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
katen-ka-za [31]
3 years ago
5

Please explain with working!!! Find the set of values of x that satisfy the inequality 9x^2-15x<6

Mathematics
1 answer:
Oksi-84 [34.3K]3 years ago
6 0

Answer:

-1/3

Step-by-step explanation:

When solving a quadratic inequality, first solve it normally like you would for a normal quadratic equation. We have:

9x^2-15x

Ignore the less than sign and replace it with an equal sign and solve the quadratic for its zeros:

9x^2-15x=6

Subtract 6 from both sides:

9x^2-15x-6=0

Divide everything by 3:

3x^2-5x-2=0

Factor. Find two numbers that equal (3)(-2)=-6 that add up to -5.

-6 and 1 works. Thus:

3x^2-6x+x-2=0\\3x(x-2)+1(x-2)=0\\(3x+1)(x-2)=0

Find the x using the Zero Product Property:

3x+1=0 \text{ or }x-2=0\\x=-1/3\text{ or }x=2

Now, we need to replace the equal signs with symbols again. To do so, we need to test which symbol to place. Let's do the first zero first.

So, the first zero is:

x=-1/3

Assume that the correct symbol is >. Thus,

x>-1/3

Now, pick any number that is greater than -1/3. I'll pick 0 since it's the easiest. Now, plug 0 back into the very original inequality. If it works, then the sign is correct, if it doesn't, then simply use the opposite one. Therefore:

9x^2-15x

0 is indeed less than six, so our first correct solution is:

x>-1/3

For the second one, do the same thing. We have:

x=2

Assume that the correct symbol is <. Thus:

x

Again, pick any number less than 2. I'm going to use 0. Plug 0 back into the original equation

9x^2-15x

Again, this is correct. Therefore, x<2 is also the correct inequality.

So together, we have:

x>-1/3 \text{ and } x

Together, we can write them as:

-1/3

(Note that we don't need to worry about the "or equal to" part since the original inequality didn't have it.)

You might be interested in
HELPPP I WILL BRAINLIST!!
charle [14.2K]

Answer:

Step-by-step explanation:

8 (x -3) +7 = 2x (4 -17)

8(x -3) +7 = 2x (-13)   here was the error because the had 13 that is incorrect

8x -24 +7 = -26x

8x -17 = -26x

-17 = -26x -8x

-17 = -34x

-17/-34 = x

1/2 =x

3 0
3 years ago
Evaluate 5xyz + 3y for x=2.5, y=12, and z=4
Reika [66]

Answer:

636

Step-by-step explanation:

5xyz+3y

5(2.5)(12)(4)+3(12)

(12.5)(48)+36

600+36

636

8 0
3 years ago
A circle with the radius of 1cm sits inside a 3cm×4cm rectangle. What is the area of the shaded region?
Tanya [424]

Answer:

8.86

Step-by-step explanation:

Im guessing you want the rectangles area

Finding circle area do radius times radius times 3.14 so 1 x 1 = 1 x 3.14 = 3.14

Rectangle area is length times width so 3 x 4 = 12 - 3.14 = 8.86

8 0
3 years ago
What is the equivalent radian measure of 600?​
pychu [463]

Answer:

=  \frac{ \theta}{180}  \times \pi \\  =  \frac{600}{180}  \times \pi \\  =  \frac{10}{3} \pi

3 0
3 years ago
M∠1 = 80 – x; and
Burka [1]

Answer:

10

Step-by-step explanation:

<em>m∠</em>2 and <em>m∠</em>1 are congruent by the Corresponding Angles Theorem; we set both expressions equal to each other:

[80 - x]° = [90 - 2x]°

+ x° + x°

______________

80° = [90 - x]°

-90° - 90°

__________

−10° = [−x]°

10° = x

I am joyous to assist you anytime.

6 0
3 years ago
Other questions:
  • Help please ASAP!!! I need to answer this correctly!!!
    7·1 answer
  • What is the sum? 3 y / Y 2 + 7 y + 10 + 2 / y + 2​
    9·1 answer
  • Is 2/3 and 4/6 equivalent fractions
    15·2 answers
  • Aleta's puppy gained3/8 pound each week for 4 weeks.Altogether, how much weight did the puppy gain during the 4 weeks
    11·1 answer
  • Suppose the scores of students on a Statistics course are Normally distributed with a mean of 563 and a standard deviation of 37
    14·1 answer
  • You measure 50 textbooks' weights, and find they have a mean weight of 37 ounces. Assume the population standard deviation is 5.
    7·1 answer
  • Write an equation that models the linear relationship in the graph?
    6·2 answers
  • A manufacturer of chocolate chips would like to know whether its bag filling machine works correctly at the 419 gram setting. It
    5·1 answer
  • Find the product. Express your answer as a mixed number in simplest form.<br><br> 2 1/6 × 4 1/2
    11·1 answer
  • Easy Points! <br> also plz help I'm stuck rn :)
    10·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!