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

Answers

Answer 1

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).

Answer 2

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,

[tex]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}[/tex]

→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.

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

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, ∞).

Related Questions

solve for x −1/2(x+2)+11/2x=3

Answers

The answer to this problem is 4/5 Hope I helped!

Using place value how to increase 2384598 by six million

Answers

6 million = 6,000,000

2,384,598 + 6,000,000 = 8,384,598

your answer is 8,384,598

hope this helps

50 POINTS!!! DO NOT ANSWER JUST FOR THE POINTS!!! IF YOU DO, ALL OF YOUR EARNED POINTS WILL BE TAKEN~~~~~~~~~~~~~~~

Refer to the graph.

The function is increasing on the interval(s):

The function is decreasing on the interval(s):

The function is constant on the interval(s):

Please explain the steps you used.

Answers

A) [-7,-4] U [4,7]; B) [-4,-1]; C) [1,4]

Which of the following is the inverse of the statement "If I like math, then I like science"? A. If I do not like science, then I do not like math. B. If I do not like math, then I like science. C. If I do not like math, then I do not like science. D. If I like science, then I like math

Answers

Original Conditional: If P, then Q

Inverse: If not P, then not Q

Using that template, the inverse would be "If I do not like math, then I do not like science" (simply insert those two "not" words keeping the order the same)

so the answer is choice C

Answer:

Option C If I do not like math, then I do not like science

Step-by-step explanation:

we know that

To find the inverse of a conditional, negating both the hypothesis and conclusion of a conditional statement

In this problem we have

"If I like math, then I like science"

therefore

the inverse is

If I do not like math, then I do not like science

Nia is three years older than half Jordans age , if Jordan is eight years old , how old is Nia?

Answers

Hello!

If Nia is three years older than half of Jordan's age, we must divide Jordan's age by 2 (to find half of his age).

Jordan is eight years old:
8 divided by 2 equals 4

4 years old is half of Jordan's age. Now, to find Nia's age, we must add 3 to half of Jordan's age (4).

4+3= 7
Nia is 7 years old.

I hope this helps answer your question! Have a great day!

Answer:

Step-by-step explanation:

An important part of customer service responsibilities of a cable company relates to the speed with which trouble in service can be repaired. Historically, the data show that the likelihood is 0.75 that troubles in a residential service can be repaired on the same day. For the first 5 troubles reported on a given day, what is the probability that fewer than 2 troubles will be repaired on the same day?

Answers

The answer to your question is
D. .2373

Hope this helps

Answer:

The probability that fewer than 2 troubles will be repaired on the same day is:

0.015576

Step-by-step explanation:

We have to use the Binomial function is n=order to calculate the probability of r successes out of the n-events.

We know that the probability of r success out of the n-events is given by:

[tex]P(X=r\ successes)=n_C_r\cdot p^r\cdot (1-p)^{n-r}[/tex]

where p is the probability of an success.

Here we have:

n=5 and r=0,1.

since we are asked to find the probability that fewer than 2 troubles will be repaired on the same day.

i.e we have to find:

[tex]P(X<2)=P(X=0)+P(X=1)[/tex]

Also p=0.75 ( since, likelihood is 0.75 that troubles in a residential service can be repaired on the same day )

Hence,

[tex]P(X=0)=5_C_0\cdot (0.75)^{0}\cdot (1-0.75)^{5-0}\\\\P(X=0)=1\cdot 1\cdot (0.25)^5\\\\P(X=0)=0.000976[/tex]

and

[tex]P(X=1)=5_C_1\cdot (0.75)^{1}\cdot (0.25)^{5-1}\\\\P(X=1)=5\cdot (0.75)\cdot (0.25)^4\\\\P(X=1)=0.0146[/tex]

Hence,

[tex]P(X<2)=0.000976+0.0146\\\\P(X<2)=0.015576[/tex]

Hence, the probability that fewer than 2 troubles will be repaired on the same day is:

0.015576

Which of the following statements is true? 0.74 < 0.80 0.61 > 0.93 0.83 < 0.94 1.548 < 0.698

Answers

0.74 < 0.80
0.83 < 0.94

Among the given statements, the only true statements are

0.74 < 0.80 and 0.83 < 0.94.

How is this so?

In both cases, the number on the left is less than the one on the right. Which makes the expression and or use of the less than symbol correct.

The greater than symbol (>) and the less than symbol (<) are used to compare two numbers or expressions to determine their relationship.

The greater than symbol (>) represents "greater than" and indicates that the number on the left side is larger than the number on the right side.

The less than symbol (<) represents "less than" and indicates that the number on the left side is smaller than the number on the right side.

For example, 5 > 3 means "5 is greater than 3," and 2 < 7 means "2 is less than 7."

Learn more about statements at:

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A rectangular plot of land has an area of 1/8 square mile. Its width is 3/20 mile.What is the length of the plot of land?

Answers

A = L * W
A = 1/8
W = 3/20

1/8 = 3/20L
(1/8) / (3/20) = L
1/8 * 20/3 = L
20/24 reduces to 5/6 miles = L <===

Suppose a line has slope 4 and passes through the point (-2, 5). Which other point must also be on the graph?

A) (2, 6) B) (-1, 9) C) (-1, 1) D) (-6, 4)

Answers

D) -6,4. because if it has a slope of 4 which is positive it has to have an uphill slope which passes through -2,5, in order for that to happen you plot it and make the line and count the rise over run till you have the slope of 4.

[tex]\bf slope = {{ m}}= \cfrac{rise}{run}\implies 4\implies \cfrac{4}{1}[/tex]

so the rise is 4 units and the run is 1 unit, ok.

now, from point -2, 5, if we move 4/1, that is, "1 unit over the x-axis, and 4 units over the y-axis", we'll find another point, now, a fraction can be positive so long both top and bottom are the same sign, so -4/-1 is the same as 4/1 and therefore, if we move +4 and +1 over the axes we get a point, or if we move -4 and -1 we also get another point, and any other subsequent points from there on.

so, hmm let's check [tex]\bf (\stackrel{x+1}{-2}~,~\stackrel{y+4}{5})\implies (-1~,~9)[/tex]

What is 10000 times 20000000

Answers

the answer to you problem given is, 200000000000

The answer is 200,000,000,000
Hope this helps you!
Have a nice day!

Math please help!!!!

Answers

Separate the numbers out into
50 x 5
7 x 5

That gets you 250 and 35
Add the numbers and you get 285, the same as 57 x 5

If you drive for 2 hours, at 60 miles per hour, you will have traveled 120 miles. this is a very common type of calculation, involving three quantities: distance, rate and time. if you know just two of these three quantities, you can always calculate the third. thus, if you want to know how much time it is going to take you to get somewhere, and you know that the distance is 120 miles and you will drive at a rate of 60 miles per hour, you can divide the 120 miles by the 60 miles per hour and obtain a time of 2 hours.

Answers

do u still need the answer

A segment has endpoints ar (-2,3) and (7,9) how long is the segment

Answers

[tex]\bf \textit{distance between 2 points}\\ \quad \\ \begin{array}{lllll} &x_1&y_1&x_2&y_2\\ % (a,b) &({{ -2}}\quad ,&{{ 3}})\quad % (c,d) &({{ 7}}\quad ,&{{ 9}}) \end{array}\qquad % distance value d = \sqrt{({{ x_2}}-{{ x_1}})^2 + ({{ y_2}}-{{ y_1}})^2} \\\\\\ d=\sqrt{[7-(2)]^2+[9-3]^2}\implies d=\sqrt{(7+2)^2+(9-3)^2} \\\\\\ d=\sqrt{9^2+6^2}\implies d=\sqrt{81+36}\implies d=\sqrt{117} \\\\\\ \boxed{117=3^2\cdot 13}\qquad \qquad d=\sqrt{3^2\cdot 13}\implies d=3\sqrt{13}[/tex]

kim has 3/4 pound servings of grapes. how many 1/8 pound servings can Kim make from his grapes

Answers

he can make 6 servings

(3/4) / (1/8) =
3/4 * 8/1 =
24/4 =
6 <=== there are 6 one-eighth pound servings

The length of a rectangle is 11 m greater than the width. The area is 42 m^2. Find the length and width.

Answers

the answer is that the width is 3 m and the length will be 14 m because 3•14 = 42m² and 3+11=14

Hello friends my name is blank I'm sorry but I need to ask a question so buy

At Avery Middle School, 273 students responded to a survey asking whether a Bulldog, a Lion, or a Tiger should be a new school mascot. Four times as many students chose Tiger. Twice as many students chose Lion as chose Tiger. How many students chose Lion?
A) 39 students
B) 78 students
C) 156 students
D) 273 students

Answers

the answer is c 156 students

Answer with Step-by-step explanation:

273 students responded to a survey asking whether a Bulldog, a Lion, or a Tiger should be a new school mascot.

Let t students chose tiger

b students chose bulldog

and l students chose lion

then, t+b+l=273

Four times as many students chose Bulldog as chose Tiger.

i.e. b=4t

Twice as many students chose Lion as chose Tiger.

i.e. l=2t

So, t+4t+2t=273

i.e. 7t=273

Dividing both sides by 7, we get

t=39

Number of students who chose lion=2t

= 2×39

= 78

Hence, Correct option is:

B) 78 students

Order pairs (x,y) that is the solution to the equation.
5x-y=4
(x,y) =

Answers

Given: 5x-y=4. Create a couple of ordered pairs by choosing x and calculating y from this equation:

x=1 results in y=1. Thus, (1,1) is a solution.
x=-3 results in -15-y=4, or -y=19, or y=-19. Thus, (-3,-19) is a solution.

x=0 results in -y=4, so that y=-4. Thus, (0,-4) is a solution.

The arctic lion's Mane Jellyfish is one of the largest known animals. Its tentacles can be as long as 120 feet. Find how this length compares to your height. Round your height to the nearest foot. 120 feet is time as long as feet.

Answers

To solve this problem, we must first know your height. So assuming that your height is 5 feet. Therefore we can divide:

120 feet / 5 feet = 24

So that the answers in the blanks are:

120 feet is 24 times as long as 5 feet

Is m=1/2 a solution of the equation 6m-8= -5

Answers

Yes correct it is a solution and here is why. :D

Add 8 to both sides

(6m = -5 + 8)

Simplify -5 + 8 to 3

(6m = 3)

divide both sides by 6

(m = 3/6)

simplify 3/6 to 1/2

Answer: m = 1/2

Is y=2x-8 and 2x-y=8 a dependent independent or inconsistent

Answers

Note that 2x-y=8 can be solved for y: y=2x-8. This is identical to the first equation. The graph of one is exactly the same as the graph of the other. Thus, the two equations are dependent.

Answer:

dependent

Step-by-step explanation:

[tex]y=2x-8[/tex] and [tex]2x-y=8[/tex]

First equation is already solve for y

LEts solve the second equation for y

[tex]2x-y=8[/tex]

Subtract 2x on both sides

[tex]-y=-2x+8[/tex]

Divide the whole equation by -1

[tex]y=2x-8[/tex]

After solving for y, both equation are same

When both the system of equation are same then it has infinite solutions.

They are said to be dependent.

3a/(a+1)^2
Give the equivalent numerator if the denominator is (a + 1)³.

Answers

Given 3a/(a+1)^2
To make the denominator a cube, you would have to multiply by 1 or (a+1)/(a+1)
yielding 3a(a+1)/(a+1)^3
(3a^2 + 3a) is the equivalent numerator

Answer:

3a(a+1)

Step-by-step explanation: for those who were confused on the other asnwer he gave a different veriation of this answer. however it is correct.

Brainliest plsss

Banks pay interest on savings accounts because

A. they can get more customers that way.

B. they want to encourage you to save.

C. they invest your money.

D. they're just very nice.

Answers

I'm gonna go with C or B cause(based on Google)Banks use the money deposited on savings accounts to lend to borrowers, who pay interest on their loans. After paying for various costs, the banks pay money on savings deposits to attract new savers and keep the ones they have.

Hey there!

Banks aren't in the business of being nice and actually get most of their revenue from their relentless overdraft fees. While it may seem like they're doing something nice or encouraging you to save your money, they're really just encouraging you to become a customer. They don't invest your money, since it needs to be present for you if you want to withdraw it.

Interest on your savings is simply a method for getting new customers.

Hope this helped you out! :-)

michael wittry has been investing inhis roth IRA retirement account for 20 years. Two years ago his account was worth $215,658. after losing 1/3 of its origional value, it then gained 1/2 of its new value back, what is the current value of his roth IRA?

Answers

let's say

a = 215,658

ok... so.. he first lost 1/3 of that

[tex]\bf \textit{\underline{lost} }\frac{1}{3}a\qquad \qquad a-\cfrac{1}{3}a\implies a-\cfrac{a}{3}\implies \cfrac{3a-a}{3}\implies \cfrac{2a}{3} \\\\\\ \textit{then he \underline{gained} }\frac{1}{2}\textit{ of }\frac{2a}{3}\qquad \qquad \cfrac{2a}{3}+\cfrac{\frac{2a}{3}}{2}\implies \cfrac{\frac{2a}{3}}{\frac{2}{1}} \\\\\\ \cfrac{2a}{3}+\cfrac{2a}{3}\cdot \cfrac{1}{2}\implies \cfrac{2a}{3}+\cfrac{2a}{6}\implies \cfrac{4a+2a}{6} \\\\\\ \cfrac{6a}{6}\implies \boxed{a}\implies 215,658[/tex]

so, his nickname might just be even steven, because, he ended up with the same original amount after the 1/2 bump.

His current value is 215658 dollars.

How to calculate a fraction of amount of a total amount ?

To calculate a fraction of amount of a total amount just multiply the given fraction to the total amount.

According to the given question

Michael wittry has been investing in his roth IRA retirement account for 20 years.

Two years ago his account was worth $215,658.

1/3rd of it's original value is

= (1/3) × 215658

= 71886 dollars.

∴ Remaining value is

=(215658 - 71886)

=143772 dollars.

After some time it gained half of it's new value back

∴ Half of this new value is

(1/2) × 143772

= 71886 dollars.

So , the current value is

(143772 + 71886)

=215658 dollars.

Actually his currect value of roth IRA is same as it was two years ago.

Learn more about fractions here :

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round 2,412 to the nearest thousands

Answers

2,000 since you're rounding to the nearest thousands.

The answer is 2,000 because 2,412 is closer to 2,000 than 3,000. Hope I helped!

A machine produces 240 bolts in 25 minutes. At the same rate how many bolts would be produced in 45 minutes

Answers

The rate per minute = 240/25 = 9.6 bolts/minute

And in 45 minutes = 45 x 9.6 = 432 bolts

In 1 minute of those 25 minutes 9.6 bolts were produced. 45*9.6=432. So in 45 minutes 432 bolts were made.

Hope that helped. :^)

386-123= estimate then find the difference

Answers

390-125= 265
Round 386 to 390 and 123 to 125

you estimate 386 to 400 and 123 to 100 so you will get
400-100=300

The outside diameter of a pipe is 5 and 7/32 inches. The walls of the pipe are 5/32 inches thick. What is the inside diameter?

Answers

check the picture below

thus

[tex]\bf 5\frac{7}{32}-\cfrac{5}{32}\implies \cfrac{5\cdot 32+7}{32}-\cfrac{5}{32}\implies \cfrac{167}{32}-\cfrac{5}{32}\implies \cfrac{162}{32} \\\\\\ \cfrac{81}{16}\implies 5\frac{1}{16}''[/tex]

The sum of three numbers is 99. The first number is 9 more than the third. The second number is 4 times the third. What are the numbers?

Answers

first number=x+9
second number=4x
third number=x
4x+x+x+9=99
6x=90
x=15
first number=24
second number=60
third number=15

Final answer:

The first number is 24, the second number is 60, and the third number is 15.

Explanation:

Let's assign variables to represent the three numbers. Let x represent the third number. Since the first number is 9 more than the third, we can write the equation:

First number = x + 9

Since the second number is 4 times the third, we can write the equation:

Second number = 4x

Now, we can add the three numbers together, according to the given information:

(x + 9) + 4x + x = 99

Simplifying this equation, we get:

6x + 9 = 99

Subtracting 9 from both sides, we have:

6x = 90

Dividing both sides by 6, we find:

x = 15

So the third number is 15. Plugging this value back into the two other equations, we find that the first number is 24 and the second number is 60. Therefore, the three numbers are 24, 60, and 15.

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A book had a length of 5 inches and a width of 8 inches. What is the perimeter of the book

Answers

26 inches hope this helps

the perimeter is 26in

12 tenths plus 9 tenths =21 tenths = ____ ones _____ tenths

Answers

2100 ones if I am thinking about this right. hope it helps

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