Given the function defined in the table below, find the average rate of change, in simplest form, of the function over the interval ≤ x ≤ 9.
Answers
The average rate of change is given by the rate of change of both variables.
"Rate" refers to a division. We want to divide the change of y, Δy, by the change of x, Δx:
Δy/Δx
("Δ" means "change").
We want to analyze the change over the interval 3 ≤ x ≤ 9.
Step 1: change of x (Δx)The change from x = 3 and x = 9 is
Δx = 9 - 3 = 6
Step 2: change of y (Δy)We observe the right column of the table. When x = 3, y = 28 and when x = 9, y = 4.
The change from y = 28 to y = 4 is
Δy = 4 - 28 = -24
Step 3: rate of changeThen, the average rate of change is:
Δy/Δx = -24/6 = -4
Answer: -4
Related Questions
Use the Distributive Property to solve the equation 2/3 (9a + 6) = 23.8
Answers
Distributive property tell us how to solve expressions in the form a(b+c), it says:
a(b+c)=ab+ac
Then,
[tex]\begin{gathered} \frac{2}{3}(9a+6)=23.8 \\ \frac{18a}{3}+\frac{12}{3}=23.8 \\ 6a+4=23.8 \\ 6a=23.8-4 \\ a=\frac{19.8}{6}=3.3 \end{gathered}[/tex]What is 4x+10(2x) - 8x
Answers
4x+10(2x) - 8x
First, multiply to solve the parentheses:
4x+20x-8x
Add and subtract
16x
Write problem as a single radical using the smallest possible root. 20
Answers
Answer::
[tex]\sqrt[30]{r^{29}}[/tex]Explanation:
Given the expression:
[tex]\sqrt[5]{r^4}\sqrt[6]{r}[/tex]First, rewrite the expression using the fractional index law:
[tex]\begin{gathered} \sqrt[n]{x}=x^{\frac{1}{n}} \\ \implies\sqrt[5]{r^4}=r^{\frac{4}{5}};\text{ and} \\ \sqrt[6]{r}=r^{\frac{1}{6}} \end{gathered}[/tex]Therefore:
[tex]\sqrt[5]{r^4}\times\sqrt[6]{r}=r^{\frac{4}{5}}\times r^{\frac{1}{6}}[/tex]Use the multiplication law of exponents:
[tex]\begin{gathered} a^x\times a^y=a^{x+y} \\ \implies r^{\frac{4}{5}}\times r^{\frac{1}{6}}=r^{\frac{4}{5}+\frac{1}{6}} \\ \frac{4}{5}+\frac{1}{6}=\frac{24+5}{30}=\frac{29}{30} \\ \operatorname{\implies}r^{\frac{4}{5}}\times r^{\frac{1}{6}}=r^{\frac{4}{5}+\frac{1}{6}}=r^{\frac{29}{30}} \end{gathered}[/tex]The resulting expression can be rewrittem further:
[tex]\begin{gathered} r^{\frac{29}{30}}=(r^{29})^{\frac{1}{30}} \\ =\sqrt[30]{r^{29}} \end{gathered}[/tex]The single radical is:
[tex]\sqrt[30]{r^{29}}[/tex]Tiffany works at a lawnmower store.Part AA portion of Tiffany's monthly salary is based on commission. She earns 21% of everything she sells. This month she sold $27,000 worth of lawnmowers. Howmuch was her sales commission this month?Part BThe store purchased one riding lawn mower for $1,500 and sold it for $2025. What percentage was the markup for the mower?PartTiffany earns $15 per hour. The store offers her a raise-a 2% increase per hour. After the raise, how much will Tiffany make per hour?
Answers
1) Gathering the data
Part A
Tiffany's Commission: 21%
Sales Revenue: 27,000
2) In this case, we can figure out how much has she earned by doing this:
[tex]27,000\text{ }\times0.21=5,670[/tex]Part B)
$1,500
$ 2,025
We can solve it in 2 steps. Firstly let's find the equivalence of 2025 in percentage.
1500-------100%
2025- ----x
1500x = 202500
x=202500/1500
x =135%
Now we need to subtract from 100%. 135%-100%= 35%
So the percentage (markup) was 35%. That lawnmower was sold 35% above the price.
Part C)
$15 per hour
2% per hour (0.02)
In this, case we need a simple calculation multiplying that 15 by (1 +0.02)
15 x ( 1 +0.02)
15 x (1.02)
15.3
After the raise, Tiffany earns $15.30 per hour
Harry fills up his Jeep with gasoline and notes that the odometer reading is 23,529.6 miles. The next time he fills up his Jeep, he pays for 10 gallons of gasoline he notes his odometer reading is 23,640.6 miles. How many miles per gallon did he get? (Round the answer to the nearest 10th if necessary.)
Answers
Answer:
11.1 miles per gallon
Explanation:
Given;
Odometer reading when the jeep is filled up with gasoline = 23,529.6 miles
Odometer reading when the jeep is filled up with 10 gallons of gasoline =23,640.6 miles
We can now go ahead and determine how many miles per gallon Harry got as seen below;
[tex]\begin{gathered} \frac{(Reading\text{ when j}eep\text{ is filled with 10 gallons }-Reading\text{ when j}eep\text{ is filled up)}}{\text{Gallo of gasoline}} \\ =\frac{23640.6-23529.6}{10}=\frac{111}{10}=11.1\text{miles per gallon} \end{gathered}[/tex]So Harry got 11.1 miles per gallon
Rewrite each equation in slope intercept form . Then determine whether the lines are perpendicular . Explain your answer .. y - 6 = - 5/2 (x + 4) 5y = 2x + 6
Answers
y - 6 = - 5/2 (x + 4)
To write in slope-intercept form means to write in the form;
y= mx + b
where m is the slope and b is the intercept
y - 6 = - 5/2 (x + 4)
open the parenthesis
y - 6 = -5/2 x - 10
add 6 to both-side of the equation
y = - 5/2 x - 10 + 6
y = -5/2 x - 4
[tex]y=-\frac{5}{2}x\text{ - 4}[/tex]Next is to check whether 5y = 2x + 6 is perpendicular to the above
To do that, we have to make the equation to be in the form y=mx+ b
5y = 2x + 6
Divid through by 5
y = 2/5 x + 6/5
[tex]y\text{ = }\frac{2}{5}x\text{ + }\frac{6}{5}[/tex]The slope of perpendicular equation, when multiply gives minus one (-1)
The slope of the first equation = -5/2
The slope of the second equation is 2/5
Multiplying the two slopes;
(-5/2) (2/5) = -1
Hence the lines are perpendicular
complete the table of ordered pairs for the linear equation. 5x+8y=3
Answers
Given:
5x+8y=3
The objective is to fill the table using the given values of x otr y.
Let's take that, x=0 and substitute in the given equation.
[tex]\begin{gathered} 5x+8y=3 \\ 5(0)+8y=3 \\ 0+8y=3 \\ y=\frac{3}{8} \end{gathered}[/tex]Hence, the the required solution will be (0,3/8).
Let's take that, y=0 and substitute in the given equation.
[tex]\begin{gathered} 5x+8y=3 \\ 5x+8(0)=3 \\ 5x+0=3 \\ x=3-5 \\ x=-2 \end{gathered}[/tex]Hence, the the required solution will be (-2,0).
Let's take that, y=1 and substitute in the given equation.
[tex]\begin{gathered} 5x+8y=3 \\ 5x+8(1)=3 \\ 5x+8=3 \\ 5x=3-8 \\ 5x=-5 \\ x=-\frac{5}{5} \\ x=-1 \end{gathered}[/tex]Hence, the the required solution will be (-1,1).
I have a question about how to solve graphing a system of inequalities and about how to do the (0,0)
Answers
The given system of inequality is
[tex]\begin{gathered} 2x-3y>-12 \\ x+y\ge-2 \end{gathered}[/tex]At first, we must draw the lines to represent these inequalities
[tex]2x-3y=-12[/tex]Let x = 0, then find y
[tex]\begin{gathered} 2(0)-3(y)=-12 \\ 0-3y=-12 \\ -3y=-12 \\ \frac{-3y}{-3}=\frac{-12}{-3} \\ y=4 \end{gathered}[/tex]The first point is (0, 4)
Let y = 0
[tex]\begin{gathered} 2x-3(0)=-12 \\ 2x-0=-12 \\ 2x=-12 \\ \frac{2x}{2}=\frac{-12}{2} \\ x=-6 \end{gathered}[/tex]The second point is (-6, 0)
We will do the same with the second line
Let x = 0
[tex]\begin{gathered} 0+y=-2 \\ y=-2 \end{gathered}[/tex]The first point is (0, -2)
Let y = 0
[tex]\begin{gathered} x+0=-2 \\ x=-2 \end{gathered}[/tex]The second point is (-2, 0)
Since the sign of the first inequality is >, then the line will be dashed
Since the sign of the second inequality is >=, then the line will be solid
Let us substitute x, y by the origin point (0,0) in both inequalities to find the shaded part of each one
[tex]\begin{gathered} 2(0)-3(0)>-12 \\ 0-0>-12 \\ 0>-12 \end{gathered}[/tex]Since the inequality is true then the point (0, 0) lies on the shaded area
[tex]\begin{gathered} 0+0\ge-2 \\ 0\ge-2 \end{gathered}[/tex]Since the inequality is true, then point (0, 0) lies in the shaded area
Let us draw the graph
The red line represents the first inequality
The blue line represents the second inequality
The area of two colors is the area of the solution
Point (0, 0) lies in this area, then it is a solution for the given system of inequalities
Given the function f(x)={4x+7 if x<0 6x+4 if x>0 _
Answers
Given:
[tex]f(x)=\begin{cases}4x+7ifx<0{} \\ 6x+4ifx\ge0{}\end{cases}[/tex]Required:
To find the value of f(-8), f(0), f(4), and f(-100)+f(100).
Explanation:
f(-8) :
Clearly -8<0,
So
[tex]\begin{gathered} f(x)=4x+7 \\ f(-8)=4(-8)+7 \\ =-32+7 \\ =-25 \end{gathered}[/tex]f(0) :
Clearly 0=0,
[tex]\begin{gathered} f(x)=6x+4 \\ =6(0)+4 \\ =4 \end{gathered}[/tex]f(4) :
Clearly 4>0,
[tex]\begin{gathered} f(x)=6x+4 \\ f(4)=6(4)+4 \\ =24+4 \\ =28 \end{gathered}[/tex]f(-100)+f(100) :
-100<0
[tex]\begin{gathered} f(x)=4x+7 \\ f(-100)=4(-100)+7 \\ =-400+7 \\ =-393 \end{gathered}[/tex]100>0
[tex]\begin{gathered} f(x)=6x+4 \\ f(100)=6(100)+4 \\ =600+4 \\ =604 \end{gathered}[/tex][tex]\begin{gathered} f(-100)+f(100)=-393+604 \\ \\ =211 \end{gathered}[/tex]Final Answer:
[tex]\begin{gathered} f(-8)=-25 \\ \\ f(0)=4 \\ \\ f(4)=28 \\ \\ f(-100)+f(100)=211 \end{gathered}[/tex]Find the missing factor. x2 - 11x + 18 = (x - 2)( .) Enter the correct answer. 000 DONE Clear all DOO
Answers
we have the second degree polynomial
[tex]x^2-11x+18[/tex]we must find two numbers a,b such that
[tex]\begin{gathered} x^2-11x+18=(x+a)(x+b)\text{ and} \\ a+b=11 \\ ab=18 \end{gathered}[/tex]We can see that, a=-2 and b=-9 fulfill the above conditions. Therefore, we have
[tex]x^2-11x+18=(x-2)(x-9)\text{ }[/tex]The con 3720bertar What can be interpreted from the youtercept of the functionRachel must pay $37 per month to use the gymRachel must pay $20 per month to use the gymRachel must pay a $37 membership fee to join the gymRachel must pay a $20 membership fee to join the samMaria wants to rent a car. She learns that the total daily costcated using the formula C = 5x + 30. hereseS driven that day. What does the constanteseer
Answers
f(x) = 37x + 20
Answer:
Option D, $20 is the membership beause it is a fixed cost, it does not depend on the amount of months
What Is the inverse of.. (ignore pencil writing) -matrices- (there may be more than one answer
Answers
To find the inverse of the matrix, first let's find the determinant:
[tex]\begin{gathered} |A|\text{ = 3(2) - 5(1)} \\ |A|\text{ = 6 - 5} \\ |A|\text{ = 1} \end{gathered}[/tex]Then, we'll find the Adjunct of the matrix:
[tex]\begin{gathered} \begin{bmatrix}{3} & {5} & {} \\ {1} & {2} & {} \\ {} & {} & {}\end{bmatrix}\text{ : interchange }3\text{ and 2. negate 1 and 5} \\ \text{Adjunct = }\begin{bmatrix}{2} & {-5} & {} \\ {-1} & {3} & {} \\ {} & {} & {}\end{bmatrix} \end{gathered}[/tex][tex]\begin{gathered} In\text{verse of the matrix = }\frac{1}{|A|}\times\text{ adjunct} \\ A^{-1}\text{ = }\frac{1}{1}(\begin{bmatrix}{2} & {-5} & {} \\ {-1} & {3} & {} \\ {} & {} & {}\end{bmatrix}) \\ A^{-1}\text{ =}\begin{bmatrix}{2} & {-5} & {} \\ {-1} & {3} & {} \\ {} & {} & {}\end{bmatrix}\text{ (option B)} \\ \end{gathered}[/tex]What two variables can you define to write an equation to match this scenario?x = number of minutes for fruit cans and y = number of minutes for vegetable cansx = total number of minutes and y = total number of cansx = number of minutes for fruit and y = total number of cansx = total number of minutes and y = number of minutes for vegetables
Answers
An equation to correctly match this scenario would have to include both separate products. The current order which is 384 cans of food, includes both fruits and vegetables, and therefore any expression that does not include them both would give a wrong answer and the order would not be properly met.
The correct scenario is;
[tex]\begin{gathered} x=Number\text{ of minutes for fruit cans} \\ y=\text{Number of minutes for vegetable cans} \end{gathered}[/tex]This way you can produce both at a maximum without overproducing one and underproducing the other.
A straight line is 180 degrees. Find the value of X.
Answers
Given a straight line angle = 180
So, the angles (9x-100) and (40-x) are supplementary angles
So,
[tex](9x-100)+(40-x)=180[/tex]Solve for x:
[tex]\begin{gathered} (9x-x)+(40-100)=180 \\ 8x-60=180 \\ 8x=180+60 \\ 8x=240 \\ x=\frac{240}{8}=30 \end{gathered}[/tex]So, the answer will be x = 30
solve the equation for x. x/16=10
Answers
To solve further cross multiply both sides
so that
[tex]x\text{ }\times1\text{ = 16 }\times10[/tex]x = 160
Solve the equation 7-(5t-13)=-25-15b+21+5b=-19
Answers
Let's solve the following expressions:
a.) 7 - (5t - 13) = -25
[tex]\text{ 7 - (5t - 13) = -25}[/tex][tex]\text{ 7 - 5t + 13 = -25}[/tex][tex]\text{ 20 - 5t = -25}[/tex][tex]\text{-5t = -25 - 20}[/tex][tex]\text{-5t = -4}5[/tex][tex]\frac{\text{-5t}}{-5}\text{ = }\frac{\text{-4}5}{-5}[/tex][tex]\text{ t = 9}[/tex]Therefore, t = 9
b.) -15b + 21 + 5b = -19
[tex]-15b+21+5b=-19[/tex][tex]-10b+21=-19[/tex][tex]-10b=-19\text{ - 21}[/tex][tex]-10b=-40[/tex][tex]\frac{-10b}{-10}=\frac{-40}{-10}[/tex][tex]\text{ b = 4}[/tex]Therefore, b = 4
Three times a number decreased by 1 is 10 Three times the difference of a number is 1 is 10One less than three times a number is 10The quotient of a number and 3 is 10
Answers
Three times a number decreased by 1 is 10:
X is the number.
3x = three times a number.
3x - 1 = 10 (Three times a number decreased by 1 is 10)
3x = 10 + 1
3x = 11
x = 11/3
Can you help me solve the domain of this math word problem?
Answers
the domain refers to all possible values of x in the function.
since a negative time does not make sense, the smallest value of the domain is zero
on the other hand, the problem indicates that the model is considered accurate up to 100,000 years, therefore that would be the largest value of t
in conclusion, the domain of the function A(t) is
[tex]\lbrack0,100000\rbrack[/tex][ 0 , 100,000 ]
A training field is formed by joining a rectangle and two semicircles, as shown below. The rectangle is 96 m long and 64 m wide. Find the area of the training field. Use the value 3.14 for n, and do not round your answer. Be sure to include the correct unit in your answer.
Answers
To find:
The area of the training field.
Solution:
The training field is made of two semicircles and a rectangle.
The length and width of the rectangle is 96 m and 64 m. So, the area of the rectangle is:
[tex]\begin{gathered} A=l\times w \\ =96\times64 \\ =6144\text{ m}^2 \end{gathered}[/tex]The diameter of the semicircle is 64 m. SO, the radius of the semicircle is 32 m.
The area of two semicircles is:
[tex]\begin{gathered} A=2\times\frac{1}{2}\pi r^2 \\ =3.14\times(32)^2 \\ =3.14\times1024 \\ =3215.36 \end{gathered}[/tex]So, the area of the training field is:
[tex]\begin{gathered} A=6144+3215.36 \\ =9359.36 \end{gathered}[/tex]Thus, the area of the training field is 9359.36 m^2.
Find the x-intercepts and y-intercept of the following
function.
f(x) = (x+7) (x + 1)(x − 2)
Write your answer in coordinate pairs of the form (x, y).
Provide your answer below:
x-intercept: ().(
]).() and
y-intercept:
Answers
Step-by-step explanation:
there are 3 x-intercepts (the x- values when y = 0). because y is only 0, when one of the 3 factors is 0.
and that is the case for
x = -7
x = -1
x = 2
so, formally, the x- intercepts are
(-7, 0), (-1, 0), (2, 0)
the y intercept is the y- value when x = 0.
(0 + 7)(0 + 1)(0 - 2) = 7×1×-2 = -14
the y-intercept is formally
(0, -14)
Devon saw 19 adults wearing hats
Answers
Answer:
please add rest of question?
Step-by-step explanation:
Will give brainliest thank you..!
Answers
Answer:
4
Step-by-step explanation:
4
4
4
4
1 4 a) Is the above sequence arithmetic? Justify your answer. b) Write the explicit formula for the above sequence. c) Find the 18th term.
Answers
THe length of each cube is inreasing by 1. This means that the increment is in arithmetic sequence.
The formula for determining the nth term of an aritmetic sequence is expressed as
Tn = a + (n - 1)d
Where
a represents the first tem of the sequence
Common difference, d represents the difference between consecutive terms
Given that a = 3, d = 1
Tn = 2 + (n - 1)1
Tn = 2 + n - 1
Tn = 1 + n
For the 18th term, n = 18
T18 = 1 + 18 = 19
The number of boxes in the square for the 19th term is
19 * 19 = 361
I need help figuring out how to write out this problem correctly.
Answers
Answer
[tex]\frac{\sqrt{10}}{11}[/tex]Step-by-step explanation
Given the expression:
[tex]\sqrt{\frac{10}{121}}[/tex]Distributing the square root over the division and evaluating the square root at the denominator:
[tex]\begin{gathered} \frac{\sqrt{10}}{\sqrt{121}} \\ \frac{\sqrt{10}}{11} \end{gathered}[/tex]Can someone help me with this geometry question?A.Triangular prismB.Hexagonal prismC.Triangular pyramidD.Hexagonal pyramid
Answers
B. Hexagonal Prism
1) One prism is defined, in terms of naming it by the base.
2) Counting the edges of the base in this net surface, we can tell that this is a Hexagonal Prism for the base is a hexagon.
Need help asap please and thank you
Answers
Answer:
y=[tex]\frac{1}{2}[/tex]x+1
Step-by-step explanation:
y=mx+b
m is the slope of the line, which you find by counting the rise over run between two points. In this case its up one, and right two, or [tex]\frac{1}{2}[/tex].
b is the y intercept, or where the line crosses the y axis
A local band was interested in the average song time for rock bands in the 1990s. They sampled eight different rock bands and found that the average time was 3.19 minutes with a standard deviation of 0.77 minutes.
Calculate the 95% confidence interval (in minutes) for the population mean.
Answers
The 95% confidence interval (in minutes) for the population mean is of:
(2.55, 3.83).
What is a t-distribution confidence interval?The bounds of the confidence interval are given according to the following rule:
[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]
In which the parameters are described as follows:
[tex]\overline{x}[/tex] is the sample mean.t is the critical value.n is the sample size.s is the standard deviation for the sample.The distribution is used when the standard deviation of the population is not known, only for the sample.
In the context of this problem, the values of the parameters are given as follows:
[tex]\overline{x} = 3.19, s = 0.77, n = 8[/tex]
The critical value, using a t-distribution calculator, for a two-tailed 95% confidence interval, with 8 - 1 = 63 df, is t = 2.3646.
Then the lower bound of the confidence interval is calculated as follows:
[tex]\overline{x} - t\frac{s}{\sqrt{n}} = 3.19 - 2.3646\frac{0.77}{\sqrt{8}} = 2.55[/tex]
The upper bound is calculated as follows:
[tex]\overline{x} + t\frac{s}{\sqrt{n}} = 3.19 + 2.3646\frac{0.77}{\sqrt{8}} = 3.83[/tex]
More can be learned about the t-distribution at https://brainly.com/question/16162795
#SPJ1
karen recorded her walking pace in the table below. what equation best represents this relationship
Answers
Given Data:
The table given here shows time taken in the first column and the distance travelled in the second column.
First check the ration of distance /time to verify if the speed of the man is constant or not.
[tex]\begin{gathered} \frac{8.75\text{ m}}{2.5\text{ h}}=3.5\text{ m/h} \\ \frac{14\text{ m}}{4\text{ h}}=3.5\text{ m/h} \end{gathered}[/tex]As both ratios are same it means the speed of the man is constant and the distance travelled is directly proportional to the time taken and varies linealy with the time.
Now to determine the relationship between m and h we will use the same ratio of m and h which comes in the previous step.
[tex]\begin{gathered} \frac{m}{h}=3.5 \\ m=3.5h \end{gathered}[/tex]Thus, option (D) is the required solution.
Over a set of 5 chess games, Yolanda's rating increased 10 points, increased 4 points,
decreased 21 points, increased 23 points and decreased 8 points.
Her rating is now 1647.
What was her rating before the 5 games?
A. 1639
B. 1649
C. 1655
D. 1661
Answers
Answer:
C. 1655
Step-by-step explanation:
+10, +4, -21, +23, -8
Adding all those terms together we get 8
1647 + 8 = 1655
in chess, the knight (the piece shaped like a horse) moves in an L pattern.
Answers
Answer:
That is true but still remember that playing the knight at the start can be very useful.