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
If 1/2 a number is 5 more than 1/7 of that number, what is the number?​
Burka [1]

Answer:

14

Step-by-step explanation:

1/2x = 1/7x + 5

1/2x - 1/7x = 5

7/14x - 2/14x = 5

5/14x = 5

x = 5 * 14/5

x = 14

4 0
2 years ago
What is 5 divided by-6/5
klasskru [66]
-25/6. hope this helps!

6 0
3 years ago
How much coffee is in the cup, it the cup if 7 feet by 7 feet, and 1 cubic foot = 7.48052
dybincka [34]

Answer:

the volume of a cylinder is pi r^2 h = 3.14.(3.5)^2. 5.5=211.55 cubic foot

211.55 x 7.48052 =1583.36 gallons.

Step-by-step explanation:

5 0
2 years ago
HELP I NEED HELP ASAP ONEIS BRAINLY
Luba_88 [7]
Q: can you find the volume of the tank based on the opposite sides as the bases. 


This one was a tricky one lol. 

To find volume you need a formula: 

Formula for volume varies on the shape of the object.

<span><span>Cube = a 3<span>a is the side length

</span></span><span>Rectangular prism = a * b * c<span>a, b, c are the length, width, and height

</span></span><span>Cylinder = π * r 2 * h<span><span>r is the radius of the circular base</span><span>h is the height

for this one you would need the Rectangular prism formula. 

A: No you cannot find the volume because you need length, width, and height to figure out the volume of the rectangular prism. 

Hope this helped! :)

</span></span></span></span>
4 0
3 years ago
Perrys Bikes rents bikes for $17 plus $6 per hour. john paid $59 to rent a bike. For how many hours did he rent the bike?
matrenka [14]
7 hours

Let x represent hours rented
59=17+6x
42=6x
x=7
4 0
3 years ago
Other questions:
  • What type of transformation does Shape A undergo to form Shape B a
    14·1 answer
  • The difference of the reciprocals of two successive integers equals the product of their reciprocals
    11·1 answer
  • Twice a number decreased by four is greater than ten, what numbers satisfy this condition?
    7·2 answers
  • The triangular banner Inez is
    10·1 answer
  • Find the measure of arc BC. PLEASE HELP!!
    9·1 answer
  • What does "of" mean in a persent question
    9·1 answer
  • Solve the multi-step word problems. Identify any hidden questions. (1.) The teacher collected $15 from 6 students last week for
    12·2 answers
  • Dr. Mann mixed 10.357 g of chemical A, 12.062 g of chemical B, and 7.506 g of chemical C to make 5 doses of medicine. What do it
    12·1 answer
  • PLEASE HELP! QUIZ QUESTION
    15·1 answer
  • can someone please help me with this, I did it and I got 54 the answer, but 54 isn't an answer choice​
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!