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
viktelen [127]
3 years ago
10

Determine the intervals on which the polynomial is entirely negative and those on which it is entirely positive. (Enter your ans

wers using interval notation. Enter EMPTY or ∅ for the empty set.)
−x^2 + 6x − 10
I don't understand how to factor this, as as such, I can't figure out how to answer the question. Please help!
Mathematics
2 answers:
Stells [14]3 years ago
5 0
This is a parabola that opens downward.
Remember that the axis of symmetry is located at x=-b/(2a).
So the vertex is at (3,-1)
So functions slope is positive or increasing on (-co, 3] and decreasing on [3,co).

Law Incorporation [45]3 years ago
3 0

Answer with explanation:

The function for which we have to find , the intervals on which the polynomial is entirely negative and those on which it is entirely positive.

 f(x)= -x²+6 x -10

 If you will find the root of the function, there is no real root.

To find the root we will use Discriminant formula

For a Quadratic function, ax²+b x+c=0,

 x=\frac{-b+\sqrt{D}}{2a}\\\\D=b^2-4ac\\\\x=\frac{-6\pm \sqrt{6^2-4 *(-1)*(-10)}}{2*(-1)}\\\\x=\frac{-6\pm\sqrt{-4}}{-2}

→So,there is no interval in which  the polynomial is entirely negative and those on which it is entirely positive, which can be represented in interval notation using Ф.

   f(x)= -(x^2-6x+10)\\\\= - [(x-3)^2-9+10]\\\\=-(x-3)^2-1

For, any value of x,the value of f(x) will be always Negative.

To find the vertex, put ,x-3=0

 x=3

And, by putting , x= 3 ,in the equation we get

y = -1

So,Vertex = (3, -1)

⇒If you will try to find the intervals in which the function is increasing , means the curve is moving up is from (-∞, 3) and the intervals in which the function is decreasing , means the curve is moving downward is from , (3, ∞).

You might be interested in
PLEASE GUYS CAN SOMEONE HELP ME WITH THESE, POINTS TO THE KIND AND SMART PERSON TO ANSWER THESE SORT OF TEDIOUS QUESTIONS HELP A
MaRussiya [10]

Step-by-step explanation:

1.

a. true

b. false (the arc angles are relative to the center of the circle)

c. true (as the central angle of a circle is twice any inscribed angle subtended by the same arc)

d. true (but note that the arc angle of YE is again measured via the center of the circle and twice as large as the angle S)

2.

EGS is an isoceles triangle (that means both legs are equally long).

remember the extended Pythagoras for general triangles :

c² = a² + b² - 2ab×cos(C)

c being the side opposite of the angle C.

let's say c is our long baseline, since we have is opposite angle 124°, and a = b = GE = GS, we have

3.8² = a² + a² - 2aa×cos(124) = 2a² - 2a²×cos(124) =

= 2a²(1 - cos(124))

2a² = 3.8²/(1 - cos(124))

a² = 3.8²/(2(1 - cos(124)))

a = GS = sqrt(3.8²/(2(1 - cos(124)))) =

= 2.151883096... ≈ 2.2 cm

3.

circumference

16pi = 2pi×r

r = 8

area = pi×r² = pi×8² = 64pi

yes, the statement is true.

4.

a half-circle has 180°.

the arc angel AD is a full half-circle (because AD is a diameter), so it is 180°.

the angle ACB is the arc angle AB = 40°. so, the arc angle BD must be the rest of the 180° = 180 - 40 = 140°.

5.

diameter = 50 ft.

so, the radius or distance from the center to the circle arc is 50/2 = 25 ft.

the length of a chord is

c = 2×sqrt(r² - d²)

with r being the radius, d being the distance of the chord from the center.

40 = 2×sqrt(25² - d²)

20 = sqrt(625 - d²)

400 = 625 - d²

-225 = -d²

225 = d²

d = 15 cm

so, the distance of the chord from the center is 15 cm.

6.

the arc angles RE and TS are equal. that means the arc lengths of RE and TS are equal.

and that means the arc lengths of RS and ET are equal. the chords between 2 points on a circle must have the same length, when the arc lengths between these 2 points are the same.

7.

they are equally long.

as we saw in 5., the length of a chord depends on the radius of the circle and the distance of the chord from the center.

since both chords are in the same circle (with the same radius), and they both have the same distance from the center, they can only be equally long, as there is no other element to name them different.

8.

the angle NPE is half of the angle NAE (= the arc angle NE).

the arc angle NE = 63×2 = 126°

the angle PET is half of the angle PAT (= the arc angle PT).

the arc angle PT = 19×2 = 38°

the arcs NP and ET cover the rest of the whole circle circumference (360°).

so, arc angle NP + arc angle ET = 360 - 38 - 126 = 196°

but arc angles NP and ET must be equal (as per the problem definition).

therefore, 2 equal arc angles = 196°

1 arc angle = NP = 196/2 = 98°

6 0
2 years ago
Caitlyn did 6/7 of the problems on her math correctly and 4 incorrectly. She did all the problems. How many were there?
Viefleur [7K]
If \frac{6}{7} were incorrect, it means that \frac{1}{7}=4 were correct
4*7=28
There were 28 problems ;)
5 0
3 years ago
Mark and John share the sum of $40 in ratio 2:3 how much does John get​
lara [203]

Answer:

John gets 24 dollars

Step-by-step explanation:

Divide 40 into 5 because 2+3 equals 5.

Each "section" equals 8. Now, multiply that by 3(John's section)

You get 24.

4 0
3 years ago
Select two ratios that are equivalent to 2:12 A.6:40 B.12:2 C.3:24 D.1:6 E.8:48
Sever21 [200]

Answer:

E

Step-by-step explanation:

2:12 is equivalent to 8:48

7 0
3 years ago
Read 2 more answers
Due SOON!!
DedPeter [7]

Answer:

?=19

x=30

Step-by-step explanation:

5/6x - 1/5x = 19

5(5/6x) - 6(1/5x) = 19

25/30x-6/30x=19

19/30x=19

19x=19(30)

19x=570

x= 570/19

x=30

6 0
2 years ago
Other questions:
  • Choose an equation that when paired with the equation below, will create a system of equations with infinitely many solutions, o
    9·1 answer
  • Susie and her mother are planting a flower garden. It will be in the shape of a right triangle. They draw a diagram of a triangl
    14·1 answer
  • How to find missing angles parallel
    9·1 answer
  • Find the distance between the points (1, 5) and (1, -4). 3 √(41) 9
    14·1 answer
  • What is the value of t in the following equation? t + 14 = 2 712
    12·1 answer
  • Determine the multiplier in each situation below.
    13·2 answers
  • Benson is shopping for shampoo. His favorite brand comes in 5 different sizes which size is the best deal
    14·1 answer
  • What is f(x)=-2x+10 <br> when f(2)
    15·2 answers
  • A netball team has 7 boys and 4 girls. The percentage of the girls in the class
    13·1 answer
  • A box was 3/4 full.the box fell on the floor. 30 marbles fell out. this was 20% of the marbles that were in the box. how many ma
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!