PLEASE READ THIS EXPLANATION: It is an EXTREMELY foundational concept in algebra that must be understood. Ask questions in the comments if you do not understand anything because I love helping others learn! Do not be shy. :)
Alright, so let's just understand the problem. The interval [3,6] means that the smallest x-value is x=3 and the largest x-value is x=6, and they both INCLUDE x=3 and x=6 (It would exclude x=3 and x=6 if it was like interval (3,6) with parentheses). Since f(x) is an exponential function, the change per x is not consistent and its growth actually grows as it continues in the direction of infinity, so that is why the average rate of change is interesting and very much relies on what range there is. The average rate of change from x=3 to x=6 will be far smaller than the average rate of change farther down the road at x = 99999 and x = 100003.
So, how do we find the average rate of change? All you have to do is find the slope between two points. Simple as that.
So, how do we apply that here? Imagine a graph with two points, one point at x = 3 and one point at x = 6 and we do not know the y-value of either of these points. So, that's our first step!
We need to first find how much it grows at x=3 and x=6 separately to find the the y-value of these points. f(x) = 2^x for x = 3 means y = 8, and f(x) = 2^x for x = 6 means y = 64. We now have two points:
(3, 8) and (6, 64)
Now, all we have to do is find the slope between these lines. All we have to do is use the normal formula for finding slope:
(y₂ - y₁) / (x₂ - x₁) OR (y₁ - y₂) / (x₁ - x₂)
Most people use the first one, but they give you the exact same answer, so don't ever think it's impossible to use the second one. Let's just use the first formula anyway.
(3, 8) = (x₁, y₁)
(6, 64) = (x₂, y₂)
Now, let's use the formula (remember you can use either one because it won't affect your answer):
(y₂ - y₁) / (x₂ - x₁) = (64 - 8) / (6 - 3) = 56 / 3 = 18 and 2/3
So, the average rate of change is 18 and 2/3 or 18.666666667.
You and your brother had a cookie bake-off! You made a dozen cookies each with a circumference of 10 inches and your brother made a dozen cookie bars with a perimeter of 10 inches. Who used more cookie dough? Assume the cookies are the same thickness.
Answer:
Your brother (I think i'm right)
Step-by-step explanation:
Perimeter is bigger than circumferance if same "length"
Help MATH please EEEEE
Ruchi covers 3.25 Kilometres in 50 minutes. How much distance will she cover in Metres in 94 minutes?
Answer:
Distance covered by Ruchi = 61.1 km
Step-by-step explanation:
Formula of the Speed is given by,
Speed = [tex]\frac{\text{Distance covered}}{\text{Time taken}}[/tex]
Since, Ruchi coves distance = 3.25 km
Time taken to cove this distance = 50 minutes
Therefore, speed of Ruchi = [tex]\frac{3.25}{50}[/tex]
= 0.65 km per minute
Therefore, distance covered by Ruchi in 94 minutes,
0.65 = [tex]\frac{\text{Distance covered}}{94}[/tex]
Distance covered = 0.65 × 94
= 61.1 km
A car travels about 63 feet in one second. At this speed about how many feet will the car travel in 7 seconds.
Answer:
441 feetStep-by-step explanation:
First we need to make this word problem into just numbers. Since we know feet per second (fps) we will multiply this by the given amount of seconds to find the answer
63 × 7
Now solve
After solving you should get 441 which is the answer
*EXTRA*
I have included a graph but it is hard to use since it is such a narrow line but still helpful since there is the equation included
(rcostheta = 6) convert to rectangular
WILL REWARD BRAINLIEST! Is segment AB tangent to circle O shown in the diagram, for AB = 8, OB = 3.75, and AO = 10.25. Explain your reasoning and show all work in your own words.
Answer: look at the picture, it going to take my long to write so I give you a picture. In the picture it my work done for you.
Step-by-step explanation: Hope this help :D
HELP I HAVE 5 MINUETS, DONT GUESS ITS NOT ADDING BTW
Answer:
63.554
Step-by-step explanation:
V=pir^2h
r=3.4/2
h=7
V=pi(1.7)^2(7)
=63.554
Find the area of this parallelogram. Be sure to include the correct unit in your answer.
Opposite sides are equal in length and opposite angles are equal in measure. To find the area of a parallelogram, multiply the base by the height. The formula is: A = B * H where B is the base, H is the height, and * means multiply.
Answer:
A = 126 cm²
Step-by-step explanation:
The area (A) of a parallelogram is calculated as
A = bh ( b is the base and h the perpendicular height )
Here b = 14 and h = 9 , then
A = 14 × 9 = 126 cm²
David reads this advert on his country council website 70% of the area of woodland in the country is native woodland this means there are 350km squared of native woodland in the country work out the area of woodland in the country that is not native woodland
PLEASE ANSWER I WILL GIVE BRAINLIEST
Answer:B because you multiply all the similar numbers together then at the end you add them all up.
En una tienda de ropa vas a comprarte una pantalones que están de 150 a 90 euros y una camiseta de 40 a 24 ¿ tienen el mismo porcentaje de rebaja ?
Respuesta:
Sí, tienen el mismo descuento del 40%
Explicación paso a paso:
Dado :
PANTALÓN :
Precio inicial = 150
Precio con descuento = 90
Porcentaje de descuento en el precio:
(150 - 90) / 150 * 100%
60/150 * 100%
0,4 * 100
= 40%
CAMISA:
Precio inicial = 40
Precio con descuento = 24
Porcentaje de descuento en el precio:
(40-24) / 150 * 100%
16/40 * 100%
0,4 * 100
= 40%
Sí, tienen el mismo descuento del 40%
Solve for i
3 (.5i - 6 ) = 12
Answer:
15i-18=12
15i=12+18
15i=30
i=30/15
i=2
us
Complete the square
to find the vertex
of this parabola.
x2-14x+4y+29=0
( , )
Answer:
y=3x+29
Step-by-step explanation:
4y=12x+29
4y/4=12x+29/4
y=3x+29
Answer:
(7,5)
Step-by-step explanation:
Show you work please no links
Answer:
always catchin em lackin
Step-by-step explanation:
The image below is a kite. Find the value of x.
Answer:
x=55.5
Step-by-step explanation:
2x=111
Isolate x by dividing both sides by 111
x=55.5
Find c. Round to the nearest tenth:
Answer:
c=56.3
Step-by-step explanation:
Sorry for the bad writing and diagram haha
DUE AT 12 SO LIKE HURRY
Arthur's brother wants to borrow some money. Arthur decided to lend him $1000 at 2% simple interest. If the loan will cost his brother $50, how much time does he have before he has to pay Arthur back. (See Example 2 in your notes.)
a
2 years
b
2.5 years
c
3 years
d
3.5 years
Answer:
2.5
Step-by-step explanation:
Answer: b. 2.5 years
Step-by-step explanation:
The formula for Interest is:
= principal × rate × time
Then, we slot in the values given which will be:
Interest = principal × rate × time
50 = 1000 × 2% × Time
50 = 1000 × 0.02 × Time
50 = 20 × Time
Time = 50/20
Time = 2.5 years
He has 2.5 years to pay back
Enter a positive value for b that makes this statement true: 16 x b is greater than 16 but less than 32.
Answer:
24
Step-by-step explanation:
24
Answer:
1.5
Step-by-step explanation:
16 x 1.5 =24
24 is greater than 16 and less than 32
HELPP HELPP HELPP HELPP HELP PLZ
Answer:
Volume= 216 cubic yards
Surface area: 276 square yards
Step-by-step explanation:
Find volume of rectangular prism:
V= lxwxh
V= 3x18x4
= 216 cubic yards
Find surface area:
SA= 2 x (front/back area) + 2 x (right/left area) and 2 x ( bottom/top area)
Front and Back Area:
A= l x w
A = 18 x 3
= 54 square yards
Right/ left Area:
4 x 3
= 12 square yards
Top/ Bottom Area:
18 x 4
= 72 square yards
54^2+12^2+72^2
= 108+24+144
=276 square yards
Answer:
DOUBLE CHEESS SANDWICH
Step-by-step explanation:
The hypotenuse of a right triangle is 75 m. One of the legs measures 45 m. What is the length of the missing leg?
Answer:
60 m
Step-by-step explanation:
A^2+b^2=c^2
a^2+45^2=75^2
a^2+2025=5625
a^2=3600
a=60
Helps are really appreciated!!
Answer:
a) 58.24 square centimeters
b) 5cm
Step-by-step explanation:
a) Area of a parallelogram
The formula for the Area of a parallelogram = Base × Height
Height : 5.2cm
Base : 11.2cm
Area = 5.2 cm × 11.2cm
= 58.24 square centimeters
b) Volume of a cuboid
The formula for the Volume of a cuboid = Length × Width × Height
7cm = Width
3cm = Length
y = Height
Volume = 105cm³
We are to find y
Hence,
105cm³ = 7cm × 3cm × y
y = 105cm³/7cm × 3cm
y = 5cm
One of the legs of a right triangle measures 14 cm and the other
leg measures 9 cm. Find the measure of the hypotenuse. If
necessary, round to the nearest tenth.
Answer:
16.6
Step-by-step explanation:
[tex]14^{2}+9^{2}= 277\\[/tex]
[tex]\sqrt{277}[/tex]=16.6(rounded)
i think its like 126
Mr. Sims wants to buy a new truck. He sold his old truck for $3,582, and he has $4,979 in the bank. If a new truck costs $9,005, how much more money does he need in order buy the new truck?
Answer:
$444
Step-by-step explanation:
3,582 + 4,979 = 8,561
9,005 - 8,561 = 444
what equation is solved by graphed systems of equations
Answer:
its 7x+3=x-3
Step-by-step explanation:
it is
Jason represented the values of his 35 baseball cards in a histogram and in a stern-and-leaf plot. Which of these best describes the graph and characteristic that allow Jason to find the median value of his 35 baseball cards?
are there any choices?
Step-by-step explanation:
4
−5
x+
5
2
=
30
−13
Answer:
2 ...........
What is the value of the y-coordinate of point A
Answer:
there's no pic
Step-by-step explanation:
can you re attach it plz I might be able to help
Pls explain how to do this
Answer:
3 1/12 miles
Step-by-step explanation:
[tex]6\frac{3}{4} -3\frac{2}{3} \\\\=\frac{27}{4} -\frac{11}{3}\\\\ =\frac{81}{12} -\frac{44}{12} \\\\=\frac{37}{12}\\\\=3\frac{1}{12}[/tex]
Make them into mixed fractions and then find the least common denominator (12). solve.
Use the tabel to answer the question what rule describes the function F(x)?
A) f(x)=x+3
B) f(x)=x+4
C) f(x)=3x+2
D) f(x)=5x
A large bag of marbles contains red (R) and blue (B) marbles. Marbles are pulled one at a time, recorded, and placed back in the bag. Estimate the percentage of blue marbles in the bag.
R R R B R R R R R R B R R R B
A. 60%
B. 80%
C. 25%
D. 20%
Answer: 20%
Step-by-step explanation:
3/15= 1/5= 20%
