Mathematics High School

WILL GIVE BRAINLIEST-What is the average rate of change of the function on the interval from x = 0 to x = 2?

f(x)=250(0.5)x

Answers

Answer 1
Average=  f(2)−f(0)/2−0
=62.5−250/ 2-0
= −93.75
Answer 2

The average rate of change of the function will be -93.75.

What is the average rate of change?

It is the average amount by which the function changed per unit throughout that time period. It is calculated using the slope of the line linking the interval's ends on the graph of the function.

Given that the interval from x = 0 to x = 2 and the function is [tex]f(x)=250(0.5)^x[/tex].

Calculate the value of the function at x = 0 and x = 2

[tex]f(x)=250(0.5)^x[/tex].

[tex]f(0)=250(0.5)^0=250\\f(0)=250(0.5)^2=62.5[/tex].

The average rate of change will be calculated as,

Rate of change = ( 62.5 - 250 ) ( 2 - 0)

Rate of change = -93.75

Therefore, the average rate of change of the function will be -93.75.

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Related Questions



What is the value of the expression when a = 4, b = 3 ,and c = 10?

3a/4b−c

1
4
6
12

Answers

The answer is C. 6. I hope this helps!

Brock is a plumber. He charges a flat rate of $40 to visit a house to inspect it's plumbing. He charges an additional $20 for every hour he spends inspecting or making repairs.

Which graph below correctly shows the price of using Brock's plumbing service vs time?

Answers

it would be graph W because the cost will increase, so that gets rid of Y... It has to start at 40 for the original cost, getting rid of Z and X

W is correct. the red line starts at 40 which is the initial fee

 then it crosses 60 and 1.0 and 80 at 2.0 which is 20 dollars for 1 hour

What is 120 degrees in radians?

Answers

Answer:

[tex]\frac 23 \pi [/tex]

Step-by-step explanation:

120 degrees is one third of the whole circle, or [tex] \frac 13 2\pi [/tex]

Answer:

the answer is 2pi/3

is (3,4) a solution of y=-x+5

Answers

3=x
4=y

4=-3+5

So no it’s not.

Which is an equation of the line with x-intercept 2 and y-intercept 12?

Answers

Your answer should be y=2x+12

If you know how to do this, can you show the work, please?
Thanks

Answers

Answer: The original area of the square is 64 square feet

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

Let x be the original side length of the square. The original area is therefore going to be x*x = x^2. For now we don't know the area but once we figure out x, we can compute the area.

The original side length x is increased by 7 ft to jump up to (x+7) ft
At the same time, the other dimension is reduced to (x-2) ft, which is a decrease of 2 ft

The old square is x ft by x ft with area x*x = x^2

The new rectangle is (x+7) ft by (x-2) ft

Let's find the area of this rectangle

Have a look at the image attachment to see how to multiply out (x+7)*(x-2) using the box method

The terms in red are x^2, 7x, -2x and -14 which are found by multiplying the headers

x times x = x^2
x times 7 = 7x
-2 times x = -2x
-2 times 7 = -14

The like terms are 7x and -2x which combine to 5x

Overall the result of multiplying out (x+7)*(x-2) is x^2+5x-14

Note: we can get the same result if we use the FOIL or distribution rule. The box method is a handy way to visually keep track of all the terms.

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

The area of the rectangle, in terms of x, is x^2+5x-14

We are told that the area is 90 square feet

So equate the two expressions and solve for x

x^2+5x-14 = 90
x^2+5x-14-90 = 90-90
x^2+5x-104 = 0
(x-8)(x+13) = 0 ... see note below
x-8 = 0 or x+13 = 0
x = 8 or x = -13

note: find two numbers that multiply to -104 and add to 5. Those numbers are -8 and 13 which helps us factor

We ignore x = -13 as a negative side length makes no sense

The only practical root is x = 8

The side length of the original square is 8 feet

The area is
x*x = 8*8 = 64 square feet

We can check the answer by adding 7 to 8 to get 15, and subtracting 2 from 8 to get 6. The 8 by 8 square turns into a 15 by 6 rectangle. Since 15*6 = 90, we have confirmed the right answer. 

If one quart is the same amount as 2 pints, how many pints are in 8 quarts?

Numerical Answers Expected!

Answers

just do a proportion to set up your problem so you would have (1/2)=(8/x) then solve for x. which you would get 16

Answer:

16!

Step-by-step explanation: Hope this helps.... you made this in 2017 its 2020 now-

1. Can √72 be completely simplified if it is broken up as √72=√9x8, explain why or why not?

2. How do you determine the result of taking the square root of a variable raised to an even power? For example √x∧28?

Answers

sqrt72 = sqrt(9x8) = 3sqrt8 = 3(sqrt(4x2)) = 3(2sqrt2) = 6 sqrt(2)

2. sqrt x = x^½. Rules of indices states for a power of a power, you times them.
so (x^28)^½ = x^14

Maybelle looked at a hotel. She waited a week before she decided to book nights at that hotel, and now the prices have increased. The original price was $1195. The price for the same room and the same number of nights is now $2075. What is the percent increase? Round to the nearest whole percent. Explain and Show your work.

-20 points. Better yet, 30 points!! Please help!

Diff in price = %
_________ _________ thats the formula i think...
original price 100

Answers

The formula for percent increase is (final-initial)/initial*100
Plug in to get (2075-1195)/1195*100
880/1195*100
.7364*100
73.64% rounding we get
74%

HELP PLEASE:

What is the point-slope form of the line with slope 25 that passes through the point (−4, −7)?

y−7=2/5(x−4)
y+7=2/5(x+4)
y+4=2/5(x+7) ​
y−4=2/5(x−7)

Answers

y - y1 = m(x - x1)
slope(m) = 2/5
(-4,-7)....x1 = -4 and y1 = -7....pay attention to ur signs
now we sub
y - (-7) = 2/5(x - (-4)...not done yet
y + 7 = 2/5(x + 4) <===

Answer:

Correct option is:

y+7=2/5(x+4)

Step-by-step explanation:

The point-slope form of the line with slope m and passing through the point (x1,y1) is given by:

y-y1=m(x-x1)

Here, we are given line with slope m=2/5

and passing through (x1,y1)=(-4,-7)

i.e. x1= -4 and y1= -7

[tex]y-(-7)=\dfrac{2}{5}(x-(-4))[/tex]

[tex]y+7=\dfrac{2}{5}(x+4)[/tex]

Hence, Correct option is:

y+7=2/5(x+4)

PLZ HELP
Mrs. Kuss received a $50 Itunes gift card for her birthday. She bought one album for $9.99 and would like to see how much money she has left to buy single songs. If each song costs $1.29, how many songs can Mrs. Kuss buy with her remaining money? Show your work.

Answers

Mrs kiss can buy about 31 songs

50.00-9.99 = 40.01
40.01 / 1.29 = 31.0
She initially has $50 and she bought an album of $9. 99 so you subtract those $9.99 from $50 and you are left with $40.01, now you can either divide it by $1.29 to skip the long process or subtract $1.29 at a time. Once you do so, you will get an answer of 31 more songs with $0.02 left. YOU'RE WELCOME :D

A girl starts to walk to her school, which is 20 miles away, at 6:50 and at a rate of 3 miles per hour. After a while, her dad picks her up and drives her through the remainder of the way at 30 miles per hour. If they arrived at school at 9:00, how far did she walk?

Answers

The girl walked 5 miles.

Answer:

She walked 5 mi

Which of the following list of ordered pairs is a function?!!!

Answers

the answer will be a
I think A. will be the answer because how the numbers show that its increasing by every time so i would choose A as the best answer.

Give the first four nonzero terms of the series about x=8 representing the function x^(1/3)

Answers

empire state building

$40 is discounted into $32 what is the percent decrease

Answers

about 28.5 percent is the decrease I hope this helps :)

A packet of biscuits has a mass of 1 1/3 kg. Jason eats 2/5 of the packet. What is the mass of biscuits left?

Answers

11 / 3 = 55 / 15;
2 / 5 = 6 / 15;
So. 11 / 3 - 2 / 5 = 55 / 15 - 6 / 15 = 49 / 15 = 3.26 kg is the mass of biscuits left.

The mass of biscuits left after Jason eats 2/5 of the packet is approximately 0.8 kg.

To find the mass of the biscuits left after Jason eats 2/5 of the packet, we need to calculate the mass of the biscuits he ate and then subtract it from the initial mass of the packet.

Given:

Mass of the packet of biscuits = 1 1/3 kg

First, let's convert 1 1/3 kg to an improper fraction:

1 1/3 = 3/3 + 1/3 = 4/3 kg

Now, to find the mass of the biscuits Jason ate, we can use the fact that he ate 2/5 of the packet:

Mass of biscuits Jason ate = (2/5) * (4/3) kg

Now, perform the multiplication:

Mass of biscuits Jason ate = (8/15) kg

To find the mass of biscuits left, we subtract the mass Jason ate from the initial mass of the packet:

Mass of biscuits left = 4/3 kg - 8/15 kg

To subtract fractions, we need to find a common denominator, which is 15 in this case:

Mass of biscuits left = (20/15) kg - (8/15) kg

Now, perform the subtraction:

Mass of biscuits left = 12/15 kg

Finally, let's simplify the fraction:

Mass of biscuits left = (12/15) * (1/3) kg

Mass of biscuits left ≈ 0.8 kg

Therefore, the mass of biscuits left after Jason eats 2/5 of the packet is approximately 0.8 kg.

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How to solve 5x-9y=7 and -3x+7y=-5 using any method

Answers

You can solve this by graphing
The x value will give 0.5 and the y value will be equal to -0.5
I hope this helps.
YOU'RE WELCOME :D

Given 11 is conguent to 3, which lines, if any, must be parallel based on the given information? Justify your conclusion


A. a || b, Converse of the Alternate Exterior Angles Theorem

B. c || d, Converse of the Same-Side Interior Angles Theorem

C. a || b, Converse of the Corresponding Angles Theorem

D. not enough information to make a conclusion

Answers

To draw a conclusion with parallel lines, you need two lines cut by a transversal. You don't have that situation here, so you cannot draw any conclusion about parallel lines.

if MN = PQ AND PQ = RS then MN = RS

Answers

The answer for this problem would be : true

What is the next term in the sequence 1/2 1/6 1/18 1/54

Answers

1/162
2*3=6
6*3=18
18*3=54
54*3=162

For an arithmetic sequence where a1 = 13 and the common difference is 3, find s7.

A. 162
B. 157
C. 154
D. 151

Answers

sn=n/2[2a+(n-1)d]
s7 means n=7

a7=7/2[2(13)+(7-1)(3)]=7/2(44)=154

Ans:C

Answer:

C. 154

Step-by-step explanation:

Here we have given that,

First Term a₁ = 13

Common Difference d = 3

Term (n ) = 7

so, we have arithmetic sequence: 13, 16, 19, 22,... and so on

Thus Sum of first 7 terms = [tex]\frac{n}{2} [2a+(n-1)d][/tex]

                                          = 7÷2 [2*13 + (7 - 1)*3 ]

                                          = 3.5 [ 26 + 21 ]

                                          = 154

                                           

The function f(x) is shown in the graph.

What is the equation for f(x)?



Enter your answer in the box.
f(x)=_______

Answers

   f(x) =   (-5/6)x  −  1  .
___________________________________

When the function f(x) is divided by x-2 the quotient is 3x^2+8x-4 and the remainder is 9 find the function f(x) and write the result in standard form?

Answers

dividend ÷ divisor = quotient + remainder
∴ dividend = divisor(quotient) + remainder  ... there is a reason why I am not multiplying the remainder by the divisor in this case... your remainder is not represent as a fraction with the divisor as the denominator..

[tex]f(x)=(x-2)(3x^2+8x-4)+9=3x^3+8 x^{2} -4x-6 x^{2} -16x+8+9[/tex]
[tex]f(x)=3x^3+2x^2-20x+17[/tex]

The expression for the function f(x) in standard form is f(x) = 3x³ + 2x² - 20x + 17 if the function f(x) is divided by x-2.

What is a function?

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

It is given that:

When the function f(x) is divided by (x - 2) the quotient is 3x² + 8x - 4 and the remainder is 9

By using the division algorithm:

f(x) = (x - 2)(3x² + 8x - 4) + 9

After simplification:

f(x) = 3x³ + 8x² - 4x - 6x² - 16x + 8 + 9

f(x) = 3x³ + 2x² - 20x + 17

Thus, the expression for the function f(x) in standard form is f(x) = 3x³ + 2x² - 20x + 17 if the function f(x) is divided by x-2.

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Bella babysits for two families each weekend. One family pays her $20. The other family pays her $22. Which expression represents the amount of money Bella has been paid after w weekends?

Answers

y=w(20+22). That uses the distributive property. for a simpler answer, use y=20w+22w.

Johnny is reading a novel for the read-a- Thon. The ratio of the number of pages she read to the pages that remain to be read is 7:3. If the book contains 500 pages in all, how many pages did Johnny reed and how many pages remain left?

Answers

There are several ways to answer this question and I will use this approach. Since Johnny reads at a ratio of 7:3 it can be stated that for every 10 pages in a book containing 500 pages Johnny will read 7 of those pages. There are 50 groups of 10 in a 500-page book (50 x 10). Take the ration 7:3 times 50 and use the distributive property:  7:3(50) = (7 x 50):(3 x 50) = 350:150. Based on this Johnny has read 350 pages and has 150 pages remaining.

hich is an example of a proportional relationship?

A.The yogurt shop charges .30 per pound.
B.The yogurt shop charges .30 per pound plus $1.00 for the cup.
C.John ran 2 miles in 15 minutes then ran 3 miles in 20 minutes.
D.The car travelled 40 mph for half an hour and then travelled 60 mph for 2 hours

Answers

B im sure plz like and put 5star

Please Help With This. What is the equation of the line shown in this graph? Answer your answer in the box.

Points are:
(-2,-3) (3,-3)

Answers

[tex]\bf \begin{array}{lllll} &x_1&y_1&x_2&y_2\\ % (a,b) &({{ -2}}\quad ,&{{ -3}})\quad % (c,d) &({{ 3}}\quad ,&{{ -3}}) \end{array} \\\\\\ % slope = m slope = {{ m}}= \cfrac{rise}{run} \implies \cfrac{{{ y_2}}-{{ y_1}}}{{{ x_2}}-{{ x_1}}}\implies \cfrac{-3-(-3)}{3-(-2)} \\\\\\ \cfrac{-3+3}{3+2}\implies \cfrac{0}{5}\implies 0[/tex]

[tex]\bf \stackrel{\textit{point-slope form}}{y-{{ y_1}}={{ m}}(x-{{ x_1}})}\implies y-(-3)=0[x-(-2)] \\\\\\ y+3=0\implies y=-3[/tex]

The solution to f - (-4) = 12 is f = 8.

True or False

Answers

Answer is true. two -'s turn into + (8+4=12)
True, because 8 +4=12. It's "+4" because 2 negatives make a positive.

Can someone please just explain what I need to do? I'm so confused

The length of a text messaging conversation is normally distributed with a mean of 10 minutes and a standard deviation of 4 minutes. What is the probability that a conversation lasts longer than 20 minutes?

Answers

Durant missed the preseason finale against Sacramento, allowing Nick Young to get experience starting and score 15 points.

A trail is 2940 miles long. it begins in city a and ends in city
b. manfred has hiked three sevenths 3 /7 of the trail before. how many miles has he​ hiked?

Answers

Final answer:

Manfred has hiked 1260 miles of the trail, which is calculated by multiplying the total length of the trail (2940 miles) by the fraction of the trail he has completed (3/7).

Explanation:

To calculate the distance Manfred has hiked on the trail, we multiply the total length of the trail by the fraction of the trail he has completed. In this case, Manfred has hiked three sevenths (3/7) of the trail. The total distance of the trail is 2940 miles.

Distance Hiked = (Total Distance of Trail) × (Fraction of Trail Completed)

Distance Hiked = 2940 miles × (3/7)

Distance Hiked = 2940 miles × 0.4286

Distance Hiked = 1260 miles

Therefore, Manfred has hiked 1260 miles of the trail.

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