a) The average rate of change of a function over an interval is the change in the function's output (f(b) - f(a)) divided by the change in the function's input (b - a). So, to find the average rate of change of f over the interval -4 <= x <= 3, we can use the formula:
(f(3) - f(-4)) / (3 - (-4)) = (sqrt(25 - 9) - sqrt(25 - 16)) / (3 - (-4)) = (-2sqrt(7) + 4sqrt(3)) / 7
b) To find the derivative of f(x), we need to use the power rule and the chain rule. The power rule states that the derivative of x^n is nx^(n-1), and the chain rule states that the derivative of f(g(x)) is f'(g(x)) * g'(x).
So, the derivative of f(x) = sqrt 25 - x^2 is:
-2x
c) To find the equation of the line tangent to the graph of f at x = -3, we need to use the point-slope form of a line, which is:
y - y1 = m(x - x1)
where m is the slope of the line (which is f'(-3) = -6), (x1, y1) is the point on the graph where the line touches (which is (-3, f(-3)) = (-3, sqrt(25 - 9) = 2sqrt(7))
so we have: y - 2sqrt(7) = -6(x + 3)
d) To check if g(x) is continuous at x = -3, we need to check if the limit of g(x) as x approaches -3 exists and is equal to g(-3).
Since g(x) = f(x) for -5 <= x <= -3 and g(x) = x + 7 for -3 <= x <= 5, we have:
g(-3) = f(-3) = sqrt(25 - 9) = 2sqrt(7)
and the limit of g(x) as x approaches -3 is:
lim x->-3 g(x) = lim x->-3 (x + 7) = -3 + 7 = 4
Since g(-3) = 2sqrt(7) and lim x->-3 g(x) = 4, g(x) is not continuous at x = -3.
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Estimate number of jelly beans in 1 litre jar.
Michelle has four white socks two black socks and two gray socks in her drawer she pulled that one sock on the drawer without looking she's not put it back then Michelle Pulls a second Sock from the drawer .what is the probability that Michelle pulls two white socks from the drawer a.3/14 b. 3/16 c. 1/16 d. 1/2
Answer:
3/14
Step-by-step explanation:
prob for the 1st sock=4/8=1/2
prob for the 2nd sock=3/7(there's 7 socks left now and only 3 were white since she pulled one out and didn't put it back)
so the prob of both being white is 1/2*3/7=3/14
what is 8 1/4/d=2/11
[tex]8\frac{1}{4}d =\frac{2}{11}[/tex]
a) Simplify both sides of the equation.
[tex]\frac{33}{4}d=\frac{2}{11}[/tex]
b) Multiply both sides by 4/33.
[tex](\frac{4}{33} ) \times (\frac{4}{33}d)=(\frac{4}{33}) \times (\frac{2}{11} )\\[/tex]
d = [tex]\frac{8}{363}[/tex]
[tex]8\frac{1}{4} \div d=\frac{2}{11}[/tex]
= [tex]\frac{33}{4d} =\frac{2}{11}[/tex]
a) Cross Multiply.
[tex](33)\times(11)=2\times 4d[/tex]
[tex](363) =8d[/tex]
b) Flip.
[tex]8d=(363)[/tex]
c) Divide both sides by 8
[tex]\frac{8d}{8} = \frac{363}{8}[/tex]
[tex]d=\frac{363}{8}[/tex]
Please help, I need answers ASAP.......
Answer:
hope it is helpful to you
pls help me, i need to get my grade up as soon as I can
Answer:
106 and 93
Step-by-step explanation:
The whole thing has to add up to 360
what is the answer to 4^43
Answer:
7.737
Step-by-step explanation:
hi can someone pls help me
:)
What is the slope of the linear regression prediction equation if a person with 12 years of schooling
On solving the provided question, we can say that the e slope of the linear regression prediction equation if a person with 12 years of schooling is 1.
what is linear regression?When modeling the relationship between a scalar answer and one or more explanatory variables in statistics, linear regression is a linear method. Simple linear regression is used when there is only one explanatory variable. The procedure is known as multiple linear regression if there are numerous. A straight line is used to evaluate the relationship between the independent and dependent variables in a regression model known as simple linear regression. Both factors ought to be quantitative. The effect of the independent variable on the dependent variable is examined using simple linear regression. The second scenario, known as multiple linear regression, examines how various independent factors affect the dependent variable.
the e slope of the linear regression prediction equation if a person with 12 years of schooling
a. 1(correct)
b. 12
c. 13
d. 1,500
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A cone and a sphere have the same volume the base of the cone has a radius of 8 feet and the sphere has a radius of 6 feet what is the height of the cone?
Step-by-step explanation:
Volume of Cone=
[tex] \frac{1}{3} \pi \: r {}^{2} h[/tex]
Volume of Sphere=
[tex]\frac{4}{3} \pi \: r {}^{3} [/tex]
Since VC = VS
[tex] \frac{1}{3} \times 3.14 \times 8 {}^{2} \times h = \frac{4}{3} \times 3.14 \times 216[/tex]
66.99h = 904.32
h = 904.32 ÷66.99
h= 13.5 feet
Has a slope of 2/3 and passes through the point (-12, 3) in y intercept form
Alonzo went to a baseball game. The game started at 10:50 AM, and it was 3 hours 27 minutes long. When did the game end? PLEASE ANSWER IT I NEED IT
Answer:
The game ends at 2:17 PM.
Step-by-step explanation:
The basketball game started at 10 hours and 50 minutes and the game lasted 3 hours and 27 minutes. We can use addition to find out the time. Simply add the hours and the minutes.
10 hours + 3 hours = 13 hours
50 minutes + 27 minutes = 77 minutes = 1 hour and 17 minutes
⇒ 14 hours and 17 minutes ⇒ 2:17 PM
The first rule is add 4 starting from 2. The second rule is subtract 4 starting from 28. What is the second ordered pair using the terms in each sequence? A (2, 28) B(6, 24) C (14, 16) D (10, 20)
The second ordered pair using the terms in each sequence is B (6, 24).
THE SEQUENCE PAIRThe first rule says to add 4 to the first term of the ordered pair, starting from 2. So the first term of the second ordered pair would be 2+4 = 6.The second rule says to subtract 4 from the second term of the ordered pair, starting from 28. So the second term of the second ordered pair would be 28-4 = 24.
Therefore, the second ordered pair using the terms in each sequence is B (6, 24).
The third ordered pair using the terms in each sequence would be C (14,16) and the fourth ordered pair would be D (10,20)This is because:
C (14,16) can be obtained by adding 4 to first term of B(6,24) which is 6+4 = 10 and subtracting 4 from second term of B(6,24) which is 24-4=20.
D (10,20) can be obtained by adding 4 to first term of C(14,16) which is 14+4 = 18 and subtracting 4 from second term of C(14,16) which is 16-4=12.
So the sequence list of ordered pair would be:
First order: A (2,28)
Second order: B(6,24)
Third order: C (14,16) D (10,20)
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What is the solution to the system Y 3x 7 and 6x 2y 12?
The system of equations y = 3x - 7 and 6x - 2y = 12 has no solution. That is the lines of the equation is parallel.
To solve a system of equations, you can use substitution or elimination.
One method to find the solution for this system of equations is substitution. To use this method, you can solve one equation for one variable in terms of the other variable, and then substitute this expression into the other equation.
Solving for y in the first equation:
y = 3x - 7
Then substitute the result in the second equation:
6x - 2(3x - 7) = 12
6x - 6x + 14 = 12
14 = 12
That clearly is not true and this system of equations has no solution.
--The question is incomplete, answering to the question below--
"What is the solution to the system y = 3x - 7 and 6x - 2y = 12?
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Is (1, 1) a solution to this system of equations?
4x + 14y = 18
9x + y = 10
Answer:
yes
Step-by-step explanation:
HELP DUE IN 15 MINS!
In rhombus ABCD, m∠CDE = 50°, DB = 12 ft, and AC = 16 ft
1. m∠CEB =?? degrees
2. m∠BCE =?? degrees
3. m∠ADE =?? degrees
4. ° DE =?? degrees
5. CB =?? degrees
Answer:
1.) m∠CEB = 90 degrees => The intersection is perpendicular
2.) m∠BCE = 40 degrees => 180 - (50 + 90)
3.) m∠ADE = 50 degrees => 180 - (40 + 90)
4.) DE = 6 ft => half of DB: 12/2
5.) CB = 10 ft => Using Pythagorean Theorem, solve:
=> 8² + 6² = CB²
=> 64 + 36 = CB²
=> 100 = CB²
=> [tex]\sqrt{100}[/tex] = CB
=> 10 = CB
Hope this helps!
Answer:
Step-by-step explanation:
I'm just adding the answer to 3. Give the other answerer the Brainliest.
Given a Rhombus, The diagonals bisect the angle that the diagonal is connect to
Therefore <ADE = 50 degrees, same as <CDE.
Determine whether each system of equations has no solution, one solution, or infinitely many solutions
Show work please:)
Answer:
One solutionStep-by-step explanation:
Given system:
y = -3-3(x + 9) = yThe first equation is a horizontal line, the second equation is a line with a slope of -3.
Since the lines have different slopes, they intersect at one point.
As there is one intersection, the system has one solution.
You need to split it in half then multply then add
Answer: 322in 2
Step-by-step explanation:
1. Cut it in half
2. 8*21=168 (first half)
3. 11*14=154 (second piece)
4. Add 168 and 154, equals to 322in 2
Help me pleaseeeeeee
Answer:
only y= 8x-6
Step-by-step explanation:
in order know of an equation is linear is if the equation when graphed makes a straight line the equation should be in the format y=mx+b or y=mx if it is a proportional relationship.
What is the formula for directed line segment?
The formula for a directed line segment is A = (x2 - x1, y2 - y1). It is a vector equation, meaning that it describes the direction and magnitude of a line segment, rather than its endpoint coordinates.
A directed line segment is a line segment with a starting point and an ending point, where the direction of the line can be described in terms of its magnitude and direction. To calculate the directed line segment, first calculate the difference between the x-coordinates of the start and end points, and then calculate the difference between the y-coordinates of the start and end points. The result is the vector A, which describes the magnitude and direction of the line segment.
For example, consider a line segment with start point (1, 2) and end point (4, 6). To calculate the directed line segment, first calculate the difference between the x-coordinates of the start and end points (4 - 1 = 3). Then, calculate the difference between the y-coordinates of the start and end points (6 - 2 = 4). The result is the vector A = (3, 4). This vector describes the magnitude and direction of the line segment, with the magnitude being the length of the line segment, and the direction being the direction from the start point to the end point.
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Please answer fast! this is my first question so I think I'm giving 10 points? I'm not sure how it works-
if the producer in a food chain has 1000 kcal of energy available, how much energy would each of the consumers have?
Answer:
100kcal
10kcal
1kcal
Step-by-step explanation:
Each level you go up, you only get 10% of the total energy
Need help ASAP !!! Right answer please
Answer:
[0,∞) or x ≥0
Notice that the graph doesn't go to the left of x = 0. It only goes right. This means that the domain (all possible values of x), can only be the values above 0.
can you find the proportion pwease :)
Answer: 15/10
Step-by-step explanation:
Answer:
15 cookies and 10 brownies
Step-by-step explanation:
What is the simplest form of this expression? 2m^3(-m - 3) + 7m^4
Round your answer to the nearest hundredth.
?
B
С
50°
7
9514 1404 393
Answer:
BC ≈ 5.87
Step-by-step explanation:
The law of sines is applicable.
a/sin(A) = 7/sin(50°)
Angle A is the complement of angle B, so we have ...
a = 7(sin(40°)/sin(50°))
a ≈ 5.8736974
The length of BC is about 5.87 units.
Define an exponential function, f(x), which passes through the points (0,125) and (3,8). Enter your answer in the form a*b^x
Answer:
Step-by-step explanation:
put (0, 125) in a*b^x, we get a = 125, then put (3,8) in 125*b^x, we get 125*b^3=8
b^3=8/125
b=2/5
then the answer is 125*(2/5)^x
A triangle ha an area of 142. 74 quare feet and a height of 18. 3 feet. What i the length of the bae?
A triangle having an area of 142. 74 ft^2 and a height of 18. 3 ft, has a base of 15.6 ft.
What is the area of a triangle?
In a two-dimensional plane, a triangle's area is the area that it completely encloses. A triangle is a closed shape with three sides and three vertices, as is common knowledge. The entire area occupied by a triangle's three sides is referred to as its area. Half of the product of the triangle's base and height provides the general formula for calculating the area of the triangle.
The area of the triangle is 142.74 ft^2.
The height of the triangle is 18.3 ft.
Let the base of the triangle be x.
The formula for area of a triangle is -
Area = (height × base)/2
Plugging in the values in the equation -
142.74 = (18.3 × x)/2
142.74 = 18.3x/2
18.3x = 285.48
x = 285.48/18.3
x = 15.6
Therefore, the base of the triangle measures 15.6 ft.
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What is the solution to the inequality below?
√x <9
Answer:
x<81 I hope this is the correct answer.
The red line on this graph is y=-2x-1
The dotted line is y=x.
Write the equation of the inverse of this function
Answer:
Step-by-step explanation:
Miranda conducted a survey on how many hours per day students spend surfing the internet versus how many pets they have. She surveyed ten of her classmates and recorded the data in the scatter plot below.
Use technology to determine which equation best models the data in the scatter plot.
A.
y = -0.4x + 6.3
B.
y = -7.4x + 0.7
C.
y = -0.7x + 7.4
D.
y = -6.3x + 0.4
Answer:
Step-by-step explanation:
a
PLS HELP I HAVE NO IDEA
Complete the remainder of the table for the given function
y=x/2 + 5
Answer:
Step-by-step explanation:
(-2,4)
(0,5)
(2,6)
(4,7)
Answer: 4, 5, 6, 7,
Step-by-step explanation: From the formula y = x / 2 + 5
substitute x with the value -2
It becomes -2 / 2 + 5
that equals 4
then do the same for the rest
when x = 0
y = 0 / 2 + 5
y = 5
when x = 2
y = 2 / 2 + 5
y = 1 + 5
y = 6
when x = 4
y = 4 / 2 + 5
y = 2 + 5
y = 7
I hope this was helpful