Answer:
(a) -8
(b) 6x +4 +3h
Step-by-step explanation:
Sometimes, it works well to find the general solution first, then use that to solve the specific problem. That's what we'll do here.
(b)The average rate of change on the interval [x, x+h] is defined as ...
m = (f(x+h) -f(x))/h
For the given f(x), this is ...
[tex]m=\dfrac{((3(x+h)^2+4(x+h)-4)-(3x^2+4x-4)}{h}\\\\m=\dfrac{3x^2 +6xh+3h^2+4x+4h-4-3x^2-4x+4}{h}\\\\m=\dfrac{6xh+3h^2+4h}{h}\\\\\boxed{m=6x+4+3h}\qquad\text{average rate of change on $[x,x+h]$}[/tex]
__
(a)Using the above result for the interval [-4. 0], we have x=-4 and h=4. The average rate of change on that interval is ...
m = 6(-4) +4 +3(4) = -24 +4 +12 = -8
The average rate of change on [-4, 0] is -8.
_____
Additional comment
In the above, we worked the generic problem first. That way, we only needed to expand f(x+h)-f(x) once. If you're not terribly comfortable with doing algebra on literal expressions, sometimes it is more comfortable to work the numerical problem--as this question would have you do. This lets you get an idea of the kinds of operations that are involved and the way terms combine.
We note that the average rate of change is the instantaneous rate of change (derivative of the function) at the midpoint of the interval. That derivative is the value of m when h=0: 6x+4. The midpoint of the interval [-4,0] is x=-2, and the derivative there is 6(-2)+4 = -8, as above.
A beverage distributor has a facility that bottles beer. Beer bottles are supposed to be filled to 12 oz but there are slight variations. As part of quality control, they randomly sample bottles of beer and measure how many ounces they contain. In the most recent sample, the found an average fill of 12.01 oz with a standard deviation of 0.89.
If one of the bottles of sampled beer was filled to 10.98 oz, what is its associated zscore?
Is this bottle an outlier?
The associated z score for filling to 10.98 oz. is -1.16.
Z scoreThe z score is used to determine by how many standard deviations the raw score is above or below the mean. It is given by:
z = (x - μ) / σ
where x is the raw score, μ is the mean and σ is the standard deviation.
Given that μ = 12.01, σ = 0.89, hence:
For x = 10.98:
z = (10.98 - 12.01)/0.89 = -1.16
The associated z score for filling to 10.98 oz. is -1.16.
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solve 9(x-11)=9 please help
Answer: 12
Step-by-step explanation:
Distribute the 9(x-11) first. If you distribute it, it becomes 9x-99
9x-99=9
Add 99 to both sides
9x=108
Divide by 9 on both sides
X=12
Rearrange the equation to isolate E:
M=
Answer:A
Step-by-step explanation:
The solution is in the file below
HELP ASAP!! I DON'T UNDERSTAND THIS EXPRESSION.
Solve for x: 5 − (x + 5) > −2(x + 4)
a
x > −8
b
x < −8
c
x > −18
d
x < −18
Answer: A. x > -8
Step-by-step explanation: have a wonderful day!!!!!!!!
Matt and Anna Killian are frequent flors on Fast-n-Go Airlines, They often fly between two cities that are a distance of 800 miles apart. On one particular trip, they
flew into the wind and the trip took 2.5 hours. The return trip with the wind behind them, only took about 2 hours. Find the speed of the wind and the speed of the
plane in still air
Pls help
Answer:
The speed of the wind is 40mph, the speed of the plane in still air is 360mph
Step-by-step explanation:
distance = speed * time
Both legs of the trip are 800 miles, let 'x' represent the speed of the plane in still air and 'w' represent the speed of the wind, then 'x+w' represents the speed with the wind and 'x-w' represents the speed into the wind
800 = (x-w)2.5
800 = (x+w)2
Rewrite equations:
800=−2.5w+2.5x;800=2w+2x
Steps: Solve 800=−2.5w+2.5x for w:
800=−2.5w+2.5x
800+2.5w=−2.5w+2.5x+2.5w(Add 2.5w to both sides)
2.5w+800=2.5x
2.5w+800+−800=2.5x+−800(Add -800 to both sides)
2.5w=2.5x−800
2.5w/2.5 = 2.5x - 800 / 2.5 (Divide both sides by 2.5)
w=x−320
Step: Substitute x−320 for w in 800=2w+2x:
800=2w+2x
800=2(x−320)+2x
800=4x−640(Simplify both sides of the equation)
800+−4x=4x−640+−4x(Add -4x to both sides)
−4x+800=−640
−4x+800+−800=−640+−800(Add -800 to both sides)
−4x=−1440
-4x/-4 = -1440/-4 (Divide both sides by -4)
x=360
Step: Substitute 360 for x in w=x−320:
w=x−320
w=360−320
w=40(Simplify both sides of the equation)
solving this system we have:
w=40
x=360
Therefore, the speed of the wind is 40mph, the speed of the plain in still air is 360mph
MATH
Help me to answer this pls
An 8-bar package of soap sells for $4.00. What is the unit rate in cost per bar
I need help please!!
help pls i give 5 stars and crown
Answer:
a) 82
b) 144
c) 75
d) 150
e) 241
f) 80
Step-by-step explanation:
There is a total of 360 degrees in a circle. To find the missing angles, you just have to add all of the other angles and subtract them from 360.
3.
Sam claims that when he completes the transformation f(x) +3, the
parent function would move three units to the left.
Part A: Do you agree or disagree? Why or why not?
Part B: What misconception do you think Sam needs to clear up?
A) Disagree, The transformation f(x) + 3 represents moving the graph vertically up by 3 units.
B) A vertical transformation involves changing the y-coordinate of the graph, while a horizontal transformation involves changing the x-coordinate of the graph.
What is Translation?A transformation that occurs when a figure is moved from one location to another location without changing its size or shape is called translation.
Since, We know that;
The transformation f(x) + 3 represents moving the graph vertically up by 3 units.
Therefore, the parent function would not move three units to the left.
It seems that Sam has a misconception about vertical and horizontal transformations.
For clarify, a vertical transformation involves changing the y-coordinate of the graph, while a horizontal transformation involves changing the x-coordinate of the graph.
Thus, We get;
A) Disagree, The transformation f(x) + 3 represents moving the graph vertically up by 3 units.
B) A vertical transformation involves changing the y-coordinate of the graph, while a horizontal transformation involves changing the x-coordinate of the graph.
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Is 20b+16c equal to 4(4b+5c)
Answer:
No
Step-by-step explanation:
Simplify : Distribute
4(4b+5c)
16b+20c
Hence, 4(4b+5c) equal to 16b+20c.
What is the constant of proportionality in dollars per granola bar?
4 granola bars is $9.00 12 granola bars is $27.00 24 granola bars is $54.00
: Have a nice day!!! :)
what is x - 2 5/8 = 6 1/4
Answer:
8 7/8 is the correct answer
Step-by-step explanation:
hope this helps
[tex]x - 2 \frac{5}{8} = 6 \frac{1}{4} [/tex]
[tex]x - \frac{21}{8} = \frac{25}{4} [/tex]
[tex]x = \frac{50}{8} + \frac{21}{8} [/tex]
[tex]x = \frac{71}{8} [/tex]
[tex]x = 8 \frac{7}{8} [/tex]
Help Solve please and explain find X and Y
Answer:
y = [tex]\frac{9}{2}[/tex][tex]\sqrt{2}[/tex]
x = 9
Step-by-step explanation:
this triangle is isosceles because the base angles are each 45°
the ratio of sides in a 45-45-90° triangle are 1 : 1 : [tex]\sqrt{2}[/tex]
so 'y' is going to also be [tex]\frac{9}{2}[/tex][tex]\sqrt{2}[/tex]
'x' will be [tex]\sqrt{2}[/tex] multiplied by [tex]\frac{9}{2}[/tex][tex]\sqrt{2}[/tex] which will be:
[tex]\frac{(9x2)}{2}[/tex] = 9
I need some help please
Answer: 6
Step-by-step explanation:
Since the 3 semicircles are identical, we know that each semicircle has a diameter of 4, meaning they each have a radius of 2.
We can use the fact that (arc length of semicircle) = (pi)(r) to get the arc length of each to be 2pi.
Meaning 2pi + 2pi + 2pi = 6pi.
U2 L6 Function Operations Quick Check
PLEASE HELP!
Answer the questions in the pictures..
Answer:
1.d
2.b
3.c
4.d
5.c
Step-by-step explanation:
1. f(x) + g(x) = x - 11.
2. f(x) - g(x) = - 3x + 9.
3. f.g = 30x² + 28x - 6, all real numbers.
4. f/g = x + 4, all real numbers, x ≠ 4.
5. It doesn't matter which discount is applied first the result is the same.
What is a composite function?When the output of one function is given to the input of another function they are called composite functions.In (fog)x which is [f{g(x)}] here the out of the function g(x) is the input of the function f(x).
1. f(x) = - 5x - 4 and g(x) = 6x - 7.
Therefore, f(x) + g(x) = - 5x - 4 + 6x - 7.
f(x) + g(x) = x - 11.
2. f(x) = 3x + 2 and g(x) = 6x - 7.
Therefore, f(x) - g(x) = 3x + 2 - (6x - 7).
f(x) - g(x) = 3x + 2 - 6x + 7.
f(x) - g(x) = - 3x + 9.
3. f(x) = 5x + 3 and g(x) = 6x - 2.
Therefore, f.g = f(x)×g(x) = f(x).g(x).
f.g = (-5x + 3)(6x - 2).
f.g = -30x² + 10x + 18x - 6.
f.g = 30x² + 28x - 6.
The domain is all real numbers no restrictions.
4. f(x) = x² - 16 and g(x) = x + 4.
Therefore, f/g = f(x)/g(x).
f/g = (x² - 16)/(x + 4)(x - 4).
f/g = (x + 4)(x - 4)/(x - 4).
f/g = x + 4.
The domain of f/g is all real numbers except x ≠ 4.
5. Let, The original amount be 100.
25% off on 100 is 75 and 10% off again is 75 - 7.5 = 67.5.
Again, 10% off on 100 is 90 and 25% off on 90 is 90×0.75 = 67.5.
So, Both way is the same.
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The table below shows the amount of lemon juice and sugar needed to make three different-sized batches of lemonade using the same recipe.
Lemon juice (\text{mL}mLstart text, m, L, end text) Sugar (\text{g}gstart text, g, end text)
Batch A 500500500 200200200
Batch B 750750750 300300300
Batch C 150015001500 600600600
Write an equation to describe the relationship between jjj, the amount of lemon juice in \text{mL}start text, m, L, end text, and sss, the amount of sugar in \text{g}gstart text, g, end text.
Answer:
j = 2.5sStep-by-step explanation:
Batch A
500 ⇒ 200, juice to sugar ratio j/s = 500/200 = 2.5Batch B
750 ⇒ 300, juice to sugar ratio j/s = 750/300 = 2.5Batch C
1500 ⇒ 600, juice to sugar ratio j/s = 1500/600 = 2.5General equation would be:
j = 2.5sAnswer: j=2.5s
Step-by-step explanation:Got answer from Khan
6/11 = c/77 solve the proportion
Hey there!
6/11 = c/11
6(77) = c(11)
6(77) = 11(c)
462 = 11c
We got the new equation above because we had to CROSS MULTIPLY.
11c = 462
DIVIDE 11 to BOTH SIDES
11c/11 = 462/11
CANCEL out: 6/6 because it give you 1
KEEP: 462/11 because it help solve for the c-value
NEW EQUATION: c = 462/11
SIMPLIFY IT!
c = 42
Therefore, your answer is: c = 42
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
Use given triangle to fill in the blank.
Answer:
[tex]\sin B=\displaystyle\frac{b}{c}[/tex]
Step-by-step explanation:
Hi there!
This is the sine ratio:
[tex]\sin\theta=\displaystyle\frac{opposite}{hypotenuse}[/tex] where "opposite" is the side opposite the angle, "hypotenuse" is the hypotenuse of the right triangle and theta is the angle.
To find sin B, we must identify which sides of the triangle are the opposite side and the hypotenuse.
The side opposite to angle B would be b.
The hypotenuse is the side opposite the right angle, and that would be c.
[tex]\sin B=\displaystyle\frac{b}{c}[/tex]
I hope this helps!
Answer:
The choice second
[tex] \sin( B) = \frac{b}{c} [/tex]
Step-by-step explanation:
sin B = opposite/hypotenuse
Explain to your guardian how you would solve the below problem
step by step. Solve the system y = 2x + 6 and 3y = 6x + 18 by using graph paper or graphing technology.
What is the solution to the system? Feel free to submit graphs.
Answer:
infinite solutions
Step-by-step explanation:
y = 2x + 6
when x = 0, y = (2 x 0) + 6 = 6 ⇒ (0, 6)
when y = 0, 0 = 2x + 6 ⇒ x = 3 ⇒ (3, 0)
Plot the two points and draw a line through them
3y = 6x + 18
divide everything by 3 ⇒ y = 2x + 6
Therefore, y = 2x + 6 equals 3y = 6x + 18
So the lines overlap (produce the same graph)
Therefore, the system will have infinite solutions
is -11/-3 positive or negative
[tex] \huge \boxed{ \tt positive}[/tex]
[tex] \\ \\ [/tex]
[tex] \longrightarrow \sf \dfrac{ - 11}{ - 3} [/tex]
[tex] \\ \\ [/tex]
[tex] \longrightarrow \sf \dfrac{ \cancel- 11}{ \cancel - 3} [/tex]
[tex] \\ \\ [/tex]
[tex] \longrightarrow \sf \dfrac{ 11}{ 3} [/tex]
Find the value of x.
(7x+ 31)
David must install fencing around a lot that is shaped like a right triangle. The side of the lot that runs east-west is 200 ft long. The side of the lot that runs north-south is 125 ft long. Calculate how many feet of fencing he will need to surround the entire lot. If necessary, round your answer to the nearest whole.
1. Observe problem
I think 200ft and 125 ft are both sides, so:
sqrt(200^2+125^2) is 25sqrt{89}
which is
235.84952
If a sprinkler waters 1/15 of a lawn in 1/3 hour, how much time will it take to water the entire lawn?
Answer:
ok so first we know that 1/3 of a hour is 20 minutes since
60*1/3=20
so every 20 minutes 1/15 of the lawn is mowed then we need to just multiply 20 by 15
20*15=300
300 minutes or 5 hours
Hope This Helps!!!
Answer:
5 Hour
Step-by-step explanation:
For 1/15 of lawn it takes = 1/3
So, for entire lawn it will take = 1/3 * 15 = 5
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[RevyBreeze]
Find the Value of X. I will mark Brainliest to whomever answers this correctly with an extra 100 points if you give a decent explanation. Any foolish or obscene answers will be taken down and reported since this is more Brainly points than most people are willing to give.
Answer:24 degrees
Step-by-step explanation:
94+41 = 135 degrees
180 - 135 = 45 degrees
111 + 45 = 156 degrees
180 - 156 = x = 24 degrees
Hope I could help :)
Please Mark brainliest
Answer:
24°Step-by-step explanation:
One angle is shared and the sum of interior angles is 180:
94° + 41° = x + 111° (excluding the shared angle)135° = x + 111°x = 135° - 111°x = 24Jake rewrites the expression 81x2 – 1 as a difference of squares so he can factor it. Which answer choice shows how Jake could rewrite the expression?
Solve the equation-7x+6=127
Answer:
The answer is -19 because 127 - -6 will equal 133 and divided by -7 will equal the answer -19.
Helped by QueenTloveHave an nice day
Answer:
-17.28
Step-by-step explanation:
-7x +6= 127
-7x = 127-6
-7x= 121
x= -17.28
would appreciate some help! :)
AABC ~ AQRS
Find the missing side length, m.
R
B
15
m
А-
С
4.
s
10
m = [?]
=
===========================================
Work Shown:
AC/QS = BC/RS
4/10 = m/15
4*15 = 10*m
60 = 10m
10m = 60
m = 60/10
m = 6
The first equation is possible because the triangles are similar. The horizontal sides AC and QS form the ratio AC/QS. This is equal to the ratio of the diagonal sides BC/RS since similar triangles have their sides in proportion.
After the equation is set up, we cross multiply and then solve for m.
5 more than one-fith of a number is equal to 5 less than one-fourth part of the same number. Find the number.
Answer:
200
Step-by-step explanation:
Let the number = x
[tex]One-fifth \ of \ a \ number = \dfrac{1}{5}x\\\\\\5 \ more \ than \dfrac{1}{5}x =\dfrac{1}{5}x+5\\\\\\one-fourth \ of \ the \ same \ number = \dfrac{1}{4}x\\\\\\5 \ less \ than \dfrac{1}{4}x=\dfrac{1}{4}x-5\\\\\\\\\dfrac{1}{5}x+5=\dfrac{1}{4}x-5\\\\\\\dfrac{1}{5}x=\dfrac{1}{4}x-5-5\\\\\\\dfrac{1}{5}x-\dfrac{1}{4}x=-10\\\\\\\dfrac{4}{20}x-\dfrac{5}{20}x=-10\\\\\\\dfrac{-1}{20}x=-10\\\\\\x= -10*\dfrac{20}{(-1)}\\\\\\x=200[/tex]
Find the perimeter and area of this trapezoid.
Answer:
area = 36 m^2
perimeter = 34m
Step-by-step explanation:
Area of a trapezoid is calculated by the following formula:
(a+b)/2 * h (a: base, b: base, h:height)
(6+12)/2 * 4 = 36 the area is 36 m^2
The perimeter is calculated by adding all side lengths or multiplying the sum of non-parallel sides by 2
Only the measure of AB=AC is missing to find it we can use the method in attached photo
and the perimeter is:
(12+5)*2 = 34