Answer:
The average rate of change of the function in this interval is of 18.
Step-by-step explanation:
The average rate of change of a function [tex]f(x)[/tex] in an interval from a to b is given by:
[tex]A = \frac{f(b) - f(a)}{b - a}[/tex]
In this question:
[tex]f(x) = x^2 + 6x[/tex]
Where x goes from 5 to 7.
This means that [tex]b = 7, a = 5[/tex]. So
[tex]f(7) = 7^2 + 6(7) = 49 + 42 = 91[/tex]
[tex]f(5) = 5^2 + 6(5) = 25 + 30 = 55[/tex]
The rate of change is:
[tex]A = \frac{f(7) - f(5)}{7 - 5} = \frac{91 - 55}{2} = 18[/tex]
The average rate of change of the function in this interval is of 18.
The rate of change of a function over a given interval is required.
The average rate of change is 18
Rate of changeThe given function is
[tex]f(x)=x^2+6x[/tex]
The interval is between [tex]x=5[/tex] to [tex]x=7[/tex]
Finding the corresponding [tex]y[/tex] values
[tex]y=5^2+6\times 5=55[/tex]
[tex]y=7^2+6\times 7=91[/tex]
The two points are
[tex](5,55),(7,91)[/tex]
The slope is
[tex]m=\dfrac{\Delta y}{\Delta x}\\\Rightarrow m=\dfrac{91-55}{7-5}\\\Rightarrow m=18[/tex]
Learn more about rate of change:
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An audio cable is 14.7 dm long. How long is the cable in meters?
Answer:
1.47
Step-by-step explanation:
It's quite easy to calculate, one decimeter is equal to 0.1 meters!
Find the volume of the cube
Answer:
You just do 3/4 × 3/4 × 3/4 to find the volume. the answer would be 27/64 in fraction form. in decimal form it would be 0.421875
Answer:
0.421875 if its wrong sorry
Step-by-step explanation:
What is the distance from 0 to point g on the number line
Answer:
?
Step-by-step explanation:
The steps of the scientific method are listed below. Check the box next to each step of the scientific method that you think communication plays an important role in.
Answer: all of them
Step-by-step explanation:
A DEPOSIT OF $600 EARNS 2.5% INTEREST FOR 6 YEAR?
Answer: $73.80 in interest over a 6 year period
Step-by-step explanation:
600*0.0205= 12.30*6=73.80
Answer:
Step-by-step explanation:
if you have 600 dollars in the bank, and 2.5% interest
600*2.5/100=15 dollars per year
6*15=90 dollars interest in 6 years
Triangle ABC has vertices A (0, 2), B (5, 4), and C (5, 0). Triangle A′B′C′ has corresponding vertices A′ (–5, –1), B′ (0, 1), and C′ (0, –3). Which of the following describes a translation that would produce triangle A′B′C′ from the pre-image of triangle ABC?
Question options:
A) To the left five units, down three units.
B) To the right five units, up three units.
C) To the right five units, down three units.
D) To the left five units, up three units.
Answer:
B
Step-by-step explanation:
Ava planned to paint 5 flowerpots. She painted 4 already. What percentage of her work is complete?
O 75%
O 80%
O 20%
O 50%
Answer:
80%
Step-by-step explanation:
4/5 = .8
.8 = 80%
Colin needs to save at least $200 for homecoming. He works 2 jobs earning $9/heur at Wawa and $25/hour mowing lawns. He only has time to work 16 hours before
homecoming.
Answer:
he would need to mow lawns for 8 hours
Step-by-step explanation:
Write an example of the Commutative Property of Multiplication.
help pleassssssseeee
Answer:
Commutative property: When two numbers are multiplied together, the product is the same regardless of the order of the multiplicands. For example 4 * 2 = 2 * 4 Associative Property: When three or more numbers are multiplied, the product is the same regardless of the grouping of the factors. For example (2 * 3) * 4 = 2 * (3 * 4)
What is the value of the expression below when w=3w=3?
10w^2 +9w-2
10w
2
+9w−2
Answer:
i dont know sorry
Step-by-step explanation:
but hi :3 how are you
A factory packed 85 teddy bears into large boxes for delivery to a toy store. Each large box held 9 teddy bears. The remaining bears was packed into a small box. How many teddy bears were packed in the small box. what i am asking is what the remainder for this question.
Answer:
9.4
Step-by-step explanation:
85/9=9.4...
I put ... at end because it continues forever the 4s I hoped I helped
Airlines A and B each operate one flight per day between the cities of Hartford and Chicago; the daily passenger volume between the two cities is 350. Because the quality of service and departure times for both airlines are similar, we assume that passengersselect the flights with equal probability and independently of one another.
Required:
a. Let X denote the number of passengers on the flight operated by airline A. Describe the exact distribution of X; name it and identify the parameters.
b. If the plane for airline A carries 210 seats there is a positive probability that more than 210 passengers will turn up, in which case not all passengers can be accommodated. Estimate the probability of "overbooking"
c. Denote by n the minimum number of seats the aircraft should contain if it is desired that the probability of exceeding the seating capacity be less than 0.01. Find n
Answer:
X ~ (350, 0.5)
0.00009
Step-by-step explanation:
Given that:
Daily passenger volume = 350
Since both airlines A and B have equal probability ;
p = 0.5
n = 350
X ~ (n, p)
X ~ (350, 0.5)
B.)
Mean, m= np = 350 * 0.5 = 175
Standard deviation, s = sqrt(np(1-p)) = sqrt(350*0.5*0.5) = sqrt(87.5)
Obtaining standardized score, Z
Z = (x - m) / s
x = 210
Z = (210 - 175) / sqrt(87.5)
Z = 35 / sqrt(87.5)
Z = 3.74
P(Z > 3.74) = 0.00009 (Z probability calculator)
Calculate and express your answer in decimal form: 1/2 x 17 *
Answer:
8.5
Step-by-step explanation:
I need the simplified expression for this please
Answer:
4x + 8
Step-by-step explanation:
1. 4(2x + 4) Multiply 2x by 4 to get 8x. Multiply 4 by 4 to get 16. You should now have the equation 8x + 16 / 2.
2. Divide the 8x and 16 by 2. You should get 4x and 8. (4x + 8).
The volleyball coach wants to buy new warm-up suits for her team. The suits cost $20. The coach has $210. How many warm-up suits can she buy?
Answer:
100
Step-by-step explanation:
because 20×10=$200
Answer:
10 suit
Step-by-step explanation:
she can buy 10 suit
210 divide 20 is 10.5
but since half aren't counted
it just 10 suit
Simplify the ratio 9:12
Four more than twice a number is the same as 8 less than three times the same
number. What is the number?
Answer:
Step-by-step explanation:
Please Help :) Thanks!
Answer:
it's C
Step-by-step explanation:
You have to plug in the inputs into the n variable to get your answer/output.
Answer:
Step-by-step explanation:
f(n)= 3n+2
hence
1) for n= -2
f(-2) = 3(-2)+2 =-6+2= -4
2) for n= -1
f(-1) = 3(-1)+2 =-1
3) for n=0
f(0)=3(0)+2 = 2
4) for n=1
f(1) =3(1)+2 =5
5) for n=2
f(2)=3(2)+2 =8
Hence "C" option is correct
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Which of the following expressions represents the distance between -2 and 1?
Pls help!!!
If John and Peter share some money in the ratio 3:4, what fraction of the money does John receive?
Answer:
So 3/7 is the fraction of the money John received.
Step-by-step explanation:
3:4, so John is 3 and Peter is 4.
Now add these up for the denominator which is 3+4=7
and put Johns value over it, Johns value is 3.
So 3/7 is the fraction of the money John received.
i giveeeeeeeeeeeeeeeee brainlilstttttt
Answer:
I think the answer is b or c
Answer:
It's the first one
Step-by-step explanation: give me brainlist LOL
HELP ME PLEASE!!! this dosent make sense
Answer:
I think it would be D not sure tho hope this is helpful
Answer:
B
Step-by-step explanation:
The correct answer is B because in A and C, the gray area is not under the blue line since y has to be less than the equation. It is not D because the equation does not have a negative slope and in this inequality, it is also not equal to. Because the line in D is not a dotted line, then you know it is also equal to.
63 = 7(c + 2)
so c = what
Answer:
c=7
Step-by-step explanation:
63=7c+14
49=7c
7=c
c=7
Maximum carrying capacity
Express (x+8)squared as a trinomial in standard form
Step-by-step explanation:
(x + 8)²
= (x + 8)(x + 8)
= x² + 2(x)(8) + 8²
= x² + 16x + 64.
The binomial expression (x + 8)² is converted into trinomial in standard form x² + 16x + 64.
What is a polynomial?A polynomial expression is an algebraic expression with variables and coefficients. Unknown variables are what they're termed. We can use addition, subtraction, and other mathematical operations. However, a variable is not divisible.
The expression is given below.
⇒ (x + 8)²
Simplify the expression, then we have
⇒ (x + 8)²
⇒ x² + 8² + 2·8·x
⇒ x² + 16x + 64
The binomial expression (x + 8)² is converted into trinomial in standard form x² + 16x + 64.
More about the polynomial link is given below.
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Simplify sin^2y/sec^2 y−1 to a single trigonometric function
Answer:
[tex] \frac{ { \sin}^{2} y}{ { \sec}^{2}y - 1 } = { \cos }^{2} y[/tex]
Step-by-step explanation:
We know that [tex] { \tan }^{2} y = { \sec }^{2} y - 1[/tex]
Also , [tex] { \tan}^{2} y = \frac{ { \sin }^{2} y}{ { \cos }^{2}y } [/tex]
So ,
[tex] \frac{ { \sin }^{2}y }{ { \sec }^{2}y - 1 } = \frac{ { \sin}^{2} y}{ { \tan }^{2} y} = \frac{ { \sin }^{2}y }{ \frac{ { \sin}^{2} y}{ { \cos}^{2}y } } = { \cos }^{2} y[/tex]
What does "of" mean in a persent question
Answer:
existing or occurring now
What quantity is being measured: 54ON
Answer:
Force
Step-by-step explanation:
The n at the end stands for newtons and this is the measurement for force.
HOPE THIS HELPED
It can be helpful to classify a differential equation, so that we can predict the techniques that might help us to find a function which solves the equation. Two classifications are the order of the equation -- (what is the highest number of derivatives involved) and whether or not the equation is linear . Linearity is important because the structure of the the family of solutions to a linear equation is fairly simple. Linear equations can usually be solved completely and explicitly. Determine whether or not each equation is linear:
Answer:
The equations are not given but the clue to your answer is given below:
Step-by-step explanation:
So the question above talks generally about differential equations (equations whose derivatives can be found) and then describes them thus - the order of a differential equation and the linearity status of a differential equation.
To determine whether or not each of the absent equations is linear, check for the following characteristics of linearity:
1. The maximum number or power that any variable in a linear equation is raised to is 1.
Example: 2x² + 6y = 43y is NOT a linear equation because some or all (in this case, variable x) of the variables in it are raised to a power greater than 1. Variable x is raised to the power of 2.
2. An equation (a linear equation, in this case) contains an 'equal to' sign. This is the reason why it's called an equation. There is a mathematical expression on each side of the equal to sign. Take note of this, just incase one of the options in your question has no equal to sign.
Example: 2x + 6y is NOT a linear equation. It is a linear expression. It contains no equal to sign that compares two distinct mathematical expressions.
3. A linear equation usually has not more than two variables. It is not complex or difficult to solve.
Example: 2x + 6y = 43z is NOT a linear equation.
— 3 + 5 + 6g = 11 – 3g
Given : −3 + 5 + 6g = 11 − 3g
To find : The variable g
Solution:
Isolate and solve for the variable g in the equation −3 + 5 + 6g = 11 − 3g
Steps:
−3 + 5 + 6g = 11 − 3g
2 + 6g = 11 − 3g
6g = −3g + 9
9g = 9
g = 1
Hence,
Answer: g = 1