[tex]\text{Given that,}\\\\f(x)= \dfrac{x+1}{x-1}\\\\\\f'(x)=\lim\limits_{h \to 0} \dfrac{f(x+h) - f(x) }{h}\\\\\\ ~~~~~~~~=\lim\limits_{h \to 0} \dfrac{\left( \tfrac{x+h+1}{x+h-1}\right) - \tfrac{x+1}{x-1}}{h}\\\\\\~~~~~~~~=\lim\limits_{h \to 0} \dfrac{\tfrac{(x+h+1)(x-1) - (x+1)(x+h-1)}{(x+h-1)(x-1)}}{h} \\\\\\~~~~~~~~=\lim\limits_{h \to 0} \dfrac{\tfrac{x^2-x+hx-h+x-1 - x^2-xh+x-x-h+1}{(x+h-1)(x-1)}}{h}\\\\\\~~~~~~~~[/tex]
[tex]~~~~~~~=\lim\limits_{h \to 0} \dfrac{\tfrac{-2h}{(x+h-1)(x-1)}}{h}\\\\\\~~~~~~~~=\lim\limits_{h \to 0} \dfrac{-2}{(x+h-1)(x-1)}\\\\\\~~~~~~~~=\dfrac{-2}{(x+0-1)(x-1)}\\[/tex]
[tex]\\\\~~~~~~~~=\dfrac{-2}{(x-1)(x-1)}\\\\\\~~~~~~~~=\dfrac{-2}{(x-1)^2}[/tex]
The recursive formula for an arithmetic sequence is:
{a1 = -6
{an-an-1+2
What is the 3rd term in the sequence?
A. - 2
B. -4
C. -10
D. -18
The transformation of triangle ABC is an example of what?
Answer:
The relation between preimage and image
Step-by-step explanation:
help me help me help me
Answer:
For the third one,
3, 8, 15, 24, 35, 48, 63
For the fourth one,
4, 6, 10, 18, 30, 46, 66
Step-by-step explanation:
In a writing competition, the first place winner receives 1/2 of the prize money. The second runner up receives 1/4 of what the winner won. What was the total amount of prize money distributed if the winner receives $8000
Answer:
10,000 is the total amount of.money that was distributed
Mrs. Becker drives past the Route 50 drawbridge light every morning on the way to
work. Eight out of 10 times, the traffic light is red. There are only 25 days of school le
how many of those days should she expect to get stopped at that light?
Answer:
20 days
Step-by-step explanation:
1) [tex]\frac{8}{10}[/tex] must be written as a fraction where the denominator is 25 since there are 25 days of school.
[tex]\frac{8}{10} = \frac{x}{25}[/tex]
2) Cross multiply them.
[tex]10(x) = 25(8)[/tex]
[tex]10x = 200[/tex]
3) Solve for [tex]x[/tex].
[tex]x = \frac{200}{10}[/tex]
[tex]x = 20[/tex]
15 There are 30 students in a class. 1 5 like football. How many students do not like football?
A babysitter charges a rate of $15 per hour. how long was the babysitter there if she makes 40
Answer:
2.7
Step-by-step explanation:
15/1 = 40/x
Cross multiply: 40/15
Divide: 2.66
Round up: 2.7
2.7 times 15= 40.5
Answer:
2hrs. 40mins.
Step-by-step explanation:
A babysitter charges a rate of $15 per hour. How long was the babysitter there if she makes $40?
x = hours she babysat
Equation:
15x = 40
Divide to isolate x:
15x = 40
/15 /15
x = 8/3 hrs.
Now, we convert into hours and minutes, since she did work for more than an hour, to earn the $15 each hour.
We know that there are 60 mins. in an hour
60 * 8/3
480/3
160 mins.
Convert into hour and mins:
1 hr. = 60 mins
160/60 = 2 40/60 ==> 2 2/3
Convert 2/3 into mins to add to the hours:
60 * 2/3
120/3 = 40
2hrs. + 40 mins.
2hrs. and 40mins
Therefore, the babysitter was there for 2hrs. 40mins.
Hope this helps!
A certain number added to its square is equal to 90. What is/are the number(s) that work?
Answer:
9,-10
Step-by-step explanation:
Let u be a number.
[tex]u + {u}^{2} = 90[/tex]
[tex]u {}^{2} + u - 90 = 0[/tex]
[tex](u + 10)(u - 9) = 0[/tex]
[tex]u = - 10[/tex]
or
[tex]u = 9[/tex]
9, -10
Tracy has 40 feet of material to make the perimeter of a rectangular sandbox for her little brother.
What rectangle with whole-number side lengths would give the sandbox with the greatest area?
Answer:
11 and 9
Step-by-step explanation:
With a width of 11 and a length of 9 the area of the rectangle would be
11 * 9 = 99
By adding 11 and 9, then mulitplying it by 2 we get the perimeter
11 + 9 = 20
20 * 2 = 40
Is 10 times as much as 0.007
Answer:
10 x 0.007 = 0.07
Step-by-step explanation:
im not sure if thats what you meant
solve the system of equations:
-3x + 7y = -15
3x + 5y = 15
what do X and Y equal?
Answer:
x=5
y=0
Step-by-step explanation:
Let's solve the system of equations through elimination
Solving by elimination is when you add or subtract one equation by the other to eliminate one variable
In this case, adding 3x and -3x would cancel each other out so we should add the equations
[tex]-3x + 7y = -15\\+(3x + 5y = 15)\\0+12y=0\\12y=0[/tex]
Now solve for y
Divide both sides by 12 to isolate y
[tex]12y=0\\\\\frac{12y}{12} =\frac{0}{12} \\\\y=0[/tex]
Now sub in the value of y into one of the original equations and solve for x
[tex]3x+5y=15\\3x+5(0)=15\\3x=15\\[/tex]
Divide both sides by 3 to isolate x
[tex]\frac{3x}{3} =\frac{15}{3} \\x=5[/tex]
Determine the discriminant for the quadratic equation -3=x2+4x+1. Based on the discriminant value, how many
number solutions does the equation have?
real
Discriminant = b2-4ac
O 0
O 1
O 2
O 12
Number of solution for the given quadratic equation as Discriminant=0 is equals to 1.
What is quadratic equation?" Quadratic equation is defined as the polynomial containing variables with highest exponent equals to 2."
Formula used
For quadratic equation
[tex]ax^{2} +bx+c=0[/tex]
Discriminant = b²-4ac
According to the question,
Given quadratic equation
[tex]-3 = x^{2} +4x+1[/tex]
⇒[tex]x^{2} +4x+1 +3 =0[/tex]
⇒[tex]x^{2} +4x+4 =0[/tex]
Here, a=1 , b= 4 , c =4
Substitute the value in the formula we get,
Discriminant = [tex]4^{2} - 4(1)(4)[/tex]
= [tex]16 -16[/tex]
= 0
Number of solution discriminant =0 is 1.
[tex]x^{2} +4x+4 =0[/tex]
⇒[tex](x+2)^{2} =0[/tex]
⇒[tex]x= -2[/tex] has unique solution.
Hence, number of solution for the given quadratic equation as Discriminant=0 is equals to 1.
Learn more about quadratic equation here
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Find the area
A. 300 units
B. 520
C. 500 units
Answer:
b.520 units
Step-by-step explanation:
find the area of the bigger triangle the base is 20 which is 10×2 while the height is 28. 1/2×20×28=280units find the area of the smaller triangle. the base is also 20 while the height is 24. 1/2×20×24=240. sum the areas of the two triangles. 280+240=520units
Dan made $5000 in taxable income last year.
Suppose the income tax rate is 10% for the first $7500 plus 15% for the amount over $7500
How much must Dan pay in income tax for last year?
well, we know is 10% for the first 7500, but Dan only made 5000 of taxable income, so he's in that range of 0 - 7500, so he only gets to pay 10% of 5000.
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{a\% of b}\\ \cline{1-1} \\ \left( \cfrac{a}{100} \right)\cdot b \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{10\% of 5000}}{\left( \cfrac{10}{100} \right)5000}\implies 500[/tex]
Mae has 36 orange slices. She will fill each of
7 bags with the same number of orange slices.
How many slices will be in each bag? How many
slices will be left over?
Answer:
5 orange slices will be in each bag with 1 left over
Step-by-step explanation:
36 ÷ 7 = 5 with a remainder of 1
Solve for x in the equation x2-12x+36 = 90
X
=
O X=6+3/10
O x=6+217
X
X= 12+3^22
X= 12+3/10
Answer:
Step-by-step explanation:
hello : (x-6)² = 90 .....continu
The number of peanuts in bags is normally distributed with a mean of 172.5 peanuts and a standard deviation of 1.9 peanuts.
What is the z-score of a bag containing 168 peanuts?
−2.37
−2.06
−1.32
−1.05
Rodney says that he can draw two rectangles that have the same areas but different perimeters.
Which of the following pairs of rectangles could Rodney draw?
Select all that apply.
LIVE
A rectangle with side lengths 4 cm and 6 cm and a rectangle with side lengths 2 cm and 12 cm
LIVE
A rectangle with side lengths 4 cm and 6 cm and a rectangle with side lengths 2 cm and 8 cm
LIVE
A rectangle with side lengths 3 cm and 6 cm and a rectangle with side lengths 2 cm and 9 cm
LIVE
A rectangle with side lengths 5 cm and 6 cm and a rectangle with side lengths 2 cm and 9 cm
LIVE
A rectangle with side lengths 5 cm and 4 cm and a rectangle with side lengths 2 cm and 7 cm
Answer:
A rectangle with sides lengths 4cm and 6cm and a rectangle with side lengths 2cm and 12 cm...
The points (4,7) and (r. – 5) lie on a line with slope – 3. Find the missing coordinate r
Answer:
[tex]r=\frac{14}{3}[/tex]
Step-by-step explanation:
Set up an equation and solve for r using the formula for slope:
[tex]\frac{5-7}{r-4}=-3\\ \\-2=-3(r-4)\\\\-2=-3r+12\\\\-14=-3r\\\\\frac{14}{3}=r[/tex]
Which point is located at (-1, 1 1/4)
A
B
C
D
Answer: Point A.
Step-by-step explanation: To find the location of points such as (-1, 1 1/4), you need to know what part of the point is the x-axis and the y-axis. The first part of the point is the x-axis, which is the horizontal line that goes left to right on the coordinate graph. The first part of the point (-1, 1 1/4), is -1. The second part of the point is the y-axis, which is the vertical line that goes up and down on the coordinate graph. The second part of the point (-1, 1 1/4), is 1 1/4. Therefore, we first find the x-axis to the point (-1, 1 1/4), which is -1, and so far, point A is the only option that matches. However, we need to make sure that the point (-1, 1 1/4)'s y-axis matches to point A as well. The y-axis to the point (-1, 1 1/4) is 1 1/4 so we need to go up 1 1/4 times, and the point that matches these actions is point A. Therefore, that's your answer.
Let me know if this is right! :)
The doubling time of a population of flies is 8 hours. By what factor does the population increase in 34 hours? By what factor does the population increase in 1 week ?
Answer:
19.017 in 34 hours2,097,152 in 1 weekStep-by-step explanation:
An exponent is used to signify repeated multiplication. When the population doubles, it is multiplied by 2. The number of times the population has doubled will be an exponent of 2.
a)In 34 hours, the population will have doubled 34/8 = 4.25 times. The multiplier is 2 with an exponent of 4.25:
factor = 2^4.25 ≈ 19.027
__
b)The population will double 24/8 = 3 times each day. After 7 days, the population will have doubled 7×3 = 21 times. The multiplication factor is ...
factor = 2^21 = 2,097,152
joshua drinks 8 cups of water a day. The recommended daily amout is given in fluid ounces.How many fluid ounces of water does he drink each day?
Question:
Joshua drinks 8 cups of water a day. The recommended daily amout is given in fluid ounces. How many fluid ounces of water does he drink each day?
What were being asked:
How many fluid ounces of water does he drink each day?
Answer:
The answer is
→ 64 fluid ounces
Step-by-step explanation:
1 cup of water = 8 fluids.
8 cups of water x 8 fluids = 64 ounces
Therefore, your answer is 64 fluid ounces.
Hope this helped! :^)
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Submitted on 4/18/2022 at 4:08 PM
(To avoid plagarism, by users whom decide to copy.)
On Friday, Hayley has purchased more flour and eggs, but only has 22 cups of sugar and 4 sticks of butter. Which combination of loaves of zucchini bread and banana bread can Hayley make?
Answer:
It is C
Step-by-step explanation:
A culture started with 6000 becteria. after 3 hours it grew to 7200 becteria. Predict how many bacteria will be present after 19 hours. Round your answer to the nearest whole number. p=ae^kt
Answer: 13,600.
Step-by-step explanation: every hour is 400 bacteria produced. 400x19= 7600. 7600+6000=13600
What is the value for y when x = 8
Answer:
x+y=0
8+y=0
y=8
Step-by-step explanation:
correct me if I'm wrong
Answer:
D. 44
Step-by-step explanation:
y = (8 x 5) +4
y= 40 + 4
y= 44
Simplify the expression. (–8.6)0
A)–1
B)–8.6
C)1
D)0
Answer: D
Explanation: Anything times 0 is 0.
A babysitter charges a rate of $15 per hour. how long was the babysitter there if she makes $5
Answer:
20 mins.
Step-by-step explanation:
A babysitter charges a rate of $15 per hour. How long was the babysitter there if she makes $5?
x = hours she babysat
Equation:
15x = 5
Divide to isolate x:
15x = 5
/15 /15
x = 1/3 hrs.
Now, we convert into minutes, since she didn't work for a whole hour, to earn the $15
We know that there are 60 mins. in an hour
60 * 1/3
60/3
20 mins.
Therefore, the babysitter was there for 20 mins.
Hope this helps!
On January 1, 2022 Hideki Matsuyama provides services in exchange for a $10,000 zero-interest bearing note due in 4 years. The effective interest rate for a note of this type is 15 percent. How much revenue does Hideki recognize on January 1, 2022?
Answer:
Revenue=$6000
Step-by-step explanation:
A = PRT
100
A= (10,000×4×15)/100
= (10,000×60)/100
= 600,000/100
=$6000
Hideki recognizes a $17,490.06 revenue.
What is Revenue?Revenue is the total amount of income generated by the sale of goods and services related to the primary operations of the business.
Given that on January 1, 2022, Hideki Matsuyama provides services in exchange for a $10,000 zero-interest bearing note due in 4 years, and the effective interest rate for a note of this type is 15 percent,
To determine how much revenue does Hideki recognize on January 1, 2022, the following calculation must be made:
x = 10000 x 1.15^4
x = 10000 x 1.749
x = 17490.06
Therefore, Hideki recognizes a $17,490.06 revenue.
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. Mai skated miles, and Clare skated farther than that. Write an equation to Accelerated 6 Unit 6 Lesson 1 represent the relationship between the distance Mai skated ( ) and the distance Clare skated ( ).
Answer:
X over y or x/y since y is claire and she skated more
Step-by-step explanation:
since y is claire and she skated more
Y=Clarie skated
X= Mai skated
Find the measure picture below
By the vertical angle theorem, angle K is equal to the angle of measure 28 degrees.
--> so k is 28 degrees
Def. of vertical angle theorem: states that the opposite (vertical) angles of two intersecting lines are congruent
Hope that helps!
