What is the average rate of change of the function f(x)=4x^2+3x on the interval [1,5]

Answer:

4.75 feet

Step-by-step explanation:

Let the height of the flagpole be x

Sin 53 = x/12

x = 12 × Sin 53

x = 12 × 0.3959

x = 4.75 feet

Answer:

15.9

Step-by-step explanation:

The 12 ft is the adjacent side and you are trying to find the opposite side or the height of the flagpole. You use Tan. Lowercase x means multiply.

Tan 53 = X

             --------

               12

To get rid of the 12 multiply both sides of the equation by 12. so

Tan 53 x 12 = X/12 x 12

Tan 53 x 12= X

X= 15.9

Answer:

[tex]x=\frac{27+\sqrt143i}{8}{} ,\frac{27-\sqrt{143i} }{8}[/tex]

[tex]y=-9+\frac{27+\sqrt{143} i}{4} ,-9+\frac{27-\sqrt{143} i}{4}[/tex]

Step-by-step explanation:

1) Solve for 2x - y = 9

A. Solve for y.

2x - y = 9

B. Subtract 2x from both sides.

-y = 9 - 2x

C. Multiply both sides by -1.

y = -9 + 2x

D. Regroup terms.

y = 2x - 9

2) Substitute y = 2x- 9 into 4x² + 3y² - 2x + y = 16

A. Start with the original equation.

4x² + 3y² - 2x + y = 16

B. Let y = 2x - 9.

4x² + 3(2x - 9)² - 2x + 2x - 9 = 16

C. Simplify.

16x² - 108x + 234 = 16

3) Solve for x in 16x² - 108x + 234 = 16

A. Solve for x.

16x² - 108x + 234 -= 16

B. Move all terms to one side.

16x² - 108x + 234 - 16 = 0

C. Simplify 16x² - 108x + 234 - 16 to 16 x² - 108x + 218

16 x² - 108x + 218 = 0

D. Use the Quadratic Formula.

[tex]x=\frac{108+4\sqrt{143}i }{32}[/tex], [tex]\frac{108-4\sqrt{143} i}{32}[/tex]

E. Simplify solutions.

[tex]x=\frac{27+\sqrt{143} i}{8} ,\frac{27-\sqrt{143} i}{8}[/tex]

4) Substitute [tex]x=\frac{27+\sqrt{143}i }{8} ,\frac{27-\sqrt{143}i }{8}[/tex] into y = 2x - 9.

1) Start with the original equation.

y = 2x - 9

2) Let x = [tex]\frac{27+\sqrt{143} i}{8} ,\frac{27-\sqrt{143}i }{8} .[/tex]

[tex]y=2*\frac{27+\sqrt{143} i}{8} -9,2*\frac{27-\sqrt{143}i }{8} -9[/tex]

3) Simplify

[tex]y=-9+\frac{27+\sqrt{143}i }{4} ,-9+\frac{27-\sqrt{143i} }{4}[/tex]

Answer:

[tex]x=-1.52,2.19[/tex]

Step-by-step explanation:

Hi there!

[tex]3x^2 - 2x - 10 = 0[/tex]

Use the quadratic formula:

[tex]x=\displaystyle\frac{-b\pm\sqrt{b^2-4ac} }{2a}[/tex] in the form [tex]ax^2+bx+c=0[/tex]

Plug in the a, b and c values

[tex]x=\displaystyle\frac{-(-2)\pm\sqrt{(-2)^2-4(3)(-10)} }{2(3)}\\\\x=\displaystyle\frac{2\pm\sqrt{4+120} }{6}\\\\x=\displaystyle\frac{2\pm\sqrt{124} }{6}\\\\x=\displaystyle\frac{2\pm2\sqrt{31} }{6}\\\\x=\displaystyle\frac{1\pm\sqrt{31} }{3}\\\\x=-1.52,2.19[/tex]

I hope this helps!

Answer:

  44.5 km on a bearing of 134.1°

Step-by-step explanation:

A suitable vector calculator will tell you the location of the ship from port is ...

  21∠32° +45∠287° = 44.5∠-45.9°

The bearing of the port is in the reverse direction, so 180° added to this:

  180° +(-45.9°) = 134.1°

The distance from port is 44.5 km. The bearing of the port is 134.1°.

_____

Additional comment

The distance from port is perhaps most easily found using the Law of Cosines. It is the third side of a triangle with sides 21 and 45. The included angle is (287° -(180° +32°)) = 75°. The distance is then ...

  c = √(a² +b² -2ab·cos(C)) = √(21² +45² -2·21·45·cos(75°)) ≈ √1976.83

  ≈ 44.5 km

The angle between the 32° bearing and the bearing from the port to the ship can be found using the Law of Sines.

  B = arcsin(b/c·sin(C)) = arcsin(45/44.5sin(75°)) ≈ 77.9°

so, the bearing angle from the ship to the port is ...

  180° +(32° -77.9°) = 134.1°

__

Bearings are measured clockwise from north. A diagram can be helpful.

Answer:

7. The area should be 32. Multiply 5 by 4 to get 20. Find the missing length to multiply by 3, which is 4, and multiply. 3 * 4 = 12. Add 20 + 12 and get 32 cm.

8. The area should be 70. You did pretty well, but when finding the area of a triangle, divide the product by 2, or multiply by 0.5. 5 * 8 = 40/2 or 40 * 0.5 which both equal 20. 50, plus the area of the triangle, 20, will get you 70.

Answer:

4.38, aka 219/50

Step-by-step explanation:

Answer:

14

Step-by-step explanation:

The number of elements in M is 31, so let's make set M the set of the first 31 natural numbers.

M = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31}

Set N has 18 elements. We need to choose 18 elements to place in set N.

The union of sets M and N has 35 elements. That means that since set M contributes 31 elements to the union, set N only contribute 4 new elements to the union. That means that 14 of the 18 elements in N are in common with set M.

Set N can be:

N = {18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35}

Answer: 14

Answer:

x = - 10, x = - 6

Step-by-step explanation:

x² + 16x + 60 = 0

Consider the factors of the constant term (+ 60) which sum to give the coefficient of the x- ter (+ 16)

The factors are + 10 and + 6 , since

10 × 6 = 60 and 10 + 6 = 16 , then

(x + 10)(x + 6) = 0 ← in factored form

Equate each factor to zero and solve for x

x + 10 = 0 ⇒ x = - 10

x + 6 = 0 ⇒ x = - 6

The population of Ohio will be 10 million in the year 1970

The population growth of Ohio is represented by the function:

[tex]P(t)=\frac{12.79}{1+2.402e^{-}0.0309t}[/tex]

P is the population in millions

t is the number of years since 1900

To find the year that the population of Ohio will be 10 million, substitute P = 10 into the function P(t) and solve for t

[tex]10=\frac{12.79}{1+2.402e^{-}0.0309t}\\\\10(1+2.402e^{-}0.0309t)=12.79\\\\1+2.402e^{-}0.0309t=\frac{12.79}{10} \\\\1+2.402e^{-}0.0309t=1.279\\\\2.402e^{-}0.0309t=1.279-1\\\\2.402e^{-}0.0309t = 0.279\\\\e^{-}0.0309t =\frac{0.279}{2.402} \\\\e^{-}0.0309t =0.116\\\\-0.0309t=ln0.116\\\\-0.0309t=-2.154\\\\t=\frac{-2.154}{-0.0309} \\\\t=69.7[/tex]

t = 70 years (to the nearest whole number)

70 years after 1900 will be 1970

Therefore, the population of Ohio will be 10 million in the year 1970

Learn more here:  https://brainly.com/question/25504185

Step-by-step explanation:

We will use the LHS to find the RHS.

Step 1: Expand the LHS by multiplying through the brackets and simplify

(sinx + cosx)(1 − sinx cosx) ≡  sinx + cosx - (sinx + cosx (sinx cosx))

                                             ≡  sinx + cosx - sin²x cosx - sinx cos²x

Step 2: Use the identity sin²x + cos²x = 1, to rewrite the equation

                                           ≡ sinx + cosx - cosx (1 - cos²x) - sinx (1 - sin²x)

Step 3: Simplify the equation by adding like terms

                                           ≡ sinx + cosx - cosx + cos³x - sinx + sin³x

                                           ≡ sin³x + cos³x                 [QED]

Reminder:

Answer:

Step-by-step explanation:

Joshua wants to buy a flat-screen TV that costs $625. He saves $62.50 each week to buy the TV. In how many weeks will he have enough money to make his purchase?

A. 8

B. 9

C. 10

D. 11

cost of television divided by weekly savings = number of weeks

625 : 62.50 = 10 weeks

Answer:

Interest: $402.20

Total Debt owed: $9,302.00

Step 1: Multiply the principal (the original amount borrowed) by the interest rate (%):  

$8,300 x 4% = 360.00 (interest for one year)

Step 2: Find out how many years she will be paying back the loan and add that number of years to the first payment year ($360). ($360 + 5years = 365 total payments) Then multiply the total number of payments by the interest rate ($365 x .04 = $14.60 interest per payment).

Step 3: Add up all the yearly interests ($14.60 per payment x 12 months = $181.20 yearly interest)

Step 4: Add the yearly interest to the total debt owed.  

$9,302 + $181.20 = $9,483.20 total debt

Total amount owing after 5 years = $8,300+($365 x .04 interest rate per payment for 60 months)=10,605.00 dollars owed in 5 years of payments. Interest owed is 10,605 x .04=$410.20 for a grand total of 10,915.20 dollars owed overall for this 4% loan which was paid back over a period of five years with twelve monthly payments per year at four percent interest rate per month ($410.20/12=$34.02).

Answer:

y = 16

Step-by-step explanation:

11y = 2(24 + 4y)

11y = 48 + 8y

3y = 48

   y = 16

The sale price is 85% of the regular price.

-If regular price is 100% and there is a 15% discount, The sale price will be 85% of reg. price.

100-15=85

Answers:

- Sale price: $25.50

-85%of 100%

-Discount: 15%

-$4.50

You can check by the following:

30-25.5=4.5

30-4.5=25.5

4.5+25.5=30

25.5+4.5=30

100-15=85

100-85=15

85+15=100

15+85=100

(Brainliest?) ^^

Answer:

y=20x+35

Step-by-step explanation:

if a plumber who is just starting out offers low rates to attract new customers. He charges $35 to visit a client's home, plus an additional $20 per hour. Then y=20x+35 is equation that shows how the cost of a visit, y, depends on its duration in hours, X.

Two or more expressions with an Equal sign is called as Equation.

Given that

a plumber who is just starting out offers low rates to attract new customers

Plumber charges $35 to visit a client's home, plus an additional $20 per hour.

Let the charges per hour be denoted by x.

and it is given that y is cost of a visit.

We are required to write equation for cost of a visit y.

y equal to twenty x plus thirty five.

y=20x+35

Hence if a plumber who is just starting out offers low rates to attract new customers. He charges $35 to visit a client's home, plus an additional $20 per hour. Then y=20x+35 is equation that shows how the cost of a visit, y, depends on its duration in hours, X.

To learn more on Equation:

https://brainly.com/question/10413253

#SPJ5

Answer:

Down here ↓↓↓↓↓↓

Step-by-step explanation:

Anything below 1 is a reduce

Anything above 1 is an enlarge

Anything equal to 1 is a preserve

1. Reduce, 0.75 < 1

2. Reduce,  4/5 < 1

3. Enlarge,  4.2 > 1

4. Preserve, 8/8 = 1

5. Enlarge, 7/2 > 1

6. Preserve, 1 = 1

7. Reduce, 0.1 < 1

8. Enlarge, 1 2/3 > 1

9. Enlarge, 12 > 1

-Chetan K

Answer:

D - Two.

Step-by-step explanation:I took the test and this was the correct answer.

Answer:

91°

Step-by-step explanation:

The angles are consecutive interior angles (CIA) which add up to 180°.

180 - 89 = 91

In other words, everything but point R.

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

Explanation:

The term "collinear" means "points that fall on the same straight line". Any two points are always guaranteed to be collinear; however the same can't be said for any 3 random points.

In this case, points P, Q and S are all on the vertical y axis which is why they are collinear.

The graph is shown below.

Answer:

40, 60, 80

Step-by-step explanation:

angles are 40, 3x, 4x

40+ 3x + 4x = 180

40 + 7x = 180

7x = 180 - 40

7x = 140

x = 20

so the angles are 40, 60, 80

Answer:

19.2

Step-by-step explanation:

You have to trust me, this answer is correct. But here's my solution:

With the formula

Distance=Speed multiplied by Time, we can infer that Speed=Distance/Time.

But we only have one variable (Speed) in the two we need (Speed and Time), we have to pretend we have both variables. You can put the time as 1 hour because that's the most basic unit. Note that this strategy will also work with 2 hours, 3 hours, or any measure of time.

So now for distance, let's see how fast a car can travel 24 miles. When going at 24 mph, then it'll take 1 hour. With 16 mph, then it'll take 1 hour and 30 minutes, so 1.5 or 3/2 hours.  

Now we have the distance, which is 2 times 24 (Because the 24 mph and 16 mph both traveled 24 miles), equaling 48, and time, which is 1 hour plus 1.5 hours, which is 2.5 hours.

Now we use the formula Speed=Distance/Time, with 48/2.5=19 1/5 or 19.2

DUBS

(Please consider giving a Brainliest. I spent lots of time on this, and it's honestly the best answer out of all!)

Answer:

Should be

Step-by-step explanation:

Answer: Yes

Step-by-step explanation:

Using the formula a^2+b^2=c^2, take the square of 6 (6x6=36) and 8 (8x8=64) and add them together to get the square of 10 (10x10=100) 64+36 does equal 100. Remember that the biggest number is c and the two sides a and b have to add to get c.

Answer:

Slope = - ⅖

Y-intercept = (0, 4), where b = 4

Step-by-step explanation:

Given the linear equation in standard form, 2x + 5y = 20, where A = 2, B = 5, and C = 20:

Start by transforming the standard equation into its slope-intercept form, y = mx + b, where m = slope, and b = y-intercept.

Subtract 2x from both sides:

2x -2x + 5y = - 2x + 20

5y = -2x + 20

Divide both sides by 5 to isolate y:

[tex]\frac{5y}{5} = \frac{-2x + 20}{5}[/tex]

y = - ⅖x + 4 ⇒ This is the slope-intercept form where the slope, m = -⅖, and the y-intercept, b = 4.  The y-intercept is the point on the graph where it crosses the y-axis, and has coordinates of (0, b). The y-coordinate is the value of b in the slope-intercept form. Therefore, the y-intercept is (0, 4).

Answer:

18

Step-by-step explanation:

18devided by 3 is 6 and 18 divided by 2 is 9

The number that has prime factors of 2 and 3 is 18.

Prime factors are factors that are prime numbers. Prime numbers are numbers that are divisible by one and itself. Examples are 2 and 3.

What are the factors of the numbers between 14 and 19?

To learn more about  factors, please check: https://brainly.com/question/26073850

Answer:

33 miles

Step-by-step explanation:

The cyclist traveled for 3 hours ar 11 miles per house to find how many miles she traveled simply multiply the speed times the amount of time traveled 11 times 3 is 33

1 hour = 11 miles

3 hours = 11 x 3 miles

             = 33 miles.

Ans: 33 miles

I know this is already answered but I was bored lol.

See drawing attached below.

Corresponding angles and sides are congruent to each other. Thus,

∠L corresponds to ∠H

∠J corresponds to ∠P

HU corresponds to LO

PO corresponds to JU

LP corresponds to HJ

∠U corresponds to ∠O

Answer:

thanks for the points bye bye for now love u fin and I will