f(x)=9-x^2
Average rate of change
x=0 to x=3
x=-1 to x=5
x=-2 to ×=2
we know that
The average rate of change is equal to
[tex]\frac{f\mleft(b\mright)-f(a)}{b-a}[/tex]Part 1) we have
a=0
b=3
f(a)=f(0)=9-(0)^2=9
f(b)=f(3)=9-(3^2)=0
substitute the given values in the expression above
[tex]\frac{0-9}{3-0}=-\frac{9}{3}=-3[/tex]the rate of change is -3
Part 2) we have
a=-1
b=5
f(a)=f(-1)=9-(-1)^2=8
f(b)=f(5)=9-(5)^2=-16
substitute the given values in the expression above
[tex]-\frac{16-8}{5-(-1)}=\frac{8}{6}=\frac{4}{3}[/tex]the rate of change is 4/3
Part 3) we have
a=-2
b=2
f(a)=f(-2)=9-(-2)^2=5
f(b)=f(2)=9-(2)^2=5
substitute
[tex]\frac{5-5}{2-(-2)}=\frac{0}{4}=0[/tex]the rate of change is zero
I need help with this question causey teacher didnt teach this to us.3(5-p) - 2(5 + p) = 3(p+1). Find p
Explanations:
The given equation is:
3(5 - p) - 2(5 + p) = 3(p + 1)
Step 1: Expand all the brackets
15 - 3p - 10 - 2p = 3p + 3
Step 2: Collect like terms ( That is, let everything that has p go together)
15 - 10 - 3 = 3p + 3p + 2p ( Note that the sign changes when anything crosses the equality sign)
2 = 8p
Step 3: Divide both sides by 8
2/8 = 8p/8
1/4 = p
p = 1/4
p = 0.25
An airplane flying against the wind travels 280 miles in the same amount of time it would take the same plane to travel
420 miles with the wind. If the wind speed is a constant 70 miles per hour, how fast would the plane travel in still air?
The speed of plane in still air is 150 miles per hour.
What is speed?
Speed is measured as the ratio of distance to the time in which the distance was covered. Speed is a scalar quantity as it has only direction and no magnitude.
speed = distance/time
Let s = speed in still air
then(s-70) = ground speed against the wind
and
(s+70) = ground speed with the wind
Write a time equation; time = distance/speed
time against = time with still air
280/(s-30) = 420/(s+30)
Cross multiply
420(s-70) = 280(s+70)
420s - 29400 = 280s + 19600
420s-280s = 19600+29400
140s=49000
s = 49000/140
s = 350 mph
To know more about speed, visit:
https://brainly.com/question/13943409
#SPJ9
5 ft12 ftWhat is the length of the hypotenuse?
I think these are the lengths of the legs
hypotenuse^2 = 5^2 + 12^2
hypotenuse^2 = 25 + 144
hypotenuse^2 = 169
hypotenuse = 13
The table represents the volume, y cubic units, of a cube with side lengths of x units.x:0, 1, 2, 3y:0, 1, 8, 27Does the table represents a linear function
No, the table does not represent a linear function
Explanation
Linear functions are those whose graph is a straight line. A linear function has the following form. y = f(x) = a + bx. it has one independent variable and one dependent variable. The independent variable is x and the dependent variable is y
Step 1
graph
[tex]y=x^3[/tex]so, the graph does not represent a linear function , Also
the volume of a cube is given by
[tex]\text{Volume}=Side^3^{}[/tex]the exponent of the function is 3, and for a linear function the exponent in the varialbe must be 1,
what are all the possible values of 'a' in -3≤a≤3
We have the next
[tex]-3\le a\le3[/tex]The possible values of 'a' for this are
[tex]\mleft[-3,3\mright][/tex]the value of a could be all the values between -3 and 3 including -3 and 3
ANSWER
[-3,3]
Question 3 of 10How many solutions does the nonlinear system of equations graphed belowhave?10X10
Answer:
B. Zero
Explanation:
The solutions of the system of equation are the points where the graph intersect. In this case, the red function and the blue function doesn't cross each other. So, the system formed by these non linear equations has no solutions.
Therefore, the answer is:
B. Zero
Answer:two
Step-by-step explanation:
Shelby is searching online for airline tickets. Two weeks ago, the cost to fly from to was $210. Now the cost is $305. What is the percent increase? What would be the percent increase if the airline charges an additional $50 baggage fee with the new ticket price?
The percentage increase of the airline ticket is 45.24%
Percentage IncreaseThe concept of percent increase is basically the amount of increase from the original number to the final number in terms of 100 parts of the original. An increase of 5 percent would indicate that, if you split the original value into 100 parts, that value has increased by an additional 5 parts.
Mathematically, the percentage increase of a quantity can be written as
[tex]\% increase =\frac{change in quantity}{original quantity} * 100[/tex]
Let's substitute the values given into the equation and find the percentage increase.
[tex]\% increase =\frac{change in quantity}{original quantity} * 100\\\% increase = \frac{305 - 210}{210} *100\\\% increase = 45.24\%[/tex]
The increase in percentage of the ticket price is 45.24%
If the airline charges an additional $50 with the new ticket price, the percentage increase will remain the same because assuming the baggage fees is also applicable to the old price, there won't be an change in the percentage increase.
Learn more on percentage increase here;
https://brainly.com/question/23885199
#SPJ1
3.Ronald loves to compete in triathlons. At a race a few months ago, hefinished in 290 minutes. At a race yesterday, he took 10% more time tofinish. What was his time at yesterday's race?
Explanation:
First we have to get 10% of 290 minutes:
[tex]290\times\frac{10}{100}=290\times0.1=29[/tex]If yesterday took him 10% MORE time to finish the race, it means that it took him 290min as a few months ago plus another 29 minutes
Answer:
Ronald's time at yesterday's race was 319 minutes
Hi there I need help what is 39 dollars plus two rolls of pennies equals
Answer:
41
Step-by-step explanation:
Factorise2rs-4rt-6t+3s
Given expression:
[tex]2rs\text{ - 4rt - 6t + 3s}[/tex]Collect like terms:
[tex]=\text{ 2rs - 4rt - 6t + 3s}[/tex]Next, we bring the common terms:
[tex]=\text{ 2r(s - 2t) -3(2t - s)}[/tex]Re-writing the expression:
[tex]=\text{ -2r(2t - s) -3(2t -s)}[/tex]Since we have a common term on either side of the negative sign, we can write:
[tex]=\text{ (-2r -3)(2t-s)}[/tex]Answer:
[tex]=\text{ (-2r-3)(2t -s)}[/tex]Let us verify the answer:
[tex]\begin{gathered} (-2r\text{ -3)(2t-s)} \\ =-2r(2t\text{ -s) -3(2t -s)} \\ =\text{ -4rt + 2rs -6t + 3s} \end{gathered}[/tex]Find the are of the circle below.
To find the area of the circle with diameter = 18 cm
We will use the formula:
[tex]\text{Area of a cirlce = }\pi r^2[/tex]where r= radius of the circle
From the quesion diameter = 18 cm
radius = diameter/2
radius = 18cm/2 = 9 cm
substituting r = 9cm into the formula
[tex]Area\text{ of a circle = }\pi(9)^2[/tex][tex]A\text{rea of the circle }=\text{ 81}\pi cm^2[/tex]The above answer is when we are to leave the answer in terms of π
Otherwise if π is given to be 3.14 or 22/7 , we will simply substitute into the formula
That is given that π= 3.14
[tex]\text{Area of the circle = 81 }\times3.14=254.34cm^2[/tex]
Let C be the boundary of the square with vertices (0,0),(1,0),(1,1) and (0,1) oriented the in the counter clockwise sense. Then the value of the line integral [tex]\oint_ { \rm C} \rm {x}^{2} {y}^{2} dx + ( {x}^{2} - {y}^{2} )dy \\ [/tex] is ________. (rounded of two decimal places)
By Green's theorem,
[tex]\displaystyle \oint_C x^2y^2 \, dx + (x^2-y^2) \, dy = \iint_{[0,1]^2} \left(\frac{\partial(x^2-y^2)}{\partial x} - \frac{\partial(x^2y^2)}{\partial y}\right) \, dx \, dy \\\\ ~~~~~~~~ = \int_0^1 \int_0^1 (2x - 2x^2y) \, dx \, dy \\\\ ~~~~~~~~ = \int_0^1 \left(1-\frac23 y\right) \, dy \\\\ ~~~~~~~~ = 1 - \frac13 = \frac23 \approx \boxed{0.67}[/tex]
The graph of an arithmetic sequence is shown.What is the value of the 7 th term?Round your answer to the nearest tenth. Add a decimal point and a zero if youranswer is a whole number (for example, 10 would be entered as 10.0)
10.0
Explanation
an arithmetic sequence is given by the expression
[tex]\begin{gathered} a_n=a_1+(n-1)d \\ \text{where} \\ a_{_1}\text{ is the first term} \\ \text{and d is the common diference} \end{gathered}[/tex]in the graph , to know the value of the 7 th terms, we need to take the value that y takes, when x= 7
so
therefore, the answer is
10.0
I hope this helps you
use the four value for x to make a function table. than stage the range of the function
we get that the function is x-10, and the values to replace are: -1,0,1,2
so the answer is:
[tex]\begin{gathered} -1-10=-11 \\ 0-10=-10 \\ 1-10=-9 \\ 2-10=-8 \end{gathered}[/tex]Hey can someone please help me? I would appreciate it.
Answer:
8/3 or 2.67
Step-by-step explanation:
your explanation is in the image below hope this helps sorry if wrong
Snow is accumulating at a rate of 0.5 inches per hour. Calculate the amount, in inches of snow that will accumulate in 24 minutes.
Given:
Accumulation rate = 0.5 inches per hour
time = 24 minutes
First, convert minutes into hours:
1 hour = 60 minutes
24 / 60 = 0.4 hours (divide by 60)
Now, simly multiply the rate by the number of hours
0.5 in/h x 0.4 h = 0.2 in
Answer: 0.2 inches
What is the length of AB? round your answer to the nearest hundred.
In order to calculate the length of the line AB, you use the following formula for the distance between points in the coordinate plane:
d = √((x2-x1)²-(y2-y1)²)
That is, it is only necessary to have a pair of points with coordinates (x1,y1) and (x2,y2). In this case you have two points A=(-5,-4)=(x1,y1) and B=(-3,3)=(x2,y2), then, by replacing these values into the formula for the distance you have:
d = √((3-(-3))²-(-5-4)²)
d = √((3+3)²+(-9)²)
d = √(36+81) = √(117) = 10.8166 ≈ 10.82
Hence, the length of the line AB is 10.82
Can you guys please help me on this question ?
Solution
Therefore, the correct option is D.
Find the y-intercept of the line on the graph.
Answer:
-2
Step-by-step explanation:
The y intercept is where the line crosses the y axis. It crosses at the point (0,-2)
when you multiply by a power of 10 the decimal point moves how many places
If we have a number X and we multiply it by a power of 10, then:
[tex]x\text{ }\ast\text{ }10^{n\text{ }}=\text{ x followed by n zeros}[/tex]Example:
x = 7 and we want to multiply it by 1,000
[tex]7\text{ }\ast\text{ 1,000 = 7 }\ast\text{ }10^{3\text{ }}=\text{ 7, 000 (3 zeros, the same quantity of the power)}[/tex]Another example:
x = 27 and we want to multiply it by 1 million
[tex]27\text{ }\ast\text{ 1,000,000 = 27 }\ast10^{6\text{ }}=\text{ 27,000,000 (6 zeros, the same quantity of power)}[/tex]Solve for X with intersecting chords
We apply the secant-angle theorem,
[tex]\frac{156+54}{2}=105^0[/tex]Then,
[tex]\begin{gathered} x+105^0=180^0\text{ (angle in a straight line)} \\ x=180^0-105^0 \\ x=7^{}5^o \end{gathered}[/tex]Therefore, x=75 degr
what is the massive objects the planets of the solar system orbit
The planets orbit around stars. Our solar system is an example of that, all the planets in our system orbit around a star, the Sun.
Hence, the answer is stars.
Area of Composite Figures Find the area of each figure. Round to the nearest tenth if necessary.
The Area of the composite shape is the sum of the areas of the triangle and that of the square
Area of square = length x breadth =>
[tex]\begin{gathered} \text{Area of square = 10 m x 6m } \\ \Rightarrow60m^2 \end{gathered}[/tex]Area of Traiangle = 1/2 (base x height)
=>
Determine the required value of the missing probability to make
the distribution a discrete probability distribution.
X
3
45
4
5
6
P(x)
0.24
?
0.28
0.26
The value that completes the probability distribution is 0.22
How to determine the missing value?The distribution of the discrete probability distribution is given as
x 3 4 5 6
P(x) 0.24 ? 0.28 0.26
Represent the blank value in the distribution with the variable y
So, we have the following representation:
P(x) 0.24 y 0.28 0.26
The sum of probabilities in a distribution is 1
So, we have
0.24 +y + 0.28 + 0.26 = 1
Evaluate the sum
y + 0.78 = 1
Evaluate the like terms
y = 0.22
Hence, the missing value is 0.22
Read more about probability distribution at
https://brainly.com/question/27701525
#SPJ1
For a field trip 30 students rode in cars and the rest filled four buses how many students were in each bus if 258 students were on the trip.
Total students: 258
Students that rode in cars = 30
258 - 30 = 228 students left
There are 4 busses ( assuming that each bus has the same number of students)
Students in each bus = students left / number of buses = 228 / 4 = 57
Answer: 57 Students
Assume that a triangle ABC has standard labeling. Determine wether SAA, ASA, SSA, SAS or SSS is given. Then decide wether the law of sines or the law of cosines should be used to begin solving the triangle.a, c and B
Answer:
Explanation:
I need help on a problem
Triangle BOX = Triangle DEA by Angle Side Angle
Write an equation in the form y suggested by the pattern in the table. т
I'll pick uo two points from the table.
P1 = (5, 11)
P2 = (7, 13)
1.- Find the slope
slope = (y2 - y1) / (x2 - x1)
Substitution
slope = (13 - 11) / (7 - 5)
Simplification
slope = 2/2
Result
slope = 1
2.- Find the equation of the line
y - y1 = m(x - x1)
Substitution
y - 11 = 1(x - 5)
Simplification
y = x - 5 + 11
Result
y = x + 6
This is the answer to your question
can someone help me with this please, I need this by tomorrow pleaseeee
In the given figure,
There are non-parallel lines,
Hence these angles are formed by the non-parallel lines.
This means they do not have any relation, i.e., they are not necessarily congruent to each other.
What are Intersecting lines?They are referred to be intersecting lines when two or more lines in a plane cross each other. The point of intersection, which can be found on all intersecting lines, is the common point shared by the intersecting lines. The intersecting lines (two or more) always meet at a single location. Any angle can be used to intersect the intersecting lines. This angle is always larger than zero and less than 180 degrees. Vertical angles are created by two lines intersecting. With a common vertex, the vertical angles are opposite angles (which is the point of intersection). Curved lines, not straight ones, are what intersect at several points.To learn more about Intersecting Lines, refer to:
https://brainly.com/question/11297403
#SPJ13
According to the Rational Root Theorem, which of the following could be a root of p(x)=3x3−5x2+4? Select all that apply.
SOLUTION
The rational root theorem, also called rational root test theorem state that for a polynomial equation in one variable with integer coefficients to have a solution (root) that is a rational number, the leading coefficient (the coefficient of the highest power) must be divisible by the denominator of the fraction and the constant term (the one without a variable) must be divisible by the numerator.
Given the polynomial
[tex]p(x)=3x^3-5x^2+4[/tex][tex]\begin{gathered} \text{Leading co}eficient\text{ =3} \\ \text{Constant term =4} \end{gathered}[/tex]The factor of the constant term is
[tex]\pm1,\pm2,\pm4_{}[/tex]The factors of the Leading coefficient are
[tex]\pm1,\pm3[/tex]The root of the p(x) are
[tex]\begin{gathered} \frac{p}{q} \\ \text{where p=factors of the constant term } \\ q=\text{factor of leading coefficient } \end{gathered}[/tex]hence , the possible root of p(x) are
[tex]\pm1,\pm\frac{1}{3},\pm2,\pm\frac{2}{3},\pm4,\pm\frac{4}{3}[/tex]Hence
root of p(x) are 2/3, -2, and 1
