what is the average rate of change of f over the interval [-3,9]
Answers
Answer:
According to the graph, f(−3)=3 and f(9)=-7
-7-3/9-(-3)= −10/12
Therefore the answer is -5/6
From Khan
The average rate of change over the interval [-3,9] will be 63 units per one unit change in y - value.
What is Polynomial? What are exponents? What is the general equation of a straight line? A polynomial is defined as an expression which is composed of variables, constants and exponents, that are combined using mathematical operations such as addition, subtraction, multiplication and division.An exponent is a number that is placed as a superscript over a number. In other words, it indicates that the base is raised to a certain power. Tis expression means that -[tex]b^x = \underbrace{b \times \dots \times b}_{x \text{ times}}[/tex]
The general equation of a straight line is : y = mx + cwhere : [m] → is slope of line and [c] → is the y - intercept
We have the following function -
f(x) = x³ - 9
The average rate of change would be -
r = {720 - (- 36)}/{9 - (- 3)}
r = 756/12
r = 63
Therefore, the average rate of change over the interval [-3,9] will be 63 units per one unit change in y - value.
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what is the average rate of change of f(x) = x³ - 9 over the interval [-3,9] ]
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Related Questions
PLEASE HELPPPP Wilson is thinking about buying a house for $249,000. The table below shows the projected value of two different houses for three years. Number of years 1 2 3 House 1 (value in dollars) 253,980 259,059.60 264,240.79 House 2 (value in dollars) 256,000 263,000 270,000 Part A: What type of function, linear or exponential, can be used to describe the value of each of the houses after a fixed number of years? Explain your answer. (2 points) Part B: Write one function for each house to describe the value of the house f(x), in dollars, after x years. (4 points) Part C: Wilson wants to purchase a house that would have the greatest value in 45 years. Will there be any significant difference in the value of either house after 45 years? Explain your answer, and show the value of each house after 45 years. (4 points) (10 points)
Answers
Part A
House 1: we make exponential can be used to describe the
value of house 1. After 1 year, 253480 = 249000 x 1.02
After 2 years, 259059.6 = 25398×1.02. After 3 years 264240.79 =259059.60x1.02.
House 1: we make linear. 256000=249000 + 1000.263000 = 256000 +7000.270000=263000 + 1000.
Part B.
House 1: f(x)=249000 1.02x [genometic sequence]
House 2: f(X) = 24900 + 1000x [arithmetic progression]
Part C
House 1: f(45)=249000×1.02 45 = 607025.697
House 2: f(45) = 249000 +7000x45 = 564000
"House 1 is an arithmetic sequence that increases in price each year while House 2 is an arithmetic sequence that only increases by 1000 per year.
What are word problems in mathematics?
In computational mathematics, a word problem is a problem of deciding whether two given expressions are equivalent with respect to a set of rewriting identities. A prototypical example is the word problem for groups, but there are many other instances as well.
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Read Explain 3 Parts A and B and complete Your Turn #8 below (adapted from Lesson 6.1).
8.
According to the data from the U.S. Census Bureau for 1990-2009, the number of
commercially owned automobiles in the United States can be modeled by the function
A(x) = 1.4x – 130.6x² + 1831.3x + 128,141, where x is the number of years after 1990
and A(x) is the number of automobiles in thousands. The number of privately-owned
automobiles in the United States can be modeled by the function
P(x) = -x + 24.9x² – 177.9x + 1709.5, where x is the number of years after 1990 and
P(x) is the number of automobiles in thousands. Estimate the total number of automobiles
owned in 2005.
Answers
Answer: 130875 automobiles
Step-by-step explanation:
To estimate the total number of automobiles owned in 2005, let's first find the number of years
2005 - 1990 = 15 years
Given that the Commercially owned automobiles in the United States can be modeled by the function
A(x) = 1.4x – 130.6x² + 1831.3x + 128,141, where x is the number of years after 1990
and A(x) is the number of automobiles in thousands.
Substitute 15 for x in the function
A(x) = 1.4(15) – 130.6(15)² + 1831.3(15) + 128,141
A(x) = 21 - 29385 + 27469.5 + 128141
A(x) = 126246.5 automobiles
The number of privately-owned automobiles in the United States can be modeled by the function
P(x) = -x + 24.9x² – 177.9x + 1709.5, where x is the number of years after 1990
Substitute 15 for x in the function
P(x) = -(15) + 24.9(15)² – 177.9(15) + 1709.5
P(x) = -15 + 5602.5 - 2668.5 + 1709.5
P(x) = 4628.5 automobiles
The total automobile = A(x) + P(x)
Substitutes for A(x) and P(x)
The total automobile = 126246.5 + 4628.5
= 130875
Therefore, the total number of automobiles owned in 2005 is 130875 automobiles
A tiling company completes two jobs. The first job has $1200 in labor expenses for 40 hours worked, while the second job has $1560 in labor expenses for 52 hours worked. The relationship between the labor expenses and the hours worked is linear. Which equation can be used to calculate the y-intercept of the linear equation? 1200 = 40 (40) + b 1560 = 30 (40) + b 1560 = 30 (52) + b 1200 = 52 (30) + b
Answers
Answer:
1560 = 30(52) + b
Step-by-step explanation:
First job has $1200 in labor expenses for 40 hours worked,
Point (x,y)
(40, 1200
Second job has $1560 in labor expenses for 52 hours worked.
Point (x,y)
(52,1560
Slope of the line, m
m=1560-1200/52-40
=360/12
=30
Slope intercept,y
y=mx+b
Where,
b= y intercept
y=30x+b
points: (40,1200) and
(52,1560)
Equation to find y-intercept
y=30x+b
For point (40,1200)
1200 = 30(40) + b
y=30x+b
For point (52,1560)
1560 = 30(52) + b
The correct equation is
1560 = 30(52) + b
Answer: It is C
Step-by-step explanation:
math
graph y=3/4x+2 on a graph
Answers
Explanation:
Here is a picture:
In the diagram, AC and PR are vertical lines, while CB is a horizontal line segment. If CR : RB = 2 : 3, what are the coordinates of point Q? A. (-2, -4) B. (-1, -5) C. (-3, -3) D. (0, -6)
Answers
Answer:
A. (-2,-4)
Step-by-step explanation:
If CR:RB is 2:3, and C is (-4,-7), then R is (-2,-7)
You can stop here because only A has the x value as -2.
If you want to look at the y value also, -4 is 2/5 of the way between -2 and -7, which has the same 2:3 proportion.
WILL MARK BRAINLIEST PLEASE HELP!!!!! in your own words what does it mean to have one solution in a liner equation what does it mean to have no solutions in a liner equation what does it mean to have infinite solutions in a liner equation
Answers
Answer:
One solution: When the graphs intersect at one point
No solution: This means that the lines are parallel or that there is no answer to the equation
Infinite solutions: This means that any value for the variable would make the equation true
Step-by-step explanation:
THE ANSWER IS NOT 12 OR 36 SO DO THE RSM ANSWER PLS ASAP PLS OH PLS 0-0 a * b=ba−ba+ab, find (2*3)×(3*2).
Answers
72 if * is exponents
Solve |3x + 9| + 6 = 6 Question 5 options: A) x = 3 B) x = 3 or x = –3 C) No solutions D) x = –3
Answers
Answer:
Hey there!
We have |3x + 9| + 6 = 6. Subtracting 6 from both sides gives us |3x + 9| = 0.
3x+9=0
3x=-9
x=-3
Hope this helps :)
Answer:
-3
Step-by-step explanation:
Subtracting 6 from both sides yields |3x + 9| = 0. For this to be true, 3x + 9 must be 0, and so x must be -3.
A rectangle on a coordinate plane is translated 5 units up and 3 units to the left. Which rule describes the translation?
O (x,y) - (x + 5, y-3)
(x, y) - (x + 5, y + 3)
(x,y) - (x-3, y + 5)
O (x,y) - (x + 3, y + 5)
Answers
Answer:
[tex](x,y)\rightarrow(x-3,y+5)[/tex]
Step-by-step explanation:
"5 units up" would be "5 added to the current y-value".
"3 units to the left" would be "3 subtracted from the current x-value".
So, the translation rule is:
[tex](x,y)\rightarrow(x-3,y+5)[/tex]
Therefore, Option C should be the correct answer.
Brainilest Appreciated.
The Rule describes the translation is : (x, y) - (x - 3, y + 5)
We have a rectangle on a coordinate plane is translated 5 units up and 3 units to the left.
We have to determine which of the given rules describes the translation.
A point P(3, 3) is translated 10 units up and 4 units to the left. What will be the new coordinates of this point P?The new coordinates of this point P will be - P'( - 1, 13).
According to the question, we have -
Upward translation = 5 units
When the upward translation will take place then, each and every point that lies on that rectangle will have its y - coordinate shifted upwards by +5 units.
Leftward Translation = 3 units
When the leftward translation will take place then, each and every point that lies on that rectangle will have its x - coordinate shifted by - 3 units
to the left.
Hence, rule describes the translation is : (x, y) - (x - 3, y + 5).
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If you're good at bearings pls help mee
What is the true bearing of Milton from Binji?
Answers
The leading 0 is important with true bearings. Any true bearing must be three digits.
======================================================
Explanation:
It's not stated, but I'm assuming that Binji and Congo form a flat horizontal line.
B = Binji's location
M = Milton's location
C = Congo's location
The given angles are M = 76 and C = 38. The missing angle is
B = 180-M-C
B = 180-76-38
B = 66
Subtract this from 90 to get 90-66 = 24
The true bearing of Milton from Binji is 024 degrees
In other words, if you are at Binji's location, face directly north, and turn 24 degrees clockwise (turn to the right), then you'll be facing Milton's location.
-------------
Extra info:
In terms of compass notation, the true bearing of 024 degrees converts to N 24 E. This is the same as E 66 N, though convention usually has north used more often (since it's a common reference point with compasses).
N 24 E = start facing north, turn 24 degrees to the east
E 66 N = start facing east, turn 66 degrees to the north
Two ants, Andy and Ashley, went to visit their friend. Andy crawled the whole way, but Ashley spent half of the way riding on a caterpillar, which was two times slower than crawling. Ashley spent the second half of the journey riding on a grasshopper, which was 5 times faster than crawling. Which ant got to their friend's house first, if they left at the same time? PLZ EXPLAIN IT VERY SIMPLE
Answers
Answer:
Andy
Step-by-step explanation:
Ashely rode the caterpillar till the half of her journey. And Andy crawled all the way.
Crawling is twice as fast as riding the caterpillar, so by the time Ashley got to the half of her journey, Andy would have already reached their friends house.
Answer:
Andy
Step-by-step explanation:
Please see attached picture for full solution.
Two passenger trains traveling in opposite directions meet and pass each other. Each train is 1/12 mi long and is traveling 50 mph. How many seconds after the front cars of the trains meet will their rear cars pass each other?
Answers
Answer:
6 seconds
Step-by-step explanation:
Total distance between the 2 rear cars = [tex]\\\frac{1}{12} + \frac{1}{12} = \frac{1}{6}\\\\\\\\\\Relative speed of the trains = 50 + 50 = 100 mphT = \frac{Distance}{Speed} = \frac{1}{6} * \frac{1}{100} = \frac{1}{600} hours\\T = \frac{1}{600} hours or \frac{3600}{600} = 6 seconds[/tex]
Mr. Weaver invested part of his $6000 inheritance in an account that earns 4%
simple interest and the other part in an account that earns 7% simple interest.
How much did he invest in each account if the two accounts earned $360 after
the first year?
Answers
Answer:
Mr. Weaver invested $ 2,000 in the 4% simple interest account and $ 4,000 in the 7% simple interest account.
Step-by-step explanation:
1. Let's review the information given to us to answer the question correctly:
Amount of the inheritance = $ 6,000
Interest rate of the first part = 4% simple
Interest rate of the second part = 7% simple
Interest of the accounts after the first year = $ 360
2. How much did he invest in each account?
For answering the question, we will use the following equation:
x = Amount invested in the first account
6,000 - x = Amount invested in the second account
0.04x + 0.07 * (6,000 - x) = 360
0.04x + 420 - 0.07x = 360
-0.03x = 360 - 420 (Subtracting 420 at both sides)
-0.03x = -60
x = -60/-0.03
x = 2,000 ⇒ 6,000 - x = 4,000
Mr. Weaver invested $ 2,000 in the 4% simple interest account and $ 4,000 in the 7% simple interest account.
what is the nth term of this sequence 7, 9, 11, 13
Answers
Answer:
The nth term of the sequence is
5 + 2nStep-by-step explanation:
The sequence above is an arithmetic sequence
For an nth term in an arithmetic sequence
A(n) = a + ( n - 1)d
where a is the first term
n is the number of terms
d is the common difference
From the question
a = 7
d = 9 - 7 = 2 or 11 - 9 = 2
So the nth term for the sequence is
A(n) = 7 + ( n - 1)2
= 7 + 2n - 2
A(n) = 5 + 2nHope this helps you
is the graph increasing decreasing or constant
Answers
Step-by-step explanation: aumentado pois ele define uma certa quantidade de aumentação
A
Andrea has a $25 gift card
to a art store. She buys four
canvases that are each the same
price. If she now has $2.20 on
her gift card,
what was the price of
each canvas?
Equation:
Solution:
Answers
Answer:
$5.70
Step-by-step explanation:
First we have to find out how much she spent. SO we do 25-2.20 which is 22.80. Then we have to divide by 4 since she buys four canvases that are the same price. SO 22.80/4=$5.70
Answer: 5.70
Step-by-step explanation:
Gift card = 25
Canvases = x
Since Andrea is buying four canvases, we can say that it is 4x.
Remaining balance = 2.20
Let's set up our equation. To set it up, we can write it like this
4x+2.20= 25
Now, subtract 2.20 on each side
4x = 22.8
Now divide, and you get around 5.70
So, each canvas was $5.70
If one factor of 6.x2 + 5x – 6 is
3.x - 2, the other factor is
A.
3.x + 3
B. 6x + 3
C. 2x + 3
D. 2.x - 3
Answers
You have many ways to solve this!
You could...
A) multiply all the answer choices by 3x-2 and see what matches
B) Factor the trinomial
C) Divide the trinomial by the binomial using long division
Which of the following relations is not a function? x y 0 1 1 4 -1 4 x y 0 2 1 3 1 -3 x y 0 -2 1 -3 -2 5 x y 0 -2 1 -2 2 -2
Answers
Answer:
-1 4 x y
Step-by-step explanation:
Alice is building a caterpillar habitat for some caterpillars she found in her back yard. She plans to cover all sides of the habitat with screen so the caterpillars get plenty of fresh air. What is the total amount of screen that Alice will need for her habitat? Give an exact answer (do not round).
Answers
Answer:
3.04 m²
Step-by-step explanation:
Surface Area =0.8x0.4 = 0.32 (two of these - one on each end)
1x0.4=0.4 (two of these - top and bottom) (Strange to cover bottom with screen, but have to follow the directions.)
1x0.8=0.8 (two of these - front and back)
TOTAL = 0.32+0.32+0.4+0.4+0.8+0.8=3.04
Total amount of screen that Alice will need for her habitat is 3.04 meter square
What is Surface area?The surface area of a solid object is a measure of the total area that the surface of the object occupies.
Given,
Dimensions of the Caterpillar habitat is,
Width w=1 meter
Length l= 0.4 meter
Height h= 0.8 meter
Surface area = 2lw+2lh+2hw
=2×0.4×1+2×0.4×0.8+2×0.8×1
=0.8+0.64+1.6
=3.04 meter square
Hence, Total amount of screen that Alice will need for her habitat is 3.04 meter square
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Which of the following is equivalent to log34
Answers
hope it helps u...
plz mark as brainliest...
A 2-digit number is increased by 36 when the digits are reversed. The sum of the digits is 10. What is the original number?
Answers
====================================================
Work Shown:
T = tens digit of the original number
U = units digit of the original number
U+T = 10 since the digits add to 10. Solve for U to get U = 10-T
10T+U = original number
10U+T = new number where digits are reversed
-----------
new number = (old number) + 36
10U+T = (10T+U)+36
10U+T = 10T+U+36
10(10-T)+T = 10T+10-T+36 ... plug in U = 10-T
100-10T+T = 10T+10-T+36
-9T+100 = 9T+46
100-46 = 9T+9T
54 = 18T
18T = 54
T = 54/18
T = 3 is the tens digit of the original number
U = 10-T
U = 10-3
U = 7 is the units digit of the original number
10T+U = 10*3+7 = 30+7 = 37 is the original number
73 is the reversed number.
73-37 = 36 is the difference, showing that 37 increased by 36 leads to 73. The answer is confirmed.
Answer:
37
Step-by-step explanation:
phillp asked 100 students they favourite crisps out of ready salted, cheese and onion, and salt and vinegar. 35 students are boys 12 of these boys liked cheese and onion the best 9 girls liked ready salted the best 25 out of 41 students woh liked salt and vinger the best were girls work out the total number of students who liked ready salted the best.
Answers
Answer:16 students liked ready salted
Step-by-step explanation:
35 students = boys
65 students = girls
Boys:
12/35 like cheese and onion
16/35 like salt and vinegar
7/35 like ready salted
Girls:
9/65 like ready salted
25/65 like salt and vinegar
31/65 like cheese and onion
Solve for x .........
Answers
Answer:
x = 29/20 or x = 1.45
Step-by-step explanation:
6/x + 5/(4x) = 5
Multiply all terms by x and cancel.
6 + 5/4 = 5x
Combine terms on the left side of the equation.
29/4 = 5x
Divide both sides by 5.
29/4/5 = (5x)/5
29/20 = x
Answer:
x = 29/20Step-by-step explanation:
[tex] \frac{6}{x} + \frac{5}{4x} = 5[/tex]
Multiply through by the LCM
The LCM of x and 4x is 4x
So we have
[tex] {4x} \times \frac{6}{x} + {4x} \times \frac{5}{4x} = 5 \times {4x} \\ \\ 24 + 5 = 20x \\ \\ 20x = 29 \\ \\ x = \frac{29}{20} \: \: \: or \: \: \: 1 \frac{9}{20} [/tex]
Hope this helps you
A basket of fruit contains 4 bananas, 3 apples, and 5 oranges. You intend to draw a piece of fruit from the basket, keep it, and then draw a 2nd piece of fruit from the basket. What is the probability of selecting two oranges in a row from the basket if you are blindfolded?
Answers
Answer:
5:12 or 4:11
Step-by-step explanation:
there are a total of 12 pieces of fruit including 5 oranges the first draw then on the second draw there are now 11 total pieces of fruit and 4 oranges
A submarine is only allowed to change its depth by rising toward the surface in 60 meter stages. If the submarine starts off at 340 meters below sea level, what is its depth after 4 stages of rising to the surface.
Answers
Answer:
100
Step-by-step explanation:
340 - (4 * 60) = 100
The depth of the submarine after 4 stages of rising to the surface will be 100 meters.
What is an expression?Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
It is given that a submarine is only allowed to change its depth by rising toward the surface in 60-meter stages. The submarine starts off at 340 meters below sea level.
The depth of the submarine after 4 stages will be calculated as below:-
depth = 4 x 60 = 240
depth from the surface = 340 - 240 100 meters
Therefore, the depth of the submarine after 4 stages of rising to the surface will be 100 meters.
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solve and answer the following prism
Answers
Answer:
1st) Surface Area = 178.7 cm²
Volume = 105 cm³
2nd) Surface Area = 51 m²
Volume = 15 m³
Step-by-step explanation:
1st) 1/2x2.5x7=8.75 (2 of these - one on each end)
7x12=42
12x2.5=30
12x7.433=89.20
S.A=8.75+8.75+42+30+89.2=178.7
Volume=8.75x12=105
2nd) 1/2x3x2=3 (two of these - one on each end)
5x4=20
5x3=15
5x2=10
S.A.=3+3+20+15+10=51
Volume = 3x5=15
What is the x-coordinate of point P on the coordinate grid?
Answers
Answer:
-3/2
Step-by-step explanation:
We have to see where the point lies, check the x-axis from the graph.
(-3/2, 1/2)
x = -3/2
-3/2
Step-by-step explanation:
We have to see where the point lies, check the x-axis from the graph.
(-3/2, 1/2)
x = -3/2
Using everyday knowledge, indicate whether the if-then statements are correct forward-only or both forward and reverse.
Statement 1: If Bo is Mel's sibling, then Melis Bo's sibling.
Statement 2: If the sprinklers are on, then the grass is wet.
Answers
Answer:
1. Both forward and backward
2. Only forward
Step-by-step explanation:
The reason Statement 1 can be both forward and reverse is because is Bo and Mel are related then it will word forward and backward.
The reason Statement 2 can be only forward is because is the sprinklers are on then the grass is wet will work since it is saying ONLY the sprinklers are on. If it is reverse and the grass is wet if the sprinklers are ONLY on than that is false since if it rains than the grass can also be wet. So there are multiple ways that the grass can be wet hence the answers.
Answer:
Using everyday knowledge, indicate whether the if-then statements are correct forward-only or both forward and reverse. Statement 1: If Bo is Mel’s sibling, then Mel is Bo’s sibling. / Statement 2: If the sprinklers are on, then the grass is wet.
Step-by-step explanation:
Which of the following are accurate descriptions of the distribution below?
Answers
Answer:
the most years of experience is 2, and the least years are 10 years
Step-by-step explanation:
Hi . I need help with the question below and the one in the picture.
(1.) Four girls shared a certain sum of money. The first received ½ of it , The second received ¼ and the third received 1/5 of it . If the fourth girl received 25 Kobo , what was the original sum of money.
(a). N6.00
(b). N5.00
(c). N4.50
(d). N3.50
(e). N2.50
Note : 100kobo = N1
Workings Please.
Answers
Answer:
1) N5.00
2) N1.50
Step-by-step explanation:
1) 1/2+1/4+1/5=10/20+5/20+4/20=19/20=95%
That means the 4th girl received 5%.
25 is 5% of 500
500 Kobo is N5.00
2) He lost 55%, so they means he has 45% left.
67.5 is 45% of 150
(67.5/0.45=150)
150Kobo is N1.50