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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, ∞).

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Trigonometry, can anybody help??
WINSTONCH [101]

Answer:

angle B: 39

AC: 7.288

AB: 11.58

(note: you cut off the part about rounding so make sure that it's rounded correctly before you put in your answer)

Step-by-step explanation:

To solve this we will use SOH, CAH, TOA

we have the angle and the one opposite to it which means we can use either SOH or TOA

let's use TOA

tan(51)=(9/x)

x= 7.288

We can now use pahtagaryous theroem to solve for the hyptonouse

we have

9²+7.288²=C²

C=11.58

Finally, to find angle B we will recall that the angles of a triangle must add to 180.

51+90+a=180

a=39

5 0
3 years ago
Please help answer these questions. My teacher said they were really easy but I just don't understand. Will mark brainliest !!!
kodGreya [7K]

Answer:

1.  A = 59

2.  A = 43

Step-by-step explanation:

If we have a right triangle  we can use sin, cos and tan.

sin = opp/ hypotenuse

cos= adjacent/ hypotenuse

tan = opposite/ adjacent


For the first problem, we know the opposite and adjacent sides to angle A

tan A = opposite/ adjacent

tan A = 8.8 / 5.2

Take the inverse of each side

tan ^-1 tan A = tan ^-1 (8.8/5.2)

A = 59.42077313

To the nearest degree

A = 59 degrees


For the second problem, we know the  adjacent side and the hypotenuse to angle A

cos A = adjacent/hypotenuse

cos A = 15.3/21

Take the inverse of each side

cos ^-1 cos A = cos ^-1 (15.3/21)

A = 43.23323481

To the nearest degree

A = 43 degrees


6 0
3 years ago
What's 75% off of 4.97
Alenkasestr [34]
That would be 1.2425
7 0
3 years ago
Read 2 more answers
Write 21/4 as a decimal. Round to three decimal places
Nadusha1986 [10]

5.250

To change a fraction to a decimal fraction divide the numerator by the denominator.

that is 21 ÷ 4 = 5.250 ( to 3 decimal places )


5 0
3 years ago
Read 2 more answers
An ice-cream truck sells milkshakes for $3.50 and cones for $2. On Wednesday, a total of 45 milkshakes and cones were sold, and
AnnZ [28]

Answer:

247.5

Step-by-step explanation:

i added £3.50 and £2 then times it by 45 milkshakes

5 0
3 years ago
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