What is the average rate of change of the functionf (x) = 20(1/4)^xfrom x = 1 to x = 2?​

Answers

Answer 1

Step-by-step explanation:

the average rate of change of a function f(x) between two values of x is

(f(x2) - f(x1)) / (x2 - x1)

f(x) = 20× (1/4)^x

x1 = 1

x2 = 2

f(x2) = 20× (1/4)² = 20/16 = 5/4

f(x1) = 20× (1/4)¹ = 20/4 = 5

(5/4 - 5) / (2 - 1) = (5/4 - 20/4) / 1 = -15/4

the average rate of change is -15/4.


Related Questions

find the inverse of the function F(x)=x-3​

Answers

Answer:

f¹(x) = x - 3

To find the inverse of a function, just "trade" and y and solve for the "new" y. The graph of the inverse is the reflection of the original function over the line y = x.

Rewrite the function f(x) = x + 3

as the equation y = x + 3

Trade x and y.

x = y + 3

Solve for the "new" y.

= y + 3

3 - 3

Subtract 3 from both sides

y = x= 3

The symbol for the inverse is f-¹(x)

f¹(x) = x - 3

Step-by-step explanation:

brainlies me plss

[tex]f(x) = x -3 \\\\\text{Write f(x) as}~ y = x -3}\\\\\text{Now replace x and y,}\\\\x = y-3\\\\\text{Solve for y:}\\\\y = x+3 \\\\\implies f^{-1}(x) = x +3 ,~ \text{This is the inverse of given function.}[/tex]

Please help
Solve.
(5√5)^−2x+1 = 1/5 ⋅ 125^x−3

Enter your answer in the box. Enter any fraction as a simplified fraction.

Answers

Answer: 125x=0.04x+20

Step-by-step explanation: (5√5)−2x+1=

1

5

(125x)−3

0.008x+1=

1

5

(125x)−3

Step 1: Flip the equation.

1

5

(125x)−3=0.008x+1

Step 2: Add 3 to both sides.

1

5

(125x)−3+3=0.008x+1+3

1

5

(125x)=0.008x+4

Step 3: Divide both sides by 1/5.

1

5

(125x)

1

5

=

0.008x+4

1

5

125x=0.04x+20

The  value of x is 46.

What are Exponents and power?

Exponents and powers can be used to represent extremely big or extremely small numbers in a more straightforward fashion.

The number of times a number is multiplied by itself is defined by the exponent. The power is an expression that displays the same number or factor being multiplied repeatedly.

Given:

[tex](5\sqrt{5} )^{-2x+1 }= 1/5 * 125^{x-3}[/tex]

ow, using exponents and powers

[tex](5\sqrt{5} )^{-2x+1 }= 1/5 * 125^{x-3}[/tex]

[tex](5\sqrt{5} )^{-2x+1 }= 1/5 * 5 ^{3(x-3)\\[/tex]

[tex](5\sqrt{5} )^{-2x+1 }= 5^{3x - 9 - 1}[/tex]

[tex](5\sqrt{5} )^{-2x+1 }= 5^{3x -10}[/tex]

[tex]5^{3/2(-2x+ 1)}= 5^{3x - 10}[/tex]

[tex]5^{-x+ 3/2}= 5^{3x -10}[/tex]

Now, Comparing

-x+ 3/2 = 3x- 10

-x - 3x = -10 - 3/2

-4x = -23/2

x= 46

Hence, the value of x is 46.

Learn more about Exponents and powers here:

https://brainly.com/question/15722035

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S.7.G.1.1
Question
In a drawing of a bus, the length is 5 cm. If the scale used
is 1 cm: 9 ft, what is the actual length of the bus?

Answers

9x5 =45 so the actual Length would be 45 feet

Which methods of evaluating a capital investment project ignore the time value of money?

Answers

Answer: Varies

Step-by-step explanation:

It involves any that is not concerned with making a profit.

Guided Practice


Write the equation of the parabola in vertex form. The vertex is (3, 2) and the parabola passes through the point (0, 38). Create a rough sketch of the graph to use as a visual aid.


A.
y = 4(x + 3)2 + 2


B.
y = (x + 3)2 + 2


C.
y = 19(x − 2)2 + 3


D.
y = 4(x − 3)2 + 2

Answers

Answer:

D.

y = 4(x − 3)^2 + 2

Step-by-step explanation:

A.    y = 4(x + 3)^2 + 2   = ( − 3 ,  2 )

B.    y = (x + 3)^2 + 2     = ( − 3 ,  2 )

C.    y = 19(x − 2)^2 + 3  = ( 2 ,  3 )

D.    y = 4(x − 3)^2 + 2   = ( 3 ,  2 )

number of heads: 0,1,2,3 Frequency: 16,38,34,12 Find the median​

Answers

Answer:

the median of 0 1 2 3 16 38 34 12 is 9.5

An arrow is shot at an angle 32 degree from the horizontal. If it's height is increasing at 200 km/hr, how fast is the arrow itself going?

Answers

Check the picture below.

Bearing in mind that the angle is not changing all the wihle, namely is constant

[tex]tan(32^o)=\cfrac{y}{x}\implies x = \cfrac{y}{tan(32^o)}\implies x = \cfrac{1}{tan(32^o)}y \\\\\\ \stackrel{\textit{taking the derivative on bot sides}}{\cfrac{dx}{dt}=\cfrac{1}{tan(32^o)}\cfrac{dy}{dt}}\implies \cfrac{dx}{dt}=\cfrac{1}{tan(32^o)}200\implies \cfrac{dx}{dt}\approx 320.07~\frac{km}{hr}[/tex]

positive and negative relationships are both examples of linear relationships


A. True

B false ​

Answers

Answer: A. True.

Step-by-step explanation:

A relationship is linear when the points on a scatterplot follow a somewhat straight line pattern. This is the relationship that we will examine. Linear relationships can be either positive or negative. Positive relationships have points that incline upwards to the right. As x values increase, y values increase.

URGENT WILL GIVE BRAINILY
Alex drives at a speed of 60 miles per hour. How long will it take to drive 330 miles?​

Answers

Answer:

5.5 hours

Step-by-step explanation:

time = distance/speed

t = 330/60

t = 5.5 hours

What is the algebraic expression for the following word phrase: the product of 7 and the difference of x and y?

Answers

Answer:

7(x-y)

Step-by-step explanation:

difference of x and y=x-y

product of 7=7 times the expression

so,

Answer is 7(x-y)

A line has a slope of 5 and passes through the point (1,5). What is its equation in
slope-intercept form?

Answers

Answer:

[tex]y=5x[/tex]

Step-by-step explanation:

Insert the information into the point-slope formula to find slope-intercept form.

[tex]y-y_1=m(x-x_1)\\\\y-5=5(x-1)\\\\y-5=5x-5\\\\y=5x[/tex]


You buy a $266,000 home.with. a.down payment of 21%. Find the amount of the down payment and the mortgage amount.
down payment mortgage amount

Answers

The answer is $210,140

What is the equation of this line in standard form?


6x−7y=11

6x−7y=−11

7x−6y=11

6x−5y=−13

Answers

9514 1404 393

Answer:

  (b)  6x −7y = −11

Step-by-step explanation:

Perhaps the easiest way to approach this is to look at the y-intercept. To find it, set the value of x to zero, and divide by the y-coefficient. The y-intercepts of these equations are ...

  a) 11/-7 = -1 4/7

  b) -11/-7 = 1 4/7 . . . . possible candidate

  c) 11/-6 = -1 5/6

  d) -13/-5 = 2 3/5

The only y-intercept that matches the graph is the one for equation ...

  6x -7y = -11

_____

You can use any of several other strategies to verify this choice:

1) Putting the given point values into the equation:

  for (-3, -1): 6(-3) -7(-1) = -18 +7 = -11 . . . . yes

  for (1/2, 2): 6(1/2) -7(2) = 3 -14 = -11 . . . . yes

__

2) Finding the equation from the given points.

  m = (y2 -y1)/(x2 -x1) = (2 -(-1))/(1//2 -(-3)) = 3/(3 1/2) = 6/7

Then the point-slope equation is ...

  y -k = m(x -h) . . . . . . line with slope m through point (h, k)

  y -(-1) = 6/7(x -(-3)) . . . . . substitute known values

  7y +7 = 6x +18 . . . . multiply by 7, simplify

  6x -7y = -11 . . . . . . . add -18 -7y to both sides

what are the solutions to the system

Answers

[tex]10+y=5x+x^2~~~~.....(i)\\\\5x+y =1~~~....(ii)\\\\\text{From (i):}\\\\10+y = 5x +x ^2\\\\\\\implies y = 5x +x ^2 -10\\\\\text{Substitute y in equation (ii):}\\\\5x+5x+x^2-10=1\\\\\implies x^2 + 10x -11 =0\\\\\implies x^2 +11x -x -11=0\\\\\implies x(x+11) -(x+11) =0\\\\\implies (x-1)(x+11) =0\\\\\implies x =1 ~~ \text{or}~~ x = -11\\\\\text{Substitute x =~1 in equation (ii):}\\ \\5+y =1 \implies y =-4[/tex]

[tex]\\\text{Substitute}~ x =-11~ \text{in equation (ii):}\\\\\ 5(-11) + y = 1 \implies y = 1 +55 = 56 \\\\\text{Hence} (x,y) = (-11,56) ~~\text{and}~~ (x,y)=(1,-4)[/tex]

Point-Slope Form of a Line

Answers

Y - y1 = m( x - x1 )

which could be the function graphed below ??

Answers

Answer:

D  [tex]\sqrt{x+4}[/tex]

Step-by-step explanation:

A number x increased by 4 is less than or equal to 27.

Answers

Any time you need to change a word problem involving a variable and you are not sure how to do it, ask yourself how would I tackle this problem with a known number and then trace what operation was used.

If I asked you what is the result if the number 7 is increased by 4, you would likely say 11. Tracing your work, you realize that you added 7 + 4 = 11.

Thus a number (e.g. n) increased by 4 is simply:

n + 4

Answer:

x + 4 < 27

-4. -4

x > 24

Step-by-step explanation:

put lines under signs

Express 0.03 as a percentage of 1

Answers

Answer:

3%

Step-by-step explanation:

[tex] \frac{0.03}{1} \times 100[/tex]

0.03=3/100 So

[tex] \frac{3}{100} \div 1 \times 100[/tex]

=3%

0.03 will be 3% but if it was 0.3 it would be 30% remember this for class

100.00 decreased by 20%
Please help

Answers

Answer: If Percentage decrease % = 20%, (1 - Percentage decrease %) = 1 - 20% = 100/100 - 20/100 = 80/100 = 0.8 => Percentage decreased number = 0.8 × Initial value

Step-by-step explanation: Number 100 decreased by 20% (20 percent) of its value (percentage decrease) and calculated absolute change (actual difference)

Write the quadratic function in f(x)=a(x−h)2+k form whose graph is shown below.



The graph shows a downward facing parabola with vertex (negative 3, 4) and y-intercept (0, negative 5).

Answers

[tex]~~~~~~\textit{vertical parabola vertex form} \\\\ y=a(x- h)^2+ k\qquad \begin{cases} \stackrel{vertex}{(h,k)}\\\\ \stackrel{"a"~is~negative}{o pens~\cap}\qquad \stackrel{"a"~is~positive}{o pens~\cup} \end{cases} \\\\[-0.35em] ~\dotfill[/tex]

[tex](\stackrel{h}{-3}~~,~~\stackrel{k}{4})\qquad \implies f(x) = a[x-(-3)]^2+4\implies f(x) = a(x+3)^2+4 \\\\\\ \textit{we know that} \begin{cases} x=0\\ f(x) = -5 \end{cases}\implies -5=a(0+3)^2+4\implies -5=9a+4 \\\\\\ -9=9a\implies \cfrac{-9}{9}=a\implies \boxed{-1=a}~\hfill \blacktriangleright f(x)=-(x+3)^2+4 \blacktriangleleft[/tex]

simplify 5 − 2(2.5 − 6.7)^2

Answers

Answer:

-30.28

Step-by-step explanation:

You are in charge of financial services and must calculate overtime pay for employees in your division. Due to a heavy workload, an employee had to do 35 hours of overtime in two weeks. Seven of these hours are at "double time" (i.e. twice usual pay), the rest are at "time-and-a-half". The employee's usual pay is $375 a week at $10 an hour. How much overtime money should the employee be paid for the two week period?

Answers

Answer:

$2,100

Step-by-step explanation:

'regular' pay is 375/10 or $37.50 per hour

'time-and-a-half' would be 37.50 + 18.75 = $56.25 per hour

'double time' would be (2)37.50 = $75.00

35 hours in 2 weeks and 7 hours at 'double time' and 28 at 'time-and-a-half'

so:

(7)75 + (28)56.25 = 525 + 1575

Total overtime pay for 2-week period is $2,100

Alice uses a table to record the number of black cars, b, that passed by her house in h hours.
b is directly proportional to h.

Answers

Answer:

1/2

Step-by-step explanation:

b is directly proportional to h.

b = kh

take any (h, b) point

using (28, 14)

14 = k(28)

Divide both sides by 28

1/2 = k

1/2


28. Marta Sanchez purchased a sweater for $15.67, a pair of socks for $2.13, and a bracelet for $6.78. For all
purchases she must pay the state sales tax of 7.5% and the county tax of 0.5%. What is the tax on her
purchases?

Answers

Answer:

$ 1.94

Hope I helped

A basket containing 150mangoes cost 450 find the selling price of an orange if it is to be sold at a profit of 5%

Answers

Answer:

The selling price cost 472.5

Step-by-step explanation:

Let's find the profit first.

To find that, let's turn 5% to decimal form.

5 % = 0.05

Then, lets multiply it to the initial price which is 450

450 * 0.05 = 22.5

So the profit costs 22.5

Now, let's add the profit to the initial cost to find the selling price

450 + 22.5 = 472.5

That's it.

The difference of twice a number and 7 is 20. Find the number.

Answers

Answer:

twice the difference gives 2(difference). 7 = 14  20 = 40

Step-by-step explanation:

A right triangle with a hypotenuse of square root of 61 has an area of 15 square inches. Find the lengths of the other two sides.



Answers

The lengths of the other two sides are 6 inches and 5 inches

Let b represent the base of the right triangle, h represent the height of the right triangle and x represent the hypotenuse.

Since the area of the triangle is 15 in², hence:

Area(A) = (1/2) * base * height

15 = (1/2)bh

bh = 30  

b = 30/h         (1)

Applying Pythagoras theorem also:

x² = b² + h²

(√61)² = b² + h²

61 = (30/h)² + h²

61 = 900/h² + h²

61h² = 900 + h⁴

h⁴ - 61h² + 900 = 0

h = -6, -5, 5, 6

Since the length cant be negative, hence h = 5 or h = 6

When h = 5; b = 30/5 = 6

When h = 6; b = 30/6 = 5

Therefore the lengths of the other two sides are 6 inches and 5 inches

Find out more at: https://brainly.com/question/2773823

1. Transplant operations have become routine. One common transplant operation is for kidneys. The most dangerous aspect of the procedure is the possibility that the body may reject the new organ. There are several new drugs available for such circumstances and the earlier the drug is administered, the higher the probability of averting rejection. The New England Journal of Medicine recently reported the development of a new urine test to detect early warning signs that the body is rejecting a transplanted kidney. However, like most other tests, the new test is not perfect. In fact, 20% of patients that experience kidney rejection and 9% of patients that do not experience kidney rejection receive a test result that proves to be incorrect. Physicians know that in about 30% of kidney transplants the body tries to reject the organ. If the new test has a positive result (indicating early warning of rejection), what is the probability that the body is attempting to reject the kidney?

Answers

Using conditional probability, it is found that there is a 0.7921 = 79.21% probability that the body is attempting to reject the kidney.

Conditional Probability

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]

In which

P(B|A) is the probability of event B happening, given that A happened. [tex]P(A \cap B)[/tex] is the probability of both A and B happening. P(A) is the probability of A happening.

In this problem:

Event A: Positive test.Event B: Body attempting to reject the kidney.

The percentages associated with a positive test are:

80% of 30%(experience kidney rejection).9% of 70%(do not experience kidney rejection).

Hence:

[tex]P(A) = 0.8(0.3) + 0.09(0.7) = 0.303[/tex]

The probability of both a positive test and the body attempting to reject the kidney is:

[tex]P(A \cap B) = 0.8(0.3) = 0.24[/tex]

Hence, the conditional probability is:

[tex]P(B|A) = \frac{0.24}{0.303} = 0.7921[/tex]

0.7921 = 79.21% probability that the body is attempting to reject the kidney.

A similar problem is given at https://brainly.com/question/25553471

In grade 10, the ratio of boys to girls is 2: 3. There are 75 girls. How many are boys?

HELP PLEASE .. I WILL GIVE A BRAINLIEST !

Answers

Answer:

150

Step-by-step explanation:

The ration is 2/3 in this example means they are twice as many boys than girls. If boys = 2/3, than girls = 1/3.

So, to find the answer, you must multiply 75 by 2, which is 150.

You don't need this, but they are 75 + 150 = 225 boys and grils in grade 10.


I need the answer and how you done it please

Answers

Answer:

x=11/17

Step-by-step explanation:

determine the defined range

11/x  17

11/x =17 then x is canceled out  

11=17x

17x=11 dividing both sides

x=11/17

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