Answers
Answer:
The average rate of change of the function [tex]g(x)=x^2+10x+18[/tex] over the interval [tex]-11 \leq x\leq -1[/tex] is -1
Step-by-step explanation:
We are given the function [tex]g(x)=x^2+10x+18[/tex] over the interval [tex]-11 \leq x\leq -1[/tex]
We need to find average rate of change.
The formula used to find average rate of change is : [tex]Average \ rate \ of \ change=\frac{g(b)-g(a)}{b-a}[/tex]
We have b=-1 and a=-11
Finding g(b) = g(-1)
[tex]g(x)=x^2+10x+18\\Putting \ x=-1\\g(-1)=(-1)^2+10(-1)+18\\g(-1)=1-10+18\\g(-1)=9[/tex]
Finding g(a) = g(-11)
[tex]g(x)=x^2+10x+18\\Putting \ x=-11\\g(-11)=(-11)^2+10(-11)+18\\g(-1)=121-110+18\\g(-1)=29[/tex]
Finding average rate of change
[tex]Average \ rate \ of \ change=\frac{g(b)-g(a)}{b-a}\\Average \ rate \ of \ change=\frac{9-29}{-1-(-11)}\\Average \ rate \ of \ change=\frac{-10}{-1+11}\\Average \ rate \ of \ change=\frac{-10}{10}\\Average \ rate \ of \ change=-1[/tex]
So, the average rate of change of the function [tex]g(x)=x^2+10x+18[/tex] over the interval [tex]-11 \leq x\leq -1[/tex] is -1
Related Questions
jerry bought 5 candy bars for $14.75. if the king size candy bar cost $3.75 and a regular size candy bar cost $1.75, how much of each candy bar did he buy?
one equation looks like:
3.75x+1.75y=14.75
Answers
Answer:
King size(x): 3
Regular size(y): 2
Steps:
System of Equations:
x+y = 5
3.75x+1.75y = 14.75
Multiply 3.75 on all sides.
3.75x+3.75y = 18.75
3.75x+1.75y = 14.75
Subtract top and bottom
2y = 4
/2 /2
y = 2
After you know regular size amount, figure out king size ----3.
5-2 = 3.
Decide whether the pair of lines is parallel, perpendicular, or neither.
Ly: 2x + 3y = 8
L2:3x + 2y = 7
Choose the correct answer below.
A. The lines are neither parallel nor perpendicular.
B. The lines are perpendicular.
C. The lines are parallel.
Answers
Answer:
A
Step-by-step explanation:
We can solve for y for both of the lines' equations to get the point-slope form.
L1: [tex]y=\frac{-2}{3} x+\frac{8}{3}[/tex]
L2:[tex]y=\frac{-3}{2}x+\frac{7}{2}[/tex]
So, the slopes of the two lines are [tex]\frac{-2}{3}[/tex] and [tex]\frac{-3}{2}[/tex].
Remember that parallel lines have the same slope, and perpendicular lines have opposite and reciprocal slopes. These slopes are reciprocal but not opposite.
Hope this helps!
Help me Please!!!!! I will give brainliest to the person who does it first
Answers
Answer:
5x + 3y - 4
This expression has three terms (5x, 3y, and -4), 2 different variables (x and y), and a constant (-4)
Step-by-step explanation:
#teamtrees #WAP (Water And Plant)
Round 958.989730738 to the nearest hundred
Answers
Answer:
958.990
Step-by-step explanation:
958.990 is the Round off to the nearest hundred.
What is rounding a number to some specific place?Rounding some number to a specific value is making its value simpler (therefore losing accuracy), mostly done for better readability or accessibility.
Rounding to some place keeps it accurate on the left side of that place but rounded or sort of like trimmed from the right in terms of exact digits.
The digit 5 acts as a limit.
If the digit on right is 5, and after it there is only zeros or no value, then we round up (increase by 1, as we did in 347500 -> 34800 ) (Well there are many detailed rules of rounding)
WE have to Round 958.989730738 to the nearest hundred.
Hence, 958.990 is the Round off to the nearest hundred.
Learn more about rounding numbers here:
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-3x - 4y = 5
- 2x + 3y = -8
Answers
Answer:
x = 1 ,y = -2
Step-by-step explanation:
Solve the following system:
{-4 y - 3 x = 5 | (equation 1)
3 y - 2 x = -8 | (equation 2)
Subtract 2/3 × (equation 1) from equation 2:
{-(3 x) - 4 y = 5 | (equation 1)
0 x+(17 y)/3 = -34/3 | (equation 2)
Multiply equation 2 by 3/17:
{-(3 x) - 4 y = 5 | (equation 1)
0 x+y = -2 | (equation 2)
Add 4 × (equation 2) to equation 1:
{-(3 x)+0 y = -3 | (equation 1)
0 x+y = -2 | (equation 2)
Divide equation 1 by -3:
{x+0 y = 1 | (equation 1)
0 x+y = -2 | (equation 2)
Collect results:
Answer: {x = 1 ,y = -2
In the figure below, points J, K, and L are the midpoints of the sides of AXYZ.
Suppose JK=38, X2=96, and YX=56.
Find the following lengths.
Answers
Answer:
28 ; 76 ; 38
Step-by-step explanation:
KL = [tex]\frac{XY}{2}[/tex] = [tex]\frac{56}{2}[/tex] = 28 units
YZ = 2 × JK = 38 × 2 = 76 units
LZ = 76/2 = 38 units
The lengths are: KL = 28 units, YZ = 76 units and LZ= 38 units.
What is Mid point theorem?The line segment in a triangle connecting the midpoint of two sides of the triangle is said to be parallel to its third side and is also half the length of the third side, according to the midpoint theorem.
Given:
J, K, and L are the midpoints of the sides of ΔXYZ.
JK=38, X2=96, and YX=56.
Now, using Mid point theorem
JK= 1/2 YZ
38 = 1/2 YZ
YZ= 2 x 38
YZ = 76 units.
and, KL= 1/2 YX
KL = 1/2(56)
KL= 28
LZ = 1/2 (YZ)
LZ = 1/2(76)
LZ = 38 units
Learn more about Mid point theorem here:
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24 21 is 60% of what number?
Answers
Answer:
could u explain it better
Answer: either I don't remember if you use the % or the number ok
Hope this helps
2421 × 60 = 145260
2421 × 60% = 1452.6
Step-by-step explanation:
What is the average rate of change of the function f(x) = 2x2 + x + 5 over the interval −2 ≤ x ≤ 2?
A. −4 B. −1 C. 1 D. 4
Answers
Answer:
d
Step-by-step explanation:
The average rate of change the function f(x) = 2x² + x + 5 is 1.
So, Option C is correct.
The average rate of change
The average rate of change in a function is the rate at which one value changes with respect to another value.
Given function: [tex]f(x)=2x^2+x+5[/tex] on interval [tex][-2,2][/tex]
Therefore,
Average rate of change = [tex]\frac{f(2)-f(-2)}{2-(-2)}[/tex]
[tex]f(2)=2(2)^2+2+5\\f(2)=15\\f(-2)=2(-2)^2-2+5\\f(2)=11[/tex]
Substitute the values,
Average rate [tex]=\frac{15-11}{2+2}[/tex]
Average rate [tex]=\frac{4}{4}[/tex]
Average rate [tex]=1[/tex]
So, the average rate of change is [tex]1[/tex]
Option C is correct.
Find out more information about the average rate of change here:
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the table shows the number of calories jane burns while exercising. How many calories would she burn for 29 minutes. Explain. Please help me! if u don't know this then don't answer!
Answers
Answer:
319
Step-by-step explanation:i just did it
I am having trouble understanding this: Sam bought 86 pounds of flour for his bakery. Every day he used the same amount of flour to make bakery items. After 10 days, Sam was left with 25.2 pounds of flour. On average, how many pounds of flour did Sam use each day?
A. 3.01 Pounds
B. 5.65 Pounds
C. 6.08 Pounds
D. 11.12 Pounds
Please also include an explanation. Thanks!
Answers
Answer:
the average amount of flour used each day=6.08 pounds
Step-by-step explanation:
Sam bought 86 pounds of flour for his bakery.
Every day he used the same amount of flour to make bakery items.
After 10 days, Sam was left with 25.2 pounds of flour.
Now we are asked to find the average pounds of flour that Sam used each day.
Total amount of flour used=86-25.2=60.8 pounds.
As he used the flour equal amount each day for 10 days.
So, the average flour used each day=
amount of flour used/ number of days=60.8/10=6.08.
the average amount of flour used each day=6.08 pounds
Answer:
C
Step-by-step explanation:
So since Sam have 25.2 leftover pounds of flour, we can subtract that from 86, knowing that will be left over in the end. Next, we divide the number left. 86 - 25.2 = 60.8
Finally, divide that by 10, since there are 10 days.
We end up with 6.08 pounds.
If (x+k) 2 (x+2) = x² +14x²+60x+72
Find the value of k.
I will give brainliest
Answers
George C.
Jul 24, 2018
(
x
+
2
)
(
x
+
6
)
2
=
0
Explanation:
Given:
x
3
+
14
x
2
+
60
x
+
72
=
0
By the rational roots theorem, any rational zeros of the given cubic are expressible in the form
p
q
for integers
p
,
q
with
p
a divisor of the constant term
72
and
q
a divisor of the coefficient
1
of the leading term.
That means that the only possible rational zeros are:
±
1
,
±
2
,
±
3
,
±
4
,
±
6
,
±
8
,
±
9
,
±
12
,
±
18
,
±
24
,
±
36
,
±
72
In addition, note that all of the coefficients are positive and the constant term is non-zero. As a result, any real zero (rational or otherwise) of this cubic must be negative.
So that leaves rational possibilities:
−
1
,
−
2
,
−
3
,
−
4
,
−
6
,
−
8
,
−
9
,
−
12
,
−
18
,
−
24
,
−
36
,
−
72
We find:
(
−
2
)
3
+
14
(
−
2
)
2
+
60
(
−
2
)
+
72
=
−
8
+
56
−
120
+
72
=
0
So
x
=
−
2
is a zero and
(
x
+
2
)
a factor:
x
3
+
14
x
2
+
60
+
72
=
(
x
+
2
)
(
x
2
+
12
x
+
36
)
Without trying any more of our "possible" zeros, we can recognise the remaining quadratic factor as a perfect square trinomial:
x
2
+
12
x
+
36
=
x
2
+
2
(
x
)
(
6
)
+
6
2
=
(
x
+
6
)
2
So the factored form of the given cubic equation can be written:
(
x
+
2
)
(
x
+
6
)
2
=
0
An amount of $2,535.00 is deposited in a bank paying annual interest rate of 5.3% compounded quarterly find the balance after 3 years
Answers
$134.35 per year x 3 years = $406.05
$2,535.00 + $406.05 = $2,941.05
Answer : $2,941.05
Answer:
2968.78
Step-by-step explanation:
took the test
Which of these is an example of a literal equation?
A. 6+ 30 = 62
B. 3x - 4y
C. 12 = 9 + 3x
D. ax - by=k
Please help
Answers
A literal equation is an equation with more than one variable. It consists primarily of letters. Another example of a literal equation is A=1/2h(a+b).
Hope this helps!
My subtotal at the bookstore came to $11.76. What is my total with 7% sales tax added on? SHOW UR WORK
Answers
X=7% find the 7%
$11.76/100*7=$0.8232
Round it and it’s $0.82
$11.76+$0.82=$12.58 the total
Independent activity 4
Ano po sagot
Answers
9514 1404 393
Answer:
A, B, C, E, D
F, G, H, I, J
Step-by-step explanation:
You can go at this a couple of ways.
Consider the squares of number 1 through 9.
[tex]\begin{array}{cccccccccc}n&1&2&3&4&5&6&7&8&9\\n^2&1&4&9&16&25&36&49&64&81\end{array}[/tex]
Then when the number under the radical is close to n², the root on the number line will be close to n.
The other way you can do this is to find the square root using your calculator.
√10 ≈ 3.2 ⇒ A√35 ≈ 5.9 ⇒ B√48 ≈ 6.9 ⇒ C√71 ≈ 8.4 ⇒ E√54 ≈ 7.3 ⇒ D√19 ≈ 4.4 ⇒ F√89 ≈ 9.4 ⇒ G√6 ≈ 2.4 ⇒ H-√20 ≈ -4.5 ⇒ I-√2 ≈ -1.4 ⇒ JBrainlest - pls help thank you sm in advance
Answers
Answer
17
Step-by-step explanation:
hope this helps
Chang knows one side of a triangle is 13 cm. Which set of two sides is possible for the lengths of the other two sides of this triangle?
05 cm and 8 cm
06 cm and 7 cm
0 7 cm and 2 cm
O 8 cm and 9 cm
Answers
Answer:
8 cm and 9 cm
Step-by-step explanation:
a + b > 13
1). 5 + 8 = 13
2). 6 + 7 = 13
3). 7 + 2 = 9 < 13
4). 8 + 9 = 17 > 13
15,000,015,969+5,000,003
Answers
The sum of 2 numbers is 15 and their difference is 1. What are the 2 numbers?
Answers
Answer:
7 & 8
Step-by-step explanation:
they are one integer apart, and if you add the two up, it makes 15
Hope this helps!
Please tell me if I am wrong.
Have a good day!
Working together, Candice and Ximena painted a fence in 8 hours. Last year, Ximena painted the fence by herself. The year before, Candice painted it by herself, but took 12 hours less than Ximena took. How long did Candice and Ximena take, when each was painting alone?
Answers
Answer: Time taken by Ximena to paint the fence alone = 24 hours
Time taken by Candice to paint the fence alone = 12 hours
Step-by-step explanation:
Let x= Time taken by Ximena to paint the fence alone .
Time taken by Candice to paint the fence alone = x-12
As per given , we have
[tex]\dfrac{1}{x}+\dfrac{1}{x-12}=\dfrac{1}{8}\\\\\Rightarrow\ \dfrac{x-12+x}{x(x-12)}=\dfrac{1}{8}\\\\\Rightarrow\ 8(2x-12)=x^2-12x\\\\\Rightarrow\ 16x-96=x^2-12x\\\\\Rightarrow\ x^2-12x-16x+96=0\\\\\Rightarrow\ x^2-28x+96=0\\\\\Rightarrow\ x^2-4x-24x+96=0\\\\\Rightarrow\ x(x-4)-24(x-4)=0\\\\\Rightarrow\ (x-4)(x-24)=0\\\\\Rightarrow x=4, 24[/tex]
if x= 4
Time taken by Ximena = 4 hours
Time taken by Candice = 4-12 hours =-8 hours which is not possible. (time cannot be negative)
Therefore, x= 24
Such that
Time taken by Ximena to paint the fence alone = 24 hours
Time taken by Candice to paint the fence alone = 24-12=12 hours
In a fruit cocktail, for every 18 ml of orange juice you need 3 ml of apple juice and 54 ml of coconut milk. What is the ratio of apple juice to coconut milk to orange juice expressed in its simplest form?
Answers
Answer:
1:18:6
Step-by-step explanation:
3:54:18
This equals 1:18:6
Find the solution(s) to the system of equations. Select all that apply.
y= x2 - 4
y=-x-2
A. (-2,0)
B. (0-4)
C. (1, -3)
D. (2,0)
Answers
The solution to a system of equations is where the lines intersect, which are: A. (-2,0) C. (1, -3)
What is the Solution to a System of Equations?When a system of equations is represented on a graph, the solution to the system of equations is simply the coordinates of the points where the line of the equations intersect.
Thus, the lines intersect at (-2,0) and (1, -3). Therefore, the solution to the system of equations are: A. (-2,0) C. (1, -3)
Learn more about the solution to a system of equations on:
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Find the new amount given the original amount and the percent of change. 28 members; 50% decrease
Answers
y=−2/9x+3 in standard form using integers
Answers
subtract 3 and subtract y
-2/9x -y = -3
Multiply all by -9 to make integer
2x+9y = 27
93.34 divided my what equals 18.69
Answers
Answer:
4.99411449973
Step-by-step explanation:
Easy math! Just divide 93.34 by 18.69
Answer:
4.99411449973
Step-by-step explanation:
You can divide those two numbers together and to check just divide 93.34 by 4.99411449973 and you get 18.69
A foreign country uses the stellar as its currency. Before a trip to that country, Mia wants to exchange $1700 to steller's. Which of Bank A and Bank B has the better exchange rate? How many more steller's would she get if she exchanged her $1700 at the better exchange rate instead of at the other rate?
Answers
Answer and explanation:
Stellar is a Brazilian cryptocurrency that is used to facilitate low cost and flexible payment. It was renamed lumens and is denoted XLM.
One stellar lumen is currently equal to $0.219096
For the purpose of the question and since it does not specify exchange rates for each bank, let's assume:
Bank A= 0.219097 to 1 US dollar
Bank B= 0.219099 to 1 US dollar
Using Bank A to exchange $1700 for stellars= $1700*0.219097= 372.464 stellars
Using Bank B to exchange $1700 for stellars= $1700*0.229042= 389.3714 stellars
From the above, we can see that Bank B has a better exchange rate as it is cheaper than Bank A(gives more stellar) . She should therefore use Bank B for her exchange.
How to solve 2x2-6+10/2=
Pleasee answer this because this is super extrimely hard
THANK YOU....
Answers
Answer:
3
Step-by-step explanation:
2*2=4
10/2=5
+-6
4-6=-2+5=3
who will donate pets on adopt me only answer if you will please?
Answers
Answer:
I can, it depends on what kind of pets tho
Bob and Carl each rented the same kind of moving truck from EZ Move. There was a flat rental fee plus a charge per mile that the truck was driven. Bob's cost for his truck was $112.96 for 138 miles. Carl's cost for his truck was $142.78 for 209 miles. Which equation can be used to represent the cost of the rental truck? Round to the nearest hundredth if necessary.
Answers
Answer:
Total cost= 55 + 0.42*x
x= miles driven
Step-by-step explanation:
Giving the following information:
Bob's cost for his truck was $112.96 for 138 miles.
Carl's cost for his truck was $142.78 for 209 miles.
To calculate the fixed cost and variable cost per mile, we need to use the high-low method:
Variable cost per unit= (Highest activity cost - Lowest activity cost)/ (Highest activity units - Lowest activity units)
Variable cost per unit= (142.78 - 112.96) / (209 - 138)
Variable cost per unit= $0.42 per mile
Fixed costs= Highest activity cost - (Variable cost per unit * HAU)
Fixed costs= 142.78 - (0.42*209)
Fixed costs= $55
Fixed costs= LAC - (Variable cost per unit* LAU)
Fixed costs= 112.96 - (0.42*138)
Fixed costs= $55
Finally, the cost equation:
Total cost= 55 + 0.42*x
x= miles driven
Answer:
The answer is D
Step-by-step explanation:
MATH MIDDLE SCHOOL HELP PLS ASAP
what is y? put the correct answer
Answers
Answer:
The -2 was not distributed properly. -2 should have been multiplied by 7 and -y, which is -14 + 2yy = 3I hope this helps!