Write a quadratic equation given the roots -1/3 and 5, show your work

Answers

Answer 1

[tex] \boxed{(x - a)(x - b) = 0}[/tex]

The equation above is the intercept form. Both a-term and b-term are the roots of equation.

[tex]x = - \frac{1}{3} \\ x = 5[/tex]

These are the roots of equation. Therefore we substitute a = - 1/3 and b = 5 in the equation.

[tex](x + \frac{1}{3} )(x - 5) = 0[/tex]

Here we can convert the expression x+1/3 to this.

[tex]x + \frac{1}{3} = 0 \\ 3x + 1 = 0[/tex]

Rewrite the equation.

[tex](3x + 1)(x - 5) = 0[/tex]

Simplify by multiplying both expressions.

[tex]3 {x}^{2} - 15x + x - 5 = 0 \\ 3 {x}^{2} - 14x - 5 = 0[/tex]

Answer Check

Substitute the given roots in the equation.

[tex]3 {(5)}^{2} - 14(5) - 5 = 0 \\ 75 - 70 - 5 = 0 \\ 75 - 75 = 0 \\ 0 = 0[/tex]

[tex]3( - \frac{1}{3} )^{2} - 14( - \frac{1}{3}) - 5 = 0 \\ 3( \frac{1}{9} ) + \frac{14}{3} - 5 = 0 \\ \frac{1}{3} + \frac{14}{3} - \frac{15}{3} = 0 \\ \frac{15}{3} - \frac{15}{3} = 0 \\ 0 = 0[/tex]

The equation is true for both roots.

Answer

[tex] \large \boxed {3 {x}^{2} - 14x - 5 = 0}[/tex]


Related Questions

Simplify 4+3/7x-2-2/7x

Answers

[tex] \huge \bold{answer}[/tex]

ANSWER:

[tex]\bold{4+\dfrac{3}{7}x-2-\dfrac{2}{7}x  }[/tex] 

[tex]\bold{4-2+\dfrac{3}{7}x-\dfrac{2}{7}x   }[/tex] 

[tex]\bold{ 2+(\dfrac{3}{7}+\dfrac{2}{7})x  }[/tex] 

[tex]\bold{2+\dfrac{3-2}{7}x   }[/tex] 

[tex]\bold{\blue{2+\dfrac{1}{7}x}}[/tex]

2x-8y=16 solve for x

Answers

Answer:

x=8+4y

Step-by-step explanation:

Add 8y to both sides:

2x=16+8y

Divide both sides by 2:

x=8+4y

State true or false for each statement

Answers

Answer:

true

true

false

false

Step-by-step explanation:

I think that that is right mark brainliest if i'm right

Help me please (the problem is in the photo)

Answers

3 small 3 larger good sir

dm the answer bc its glitched heres the question Gabi tried to solve an equation step by step.

0.1(0.5m+6)=2

Answers

Answer:

m = 28

Step-by-step explanation:

The given expression is :

0.1(0.5m+6)=2

Step 1.

Use distributive property:

0.1(0.5m) +0.1(6) = 2

0.05 m+ 0.6 = 2

Step 2.

Subtract 0.6 both sides

0.05 m+ 0.6 -0.6= 2 -0.6

0.05 m = 1.4

or

0.5 m = 14

Step 3.

Divide both sides by 0.5

[tex]m=\dfrac{14}{0.5}\\\\m= 28[/tex]

Gabi's third step is not correct. It should be m = 28 instead of m = 7.

explain how you will find the sum of 4.2 and 2.14

Answers

Answer:

you find the sum by adding a "0" at the end of "4.2" and the stack add them (or however you can add them).

Step-by-step explanation:

 4.20

+ 2.14

=  6.34

Can someone help me plz?

Answers

Answer:

60 degrees

Step-by-step explanation:

The total measures of a triangle should equal 180 total. Add the three known angles to get 120. Subtract that from 180 to get 60. So, the last angle measures 60 degrees.

Plz help I need to get my grade up in a week!!

Answers

Answer:

For 13 the slope is 0

Step-by-step explanation:

I can't see 12 nor 11, but 13 is a zero slope because horizonal lines have 0 slope.

I need help whoever answers this question will be the brainliest!!!

Answers

The answer is D because the level are higher ,,please can I get brainliest

Angela baked 5 batches of lemon sugar cookies with 17.5 cups of flour. She also made 3 batches of vanilla cookies using 11.25 cups of flour. Which type of cookies required more flour per batch?

Answers

vanilla cookies require more flour per batch

vanilla cookies = 3.75 cups of flour per batch
lemon sugar cookies = 3.5 cups of flour per batch

explanation:

lemon sugar cookies -
divide # of cups by the # of batches
17.5/5= 3.5

vanilla cookies -
divide # of cups by the # of batches
11.25/3= 3.75

to double check:
multiply 3.75 by 5 and you will see 5 batches of vanilla cookies will use 18.75 cups
and 5 batches of lemon cookies takes 17.5 cups

hope this helps !!!

Wie viele US-Dollar sind 30000 Euro?

Answers

Answer:

36,902.10 US-Dollar

Step-by-step explanation:

LMNO is a parallelogram. If NM = x + 15 and OL = 3x + 5 find the value of x and then find NM and OL.

Answers

Answer:

x = 5 unit

NM = 20 unit

OL = 20 unit

Step-by-step explanation:

Given:

LMNO is parallelogram

NM = x + 15

OL = 3x + 5

Find:

x and NM and OL

So,

NM = OL

x + 15 = 3x + 5

2x = 10

x = 5

So,

NM = x + 15 = 5 + 15 = 20

OL = 3x + 5 =3(5)+5 = 20

60 of the product of one-twelfth y and two-thirds z

Answers

Answer:

(.6)(y/12)(2z/3)

yz /30

Step-by-step explanation:

27 red markers to 12 blue markers into a ratio

Answers

27 (red markers):12 (blue markers)

Write 9x² - 36x = 4y² + 24y + 36 in standard form
this is a graph of a hyperbola, if this helps.
please include the steps on how you did it
Thank you!

Answers

Answer:

9·x² - 36·x = 4·y² + 24·y + 36 in standard form is;

(x - 2)²/2² - (y + 3)²/3² = 1

Step-by-step explanation:

The standard form of a hyperbola is given as follows;

(x - h)²/a² - (y - k)²/b² = 1 or (y - k)²/b² - (x - h)²/a² = 1

The given equation is presented as follows;

9·x² - 36·x = 4·y² + 24·y + 36

By completing the square, we get;

(3·x - 6)·(3·x - 6) - 36 = (2·y + 6)·(2·y + 6)

(3·x - 6)² - 36 = (2·y + 6)²

(3·x - 6)² - (2·y + 6)² = 36

(3·x - 6)²/36 - (2·y + 6)²/36 = 36/36 = 1

(3·x - 6)²/6² - (2·y + 6)²/6² = 1

3²·(x - 2)²/6² - 2²·(y + 3)²/6² = 1

(x - 2)²/2² - (y + 3)²/3² = 1

The equation of the hyperbola  is (x - 2)²/2² - (y + 3)²/3² = 1.

a football coach is trying to decide: when a team is ahead late in the game, which strategy is better?

• play the "regular" defense.

• play a "prevent" defense that guards against long gains but makes short gains easier
the coach reviews the outcomes of 100 games

compare the probability of winning when playing regular defense with the probability of winning when playing prevent defense. draw a conclusion
based on your results.

Answers

From analysis, it is seen that the probability of winning when playing regular defense is higher than the probability of winning with *prevent* defence.

How to find the probability of Winning?

We will assume that a total of 100 games were reviewed.

50 games used regular defense method.

The remaining 50 games used the prevent defense method.

Out of the 50 regular defense games, 38 were win while 12 games were lose.

Out of 50 prevent defense game, 29 were win, while 21 games were lose.

Thus, the Probability of winning by regular defense is:

P(win | regular) = 38/50

P(win | regular) = 0.76

Probability of winning by playing prevent defense is:

P(win | prevent) = 29/50 = 0.58

From the above analysis we observe that the probability of winning by using the regular defense method is greater than the probability of winning by prevent defense method.

That is 0.76 > 0.58.

Read more about Probability of Winning at: https://brainly.com/question/24756209

#SPJ1

a. Use the domain and range of each of the following relations to determine which is a function. {(3, -3), (9, - 6), (0, -9) b. (3. - 3), (9,- 6), (3 , -9) c. {(3. – 3), (9, - 6), (9,2). (0, -9) ] d. {3, 9, 0, - 4) Please select the best answer from the choices provided A B C D​

Answers

Answer:

A.

Step-by-step explanation:

The domain is the x values, the range is the y values. The x values are not supposed to repeat and give different y values.

Chase thought that only 23 people Would come to the banquet but 48 people endd up coming what was his percent error

Answers

Answer:

the percent of people that end up coming as error is 12%

Chase made a miscalculation of 52.08% percent.

What is Percentage Error?

The percent error is the distinction between the estimated value and the actual value in relation to the actual value. In other words, the relative error is multiplied by 100 to calculate the percent error.

Given that, Chase anticipated that just 23 people would attend the event; however, 48 individuals showed up.

The general formula for percentage error:

Percentage Error(%e) = ((Estimated Number – Actual Number)/ Actual number) x 100.

Hence,

Percentage error done by chase = (23 - 48) * 100/48

Percentage error done by chase = -52.08%

Therefore, the Percentage error done by chase is 52.08%

Learn more about Percentage error here:

https://brainly.com/question/10902860

#SPJ2

Find the AREA for J(2,4) K(3,-4) L(-2, 4) M(-1,-4)

Answers

Answer:

23

Step-by-step explanation:

PLZZZZZ HELP WILL ONLY GIVE BRAINLIEST IF ANSWER IS EXPLAINED
A TV has a listed price of $775.99 before tax. If the sales tax rate is 8.75% , find the total cost of the TV with sales tax included.
Round your answer to the nearest cent, as necessary.

Answers

Answer:

0.0875

Step-by-step explanation:

Who knows how to do this I TRULY NEED HELP

Answers

it’s 59°
cause 74+47=121
180-121=59

Two less than six times a number is the same as thirteen more than a number. Find the number.​

Answers

6x - 2 = x + 13
Subtract x
5x - 2 = 13
Add 2
5x = 15, x = 3
Solution: the number is 3

The perimeter of Square three is 20.4 square units in the perimeter of square two is 27.2 square units what is the area of square one

Answers

Answer:

a=554.88

Step-by-step explanation:

20.4*27.2=

12x-19=9x+5 solve for x

Answers

Answer:

Step-by-step explanation:

Here you go mate

Step 1

12x-19=9x+5  Equation/Question

Step 2

12x-19=9x+5  Simplify

12x-19=9x+5

Step 3

12x-19=9x+5  Subtract 9x

3x-19=5

Step 4

3x-19=5  add 19

3x=24

Step 5

3x=24  Divide by 3

answer

x=8

Hope this helps

35-284+4578567-32eye

Answers

Answer:

4578286

Step-by-step explanation:

35-284+4578567-32 = 4578286

hope this helps...

4578286 I thinkkkkkkkk

What is the length of ML if the inside is 50 degrees, and the outside is 5ft? Use pi - 3.14! I'll give Brainliest!

Answers

Answer:

Ml is 30 ft beco it help in pi

What would the UNIT RATE be for 90 miles in 5 hours be

Answers

Answer:

90/5 = 18 mph

if i start my online classes at 8:02 am and end at 11:55 am how long am i doing my classes for?

Answers

Answer:3 hours and 53 minutes

Step-by-step explanation:

11 - 8 is 3.

55- 2 is 53.

The time is 3 hours and 53 minutes

What groups of people controlled Algeria at one time?

Answers

Answer:

Much of the history of Algeria has taken place on the fertile coastal plain of North Africa, which is often called the Maghreb (or Maghrib). North Africa served as a transit region for people moving towards Europe or ... After the fall of the Western Roman Empire, Algeria came under the control of the Vandal Kingdom.

Hope this helps!!

Express in the form 1:n the ratio 56:7 give your answer as a decimal ​

Answers

Answer:

decimal 8

Step-by-step explanation:

Step 1 :Rewrite the ratio as a fraction 56:7=56/7

Step 2: Divide the number by the denominator

56/7= 56/7

56/7=8

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