F (x) =2x+3^2 (x-1)3 state of degree

The exact solutions of the qudratic equation 3x^2 - 6x + 2 = 0 are:

a. negative 1 plus or minus the square root of 3 divided by

3 (x = (-1 ± √3) / 3) .So, option a is the correct answer.

To find the solutions of the quadratic equation 3x^2 - 6x + 2 = 0, we can use the quadratic formula, which states that for an equation of the form ax^2 + bx + c = 0, the solutions are given by:

x = (-b ± √(b^2 - 4ac)) / (2a)

In this case, a = 3, b = -6, and c = 2. Substituting these values into the formula, we have:

x = (-(-6) ± √((-6)^2 - 4(3)(2))) / (2(3))

x = (6 ± √(36 - 24)) / 6

x = (6 ± √12) / 6

x = (6 ± 2√3) / 6

x = (3 ± √3) / 3

Therefore, the exact solutions of the equation 3x^2 - 6x + 2 = 0 are:

a. negative 1 plus or minus the square root of 3 divided by 3 (x = (-1 ± √3) / 3)

So, option a is the correct answer.

To learn more about : quadratic

https://brainly.com/question/1214333

#SPJ11

Answer:

105$

Step-by-step explanation:

300 times 35%=105

The loss for purchasing the 300 shares was $4,806 and the percentage loss is 39% (to the nearest whole percent).

How to determine the loss

a.

Total purchase price = $12,300

Total selling price = $7,494

Loss = total purchase price - total selling price

Loss = $12,300 - $7,494

Loss = $4,806

How to determine the percentage loss

b.

Purchase price of one share is $41

Total purchase price = $12,300                                                                     Percentage Loss =  ($4,806 / $12,300) x 100%

Percentage Loss = 0.391 x 100%

Percentage Loss = 39%

Learn about loss here: https://brainly.com/question/26754747

#SPJ1

a. The loss is $4,806.

b. The loss as a percent of the purchase price is 39%.

a. The purchase price of 300 shares is 300 x $41 = $12,300.

The selling price of 300 shares is 300 x $24.98 = $7,494.

Therefore, the loss is $12,300 - $7,494 = $4,806.

b. Calculate the loss as a percent.

The loss as a percent of the purchase price is:

($4,806 ÷ $12,300) x 100% = 39.2%

Rounded to the nearest whole percent, the loss is 39%.

Learn more about loss as a percent of purchase price on:

https://brainly.com/question/762291

#SPJ1

Answer:

\(\textsf{A.} \quad (2+x)^x\left[\dfrac{x}{2+x}+\ln(2+x)\right]\)

Step-by-step explanation:

Replace f(x) with y in the given function:

\(y=(x+2)^x\)

Take natural logs of both sides of the equation:

\(\ln y=\ln (x+2)^x\)

\(\textsf{Apply the log power law to the right side of the equation:} \quad \ln a^n=n \ln a\)

\(\ln y=x\ln (x+2)\)

Differentiate using implicit differentiation.

Place d/dx in front of each term of the equation:

\(\dfrac{\text{d}}{\text{d}x}\ln y=\dfrac{\text{d}}{\text{d}x}x\ln (x+2)\)

First, use the chain rule to differentiate terms in y only.

In practice, this means differentiate with respect to y, and place dy/dx at the end:

\(\dfrac{1}{y}\dfrac{\text{d}y}{\text{d}x}=\dfrac{\text{d}}{\text{d}x}x\ln (x+2)\)

Now use the product rule to differentiate the terms in x (the right side of the equation).

\(\boxed{\begin{minipage}{5.5 cm}\underline{Product Rule for Differentiation}\\\\If $y=uv$ then:\\\\$\dfrac{\text{d}y}{\text{d}x}=u\dfrac{\text{d}v}{\text{d}x}+v\dfrac{\text{d}u}{\text{d}x}$\\\end{minipage}}\)

\(\textsf{Let}\; u=x \implies \dfrac{\text{d}u}{\text{d}x}=1\)

\(\textsf{Let}\; v=\ln(x+2) \implies \dfrac{\text{d}v}{\text{d}x}=\dfrac{1}{x+2}\)

Therefore:

\(\begin{aligned}\dfrac{1}{y}\dfrac{\text{d}y}{\text{d}x}&=x\cdot \dfrac{1}{x+2}+\ln(x+2) \cdot 1\\\\\dfrac{1}{y}\dfrac{\text{d}y}{\text{d}x}&= \dfrac{x}{x+2}+\ln(x+2)\end{aligned}\)

Multiply both sides of the equation by y:

\(\dfrac{\text{d}y}{\text{d}x}&=y\left( \dfrac{x}{x+2}+\ln(x+2)\right)\)

Substitute back in the expression for y:

\(\dfrac{\text{d}y}{\text{d}x}&=(x+2)^x\left( \dfrac{x}{x+2}+\ln(x+2)\right)\)

Therefore, the differentiated function is:

\(f'(x)=(x+2)^x\left[\dfrac{x}{x+2}+\ln(x+2)\right]\)

\(f'(x)=(2+x)^x\left[\dfrac{x}{2+x}+\ln(2+x)\right]\)

Answer:

Total amount Omar earn = $120

Step-by-step explanation:

Given:

Total amount Omar, Hala and Lujain got paid = $240

Ratio of money Omar, Hala and Lujain got paid = 5:9:10

Find:

Total amount Omar earn

Computation:

Total amount Omar earn = [Total amount Omar, Hala and Lujain got paid][Omar'ratio / Total ratio]

Total amount Omar earn = [240][5 / (5+9+10)]

Total amount Omar earn = [240][5 / (24)]

Total amount Omar earn = [24][5]

Total amount Omar earn = $120

Answer:  you would need to cross the bridge 5 times

Step-by-step explanation:

costing a total of $42.50 for each option.

hope this helps

Answer: D

Step-by-step explanation:

Hope it helps

The logarithm expression can be simplified to:

In(6x^9)-In(x^2) =7·ln(6x)

There are some logarithm properties we can use here.

log(a) - log(b) = log(a/b)

log(a^n) = n*log(a)

(these obviously also apply to the natural logarithm)

Now let's look at our expression, it says that:

In(6x^9)-In(x^2)

Using the first rule, we can rewrite this as.

In(6x^9)-In(x^2) = ln(6x^9/x^2)

Now solving the quotient in the argument:

ln(6x^9/x^2) = ln(6x^7) = 7·ln(6x)

That is the expresison simplified.

Learn more about logarithms at:

https://brainly.com/question/13473114

#SPJ1

The length of the zip wire, with a 10-degree angle to the horizontal and a distance of 25 meters between the posts, is approximately 25.35 meters.

To calculate the length of the zip wire, we can use trigonometry. Let's consider the triangle formed by the zip wire, where the horizontal distance between the two posts is 25 meters and the angle between the zip wire and the horizontal is 10 degrees.

Using trigonometric functions, we can determine the length of the zip wire. In this case, we'll use the sine function because we have the opposite side (the vertical distance) and we want to find the hypotenuse (the length of the zip wire).

The formula for sine is:

sin(angle) = opposite / hypotenuse

Rearranging the formula, we have:

hypotenuse = opposite / sin(angle)

In this case, the opposite side is the vertical distance, which is h.

So, the formula becomes:

hypotenuse = h / sin(angle)

To find h, we can use the formula for the length of the zip wire:

h = 25 * tan(angle)

Substituting this into the previous formula, we get:

hypotenuse = (25 * tan(angle)) / sin(angle)

Calculating the value, we have:

hypotenuse = (25 * tan(10°)) / sin(10°)

Using a calculator, we find:

tan(10°) ≈ 0.1763

sin(10°) ≈ 0.1736

Substituting these values, we can calculate the length of the zip wire:

hypotenuse ≈ (25 * 0.1763) / 0.1736 ≈ 25.35 meters

Therefore, the length of the zip wire is approximately 25.35 meters.

For more question on length visit:

https://brainly.com/question/28322552

#SPJ8

Answer: y=kx/w^2

Step-by-step explanation:

y is directly proportional to x

y∝x        

y=kx

y inversely proportional to the square of w.

y ∝ (1/(w)^2)

y=k/w^2

y=kx/w^2

Answer:

The percentage of hotels with rates between 120 and 144 euros is 84%.

Step-by-step explanation:

We know that the distribution of the nightly rate for a hotel in Rome is bell shaped with a mean of 138 euros and a standard deviation of 6 euros.

We want to know the proportion of hotels between 120 and 144 euros.

We can approximate the distribution to a normal distribution and calculate the z-score for both boundaries:

\(z_1=\dfrac{X_1-\mu}{\sigma}=\dfrac{120-138}{6}=\dfrac{-18}{6}=-3\\\\\\z_2=\dfrac{X_2-\mu}{\sigma}=\dfrac{144-138}{6}=\dfrac{6}{6}=1\)

Then, we can calculate the proportion as the probability of having rates between 120 and 144:

\(P=P(120<X<144)=P(-3<z<1)\\\\P=P(z<1)-P(z<-3)\\\\P=0.8413-0.0013\\\\P=0.8400\)

Then, we can conclude that the percentage of hotels with rates between 120 and 144 euros is 84%.

If you need 1 1/4 cups of sugar to make cookies, that is the amount of sugar needed for one batch of cookies. To find out how much sugar is needed to make 16 cookies, we can set up a proportion:

1 1/4 cups sugar is needed to make 1 batch of cookies

x cups sugar is needed to make 16 cookies

We can solve for x by cross-multiplying:

1 1/4 * 16 = x

20/4 = x

5 = x

Therefore, you will need 5 cups of sugar to make 16 cookies.

Answer: 60

30

Step-by-step explanation: that’s the first two, good luck!

Answer:

its a pickup line

Step-by-step explanation:

.

The summation of 5 to power of n (where n starts from 1) is determined as 625.

The sum of the expression given is calculated by using the defined expression as sated in the question to perform the summation.

The given summation expression include;

∑5ⁿ

where;

So we are going to sum the number 5ⁿ 4 times.

The expression becomes;

5ⁿ x 5ⁿ x 5ⁿ x 5ⁿ = 5⁴ⁿ

where;

n = 1

The summation becomes;

5⁴ⁿ = 5⁴ = 625

Thus, the summation of 5 to power of n (where n starts from 1) is determined as 625.

Learn more about summation here: https://brainly.com/question/24495014

#SPJ1

Answer:32

Step-by-step explanation:

24=(3/4)d multiply both sides by 4/3(the reciprocal) and you get d=32

Therefore , the solution of the given problem of ratio comes out to be percent change is 50% for the 1/2.

To construct a pair of related variables "a" with "b," whereby "b" may also be bigger than zero, apply the straightforward formula "a / b." Two ratios are combined to form one ratio. The ratio would indeed be 1:1 if there were just one guy and three women. In the group, there are fraction 3/4 girls and 1/4 boys. Parts can be a division between two or more items, a number, or a portion of the volume of a component.

Here,

Given :

Ratio  is 1/2

To convert into percentage ,

We multiply it by 100

=> 1/2 * 100

=> 50 %

Thus , percent change is 50%

Therefore , the solution of the given problem of ratio comes out to be percent change is 50% for the 1/2.

To know more about ratio visit:

brainly.com/question/13419413

#SPJ1

Answer:

1.35 square miles I think

Step-by-step explanation:

Answer:

Julie travels 1.35 miles on the same path every day.

Area = 1.35 miles

Step-by-step explanation:

What we know so far:

- It takes 2.4 miles to walk from house to school.

- The distance from the park to school is 2.1 miles.

- It takes 1.5 miles to walk from your house to the park.

The area of a triangle is 0.5 or 1/2 x base x height.

As a result, 1.5 x 1.8 divided by two equals 1.35.

So, Julie walks 1.35 miles every day on the same route.

Area = 1.35 miles

Hope this helps! :D Brainliest?

Answer:

\(r \geqslant - 16\)

Step-by-step explanation:

\( \frac{ - 10 + r}{2} \geqslant - 13\)

multiply both sides by 2:

\( - 10 + r \geqslant - 26\)

add 10 on both sides:

\(r \geqslant - 16\)

Answer:

\(r \ge -16\)

Step-by-step explanation:

To solve any equation/inequality:

1. get the variable to show up exactly once

2. isolate it

\(\frac{-10+r}{2} \ge -13\)

Multiply both sides by 2 and simplify (note that we're multiplying by a positive, not a negative, so the direction of the inequality stays the same, whereas multiplying or dividing by a negative would have changed the direction of the inequality)

\(\frac{-10+r}{2} *2 \ge -13 *2\)

\(-10+r \ge -26\)

Add 10 to both sides, and simplify

\((-10+r)+10 \ge (-26)+10\)

\(r \ge -16\)

Answer:

yes because angle 1 and 5 are congruent

Answer:

C

Step-by-step explanation:

Answer:

11.

Step-by-step explanation:

As the first decimal place is 5 we round up the whole number.

Answer:

11

Step-by-step explanation:

See image below:)

Answer:

Step-by-step explanation:

O.4

By using the property of incenter, measures of the sides and the angles will be,

JK = 21.2 units

KL = 26.63 units

JL = 28.33 units

m ∠K = 36°

Since, By the property of incenter,

PM = PN = PO = 7 units

∠MJP = ∠OJP = 32°

∠NLP = ∠OLP = 22°

By the triangle sum theorem,

m∠JKL + m∠KLJ + m∠LJK = 180°

2(m∠NKP) + 2(m∠NLP) + 2(m∠MJP) = 180°

2(m∠NKP) + 2(22°) + 2(32°) = 180°

2(m∠NKP) = 180° - 108°

m∠NKP = 36°

From ΔJMP,

tan(32°) = MP / MJ

tan(32°) = 7/MJ

MJ = 11.20

From ΔPOL,

tan(22°) = OP / OL

tan(22°) = 7/OL

OL = 17.33

From ΔKNP,

tan(36°) = NP / KN

tan(36°) = 7 / KN

KN = 9.63

Therefore, We get;

JK = JM + MK = 21.2 units

KL = LN + KN = 26.63 units

JL = JO + OL = 28.33 units

Learn more about the triangle visit;

brainly.com/question/1058720

#SPJ1

Answer:

b = 13.5

Step-by-step explanation:

2 -b/3 = -5/2

im assuming we want to find b. therefore we want b = something. so because b is on top of a fraction right now, I will multiply both sides by 3 so -b is not on top of a fraction anymore.

6 -b = -15/2

we should get rid of the divided by 2 on the other side too, to make it easier. we can do this by multiplying 2 on both sides.

12 - 2b = -15

remember, we want to isolate b. so first we should get rid of the 12 next to the 2b. we can do this by subtracting 12 on both sides!

-2b = -27  

finally, we can divide both sides by -2 and b will be isolated!

b = 13.5

Answer:

x=11

Step-by-step explanation:

You do 38/3x+3 and 19/x+7 and then cross mulitply and get 57x+57=38x+266. Then yoy subtract 57 from 266 and get 57x=38x+209. Now you have to subtract 38 from 57 and then answer will be 19. So now you have 19x=209. Finally you divide 209 by 19 and get x=11. Good luck!

Step-by-step explanation: 23 is the answer

23+24+25=72

answer:

- this is multi-step problem

16 X 1.375 = 22 songs (37.5% was added)

22 X .5 = 11 songs (50% was removed)

final answer: 11 songs.

Answer:

technology.please mark me as brainliest

Answer:

looks like it's education