Note the derivative rule
[tex]\\ \boxed{\star\bf \dfrac{d}{dx}(x^n)=nx^{n-1}}[/tex]
Let's see
[tex]\\ \rm\Rrightarrow \dfrac{d}{dx}(2^{x+1}-2^{x-1})[/tex]
[tex]\\ \rm\Rrightarrow \dfrac{d}{dx}2^{x+1}-\dfrac{d}{dx}2^{x-1}[/tex]
[tex]\\ \rm\Rrightarrow (x+1)2^{x+1-1}-(x-1)2^{x-1-1}[/tex]
[tex]\\ \rm\Rrightarrow (x+1)2^x-(x-1)2^{x-2}[/tex]
[tex]\\ \rm\Rrightarrow (x+1)2^x-(x-1)2^x/2^2[/tex]
[tex]\\ \rm\Rrightarrow (x+1)2^x-(x-1)2^x2^{-2}[/tex]
[tex]\\ \rm\Rrightarrow 2^x(x+1-(x-1)2^{-2})[/tex]
[tex]\\ \rm\Rrightarrow 2^x(x+1-x/4-1/4)[/tex]
A door's shape is made by combining a rectangle and a semicircle. What is the area of the door?
Answer:
34.28 ft²Step-by-step explanation:
Area of the door = area of the rectangle + area of the semicircle
= 7 × 4 + (3.14 × 2²)/2
= 28 + (3.14 × 4)/2
= 28 + 3.14 × 2
= 28 + 6.28
= 34.28
what is the solution for the equation -15=5(3y-10)-5y
Answer:
[tex]\Large\boxed{\sf{y=\dfrac{7}{2} }}[/tex]Step-by-step explanation:
Isolate the variable of y from one side of the equation.
-14=5(3y-10)-5y
First, switch sides.
[tex]\sf{5\left(3y-10\right)-5y=-15}[/tex]
Use the distributive property.
DISTRIBUTIVE PROPERTY:
A(B-C)=AB-AC
5(3y-10)
Multiply by expand.
5*3y=15y
5*10=50
15y-50-5y
15y-5=10y
= 10y-50
10y-50=-15
Add by 50 from both sides.
10y-50+50=-15+50
Solve.
10y=35
Then, you divide by 10 from both sides.
10y/10=35/10
Solve.
Divide the numbers from left to right.
35/10=7/2
y=7/2
Divide is another option.
7/2=3.5
[tex]\Longrightarrow: \boxed{\sf{y=\dfrac{7}{2}}}[/tex]
Therefore, the correct answer is y=7/2.I hope this helps. Let me know if you have any questions.
Answer number 14 please. Thank you.
Answer:
i already did i the previous one
btw can you send this full page of work in pdf if you could
15.
[tex] \frac{89.32}{48.50} \times 100[/tex]
Bob sells part of a 50-acre rectangular plot of land he owns so that he can still own a smaller rectangular plot within the original. After he makes the sale, Bob's remaining plot of land is half as long and half as wide as his original plot. What is the area of Bob's remaining plot of land?
Considering the area of a rectangle, it is found that the area of Bob's remaining plot of land is of 12.5 acres.
What is the area of a rectangle?The area of a rectangle of length l and width w is given by the multiplication of these dimensions, that is:
A = lw.
In this problem, both the length and the width are divided in half, hence the proportion remaining is given by:
A = 0.5l x 0.5w = 0.25lw = 25% of the initial area.
Hence:
0.25 x 50 = 12.5.
The area of Bob's remaining plot of land is of 12.5 acres.
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If 6 pairs of socks cost $6. 90, what is the price for one pair of socks
Answer:
$1.15
Step-by-step explanation:
6 pairs of socks cost $6.90.
so every sock is at least one dollar. one dollar per sock, then you take the .90 and divided between the 6 socks and you get 15, so one dollar and 15 cents per sock.
Hope this helps, have a nice day!
What is the value of the remainder?
[tex] \underline{ \boxed{ \sf{✰\: Option\:D. \:81✓ }}}[/tex]
Refer to the attachment for solution ☘️
Hope it helps
hello what is 5x6 and what is 24 divide by 50
Answer:
5×6=30
24÷50=0.49....following long division method
Tran has a credit card with a spending limit of $2000 and an apr (annual percentage rate) of 12%. during the first month, tran charged $450 and paid $150 of that in his billing cycle. which expression will find the amount of interest tran will be charged after the first month? (0.01) (300 dollars) (0.01) (450 dollars) (0.12) (300 dollars) (0.12) (450 dollars)
The expression that will find the amount of interest tran will be charged after the first month is: (0.01) (300 dollars).
ExpressionFirst step
Monthly interest rate = (Annual percentage rate ÷ Number of months in a year)
Monthly interest rate= 0.12 ÷ 12
Monthly interest rate= 0.01
Second step
Amount left = Amount charged - Amount paid
Amount left = $450 - $150
Amount left = $300
Third step
Amount of interest=Monthly rate ×Amount left
Amount of interest=(0.01) (300 dollars)
Amount of interest=$3
Therefore the expression that will find the amount of interest tran will be charged after the first month is: (0.01) (300 dollars).
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what are the mean,median,mode, and range of the data set given the altitude of lakes in feet:-11,-28,-17,-25,-28,-39,-6,and -46? i dont know the answer
Answer:
Read explanation.
Step-by-step explanation:
The average is -22.2 (mean)
-46,-39,-28,-28,-25,-17,-11.-6 You cross out the lowest and highest until you reach the middle, which is -26.5(median)
The mode is -28 as it is the most repeated number
The range is 40 as when you subtract a negative it turns into the absolute value.
PLEASE HELP
i have no clue what im doing wrong but i cannot find the answer
The sum of a number x and 2,496 is 17,344. What is the value of x?
Find the least common denominator of 11/10 and 1/15
Answer: The least common denominator is 30.
Step-by-step explanation: Look at the image I have uploaded.
Good luck!
please help im sorry i dont understand shapes and angles
Answer:
Sorry I can't answer this.
But you may use the protacter to find the angle
? = 73°
There are 7 sides in this polygon
Calculate total interior angles using (n-2) * 180
["n" denotes number of sides]
Here total interior angle: (7-2)*180 = 900°The missing angle inside the polygon:
900° - 130° -119° -130° -154° -130° -130°
900° - 793°
107°
A straight line has total 180°
? + 107° = 180°
? = 180° - 107°
? = 73°
Please Help !! What is the surface area of a cylinder with base radius 4 and height 5. Show your work .
Answer:
226.19
Step-by-step explanation:
A= 2πrh+ 2πr2= 2·π·4·5+2·π·42≈226.19467
or
S = (2 * pi * r^2) + (2 * pi * r * h)
S = (2 * pi * 4^2) + (2 * pi * 4 * 5)
S = (32 pi) + (40 pi) = 72pi = 226.08 ANS.
Answer:
251.333 (Repeating)
Step-by-step explanation:
First, you need to find the area of the circle at the top, which is [tex]\pi r^{2}[/tex]
Next, you multiply it by the height. (I did also use actual pi)
This is if it's total area, not lateral.
1. If the height is 12 inches and the diameter
is 16 inches, what is the volume?
h
Answer:
2411.52
Step-by-step explanation:
D = r x 2
R = d/2
16/2 = 8
A = πr^[tex]\pixr^{2}[/tex]
A = 3.14 x 8x8
A = 3.14 x 64
A = 200.96
V = A x H
V = 200.96 x 12
V = 2411.52
find the measure of the missing angle?
56+72+x =180 ( therefore sum of angle in a triangle)
128+x=180
x=180-128
x=52
Answer:
THE MISSING ANGLE = 52°
Step-by-step explanation:
Sum of all angles = 18°0
Let the missing angle be x°
56° + 72° + x° = 180°
x° = 180° - 72° - 56°
x° = 52°
!!PLEASE PLEASE PLEASE PLEASE MARK ME THE BRAINLIEST!!
Hayden has $20 to spend at the county fair. Admission to the fair is $5.00 per person, and tickets for food and games are $1.25 per ticket. What information is needed to calculate the amount of money that Hayden will have left after attending the fair?
Answer:
prices of food and games and tickets
PLS HELPP WHAT IS THE ANSWER???
Answer:
-220
Step-by-step explanation:
Answer:
Let us start by plugging in x=2 into all variables x and y=1 into all y's
so: The result is -220
Korey is planning to open a comic book store. he has developed the following expense breakdown for set-up and operation for the first year. korey has $8,500 in savings and $25,000 in inheritance money to use to open his store. will korey have enough to run his business for a full year? expense amount rent $10,800 insurance $3,000 store fixtures $2,700 computer and cash register $1,200 inventory $17,400 a. yes, korey will have $1,600 to spare. b. no, korey will be short $1,600. c. yes, korey will have $15,800 to spare. d. no, korey will be short $15,800.
Answer:
C. 15800 to spare
Step-by-step explanation:
All you have to do is add up the total money he has to spend money, then you add up the total cost, and subtract the total money he has to spend by the total cost, and you're left with he has 15,800 left to spare. ;)
He should make a loan from the investors about 4.6%..
What is Percentage?To determine the volume or chance of commodity in terms of 100, use the chance formula. Per cent simply means one in a hundred. With the chance formula, a number between 0 and 1 can be expressed. A number that's expressed as a bit of 100 is what it is. It's substantially used to compare and determine rates and is represented by the symbol.
Total quantum plutocrat Korey have
= Saving plutocrat heritage plutocrat
= $,500$,000
= $,500
Total quantum of charges
= Store Fixtures amount + Computer and Cash Register amount + Inventory amount +Rent amount + Insurance amount
= $2700 + $1200 + $17400 +$10800 + $3000
= $35100
So, Fund taken through loans and investor
= Total quantum of charges -Total quantum plutocrat Korey have
= $ 35100-$ 33500
= $ 1600
and, the percentage is
= 1600 x 100 / 35100
= 4.6%
He should make a loan from the investors about 4.6%.
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Hey I kinda need some help with this could u help?
Answer:
[tex]x = 13 ~~ \text{and}~~ y= 10[/tex]
Step-by-step explanation:
[tex]~~~~~~2.31 \times 10^x = 2200 \times 1.05 \times 10^y\\\\\implies 2.31 \times 10^x = 2310 \times 10^y\\\\\implies \dfrac{10^x}{10^y} = \dfrac{2310}{2.31}\\\\\implies 10^{x-y}=1000\\\\\implies 10^{x-y} = 10^3\\\\\implies x - y = 3[/tex]
[tex]\text{If x = 13 and y = 10 then the difference will be 3.}[/tex]
Twenty-one less than a number is seven. What is the number? 3 14 28 147
Answer:
Option C, 28
Step-by-step explanation:
Step 1: Make an expression
Twenty-one less than a number is 7
[tex]x - 21 = 7[/tex]
Step 2: Solve the equation for x
[tex]x - 21 = 7[/tex]
[tex]x - 21 + 21 = 7 + 21[/tex]
[tex]x = 28[/tex]
Answer: Option C, 28
Answer:
28
Step-by-step explanation:
because twenty eight subtracted by twenty one equals seven
Kate packs snow into 5 identical jars. each jar represents a different depth of snow. kate then lets the snow in each jar completely melt. the table shows the height of the liquid in each jar as it relates to the original depth of snow in the jar. a 2-column table with 5 rows. the first column is labeled snow depth (inches), x with entries 2, 4, 6, 8, 10. the second column is labeled water depth (inches), f(x) with entries 0.4, 0.8, 1.2, 1.6, 2.0. which statements are true about the relationship between the depth of the snow and the height of water in the jar after the snow is melted? select two options. the points on a graph representing the relationship lie on a line. there is 0.4 inch of water to every 1 inch of snow. a line through the points will pass through (0, 0). the function relating snow depth to water depth is quadratic. the data can be represented by f(x) = 0.2x.
The true statements include the point on the graph represents the relationship lie on a line and a line through the points will pass through (0, 0).
How to illustrate the table?From the table, the water depth changes for about (0.8 - 0.4) = 0.4 inches. Here, the function is a linear model.
In this case, the the point on the graph represents the relationship lie on a line and a line through the points will pass through (0, 0).
Learn more about graphs on:
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Answer:
A & C
Step-by-step explanation:
hope this helps
A bag contains 3red, 4white, 5green balls. Three balls are selected without replacement. Find the probability that the three balls chosen are:
A) all red
B) all green
C)one of each color
Answer:
A. 1/220 B. 1/22 C. 3/11
Step-by-step explanation:
This question uses combinations -- counting the number of ways a selection can be made from a set of objects (without arranging them after the selection is done).
Notations for combinations:
The number of ways to select r things from a set of n things is
[tex]C(n,r)=\frac{n!}{r!(n-r)!}[/tex] where the exclamation points mean factorial.
[tex]n!=1\cdot2\cdot3\ldots\cdot n[/tex] and 0! is defined to be 1.
There are two other commonly used symbols for this:
[tex]_nC_r[/tex] and [tex]n \choose x[/tex].
In all three parts, the number of ways to choose 3 balls from a set of 12 is
[tex]C(12,3) = \frac{12!}{3!(12-3)!}=\frac{12\cdot 11 \cdot 10 \cdot 9\cdot 8\cdot 7\cdot 6\cdot 5\cdot4\cdot3\cdot2\cdot1}{(3\cdot2\cdot1)(9\cdot8\cdot7\cdot6\cdot5\cdot4\cdot3\cdot2\cdot1)}[/tex]
Notice that 9 factors in the denominator cancel 9 factors in the numerator, leaving
[tex]C(12,3) = \frac{12!}{3!(12-3)!}=\frac{12\cdot 11 \cdot 10}{3\cdot2\cdot1}=220[/tex]
A. The number of ways to choose 3 red balls from the 3 red balls is C(3, 3) = 1, so the probability is 1 / 220.
B) The number of ways to choose 3 green balls from the set of 5 green balls is [tex]C(5,3)=\frac{5!}{3!(5-3)!}=\frac{5!}{3!2!}=\frac{5\cdot 4}{2}=10[/tex] out of 220, so the probability is 10/220 = 1/22.
C) The number of ways to choose 1 red is C(3, 1) = 3. Choose 1 green in C(5, 1) = 5 ways. Choose 1 white in C(4, 1) = 4 ways.
The probability is [tex]\frac{3\cdot 5 \cdot 4}{220}=\frac{60}{220}=\frac{3}{11}[/tex]
Answer:
a) 1/220
b) 1/22
c) 3/11
Step-by-step explanation:
Check the attachment.
Which side is opposite angle C?
None
BC
AB
AC
Answer:
AB
Step-by-step explanation:
opposite is AB
Which absolute value inequality is modeled by this graph?
A. y ≥ |x − 3|
B. y ≥ |x| − 3
C. y > |x + 3|
D. y > |x| + 3
Answer:
c
Step-by-step explanation:
sorry if it is wrong
What is the equation of a line in general form that does not have a y-intercept and goes through the point (3,6) ?
(** I know the answer is x-3 = 0, please EXPLAIN)
Answer:
[tex]x = 3[/tex]
Step-by-step explanation:
Step 1: Determine the equation
So we know that our equation does not have a y-intercept which means that it doesn't intersect ANYWHERE on the y-axis. Therefore, this means that our equation will be a straight vertical line that doesn't move side to side and just goes straight up and down. We also know that our point is (3, 6) which means that our x-value will be 3 and this is where the equation will be located.
There are several ways to display our answer where x = 3 is the most common way which basically means give me all of the y-values for the same x value of 3. Another way of saying it is x - 3 = 0 which either way when adding 3 to both sides gives you x = 3 which is what I usually go with.
Answer: [tex]x = 3[/tex]
Answer:
x = 3 or x - 3 = 0
Step-by-step explanation:
Given
It does not have a y-interceptPasses through the point (3, 6)Solving
If the line cannot touch the y-axis, it has to be parallel to it (in other words, the line must be vertical)Since the x-value is constant for a vertical line and it passes through the point (3, 6), the equation of the line will be :x = 3 or x - 3 = 0Dale wants to order business cards for his new job.
• Company A charges a flat fee of $0.15 per card.
• Company B charges $0.10 per card plus an additional $10.00 for delivery
Write an inequality for the amount of business cards, c, that Dale would need to buy for Company to be cheaper
Dale would need to buy more than 200 cards for Company B to be cheaper.
What is inequality?Inequality is defined as the relation which makes a non-equal comparison between two given functions.
Company A charges a flat fee of $0.15 per card.
Company B charges $0.10 per card plus an additional $10.00 for delivery
Let x = number of cards
Company A charges = $0.15x
Company B charges = $10.00 + $0.10x
For company B to be the cheaper option ( B < A )
$10.00 + $0.10x < $0.15x
$10.00 < $0.05x
subtracting positive from both sides to retains the sense of the inequality and x is positive
200 < x
x > 200
So, Dale would need to buy more than 200 cards for Company B to be cheaper.
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A train travels from Washington D.C. to New York (225 miles). The train departs at 4:55 PM and arrives in New York at 7:55 PM. What is the average speed of the train?
7:55 pm - 4:55 pm = 3 hours
225 miles / 3 hours = 75 miles per hour
Average speed = 75 miles per hour
Please help, thank you!
Answer:
Vertical Asympote, but I might be wrong, haven't done this math in years
What is the volume of the prism if its 2 centimeters long tall 12 centimeters wide and 25 centimeters long
Answer:
600 cm
Step-by-step explanation:
L*W*H SO IT WILL BE 2*12*25