 5x+8-7x=4x+1              2.

5x-7x+8=4x+1

2x+8=4x+1

-2x+8=4x+1

-2x+8-8=4x+1-8

-2x-8=4x-7

6x=-7

x=7/6

HELP!!!!! I will gove brainliest

Answers

Answer:

what do u need help on?

Step-by-step explanation:

i don't know what u need help with

............................... 6/2(1+2)

Answers

Answer:

9

Step-by-step explanation:

6/2(1+2)

=3*3

=9

Answer:

6

Step-by-step explanation:

6/2 is 3 and 1+2 is three and 3 + 3=6

The ratio of boys to girls in 6th grade is 2:3, if there were 65 students in the class, how many girls are there? How many boys are there?

Answers

Answer:

26 boys and 39 girls

Step-by-step explanation:

if you were to divide 65 by 5 then you would get 13. all you have to do is add 13 + 13 and you would get the number of boys. for the girls you add 13 + 13 + 13.

What single decimal multiplier would you use to decrease by 7% followed by a 20% decrease?

Answers

Answer:

13 percent

Step-by-step explanation:

Single decimal multiplier used to decrease by 7% followed by a 20% decrease is 0.744.

What is decimal multiplier?

A percentage multiplier is a number which is used to calculate a percentage of an amount or used to increase or decrease an amount by a percentage. In order to use a percentage multiplier to calculate the percentage of an amount, convert the percentage to a decimal by dividing by 100 ; this is the decimal multiplier.

Given,

First decrease = 7%

Second decrease = 20%

Let a number be x.

If x is decreased by 7% then the value of the number is

( (100 - 7) / 100) × x = 0.93 x

Again if 0.93 x is decreased by 20% then the value of the number      ((100 - 20) /100) × 0.93 x = 0.744 x

Hence, The single decimal multiplier is 0.744.

Learn more about decimal multiplier here:

https://brainly.com/question/16992894

#SPJ2

what is 12 to the power of 0 simplified?

Answers

Step-by-step explanation:

the answer is 1

x^0 = 1

12^0 = 1

im not that sure

Describe the end behavior of a 9th degree polynomial with a negative leading coefficient??

Answers

Answer:

Up left, down right

Step-by-step explanation:

First, polynomials with odd degrees will have end behaviors in two different directions.

Since the leading coefficient is negative, the end behavior will be up left and down right.

So, the end behavior is up left, down right.

The end behavior of a 9th-degree polynomial with negative leading coefficients is up left, downright.

We have to determine

The end behavior of a 9th-degree polynomial with a negative leading coefficient??

What is a negative leading coefficient?

If the leading coefficient is negative and the exponent of the leading term is even, the graph falls to the left and right.

What is the equation of 9th-degree polynomial?

The equation of the 9th-degree polynomial is;

[tex]\rm x^9+3x^8+4x^7+x^6+x^5+9x^3+2x^2+x+1=0[/tex]

The degree of the polynomial is 9 which is odd.

Hence, the end behavior of a 9th-degree polynomial with negative leading coefficients is up left, downright.

To know more about Polynomial click the link given below.

https://brainly.com/question/17822016

A student has some $1 and $5 bills in his wallet. he has a total of 15 bills that are worth $51. How much of each type of bill does he have?

Answers

Answer:

# of 5 dollar bills: 9

# of 1 dollar bills: 6

Step-by-step explanation:

9•5 = 45

1•6 = 6

To Check: 45 + 6=51

9 $5 bills and 6 $1 bills

what is the avrage of 4.1 ,6 ,1.3 6.5 ,1.6

Answers

Answer:

3.36

Step-by-step explanation:

4.1 +6 +1.3+6.5 +1.6=16.8

16.8/5=3.36

In order to  get the answer you add everything up and then divide from the amount of numbers there are.

The trail starts at P(−7, 6) and goes to Q(4, 6). It goes from Q to R(4, −6) and then to S(6, −6). What is the total length (in units) of the biking trail?

Answers

We know, distance between two points A( p,q) and B(r,s) is given by :

[tex]AB=\sqrt{(p-r)^2+(q-s)^2}[/tex]

So, distance between P an Q is :

[tex]PQ=\sqrt{(-7-4)^2+(6-6)^2}\\\\PQ=11\ units[/tex]

Distance between Q and R is :

[tex]QR=\sqrt{(4-4)^2+(6-(-6))^2}\\\\QR=12\ units[/tex]

Distance between R and S is :

[tex]RS=\sqrt{(4-6)^2+(-6-(-6))^2}\\\\RS=\sqrt{4}\\\\RS = 2\ units[/tex]

Therefore, total distance is 11 + 12 + 2 = 25 units.

Hence, this is the required solution.

what is the slope of the graph?

Answers

Answer:-6

Step-by-step explanation:

What is the answer to this pre-algebra equation 7x+10=3x+120

Answers

Answer:

 =[tex]\frac{55}{2}[/tex]

WILL GIVE BRAINLIEST !!!
Find the equation of the line. Use the exact numbers.

Equation: y = __x + __

Answers

Answer:

Step-by-step explanation:

y=2/3x+4. 4 is the y intercept. 2/3 is the slope. y=mx+b where m is the slope and b is the y intercept

The average attendance of a yearly Winter Wonderland exhibit at an amusement park is 2.8 × 10 5 people. How many people can be expected to attend over 4 years?

Answers

Answer:

1120000 attendees

Step-by-step explanation:

Given that:

Yearly Average attendance = 2.8 * 10^5 people

How many attendees can be expected to attend over 4 years

Average Yearly attendees * 4

(2.8 * 10^5) * 4

= 2.8 * 4 * 10^5

= 11.2 * 10^5

= 1120000 attendees

hope this pic helps.enjoy

A ream of paper contains 500 sheets, and a case of paper contains 10 reams. An office supply store gets a delivery of 400 cases. How many sheets of paper are in the delivery? Express your answer in scientific notation.

Answers

Answer:

2,000,000  or 2x10^6

Step-by-step explanation:  Multiply the total number of sheets in a ream times the total number of reams in a case times the number of cases.

The populations of Cities A and B are 1.6 x 10^5 and 1,070,000​, respectively. The population of City C is twice the population of City B. The population of City C is how many times the population of City​ A?

Answers

Answer:

13

Step-by-step explanation:

First find the population of city c 1,070,000 times 2 = 2140000

Round 2140000 to the nearest hundred thousands = 2,100,000

Third find how many places the decimal moves which is 6 places

Fourth scientific notation of 2,100,00 is 2.1 times 10^6

Fifth divided city c by the population of city a

2.1x 10^6 divided by 1.6 x 10^5

2.1 / 1.6 rounded is 1.3

10^6 divided by 10 ^ 5 is 10

Therefore 2.1 x 10^6 divided by 1.6 divided by 10^5 equals 1.3 times 10 = 13

The population of city c is about 13 times the population of city a

Drag the numbers below to put them in order from least to greatest:
-19 -12 -13 9 -4 -1

Answers

-19, -13, -12, -4, -1, 9
-19,-13,-12,-4,-1,9 because negative numbers are smaller than positive because they are not real numbers

Find the value for x
Can somebody help me?
Please

Answers

Answer:

1-7 2-6 3-6 4-4

Step-by-step explanation:

To do this, you must notice that all of these are isosceles triangles (2 of the sides are the same.) You already have 1 value on each triangle, and the length of that side is the same length as the side with the unknown value, so those are the correct answers. If I made a mistake, please correct me. Everybody makes mistakes.

Anyone know this pls help ill give brainliest :)

Answers

Answer:

30, 40, 60, 70,

Step-by-step explanation:

pattern by 10

For 3=30

      4=40

       6=60

        7=10

  Calculate the slope

           50-20/5-2

             10

Find the value of x.
(5x + 5)

Answers

5( x + 1)

I hope this helps:)

i am in need of assistance

Answers

The cars speed is 80 miles per hour

IF YOU HAVE ANSWER PLEASE ANSWER

The math teacher said, "Please ___ each expression on the board. Show your work so that I can see how you found the value."

its ether evaluate, operation or commutative

Answers

evaluate. hope this helps

There was 4/5 of a cake sitting on the counter. Daryl ate 1/3 of the left over cake. How much cake was left over after he ate?

Answers

Answer:

0.46 is the left over 23/50 is the fraction

There are screws, nuts and bolts in a tool box. The ratio of the number of
Screws to the number of nuts to the number of boits is 2:3:7. The
difference between the number of nuts and the number of bolts is 112.
Find the number of each item​

Answers

Answer:

Step-by-step explanation:

56:84:196 would be the answer

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