Find the difference quotient and simplify your answer.
f(x) = x2 – 2x + 6,
h = 0
h
f(8 + h) – f(8),
Answers
We're given that
[tex]f(x)=x^2-2x+6[/tex]
which means
[tex]f(x+h)=(x+h)^2-2(x+h)+6=x^2+2xh+h^2-2x-2h+6[/tex]
When we subtract these, several terms cancel:
[tex](x^2+2xh+h^2-2x-2h+6)-(x^2-2x+6)=2xh+h^2-2h[/tex]
So the difference quotient is
[tex]\dfrac{f(x+h)-f(x)}h=\dfrac{2xh+h^2-2h}h[/tex]
and since h ≠ 0, we can cancel it out to end up with
[tex]\dfrac{f(x+h)-f(x)}h=2x+h-2[/tex]
Now plug in x = 8 (this could have been done at any prior point):
[tex]\dfrac{f(8+h)-f(8)}h=14+h[/tex]
Related Questions
A survey was given to 277 people asking whether people like dogs and/or cats. 126 said they like dogs 112 said they like cats 90 said they don't like cats or dogs. How many said they liked both cats and dogs?
Answers
Explanation:
277-90= 187
112+126=238
238-187=51
If f(x) = x+2 and g(x) = radical x-9, find g(f(x)).
Answers
Answer:
second option
Step-by-step explanation:
Substitute x = f(x) into g(x) , that is
g(f(x))
= g(x + 2)
= [tex]\sqrt{x+2-9}[/tex]
= [tex]\sqrt{x-7}[/tex]
Find all x-intercepts and y-intercepts of the graph of the function . f(x) = - x ^ 3 + x ^ 2 + 12x If there is more than one answer, separate them with commas. Click on "None" if applicable.
Answers
Answer:
The y-intercept is (0,0)
The x-intercepts are (-3,0), (0,0), and (4,0)
Step-by-step explanation:
So we have the function:
[tex]f(x)=-x^3+x^2+12x[/tex]
And we want to solve for the x- and y-intercepts.
Y)
To solve for the y-intercept, recall that the y-intercept is when the graph touches the y-axis. At that point, the x values is 0. Thus, to find the x-intercept, substitute 0 for x:
[tex]f(x)=-(0)^3+(0)^2+12(0)[/tex]
Simplify:
[tex]f(x)=0[/tex]
So, the y-intercept is (0,0)
X)
To solve for the x-intercept(s), set the function equal to 0 and solve for x:
[tex]0=-x^3+x^2+12x[/tex]
First, factor out a negative x:
[tex]0=-x(x^2-x-12)[/tex]
Factor within the parentheses:
[tex]0=-x(x-4)(x+3)[/tex]
Zero Product Property:
[tex]-x=0\text{ or } x-4=0\text{ or } x+3=0[/tex]
Divide by -1 on the first one. Add 4 on the second one. And subtract 3 on the right:
[tex]x=0\text{ or } x=4\text{ or } x=-3[/tex]
So, our x-intercepts are:
[tex](-3,0), (0,0), (4,0)[/tex]
And we're done :)
HURRY HELP!
The formula B = 100 + 75m gives the balance (B) of a bank account after (m) months of saving. Solve for m and then use your solution to find the number of months you would need to save to have a balance of $700.
Answers
Answer:
8 Months
Step-by-step explanation:
The formula in the problem (B = 100 + 75m) can be written as this:
(B-100)/75 = M
The problem gives us the balance (B=700), which we can plug into our new formula to find the number of months (m).
(700-100)/75 = M
M = 8
I hope this helps!
-TheBusinessMan
Two consecutive EVEN numbers have a sum of 30. What are the numbers?
Answers
Answer:
14 and 16
Step-by-step explanation:
Consecutive even numbers are even numbers that follow each other from smallest to biggest for example 2,4,6,8 are consecutive even numbers. So the consecutive even numbers that have a sum of 30 are 14 and 16 (14+16=30).
HOPE IT HELPED
PLEASE HURRY
which expression is equivalent to -3 + (7x+13)
Answers
Answer: [tex]7x+10[/tex]
Step-by-step explanation:
Combine the terms;
[tex]-3+7x+13\\(7x)+(-3+13)\\7x+10[/tex]
Joseph stated that 5/4 is a whole number because it does not repeat as a decimal. Is he correct? Why or Why Not?
Answers
Answer:
It is not a whole number.
Step-by-step explanation:
5/4 is equals to 1.25
Therefore it is still a decimal and a fraction, NOT a whole number
Write the recurrence relation for the nth term which is defined by multiplying the prior term by 3 and subtracting 12.
Answers
Answer: Aₙ = 3*Aₙ₋₁ - 12
Step-by-step explanation:
Here our terms will be denoted as:
Aₙ
Where this is the n-th term of the sequence.
Now we have that the recurrence relation is defined by:
"by multiplying the prior term by 3 and subtracting 12."
Then we will have that:
Aₙ = 3*Aₙ₋₁ - 12
That is the equation to find all the terms in our sequence (remember that we need to know the initial term, A₀ in order to find all the other ones)
3(2x-4)=4(4x-1) can someone please help ?
Answers
Answer:
x=-4/5
Step-by-step explanation:
3(2x-4)=4(4x-1)
6x-12=16x-4
-10x=8
x=-8/10
x=-4/5
PLEASE HELP RIGHT AWAY: Set the left side of this equation equal to f(x) and the right side equal to g(x) . Then graph y=f(x) and y=g(x) on the same coordinate grid. (x+1)^2-2=2/x
Answers
Answer:
Step-by-step explanation:
heres the answer
which ratio is less then 15/24 a.1/2 b.7/8 c. 19/24 d. 6/8
Answers
Answer:
A. 1/2
Step-by-step explanation:
So 15/24 = 0.625
therefore you need to convert all the fractions into decimals and determine which decimal is less than 0.625
a) 0.5 ------ding ding ding correct answer :)
b) 0.875
c) 0.79
d) 0.75
If this helped, please don't forget to give me brainliest!
A pillow that usually costs $18 is marked down 25%. Use the table to find the pillow’s new price.
Answers
It would be 13.50 because 50% off of 18$ is 9$ but it’s not 50% off itS 25% off so If you take the 50% Off price of 9$ and add 4.50 (One more 1/4th) you get $13.50
The highest point in Louisiana is Driskill Mountain at 585 feet. The lowest points -8 feet in New Orleans. What is the difference in feet between the highest and lowest elevation points? PLEASE SHOW THIS ON A VERTICLE NUMBER LINE!!!!!
Answers
The answer is a 577 foot difference
Which equation represents the line that passes
through the point (1,5) and has a slope of -2?
1) y = -2x + 7
2) y = -2x + 11
3) y = 2x-9
4) y = 2x + 3
Answers
Answer:
Step-by-step explanation:
y - 5 = -2(x - 1)
y - 5 = -2x + 2
y = -2x + 7
Option 1 is the answer
An atom that becomes positively charged due to the loss of one or more electrons is referred to as a/an proton. cation. . base, ( anion.
Answers
Answer:
cation.
right on the test, Mark brainlieste
Step-by-step explanation:
Answer: cation
Step-by-step explanation: an ion formed by the loss of one or more electrons becomes positively charged and is a positive ion, or cation
What is the base of a triangle with an area of 207 in.² and a height of 18 inches
Answers
We just need to divide so we can find the base length of the triangle:
207 / 18 = 11.5
Therefore, the base length of the triangle is 11.5 inches.
Best of Luck!
Answer:
23 inches
Step-by-step explanation:
A = [tex]\frac{1}{2}[/tex] bh
207 = [tex]\frac{1}{2}[/tex] b x 18
[tex]\frac{207}{9}[/tex] = b
b = 23
Given: <1 and <2 are supplementary, and <2 and <3 are supplementary. Prove: <1 is congruent to <3
Answers
Step-by-step explanation:
If ∠1 and ∠2 are supplementary, then m∠1 + m∠2 = 180° (1).
If ∠2 and ∠3 are supplementary, then m∠2 + m∠3 = 180° (2).
From (1) we have
m∠1 + m∠2 = 180° /subtract m∠1 from both sides
m∠2 = 180° - m∠1
substitute it to (2)
(180° - m∠1) + m∠3 = 180°
180° - m∠1 + m∠3 = 180° /subtract 180° from both sides
- m∠1 + m∠3 = 0 /add m∠1 to both sides
m∠3 = m∠1 ⇒ m∠1 = m∠3 ⇒ ∠1 ≅ ∠3
Suppose your SAT score is 1180. You look up the average SAT scores for
students admitted to your preferred colleges and find the list of scores below.
Based on your SAT score of 1180, which average score below represents the
college that would be your best option?
A. 1030
B. 1470
C. 1190
D. 900
Answers
Answer:
1190
Step-by-step explanation:
In division, does the big or small letter go first?
Answers
Answer: Big number
Step-by-step explanation:
In division, does the big or small letter go first?
Answer:
In division, the big one go first.
Step-by-step explanation:
So, when you do division, you can put the big or small ones first but, preferably the big ones because it will be easier to solve the equation.
Are the functions inverses? Why or why not?
Answers
Answer:
The answer is not an inverse function.
Step-by-step explanation:
The inverse function does not reverse. In other words, f(x) = x-5/10 and h(x) =10x+5 does not mirror.
4/5, √9, -0.95, √32/8, 2.9, - √6 PLEASE order from least to greatest
Answers
Answer:
-√6 -0.95 √32/8 4/5 2.9 √9
Step-by-step explanation:
4/5, √9, -0.95, √32/8, 2.9, - √6
4/5 = 0.8
√9 = 3
√32/8 = 4√2 / 8 = √2/2 = 0.707
-√6 = -2.449
-√6 -0.95 √32/8 4/5 2.9 √9
A point on a pre-image is G(5, -2). If its image has coordinates G'(2, 1), what was the translation? (x - 3, y - 3) (x + 3, y - 3) (x - 3, y + 3) (x + 3, y + 3)
Answers
Answer:
(x - 3, y + 3 )
Step-by-step explanation:
Note G(5, - 2 ) → G'(2, 1 )
Requires 3 to be subtracted from 5 to obtain 2 and 3 to be added to - 2 to obtain 1, thus
(x, y ) → (x - 3, y + 3 ) is the translation rule
Answer:
the answer is (x - 3, y + 3 )
Step-by-step explanation:
hope this helps
Jonas is planning out his route for an upcoming race. He uses negative numbers to represent points before the finish line and positive numbers to represent points after the finish line.
On Jonas's map, there is a bridge at -91 3/4 meters, and his wife is watching him at 14 1/2 meters.
What do 0 meters represent?
Answers
Answer:
The finish line
Step-by-step explanation:
This is because, since negative numbers are used to represent points before the finish line, and positive numbers are used to represent points after the finish line, the finish line can only be represented by the number zero. Since on Jonas' map, there is a bridge at -91 3/4 metres, therefore, the bridge is 91 3/4 metres before the finish line. And, since his wife is watching at 14 1/2 metres, since this number is positive, she is 14 1/2 metres after the finish line. So, the finish line itself, will be represented by 0 metres since this is indicated a change from negative to positive.
E is the midpoint of DF. If DE = 15x and DF = 31x -11, what is DF?
Answers
Step-by-step explanation:
(31x-11)-15x=DF
DF= 16x-11
Answer:
(31x-11)-15x=DF
DF= 16x-11
Step-by-step explanation:
It should be right
help please! Will mark you as Brainliest!
Answers
Answer:
21
Step-by-step explanation:
This angle has all of the following names, except:
Answers
Answer:
its c. <vwx
Step-by-step explanation:
i got it right
Solve the following system of equations using substitution:
2x - 2y + z = 8
-y+z=4
2z=4
Answers
Answer:
Step-by-step explanation:
2z = 4
z = 2
-y + 2 = 4
-y = 2
y = -2
2x + 4 + 2 = 8
2x + 6 = 8
2x = 2
x = 1
(1, -2, 2)
The Key Club is selling personalized valentines to raise money. The print shop charges $2 for each valentine, plus a flat rate of $10 for printing. Write an equation to represent how many valentines the club can print with a budget of $125.
Answers
Answer:
2x + 10 = 125 is the answer
did it on edge
Step-by-step explanation:
whats the difference between a variable and a numeral
Answers
Answer:
a numerical variable is a variable where the measurement or number has an empirical meaning.
a variable is a category or a type
Answer:
A numerical variable is a variable where measurement or a number has a numerical meaning.
Square root !!!!!!!!
Answers
Answer:
hope this helped
Step-by-step explanation:
Step 1: Calculate. We calculate the square root of 50 to be: √50 = 7.07106781186548.
Step 2: Reduce. 7.07.
Step 3: Round. Round 7.07 so you only have one digit after the decimal point to get the answer: 7.1.