What is the average rate of change of the function below on the interval [0, 0.5]?
F(x)= x^2+7x+10/ x^2 - 7x+6
A. 8.333
B. 6.333
C. 7.666
D. 6.667
Answers
Answer:
add all the numbers and divide by 4
Step-by-step explanation:
Answer:
D
Step-by-step explanation:
F(0)= 0^2+7(0)+10/ 0^2 - 7(0)+6 = 1.67
F(0.5)= 0.5^2+7(0.5)+10/ 0.5^2 - 7(0.5)+6 = 5
\(RateofChange = \frac{F(0.5) - F(0)}{0.5 - 0} = 6.667\)
Related Questions
The graph of the function f(x) = (x - 3)(x + 1) is shown.
Ty
-10-8-6
10
8
6
-6
8
-10-
6
10
X
Which describes all of the values for which the graph is
positive and decreasing?
O all real values of x where x < -1
O all real values of x where x < 1
O all real values of x where 1
O all real values of x where x > 3
Answers
Answer:
all real values of x where x < -1
The correct statement is all real values of x where x < -1.
Option A is the correct answer.
We have,
To determine the values for which the graph of the function
f(x) = (x - 3)(x + 1) is positive and decreasing, we need to analyze the behavior of the function.
Let's consider the factors individually:
(x - 3): This factor is positive for x > 3 and negative for x < 3.
(x + 1): This factor is positive for x > -1 and negative for x < -1.
To determine the overall sign of the function, we need to consider the signs of both factors together.
When both factors are positive or both factors are negative, the function is positive.
When the factors have opposite signs, the function is negative.
From the above analysis, we can conclude the following:
When x > 3, both factors are positive, so the function is positive.
When -1 < x < 3, the factor (x - 3) is negative, while the factor (x + 1) is positive. Therefore, the function is negative.
When x < -1, both factors are negative, so the function is positive again.
Since we are looking for values where the function is positive and decreasing, we can eliminate the options that include positive and increasing regions (such as x > 3).
Thus,
The correct statement is all real values of x where x < -1.
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identify the transformation of the following functions from the parent function f(x)= 1/x
Answers
The parent function is the simplest form of the type of function in the graph is g(x) = 1/x
What is graph ?
In mathematics, a graph is a collection of points, called vertices, and lines, called edges, that connect the vertices. Graphs are used to represent networks of communication, data organization, computational devices, the flow of computation, and more. Graphs are one of the most fundamental concepts in mathematics, and they are used to model many real-world problems and situations.
The transformation from the first equation to the second one can be found by finding a, h and k for each equation.
y = a / x-h + k
Find a, h and k for
g(x)= 1/x
a = 1
h=0
k = 0
The horizontal shift depends on the value of h and The horizontal shift is described as :
f(x) = f(x+h) The graph is shifted to the left h units
f(x) = f(x-h) The graph is shifted to the right h units.
Horizontal shift depends on the value of k and The horizontal shift is described as :
f(x) = f(x+k) The graph is shifted to up k units
f(x) = f(x-k) The graph is shifted down k units.
Vertical shift : none.
The sign of a describes the reflection across the x-axis. −a means the graph is reflected across the x-axis.
Reflection about the x-axis: None
To find the transformation, compare the two functions and check to see if there is a horizontal or vertical shift, reflection about the x-axis, and if there is a vertical stretch.
Parent Function: g(x) = 1/x
Horizontal Shift: None
Vertical Shift: None
Reflection about the x-axis: None
Hence, The parent function is the simplest form of the type of function g(x) = 1/x .
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please help it's due tomorrow
Answers
Answer:
B. -414,720 x⁷y⁶
Step-by-step explanation:
To find the 4th term of the expansion of (2x - 3y²)¹⁰, we can use the binomial theorem.
The binomial theorem states that for an expression of the form (a + b)ⁿ:
\(\displaystyle (a+b)^n=\binom{n}{0}a^{n-0}b^0+\binom{n}{1}a^{n-1}b^1+...+\binom{n}{r}a^{n-r}b^r+...+\binom{n}{n}a^{n-n}b^n\\\\\\\textsf{where }\displaystyle \rm \binom{n}{r} \: = \:^{n}C_{r} = \frac{n!}{r!(n-r)!}\)
For the expression (2x - 3y²)¹⁰:
a = 2xb = -3y²n = 10Therefore, each term in the expression can be calculated using:
\(\displaystyle \boxed{\binom{n}{r}(2x)^{10-r}(-3y^2)^r}\quad \textsf{where $r = 0$ is the first term.}\)
The 4th term is when r = 3. Therefore:
\(\begin{aligned}\displaystyle &\;\;\;\;\:\binom{10}{3}(2x)^{10-3}(-3y^2)^3\\\\&=\frac{10!}{3!(10-3)!}(2x)^7(-3y^2)^3\\\\&=\frac{10!}{3!\:7!}\cdot2^7x^7(-3)^3y^6\\\\&=120\cdot 128x^7 \cdot (-27)y^6\\\\&=-414720\:x^7y^6\\\\ \end{aligned}\)
So the 4th term of the given expansion is:
\(\boxed{-414720\:x^7y^6}\)
11. Martin's suitcase has a volume of 1,080 cubic inches. Lily's suitcase measures 9 inches wide, 13 inches long, and 21 inches high. What is the combined volume of the two suitcases?
Answers
Answer: 3,348 cubic inches
Step-by-step explanation:
1. Since we know that volume= length x width x height, then we can plug our values into this equation.
2. So, we would do volume= 9 x 12 x 21.
3. 9 x 12 = 108, and 108 x 21 =2,268.
4. Now that we have both of the volumes, we have to add them together.
5. 1,080 + 2,268 = 3,348
6. The combined volume is 3,348 cubic inches.
Please explain how to do the equation to get 10 units.
Answers
9514 1404 393
Answer:
the equation comes from setting expressions for the perimeters equal to each other
Step-by-step explanation:
Each of the relations is described in terms of the shortest side of the triangle, which is what we're asked to find. It makes sense to let a variable represent that length.
shortest triangle side: s
each of the other two sides: s+1
perimeter of the triangles: s +(s+1) +(s+1) = 3s+2
__
side length of square: s-2
perimeter of square : 4(s -2) = 4s -8
__
The two perimeters are equal, so we have ...
3s +2 = 4s -8 . . . . . your equation
10 = s . . . . . . . . . . . add 8-3s
What the meaning of "A one-to-one function of P onto Q is an isomorphism of P and Q"?
Answers
A one-to-one function (also known as an injective function) from set P to set Q is an isomorphism between sets P and Q if and only if itis a function and also has a unique element.
How to explain the informationIt is a function: For every element p in set P, there exists a unique element q in set Q such that the function maps p to q.
It is a one-to-one function: For every pair of distinct elements p1 and p2 in set P, the corresponding images in set Q, denoted as f(p1) and f(p2) respectively, are also distinct. In other words, the function does not map two different elements of P to the same element of Q.
If a function from P to Q satisfies these conditions, it is said to be a one-to-one function of P onto Q and can be considered an isomorphism between the two sets.
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simplify 15a^2 * 4c * 5ab
Answers
Answer: 300a^3cb
Step-by-step explanation:
\($$Simplify the following:$$15 \times 4 \times 5 a^{2} c a b$$$$\begin{aligned}&15 a^{2} \times 4 c \times 5 a b=15 a^{2+1} \times 4 c \times 5 b: \\ \\&15 \times 4 \times 5 a^{2+1} c b\end{aligned}$$$$\begin{aligned}&2+1=3 \\ \\&15 \times 4 \times 5 a^{3} c b \end{aligned}$$$$\begin{aligned}&15 \times 4=60 \\ \\&60 \times 5 a^{3} c b\end{aligned}$$$$60 \times 5=300$$Answer:$$300 a^{3} c b$$\)
49, 34, and 48 students are selected from the sophomore, junior, and senior classes with 496, 348, and 481 students respectively.
Answers
The sampling used in this situation is Stratified sampling
In the question, students are selected from subgroups of Sophomore, Junior, and Senior classes.
We are told that 49, 34, and 48 students are selected from the Sophomore, Junior, and Senior classes with 496, 348, and 481 students respectively.
This means that the sample numbers of 49, 34 and 48 students were selected in proportion to the subgroup sizes of 496, 348, and 481 students respectively.
Thus, due to the fact that subgroups were selected & that sample number of students were also selected in proportion to their respective subgroup sizes.
This is, therefore, a stratified sampling.
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Q: 49, 34, and 48 students are selected from the Sophomore, Junior, and Senior classes with 496, 348, and 481 students respectively. Identify which type of sampling is used and why?
If there is a 4:6 ratio of dogs to cats in the store. What percentage of the store are dogs?
Answers
Answer:
40 % dogs
Step-by-step explanation:
if ratio = 4:6
the store =10:0
10=100%
1=10%
4=40%
6=60%
40:60
40%:60%
Look at the two graphs. Make two statements that compare/contrast the two graphs.
Answers
Answer:
both same as in the diffecnce of the number of addition
Step-by-step explanation:
What is the sale price of a shirt that was originally 25$ but was marked down by 33%?
Answers
Answer:
16.75
Step-by-step explanation:
33% of $25 is 8.25 You would do 25 - 8.25 = 16.75.
Answer:
13%
Step-by-step explanation:
PLEASE HELP ASAP!!! WILL GIVE BRALIEST!!
Answers
Answer:
Bree hikes for 4 kilometers per hour
Answer:
D
Step-by-step explanation:
x represents time and y represents disrtance in relation to time.
(when you look at 1 sec you can tell that the y value is 4 meaning that the realtion is y=4x)
The diagonals of the parallelogram are 10 and 12. One of its sides is 9 cm. Find the second side.
Answers
Answer:
6.4 cmStep-by-step explanation:
Given:
d₁ = 10 cmd₂ = 12 cma = 9 cmb = ?We know that the sum of squares of diagonals of the parallelogram is equal to twice the sum of the squares of the sides:
d₁² + d₂² = 2(a² + b²)Substitute the values and solve for b:
10² + 12² = 2(9² + b²)100 + 144 = 2(81 + b²)122 = 81 + b²b² = 41b = √41b = 6.4 cmThe sum of two numbers is 41. The larger number is 17 more than the smaller number. What are the numbers?
Larger number:
Smaller number:
Answers
Let x - 17 = the smaller number
x + x + 17 = 41
2x + 17 = 41
2x = 58
x = 29
x - 17 = 29 - 17 = 12
A coral reef grows 0.14 m every week. How much does it grow in 13 weeks?
Answers
Answer: 1.82 m
Step-by-step explanation:
Ratios
0.14 n 0.14 x 13 = 1.82
1. 13 1.82/1 = 1.82
What is one fifth of twenty more than half
of 80?
(A) 8
(B) 10
(C) 12
(D) 13
Answers
Answer:
(C) 12
Step-by-step explanation:
To solve this problem, we can use the following steps:
Find half of 80: 80/2 = 40
Add 20 to half of 80: 40 + 20 = 60
Find one fifth of the result: 60/5 = 12
Therefore, one fifth of twenty more than half of 80 is equal to 12. The correct answer is (C) 12.
Answer:
(C) 12
Step-by-step explanation:
What is one fifth of twenty more than half of 80
0.5 × 80 = 40
What is one fifth of twenty more than half of 80
40 + 20 = 60
What is one fifth of twenty more than half of 80
1/5 × 60 = 60/5 = 12
Consumer Price Index, 1970-2002
Year
1970
1975
1980
1985
1990
1995
2002
Source: World Almanac 2003
CPI
116.3
161.2
248.8
322.2
391.4
456.5
535.8
Describe how the CPI is related to the year.
As the year increases, the CPI decreases and then increases.
As the year increases, the CPI increases and then decreases.
As the year increases, the CPI decreases.
d. As the year increases, the CPI increases.
C.
a.
b.
Answers
The computation of the increased in salary is $500.
Here, we have,
Explanation:
Data provided in the question
Salary for the first year = $50,000
CPI increase during the year = 4%
Overstated inflation = 1% i.e. 5%
The computation of the increased in salary is shown below:
= Salary of the first year × inflation rate - salary of the first year × CPI increase during the year
= $50,000 × 5% - $50,000 × 4%
= $2,500 - $2,000
= $500
Hence, The computation of the increased in salary is $500.
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complete question:
Mark's wage contract specifies a $50,000 salary for the first year, and specifies a salary increase equal to the percentage increase in the CPI during the second year. The increase in the CPI during the year was 4.0%. If the CPI overstates inflation by 1.0% (that is, the actual price increase was 3% and not 4%), at the end of the first year Mark's salary increased by $________ more than it would have without the upward bias.
You can drive 300 miles in 5 hours. At this rate, how long will it take you to drive 150 miles?
Answers
Answer:
2.5 hours
Step-by-step explanation:
The ratio - 300: 5 is the same as 60:1
150:x should equal 60:1
You divide 150 by 60 to get your answer
Answer:
2.5 hours
Step-by-step explanation:
Just divide 5 by 2 to get the same ratio! Hope this helps
17.
Peter transports metal bars in his van.
The van has a safety notice: "Maximum Load 1200 kg".
Each metal bar has a label: "Weight 60 kg".
For safety reasons, Peter assumes that:
1200 is rounded correct to 2 significant figures, and
60 is rounded correct to 1 significant figure.
Calculate the greatest number of bars that Peter can safely put into the van if his assumptions are
correct.
Answers
Answer:
17 bars
Step-by-step explanation:
Peter wants to compute the maximum number of bars he can load safely if the load limit of 1200 kg and the bar weight of 60 kg are each rounded to the number of significant digits those numbers have.
Range of valuesThe error in a rounded number is assumed to be as much as half of the least significant digit of the number.
Peter's load limit may actually be as low as ...
1200 kg - (1/2)(100 kg) = 1150 kg . . . . . . . 1200 is rounded to nearest 100
Peter's bar weight might be as high as ...
60 kg + (1/2)(10 kg) = 65 kg . . . . . . . . . . . 60 is rounded to nearest 10
Safe loadingIf Peter has maximum-weight bars and does not want to exceed the minimum his load limit might be, the number of bars he can load is ...
(1150 kg) / (65 kg/bar) ≈ 17.7 bars
The greatest number of bars Peter can load safely is 17.
1 1/7 over 3/5
Please help
Answers
1 19/21 answer to your problem
Need urgent help with this question, thanks.
Answers
Answer:
Step-by-step explanation:
Oli and Katrina are buying a new SUV. The sticker price is $47,500. They talked to their bank (loan A) and were offered a 6 year loan at 4.5% annual interest, resulting in monthly payments of $754.02. The dealership (loan B) claims the couple will pay less interest with them because the loan is shorter, 5 years, and the interest rate is barely higher at 6%, resulting in a monthly payment of $918.31.
Answers
Answer:
Following are the answer to this question:
Step-by-step explanation:
In the given equation some information is missing, that is Loans "A and B".
Formula:
\(\bold{Total \ Payback = \ Montly \ instalment \times \ Number \ of \ Instalments} \\\\\)
calculating total amount of Loan A:
\(= $754.02 \times 72\\\\= 54289.44\)
calculating total amount of Loan B:
\(= $918.31 \times 60\\\\= 55098.6\)
Calculate loan A:
\(\bold{ \ Int = \ Total\ Payment - \ Loan}\\\\\)
\(= $ 54289.44 - $ 47500\\\\= $ 6789.44\)
Calculate loan B:
\(\bold{ \ Int = \ Total\ Payment - \ Loan}\\\\\)
\(= $ 55098.60 - $ 47500\\\\= $ 7598.60\)
The Additional value of the Int in loan B:
\(\bold{= \ Int \ in \ loan \ B - \ Int \ in \ loan \ A}\)
\(= 7598.6 - 6789.44\\\\= 809.16\)
Solve for x. See the image below!
Answers
Answer:
x = 17
Step-by-step explanation:
in such a constellation (two beams from the same point of origin cut through the same circle) the relative relation between the segments of these beams to the overall length of the beam have to be the same :
7 × (7+x) = 8 × (8+13)
49 + 7x = 8 × 21 = 168
7x = 119
x = 17
Joanna needs a book to prop up a table leg. There are 8 Math books, 4 science books, and 5 history books. She
randomly selects a book, removing it from the shelf, and then selects another book. What is the probability that
Joanna selected two math books?
Answers
Answer:22% or 64/289
Step-by-step explanation: you take 8/17 which is math books over the total of books and multiply it together. simplify into a percent (if thats allowed)
8/17 x 8/17 = 64/289
The difference of two trinomials is ___________ a trinomial.
Answer choices:
Always
Sometimes
Never
Answers
Answer:sometimes
Step-by-step explanation:
Create an exponential function that models this situation based on the time in secons in the video.
B(t)= __
Answers
Answer:
B(t) = 2*\(2^{t}\)Step-by-step explanation:
You have all correct choices.
We can use the given values and work out the equation:
B(t) = \(ab^{t}\)B(0) = 2 ⇒ a*b⁰ = 2 ⇒ a = 2B(1) = 4 ⇒ a*b¹ = 4 ⇒ 2b = 4 ⇒ b = 2The function for this situation is:
B(t) = 2*\(2^{t}\)Answer:
2(2)^t
Step-by-step explanation:
PLATO
Which of the following equations represents a linear function?
x = 3
y = 3x2
y equals negative one third times x plus 1
3x − 4 = 7
Answers
The Linear function is y equals negative one third times x plus 1
A linear function is a function that has a constant rate of change, meaning that as one variable (usually x) increases or decreases by a certain amount, the other variable (usually y) also changes by a constant amount.
Out of the four given equations, the only one that represents a linear function is the third one:
y equals negative one third times x plus 1
This is because the equation has a constant rate of change of -1/3 for any change in x. For example, if we increase x by 3, y will decrease by 1 (because 3*(-1/3) = -1). Similarly, if we decrease x by 3, y will increase by 1. This constant rate of change is what makes the equation represent a straight line when graphed.
The other three equations do not represent linear functions.
The first equation, x = 3, is not a function at all because there are multiple possible y values for the given x value of 3.
The second equation, y = 3x2, is a quadratic function because it contains an x2 term, which means that the rate of change of y with respect to x is not constant.
The fourth equation, 3x - 4 = 7, is a linear equation but not a function because for any given x, there is only one corresponding value of y. However, when the equation is solved for y, it becomes y = 3x - 3, which represents a linear function with a constant rate of change of 3.
The linear function is y equals negative one third times x plus 1
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change the given time measure to its equaivalent unit.
1.15 minutes=___seconds
2.5 days=___hours
3.120 hours=_____days
4.how many months are they in 60 days? ___?months
5.how many days there in 2 years?____
Answers
Answer:
1,900seconds 2,120hours 3,5hours 4,2months 5,720days
Step-by-step explanation:
1,15*60=900seconds
2,5*24=120hours
3,1day=24h
? 120h
120/24=5hours
4,2months
5,360*2=720days
Based on the pattern above, how many squares will be in step 4?
15
16
20
25
Answers
Part 1: 12% annual interest on 132000 for 8 days
Part 2: 12% annual interest on 106,750 for 20 days.
If it helps, it's a 5 year note. Assuming 365 days in a year.
Answers
The interest for Part 1 is approximately $385.10.
The interest for Part 2 is approximately $709.31.
To calculate the interest for Part 1 and Part 2The formula is as follows:
Interest is calculated as follows: Principal * Rate * Time
Where
Principal represents the starting sumThe interest rate is rateTime measures length in years.Part 1:
$132,000 is the principal.
(Decimal) Rate = 12% = 0.12
Time = 8 days/365 days.
How much interest is there in Part 1?
Interest is calculated as follows : $132,000 * 0.12 * (8/365) = $385.10
Therefore, the interest for Part 1 is approximately $385.10.
Part 2:
$106,750 as the principal
(Decimal) Rate = 12% = 0.12
Time = 20 days / 365 days.
How much interest will there be in Part 2
Interest is calculated as follows : $106,750 * 0.12 * (20/365) = $709.31
Therefore, the interest for Part 2 is approximately $709.31.
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