G(x)= -\dfrac{x^2}{4} + 7g(x)=− 4 x 2 ​ +7g, left parenthesis, x, right parenthesis, equals, minus, start fraction, x, squared, divided by, 4, end fraction, plus, 7 What is the average rate of change of ggg over the interval [-2,4][−2,4]open bracket, minus, 2, comma, 4, close bracket?

Answers

Answer 1

Answer:

-1/2

Step-by-step explanation:

Given the function [tex]G(x)= -\dfrac{x^2}{4} + 7[/tex], the average rate of change of g(x) over the interval [-2,4], is expressed as shown below;

Rate of change of the function is expressed as g(b)-g(a)/b-a

where a - -2 and b = 4

[tex]G(4)= -\dfrac{4^2}{4} + 7\\G(4)= -\dfrac{16}{4} + 7\\G(4)= -4 + 7\\G(4) = 3\\[/tex]

[tex]G(-2) = -\dfrac{(-2)^2}{4} + 7\\G(-2)= -\dfrac{4}{4} + 7\\G(-2)= -1 + 7\\G(-2)= 6[/tex]

average rate of change of g(x) over the interval [-2,4] will be;

[tex]g'(x) = \frac{g(4)-g(-2)}{4-(-2)}\\ g'(x) = \frac{3-6}{6}\\\\g'(x) = -3/6\\g'(x) = -1/2[/tex]


Related Questions

Evaluate the following expression if v = 5 and w = -3: 6v - w. Type the number answer only. For example: if the answer was value is 17, then you would type 17 in the blank.

Answers

Answer:

33

Step-by-step explanation:

6v - w =

6(5) - (-3) =

30 + 3 =

33

What is the image point of (-5,9) after a translation left 1 unit and down 1 unit?

Answers

Answer: (-6,8)

Step-by-step explanation:

Translation is a rigid motion inn which every point of the figure moved in the same direction and for the same distance

Translation rules are

Left c units : [tex](x,y)\to(x-c,y)[/tex]

Down c units : [tex](x,y)\to(x,y-c)[/tex]

The image point of (-5,9) after a translation left 1 unit and down 1 unit will be:

[tex](-5,9)\to(-5-1,9-1)=(-6,8)[/tex]

Hence, the image point is (-6,8).

If a population grows 3.5% per year, how much does it grow per decade? A. 35% B. 41.1% C. 38% D. 27.6%

Answers

Answer: 35%

Step-by-step explanation: It grows 3.5% every year. A decade is 10 years. 10 x 3.5% = 35% because you move the decimal one point to the right.

The population grows 41.1% per decade. Therefore, option B is the correct answer.

What is population growth and population decrease formula?

If a constant rate of growth be R% per annum, then population after n years = P(1+R/100)ⁿ.

Given that, a population grows 3.5% per year.

Now, D(n)=P(1+R/100)ⁿ

Let P=1

So, D(1)=1(1+0.035)¹

D(1)=1.035

Similarly per 10 years with the same rate

D(10)=1(1+0.035)¹⁰

= (1.035)¹⁰

= 1.41059

= 1.411-1 (Initial population is 1)

= 0.411

= 0.411×100

= 41.1%

The population grows 41.1% per decade. Therefore, option B is the correct answer.

To learn more about the population increase and decrease visit:

https://brainly.com/question/27779235.

#SPJ2

Write a real-life problem that you can solve using a 45 degree, -45 degree, -90 degree triangle with an 18-ft hypotenuse. Describe your solution

Answers

Answer:

A triangle with angles:

"45°, 45°, 90°"

Is a triangle rectangle, with two catheti of equal length.

Now, there is a lot of problems that you can solve with this:

"Suppose that you want to find the height at which you need to attach a wire in a tree, such that the distance between the tree and the ground is 18ft, and the distance between the base of the tree and the two points where the wire is fixed is exactly the same"

Well, here we have a triangle rectangle with a hypotenuse of 18 ft, with cathetus of equal length (the catheti are the tree and the distance between the base of the tree and the point where the wire is attached at the ground)

And because the catheti are equal, then the angles are 45°, 45° and 90°.

What roles did militias play in the American Revolution? Your answer:

Answers

Hey there! I'm happy to help!

A militia is a local army. During the Battle of Lexington and Concord, the local militia (called minutemen), the militia outnumbered the British at Concord and chased them all the way back to Boston. The militia aided in many American victories during the Revolutionary War.

I hope that this helps! Have a wonderful day! :D

Three friends are at a carnival. Beth goes on 2 rides for $5.00. Zane goes on 5 rides for $12How much does it cost Tina to go on 9 rides?.50.

Answers

Answer:

$22

Step-by-step explanation:

Beth=$5.00 for 2 rounds

Zane=$12 for 5 rounds

Tina=$x for 9 rounds

Find x

9 rounds=5 rounds + 2 rounds + 2 rounds

5 rounds costs =$12

2 rounds costs=$5

2 rounds costs=$5

Then,

5 rounds + 2 rounds + 2 rounds= $12 + $5 + $5

9 rounds=$22

It will cost Tina $22 to go on 9 rounds

Two pipes A and B can fill an empty tank in 3hrs and 5hrs respectively. Pipe C can empty the full tank in 6 hours. If the three pipes A, B, and Care opened at the same time, find how long it will take for the tank to be full. *​

Answers

Answer:

30/11 (hours)

Step-by-step explanation:

Pipe A can fill the tank until it is full in 3 hours.

=> In 1 hour, pipe A can fill 1/3 of tank

Pipe B can fill the tank until it is full in 5 hours.

=> In 1 hour, pipe A can fill 1/5 of tank

Pipe C can empty the full tank in 6 hours.

=> In 1 hour, pipe A can empty 1/6 of tank

Assume that we open 3 pipes A, B, and C at the same time.

Then, in 1 hour, the amount of water in tank is:

A =  1/3 + 1/5 - 1/6 = 10/30 + 6/30 - 5/30 = 11/30 (tank)

=> The time to fill up the tank is:

T = 1/A = 1/(11/30) = 30/11 (hours)

Answer:

30/11

Step-by-step explanation:

Imagine the tank can hold x litre of water

So,A can fill x/3 litre water per hour

And B can fill x/5 litre water per hour

And C can reduce x/6 litre of water per hour which is filled by A and B.

So the gross calculation per hour is:

(x/3+x/5)-x/6

=11x/30

Now suppose it tooks 'a' hour to fill the tank.

So, a(11x/30)=x

⇨ a= (30/11x)x

⇨a=30/11

I NEED HELP ASAP PLEASE!!!



Q2 If 2w + 7 = ─9, what is the value of 15 – 4w? (4 is negative)






Q3 Solve the following equations: a) 3/4(16m − 24) = –48 (24 is negative) b) –20 = 1/6(36 + 12g)

Answers

Answer:

Q2: -17

Q3: a) -5/2  b) g = -13

Step-by-step explanation:

2w+7 = -9

2w = -9 - 7

w = -16/2

w = -8

---

15 - 4w

= 15 - 4(-8)

= 15 - 32

= -17

----------------------

Q3:

a) 3/4(16m-24) = -48

16m -24 = -48 ÷ 3/4

16m = -64 + 24

16m = -40

m = -5/2

b) -20 = 1/6(36+12g)

-20 = 1/6 × 6(6+2g)

(cross out the 6 from 1/6 and 6)

-20 = 6 + 2g

-20-2g= 6

-2g = 6+20

-2g = 26

g = 26/-2

g = -13

SOMEONE PLZ HELP ASAP !!!!!!

Answers

Answer:

a = 53.13

b = 42.76

c= 0

Step-by-step explanation:

as the question said i was supposed to use a calculator which i did

a garden is 18 feet 3 inches long and 10 feet 8 inches wide. the amount of fencing needed to enclose the garden is Need help and will mark brainlist

Answers

Answer:

[tex]\boxed{57ft 10in}[/tex]

Step-by-step explanation:

Hey there!

Well if the length is 18 and 3 inches we need to find the sum of both lengths,

18ft 3in + 18ft 3in = 36ft 6in

Width- 10ft 8in + 10ft 8in = 20ft 16 in -> 21ft 4in

l + w = 57ft 10in

Hope this helps :)

plz help thanks, will give brainliest!​

Answers

Answer:

D.

Step-by-step explanation:

[tex]\frac{x^{2/3}}{y^{-3/4}}[/tex]

= [tex]x^{2/3}y^{3/4}[/tex]

= [tex]\sqrt[3]{x^2} * \sqrt[4]{y^3}[/tex]

So, D is your answer.

Hope this helps!

one-third of a number is subtracted from 11.The result is one and half times the original number. what is the number.​

Answers

If 11 is subtracted from 3 times the number, the result is the square of 5 less than the number. What are the set of numbers that satisfy

How many gallons of 30% alcohol solution and how many of 60% alcohol solution must be mixed to produce 18 gallons of 50% solution?

Answers

Answer:

x = 6 gallons (of 30% alcohol)

y = 12 gallons (of 60% alcohol)

Step-by-step explanation:

Let

x = liters of 30% alcohol

y = liters of 60% alcohol

There are two unknowns, we need two equations

x + y = 18. (1)

0.30x + 0.60y = 0.50(x+y) (2)

From (1)

x + y = 18

y = 18-x

Substitute the value of y into (2) and solve for x:

0.30x + 0.60y = 0.50(x+y)

0.30x + 0.60(18-x) = 0.50(x+18-x)

0.30x + 10.8 - 0.60x = 0.50(18)

10.8 - 0.30x = 9

-0.30x = -1.8

Divide both sides by -0.30

x = 6 gallons (of 30% alcohol)

Substitute x=6 into (1) and solve for y:

x + y = 18

6 + y = 18

y = 12 gallons (of 60% alcohol)

Simplify: (-2)(-3)+(4)(-8)

Simplify: (3)(-6)-18​

Answers

Answer:

4

Step-by-step explanation:

Answer:

-26, and -36

Step-by-step explanation:

(-2) (-3) + (4) (-8)

        6 + -32 = -26

(3) (-6) - 18

       -18 + -18 = -36

plz help ASAP!!!!!!!!!!!
WILL MARK BEAINLIST!

Answers

Answer: Choice D

If you have a single straight vertical line cross the curve at more than one point, then you do not have a function. In other words, if an x input leads to multiple outputs, then you don't have a function.

Find the mean of the given frequency distribution table

Answers

Answer:

Mean = 32.8

Step-by-step Explanation:

Mean is given as Mean = (Σfx)/Σf

First, find the mid-point, x, of each class, and multiply by the frequency (f) of the class to get fx:

Class ==> f ==> x ==> fx

0-10   =>  3   =>  5  => 15

10-20 =>  8  => 15 => 120

20-30 => 10 => 25 => 250

30-40 => 15 => 35 => 525

40-50 =>  7  => 45 => 315

50-60 =>  4  => 55 => 220

60-70 =>  3  => 65 => 195

Sum the fx of all classes together to get Σfx:

Σfx = 15 + 120 + 250 + 525 + 315 + 220 + 195 = 1,640

Σf = 3 + 8 + 10 + 15 + 7 + 4 + 3 = 50

(Σfx)/Σf = [tex] \frac{1,640}{50} [/tex]

(Σfx)/Σf = [tex] 32.8 [/tex]

Mean = 32.8

What is the answer?

Answers

The answer would be c since the ten is being subtracting

Hi how do I solve this simultaneous equation

Answers

Answer:

M (-3, -5/2)

N (3, -1)

Step-by-step explanation:

Solve the first equation for x.

4y = x − 7

x = 4y + 7

Substitute into the second equation.

x² + xy = 4 + 2y²

(4y + 7)² + (4y + 7)y = 4 + 2y²

Simplify.

16y² + 56y + 49 + 4y² + 7y = 4 + 2y²

18y² + 63y + 45 = 0

2y² + 7y + 5 = 0

Factor.

(y + 1) (2y + 5) = 0

y = -1 or -5/2

Plug back into the first equation to find x.

x = 4(-1) + 7 = 3

x = 4(-5/2) + 7 = -3

M (-3, -5/2)

N (3, -1)

solve the following (x-2)+4=3x-2

Answers

Answer:

[tex]\boxed{x = 2}[/tex]

Step-by-step explanation:

Hey there!

To find x we need to finagle it out by combining like terms and using the communicative property.

x - 2 + 4 = 3x - 2

Simplify

x + 2 = 3x - 2

-x to both sides

2 = 2x - 2

+2 to both sides

4 = 2x

Divide both sides by 2

x = 2

Hope this helps :)

Answer:

Hey there!

(x-2)+4=3x-2

x-2+4=3x-2

x+2=3x-2

4=2x

x=2

Hope this helps :)

Sally's house is located at (5, −1) and her school is located at (−9, 7). Her best friend Molly lives at the midpoint of Sally's house and school. What coordinate represents Molly's house? A. (2, −3) B. (−2, 3) C. (3, −2) D. (−3, 2)

Answers

Answer:

B. (-2, 3)

Step-by-step explanation:

Given two coordinates (x₁, y₁) and (x₂, y₂), the coordinate of their midpoint is equivalent to X = (x₁+x₂)/2 and Y = (y₁+y₂)/2.

Given the coordinate of Sally's house and  her school to be (5, −1) and  (−9, 7) respectively, the midpoint of Sall's house and school is expressed as shown;

from the coordinates, x₁ = 5, y₁ = -1, x₂ = -9 and y₂ = 7

X = (5+(-9))/2

X = 5-9/2

X = -4/2

X = -2

Y = -1+7/2

Y = 6/2

Y = 3

The coordinate of the midpoint of Sally's house and school will be expressed as (X, Y) which is equivalent to (-2, 3).

About how much farther is it to drive than to walk directly from building A to building B? Round to the nearest whole number.


183 meters

250 meters

366 meters

683 meters

Answers

Answer:

A. 183 meters

Step-by-step explanation:

Building A and building B are 500 meters apart. There is no road between them, so to drive from building A to building B, it is necessary to first drive to building C and then to building B. About how much farther is it to drive than to walk directly from building A to building B? Round to the nearest whole number. A) 183 meters B) 250 meters C) 366 meters D) 683 meters

Find distance BC

Cos (60°)=BC / AB (Adjacent divided by the hypotenuse)

Cos (60°)=1/2

BC=a

AB=500

Cos (60°)=BC / AB

1/2=a/500

1/2 * 500=a

250=a

a=250m

Find distance AC

Sin(60°)=AC/AB (opposite side divided by hypotenuse)

Sin(60°)=√3/2

AC=b

AB=500

Sin(60°)=AC/AB

√3/2=b/500

√3/2 * 500=b

250√3=b

b=433m

Distance AC and BC=AC+BC

433m+250m=683m

Subtract the distance AB from AC+BC

= 683m - 500m

=183m

Answer is A. 183 meters

Answer:

A. 183 meters

Step-by-step explanation:

sin(60) = x/500

= 433

tan(60) = 433/x

= 250

This is the driving distance. 433+250= 683. Directly walking (using hypotenuse distance) is 500.

683-500=183!

If cot^(4)x − cot^(2)x = 1, then the value of cos^(4)x + cos^(2)x is

Answers

Answer:

1

Step-by-step explanation:

[tex]cot^4x-cot^2x=1\\cot^4x=1+cot^2x\\cot^4x=cosec^2x\\ cos^4xsin^2x=sin^4x\\cos^4x=\frac{sin^4x}{sin^2x}\\cos^4x=sin^2x[/tex]------- (1)

Putting the value of [tex]cos^4x[/tex] in the equation:

[tex]cos^4x+cos^2x\\sin ^2x +cos^2x\\1[/tex]            (Using the identity [tex]cos^2x +sin^2x=1)[/tex]

Find the quotient and remainder when p (x) divides with g (x) question (i) P (x) = x raise to 4 - 3 x square +4x + 5, g (x) = x square +5 ​

Answers

Answer:  [tex]x^2-8+\dfrac{4x+5}{x^4-3x^2+4x+5}[/tex]

Step-by-step explanation:

P(x) = x⁴ - 3x² + 4x + 5

g(x) = x² + 5

         _x²_- 8                          

x² + 5) x⁴ + 0x³ - 3x² + 4x + 5

        -(x⁴ + 0x³ + 5x²)  ↓     ↓  

                         -8x² + 4x  + 5

                       -(-8x² + 0x - 40)

                                    4x + 45

[tex]\dfrac{x^4-3x^2+4x+5}{x^2+5}=\large\boxed{x^2-8+\dfrac{4x+5}{x^4-3x^2+4x+5}}[/tex]

7th Grade Math Answer ASAP Please <3

Answers

Answer:

Hey there!

Andrew made a mistake in the last step. -11.8+9.8=2, not -21.6.

Let me know if this helps :)

Gavin combines Thirty-two and two-fifths ounces of water and 7.15 ounces of lemon juice in a pitcher to make lemonade. Which is the most reasonable estimate for the amount of liquid in the pitcher? 39 ounces 42 ounces 45 ounces 47 ounces

Answers

Answer:

OPTION A is correct

39 ounces

Step-by-step explanation:

Given:

The amount of water in the pitcher= 32 ounces

The amount of lemon juice in the pitcher = 7.15 ounces

We were to calculate the most reasonable estimate for the amount of liquid in the pitcher

To do this we need to sum up the Amount of water and Amount of lemon juice in the pitcher because the water is a liquid as well as the lemon juice which is

32 ounces + 7.15 ounces

=39.15 ounces

Therefore, the Estimated amount of liquid in the pitcher is approximately 39 ounces

Help me please
!!!!!!!!!!!!

Answers

Answer:

40

Step-by-step explanation:

Angle Formed by Tangent and Secant = 1/2 (DIFFERENCE of Intercepted Arcs)

< WVT = 1/2 ( WT - UW)

3x+4    = 1/2 (( 14x +7) - (7x+11))

Distribute

3x+4    = 1/2 ( 14x +7 - 7x-11)

Combine like terms

3x+4    = 1/2 ( 7x -4 )

Multiply each side by 2

6x +8 = 7x-4

Subtract 6x from each side

+8 = x-4

Add 4 to each side

12 =x

WVT = 3x+4

        = 3*12 +4

       = 36+4

       = 40

evaluate x³ for x=2.

Answers

Answer:

8

Step-by-step explanation:

If we have anything to the third power, we are multiplying the number by itself 3 times.

If x = 2, then the expression is [tex]2^3[/tex].

[tex]2\cdot2\cdot2=8[/tex]

Hope this helped!

Answer:

8

Step-by-step explanation:

Exponents is repeated multiplication, so what we are doing in this problem is that we are multiplying 2 by itself 3 times.

2 * 2 = 4

4 * 2 = 8

(08.02)How many solutions are there for the system of equations shown on the graph? No solution One solution Two solutions Infinitely many solutions

Answers

Answer: Infinitely many solutions

Step-by-step explanation:

There are many solutions because the lines lies on top of each other.

i dont know the exact answer but its not  

One solution

Two solutions

so its most likely

Infinitely many solutions

1.2 Exit Ticket
POSSIBLE POINTS: 0.5
Below are the total number of students for each teacher in the Arts department. Round to the nearest tens place in order to estimate the total amount of
students enrolled in an art course,
132, 145, 97, 112, 128, 82
1
2
RE

Answers

Answer:

174

Step-by-step explanation:

Given

132, 145, 97, 112, 128, 82

Required

Estimate amount of students in an art class

This is calculated by obtaining the mean of the given data

[tex]Mean = \frac{\sum x}{n}[/tex]

Where n is the number of observations

So;  n = 6

[tex]Mean = \frac{132+ 145+ 97+ 112+ 128+ 82}{6}[/tex]

[tex]Mean = \frac{696}{6}[/tex]

[tex]Mean = 174.0[/tex]

Hence, the estimated number of students is 174


A. Y=2/9x
B. Y=1/4x
C. Y=1/5x
D Y=2/11x

Answers

Answer:

the slope of the line represented by the table is y = 2/11x

Step-by-step explanation:

y = mx + b

slope: (y² - y¹) / (x² - x¹)

(4 - 2) / (22 - 11) = 2/11

plug in an x and y value to find b

y = 2/11x + b

2 = (2/11)(11) + b

2 = 2 + b

b = 0

the y-intercept is 0

your equation is y = 2/11x

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The solid homogeneous cylinder is released from rest on the ramp. If = 40 , s= 0.30 and k= 0.20. Determine the magnitudes of the acceleration of the mass (W= 8lb) center G and the friction force exerted by the ramp on the cylinder. Write a short dialogueboth sides of the conversationin Spanish between you and your new Spanish instructor in complete sentences. Use the vocabulary from this lesson and the following suggestions as a guide for your answer: You may copy and paste the accented and special characters from this list if needed: , , , , , , , , , , , , , , *Note: The sample sentences/questions in parentheses are just a guide to help you form your sentences/questions. You must come up with your own original answers keeping academic integrity intact. Greet and state your name in one sentence. (e.g., Good morning, my name is ___.) Ask your instructor his or her name in one sentence. (e.g., What is your name?formal) Have your instructor reply in one sentence what his/her name is. 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