When f(x) = -3, what is x?
-29
-10
-3
-1

Solution 1

Inspecting a 7th-degree polynomial of 'n' by taking its derivatives

From the given conditions,

 2n7+n6+2n4+2n3+2n2

=(n+1)7+(n+1)5+(n+1)4+2(n+1)3+(n+1)2+2(n+1)+1.

 2n7+n6+2n4+2n3+2n2

=n7+7n6+21n5+35n4+35n3+21n2+7n+1

 +n5+5n4+10n3+10n2+5n+1

 +n4+4n3+6n2+4n+1

 +2(n3+3n2+3n+1)

 +(n2+2n+1)+2(n+1)+1.

n7-6n6-22n5-39n4-49n3-42n2-26n-9=0 .....[1].

Let A(n)=n7-6n6-22n5-39n4-49n3-42n2-26n-9.

For n>2, A(n)<n7-6n6-22n5.

Since A(n)=0,

0<n7-6n6-22n5.

0<n5(n-3+√31)(n-3-√31).

Since n>2, n>3+√31, which means n≥9 .....[2].

Now, to differentiate A(n),

A'(n)=7n6-36n5-110n4-156n3-147n2-84n-26.

A''(n)=42n5-180n4-440n3-468n2-294n-84.

A'''(n)=210n4-720n3-1320n2-936n-294.

A(4)(n)=840n3-2160n2-2640n-936.

 A(5)(n)

=2520n2-4320n-2640

=2520{(n-6/7)2-262/147}.

If A(5)(n)=0, n=6/7±√(262/147).

Therefore, A(5)(n)>0 for n≥3.

Although n≥9 according to [2], I try inspecting A(n) for n≥10.

When n≥10, A(4)(n) increases monotonously.

A(4)(10)=840000-216000-26400-936>0.

Therefore, A(4)(n)>0 for n≥10.

And when n≥10, A'''(n) increases monotonously.

A'''(10)=2100000-720000-132000-9360-294>0.

Therefore, A'''(n)>0 for n≥10.

And when n≥10, A''(n) increases monotonously.

A''(10)=4200000-1800000-440000-46800-2940-84>0.

Therefore, A''(n)>0 for n≥10.

And when n≥10, A'(n) increases monotonously.

 A'(10)

=7000000-3600000-1100000-156000-14700-840-26>0.

Therefore, A'(n)>0 for n≥10.

And when n≥10, A(n) increases monotonously.

 A(10)

=107-6000000-2200000-390000-49000-4200-260-9>0.

Therefore, A(n)>0 for n≥10 .....[3].

From [2] and [3], A(n)=0 only when 9≤n<10.

In consequence, n=9.

Answer: 5n+14-11n-2

Step-by-step explanation:

Answer:

PQ is 10.

QR is 5.

Hence, PQ=2QR

Step-by-step explanation:

We have the three points P(-1, 3); Q(7, -3); and R(4, 1).

And we want to show that PQ=2QR.

In other words, we want to show that PQ/QR=2.

So, let's find PQ and QR. We will need to use the distance formula:

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2[/tex]

To find PQ:

P is (-1, 3) and Q is (7, -3).

So, we will let P(-1, 3) be (x₁, y₁) and Q(7, -3) be (x₂, y₂).

Substitute the values into the distance formula. This yields:

[tex]d=\sqrt{(7-(-1))^2+(-3-3)^2[/tex]

Evaluate:

[tex]d=\sqrt{(8)^2+(-6)^2[/tex]

Evaluate:

[tex]d=\sqrt{64+36}=\sqrt{100}=10[/tex]

So, the distance of PQ is 10.

And to find QR:

Q is (7, -3) and R is (4, 1).

Again, we will let Q(7, -3) be (x₁, y₁) and R(4, 1) be (x₂, y₂).

Substitute appropriately. So:

[tex]d=\sqrt{(4-7)^2+(1-(-3))^2[/tex]

Evaluate:

[tex]d=\sqrt{(-3)^2+(4)^2[/tex]

Evaluate:

[tex]d=\sqrt{9+16}=\sqrt{25}=5[/tex]

So, the distance of QR is 5.

Therefore, it follows that:

[tex]\displaystyle PQ=2QR\Rightarrow \frac{PQ}{QR}=2\Rightarrow\frac{10}{5}\stackrel{\checmark}{=}2[/tex]

And we have shown that PQ=2QR.

Answer:

A)  2f / hour

B) 10 f

Step-by-step explanation:

outside temperature decreases by ; 7 F in 3 1/2 hours

a ) represent temperature change as a unit rate

To do this you will need to represent the temperature change per hour

7 f / 3.5 hours

= 7 f / 3.5 = 2 therefore the temperature change as a unit rate = 2f / hour

b) Temperature change after 5 hours

Δ temperature  in 5 hours = temperature change per hour * 5

                             = 2 F * 5 =  10 F

Answer:

Slope-Intercept Form: [tex]y=\frac{3}{2}x+6[/tex]

Slope:  [tex]\frac{3}{2}[/tex]

Y-Intercept: [tex](0,6)[/tex]

Step-by-step explanation:

STEP 1: Add 3x to both sides of the equation.

[tex]2y=12+3x[/tex]

STEP 2: Divide each term by 2 and simplify.

[tex]y=\frac{3x}{2} +6[/tex]

STEP 3: Reorder terms.

[tex]y=\frac{3}{2}x+6[/tex]

Answer:

I agree with the person up

Answer:172 days

Step-by-step explanation:

Answer:

dufenschmertz evil incorporated...

Step-by-step explanation:

after hours ;)

oh ma goawd he on x gaems mode

Look at the download below:

Answer:

150.8

Step-by-step explanation:

Answer:

DHGB

======================

1. D

2. H

3. G

4. B

Answer:

200 seconds

Step-by-step explanation:

Given rate :

Filling rate = 1/10 gallons per second

How fast can a 20 gallon pool be filled ;

Time = size of pool / filling rate

Time = 20 gallons ÷ 1/10 gallon / second

Time = 20 * 10 / 1

Time = 200 seconds

Answer:

-27

Step-by-step explanation:

ok so we have (-9) in parentheses right? And positive 3 outside of parentheses so we know 9 x 3 = 27 BUT we have a negative in front of 9 so we just put -27.

Hope this helps :D ~P.s- pls could u give brainliest to meh TYSM!

Answer:

The answer is m = 5

Answer:

m = 5

Step-by-step explanation:

5m - 3= 7m - 13

-2m-3=-13   ........ subtract 7m from both sides

-2m = -10    ......... add 3 to both sides

m = 5          ........ divide both sides by 2 and you get 5

Hope that helps! :)

Answer:

it's C had to double-check really quick sorry

Step-by-step explanation:

Answer:

-1

Step-by-step explanation:

Answer:

$530

Step-by-step explanation:

500*0.06=30

500+30=530

Therefore, the answer is $530

I think it's 2? I'm not sure though. Sorry.

Answer:

The length of DC is 2.5.

Answer:

x=-8/(a-b)

Step-by-step explanation:

Bring everything with x over to one side and everything else to the other.

ax-bx=-8

Factor out x.

x(a-b)=-8

Divide both sides by a-b

x=-8/(a-b)

Answer:

T= 20 + 35h

Step-by-step explanation:

Giving the following information:

An electrician charges $35 per hour, h, plus a $20 fee for driving to your house.

The $20 fee is a fixed cost. It will remain constant.

The $35 fee acts as a variable cost. It varies with the number of hours required to do the job.

To calculate the total cost (T), we need to use the following formula:

T= 20 + 35h

h= number of hours.

Answer:

C=20

Step-by-step explanation:

Answer:

9 days

Step-by-step explanation:

Given that:

Days whereby there was either corn or carrot = 12 days

There are 6 more days of corn than carrot.

How many days did we have corn?

Let Number of days we had carrot = x

Hence,

Number of days we had corn = x + 6

Total number of days we had either of the two = 12

Hence,

x + (x + 6) = 12

2x + 6 = 12

2x = 12 - 6

2x = 6

x = 6/2

x = 3

Number of days we had corn = x + 6 ;

Hence,

3 + 6 = 9

The best estimate of distance between the point and the origin is 15 units. this is your answer.

The  distance between the point (-25, 10) and the origin is 27units

The formula for calculating the distance between two points is expressed as:

D = √x² + y² (since the other coordinate is an origin)

Given the coordinate points  (-25, 10) and (0, 0)

Substitute

D = √(-25)² + 10²
D = √625 + 100
D = √725
D = 27unts

Hence the  distance between the point (-25, 10) and the origin is 27units

Learn more on distance here: https://brainly.com/question/2854969

#SPJ2

Answer:

21.068 rounded to the nearest 10th is 21.1

Step-by-step explanation:

To round a number to the nearest tenth , look at the next place value to the right . If it's 4 or less, just remove all the digits to the right. If it's 5 or greater, add 1 to the digit in the tenths place, and then remove all the digits to the right.

Answer:

13. Rotation 14. A

Step-by-step explanation:

I hope this was right

Answer:

1. rotation

2. the image and pre-image are always congruent to each other

Step-by-step explanation:

even thought the bottom figure is rotated, it does not change in size. It's literally a copy of the other, just rotated, thus, they are congruent.

Answer: 60%

Step-by-step explanation:

45+30=75=100%

75/10=7.5=10%

7.5*6=45=60%

Answer:

6.4

Step-by-step explanation:

Answer:

cccccccc ccccccccccccc

Answer:

since you recorded the first marble then replaced it, you drew 10 blue marbles, so therefore we can predict the next marble you drew, was blue.

Step-by-step explanation:

Step-by-step explanation:

Given parameters:

Amount of discount on goods= 20%

Original price of the good  = 700

Unknown:

Total amount he saved  = ?

Solution:

The total amount he saved will be the value of the discount charged on the original price.

 Amount of discount  = Percentage discount x original price of goods

 Amount of discount = [tex]\frac{20}{100}[/tex] x 700

 Amount of discount  = 140

The amount saved is 140

Answer:

don't know sorry byeeeee

Answer:

If you take the 2 smallest sides and put it in the pythagreon theorem to get the other side length.

Step-by-step explanation:

So if you have a triangle with side lengths, 3, 4, and 5, you can use the exact equation below.

[tex] {3}^{2} + {4}^{2} = {5}^{2} [/tex]

Because this is true, then the triangle does have a right angle.