1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
timofeeve [1]
2 years ago
13

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

Mathematics
1 answer:
Travka [436]2 years ago
8 0

\boxed{(x - a)(x - b) = 0}

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

x =  -  \frac{1}{3}  \\ x = 5

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

(x +  \frac{1}{3} )(x -  5) = 0

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

x +  \frac{1}{3}  = 0 \\  3x + 1 = 0

Rewrite the equation.

(3x + 1)(x - 5) = 0

Simplify by multiplying both expressions.

3 {x}^{2}  - 15x + x - 5 = 0 \\ 3 {x}^{2}  - 14x  - 5 = 0

<u>Answer</u><u> </u><u>Check</u>

Substitute the given roots in the equation.

3 {(5)}^{2}  - 14(5)  - 5 = 0 \\ 75 - 70 - 5 = 0 \\ 75 - 75 = 0 \\ 0 = 0

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

The equation is true for both roots.

<u>Answer</u>

\large \boxed {3 {x}^{2}  - 14x - 5 = 0}

You might be interested in
Consider the function f(x, y) = x2 + xy + y2 defined on the unit disc, namely, D = {(x, y)| x2 + y2 ≤ 1}. Use the method of Lagr
a_sh-v [17]

Answer:________________________________________

Step-by-step explanation:

5 0
3 years ago
Retha Davidson works for a word processing center keying straight copy.
Nataliya [291]

Using proportions, it is found that:

  • In an 8-hour day, she keys 48 pages.
  • For a day, her gross earnings are of $72.
  • For a week, her gross earnings are of 72 x 7 = $504.

<h3>Proportions:</h3>

This question is solved using the proportions given, which are:

  • Payment of $1.50 per page of 30 lines.
  • Retha keys 6 pages per hour.

Hence, in an 8-hour day, she keys 6 x 8 = 48 pages.

Since she earns $1.50 per page, for a day, her gross earnings are of 48 x 1.5 = $72.

Considering a week has 7 days, for a week, her gross earnings are of 72 x 7 = $504.

To learn more about proportions, you can take a look at brainly.com/question/24372153

5 0
2 years ago
Which expression best estimates 6 and three-fourths divided by 1 and two-thirds?
bixtya [17]

Answer: The expression is 7/2.

3 0
2 years ago
6^2r=800 round it to the nearest hundreth
kogti [31]

Question: solve for r: 6 ^ (2r) = 800


Answer: 1.87


Step-by-step explanation:

6 ^ (2r) = 800

log(6 ^ (2r)) = log(800)

2r log(6) = log(800)

r = log(800) / (2 log(6))

r = 1.86537641979

round

r = 1.87

log can be any logarithm function.


6^(2×1.86) = 784.734328546

6^(2×1.87) = 813.365367336


7 0
3 years ago
2x – 3y = -5
vampirchik [111]

Answer:

y = 3

Step-by-step explanation:

2x-3y = -5 --------- (1)

y = 2+x ------- (2)

substitute (2) into (1)

2x-3y = -5

2x-3( 2+x ) = -5

2x-6-x = -5

2x-x = -5+6

x = 1

substitute x = 1 into (2)

y = 2+x

y = 2+1

y = 3

4 0
2 years ago
Other questions:
  • What is the approximate positive value of the x-coordinate of the point of intersection of p(x)=5x^2-3 and q(x)=2x+1
    11·1 answer
  • The table shows the annual consumption of cheese per person in the United States for selected years in the 20th century. Let x =
    6·1 answer
  • Answer ASAP!!! First correct answer gets brainliest
    6·1 answer
  • The time that it takes to service a car is an exponential random variable with rate 1. (a) If Lightning McQueen (L.M.) brings hi
    13·1 answer
  • The elementary school students are putting on a play as a fundraiser. The student tickets cost $2.00 each and
    11·2 answers
  • Your class is learning to tie knots. Each student needs a piece of rope that is
    7·1 answer
  • EASY QUESTION
    5·2 answers
  • Jeremy tracked the temperature as a weather front crossed his region. The temperature rose 12 degrees, fell 27 degrees, and fina
    13·2 answers
  • can anyone explain how to do an equation like this and what the answer would be? i’m so confused haha. thank you! answer asap!!
    12·1 answer
  • Lol please help :))))).
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!