• {4, 7, 12, 19, … }
has 1st differences
7 - 4 = 3
12 - 7 = 5
19 - 12 = 7
and 2nd differences
5 - 3 = 2
7 - 5 = 2
• {-1, 2, 7, 14, …}
1st differences:
2 - (-1) = 3
7 - 2 = 5
14 - 7 = 7
2nd differences:
5 - 3 = 2
7 - 5 = 2
• {-2, -8, -18, -32, …}
1st differences:
-8 - (-2) = -6
-18 - (-8) = -10
-32 - (-18) = -14
2nd differences:
-10 - (-6) = -4
-14 - (-10) = -4
Answer:
Hello,
Step-by-step explanation:
I am going to explain the method with the 1th:
[tex]\begin{array}{ccccc}n & u_n&u_{n+1}-u_{n}&u_{n+2}-2u_{n+1}+u_{n}&v_{n}\\1&4&&6\\2&7&3&9\\3&12&5&2&14\\4&19&7&2&21\\...&&&\\\end{array}\\\boxed{u_{n+2}=2u_{n+1}-u_{n}+2}\\[/tex]
[tex]Let\ say\\v_{n}=u_{n}+2\\v_{n+2}=u_{n+2}+2=(2u_{n+1}-u_{n}+2)+2=2(v_{n+1}-2)-(v{n}-2)+4\\v_{n+2}=2v_{n+1}-v{n}+2\ (1)\\v_{n+3}=2v_{n+2}-v{n+1}+2\ (2)\\(2)-(1)==> \boxed{v_{n+3}=3v_{n+2}-3v_{n+1}+v_n}\\[/tex]
[tex]Caracteristic\ equation:\\P(r)=r^3-3r^2+3r-1=0\\P(r)=(r-1)^3\\v_n=\alpha+\beta*n+\gamma*n^2\\v_1=6 ==> \alpha+\beta*1+\gamma*1=6\\u_2=9 ==> \alpha+\beta*2+\gamma*4=9\\u_3=14 ==> \alpha+\beta*3+\gamma*9=14\\[/tex]
[tex]\begin{bmatrix}1&1&1\\1&2&4\\1&3&9\end{bmatrix}*\begin{bmatrix}\alpha\\\beta\\\gamma\end{bmatrix}=\begin{bmatrix}6\\9\\14 \end{bmatrix}\\\\\\\begin{bmatrix}1&1&1&6\\1&2&4&9\\1&3&9&14\end{bmatrix}\\\\\\\begin{bmatrix}1&1&1&6\\0&2&3&3\\0&2&8&8\end{bmatrix}\\\\\\\begin{bmatrix}1&1&1&6\\0&1&3&3\\0&1&4&4\end{bmatrix}\\\\[/tex]
[tex]\begin{bmatrix}1&1&1&6\\0&1&3&3\\0&0&1&1\end{bmatrix}\\\\\\\begin{bmatrix}1&1&1&6\\0&1&0&0\\0&0&1&1\end{bmatrix}\\\\\\\begin{bmatrix}1&0&0&5\\0&1&0&0\\0&0&1&1\end{bmatrix}\\[/tex]
[tex]\alpha=5\\\beta=0\\\gamma=1\\\boxed{v_n=5+0*n+1*n^2}\\\boxed{u_n=5+0*n+1*n^2-2}\\\begin{array}{ccccc}n & u_n\\1&5+1-2=4\\2&5+4-2=7\\3&5+9-2=12\\4&5+16-2=19\\...&...\\\end{array}\\[/tex]
The two bases of a trapezoid measure 14 inches and 10 inches respectively. The trapezoid's height is 8 inches. What is the area of the trapezoid?
192 square inches
1120 square inches
140 square inches
96 square inches
Answer:
A = 96 inches ^2
Step-by-step explanation:
The area of a trapezoid is given by
A = 1/2 ( b1+b2)h where b1 and b2 are the bases and h is the height
A = 1/2( 14+10)*8
A = 1/2(24)*8
A = 12*8
A = 96 inches ^2
The area of trapezoid is given
A = 1/2 (b1+b2)h where b1 and b2 is base and h is height
A = 1/2 (14+10)*8
A = 1/2 (24)*8
A = 12 * 8
A = 96 square inches ....D.2 please help I’ll mark brainliest
Answer:
At 2
Step-by-step explanation:
I think it is because it slants down instead of going up. That is the reason why I say my answer is at 2.
HOPE THIS HELPED
Father is four times the age of his daughter. If after 5 years, he would be 3 times of daughter's age, then further after 5 years, how many times he would be of his daughter's age?
Answer:
The father is 40 years old, and his daughter is 10 years old.
Step-by-step explanation:
Given that a father is four times the age of his daughter, and after 5 years, he would be 3 times of daughter's age, then further after 5 years, to determine how many times he would be of his daughter's age, the following calculation must be done:
F = 4D
F + 5 = 3D
F = 40
D = 10
40 + 5 = 3 x (10 + 5)
45 = 45
Therefore, the father is 40 years old, and his daughter is 10 years old.
It takes four or three hours to get a pair of socks and seven hours to get a pair of clothes as he spends 89 hours kidding a total of 15 pairs of socks and gloves how many pairs of each does she kinit?
Answer:
Gloves = 11 pairs
Socks = 4 pairs
Step-by-step explanation:
Given that :
Time taken to knit pair of socks = 3 hours
Time taken to knit pair of gloves = 7 hours
Total time taken to knit 15 pairs of gloves and socks = 89 hours
Let :
number of socks = x and number of gloves = y
x + y = 15 - - - - (1)
3x + 7y = 89 - - - (2)
From (1):
x = 15 - y
Put x = 15 - y in (2)
3(15 - y) + 7y = 89
45 - 3y + 7y = 89
45 + 4y = 89
4y = 89 - 45
4y = 44
y = 44/4
y = 11
From :
x = 15 - y
x = 15 - 11
x = 4
Johnson bought a wrist watch for $y and sold it at a loss of 15% Write an expression for the selling price.
A. 0.85 y
B. 0.85
C. 85 y
D. 1.159
HELPPPPP ILL GIVE BRAINLIEST
Answer:
0.85y
Step-by-step explanation:
Cost of the wrist watch = $y
Present percentage = 100%
Percentage Loss = 15%
Selling price = (Present percentage - Percentage Loss) * Cost of the wrist watch
= (100% - 15%) * y
= 85% * y
= 85/100 * y
= 0.85 * y
= 0.85y
Selling price = 0.85y
(PICTURE) 15 Points and marking Brainliest could someone please answer/explain this for me
Answer:
9. Hypotenuse = √(19.1²+11.3²) = √492.5 = 22.2 m²
10. Area = (34×40)/2 + (17²×π/2)
= 680 + 453.96
= 1133.96 cm²
Answered by GAUTHMATH
Find the area of the regular polygon. Round your answer to the nearest hundredth.
Answer:
Step-by-step explanation:
The central angle of a hexagon is 60 degrees. Drop a line from the center to the middle of the side marked 7.
Use the tan of the angle so formed (which is 30 degrees)
Tan(30)= opposite / height (which is the line you just drew).
Tan(30) = 3.5 / h
Tan(30) = 0.5774
Tan(30) = 3.5 / h multiply both sides by h
h*Tan(30) = 3.5 Divide by tan30
h = 3.5 / Tan(30)
h = 3.5 / 0.5774
h = 6.062
Now from both ends of the given side, draw 2 lines to the center. Find the area of that triangle.
Area of 1 triangle = 1/2 * b * h
area of 1 triangle = 1/2 * 7 * 6.062
Area of 1 triangle = 21.2176
There are 6 such triangles so multiply that number by 6
Answer: 6 * 21.2176
Answer: 127.31
the LCM of 30 , 45,90
Answer:
540 is the answer
Step-by-step explanation:
hope u liked!
ASAP!! can i get help on this one and can i please get a vivid explanation thank you.
Answer:
3x + 11
Step-by-step explanation:
1) Remove Parentheses:
x + 4 + 2x + 7
2) Combine Like Terms:
(2x + x) and (4 + 7)
3) Simplify:
3x + 11
Hope this helps, good luck! Have a good day. :)
Marking brainliest please explain if you can (PICTURE)
4. If 8 out of 25 snacks are healthy, how many healthy snacks will there be per 100 snacks total?
Answer:
32 of them would be unhealthy. this is because 25 times 4 equils 100, so 8 times 4 equils 32.
Answer:
32 healthy snacks
Step-by-step explanation:
-set up an equivalent fraction to keep the same proportion
8 healthy / 25 snacks = ? healthy / 100 snacks
-solve for ? healthy
8/25 = ?/100, cross multiply
25 * ? = 8*100 , divide both sides by 25
? = 800/25 = 32 healthy snacks
* you can also think that 100 is 25 four times,
so the healthy snacks are 8*4 =32
Nia solved the equation -1.98 = 5.2v + 13.1. Her answer was v = -2.9. She is fairly confident about her answer, but wants to do a quick check of her solution using estimation to make sure her answer is reasonable.
Which of the following shows a good check of her answer?
Answer:
substitute for v, when v = -2.9
Step-by-step explanation:
[tex]-1.98=5.2v+13.1[/tex]
subtract 13.1 on both sides.
[tex]-15.08=5.2v[/tex]
divide by 5.2 to isolate v
[tex]\frac{-15.08}{5.2} = \frac{5.2v}{5.2}[/tex]
[tex]-2.9=v[/tex]
substitute for v
[tex]-1.98=5.2(-2.9)+13.1[/tex]
[tex]-1.98=-15.08+13.1[/tex]
[tex]-1.98=-1.98[/tex]
The length of a rectangle is 5 cm more than the width and the perimeter is at least 61cm. What are the smallest possible dimensions for the rectangle? (Hint: Perimeter = 2L +2W)
Explanation pleaseeee
I think the length is 17.75cm and the width is 12.75 cm
I'm not entirely sure whether it's the smallest possible length but it works on the calculator
17.75*2+12.75*2=61
(b) In a sale the original prices are reduced by 15%.
(i) Calculate the sale price of a book that has an original price of $12.
$
(ii)
Calculate the original price of a jacket that has a sale price of $38.25.
Answer:
(i): $10.20
(ii): $32:51
Step-by-step explanation:
(i) 1. put the percentage of the discount into a decimal: 0.15
2. multiply 0.15 by the sale price to find the amount of the discount: $1.80
3. subtract the discount, $1.80, from the original price, $12: $10.20
(ii) 1. put the percentage of the discount into a decimal: 0.15
2. multiply 0.15 by the sale price to find the amount of the discount: $5.74
3. subtract the discount, $5.74, from the original price, $38.25: $32.51
(i) The sale price of the book of original price $12 is $10.20.
(ii) The original price of the jacket is $38.25.
What is the percentage?The percentage is a calculation method for every 100.
How to calculate the sale price?The original price of a book is $12.
In a sale the original prices are reduced by 15%.
∴ Price reduced = $(12*15%)
=$ 1.80
Hence, the sale price is = $(12-1.80)
=$10.20
What is discounted price?The discounted price is the price a buyer pays after getting a discount of marked price.
How to calculate original price?Here, the sale reduces price by 15%
The discounted price is equivalent to = (100-15)%
=85%
By the condition ,
85% = $38.25
∴100%= $(38.25/85*100)
=$ 45
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[tex]2 \sqrt{75} - \sqrt{108} + 5 \sqrt{48}[/tex]
[tex]\\ \sf\longmapsto 2 \sqrt{75} - \sqrt{108} + 5 \sqrt{48} \\\\ \sf\longmapsto 2 \sqrt{25 \times 3} - \sqrt{36 \times 3} + 5 \sqrt{16 \times 3} \\ \\ \sf\longmapsto 2 \times 5 \sqrt{3} - 6 \sqrt{3} + 5 \times 4 \sqrt{3} \\ \\ \sf\longmapsto 10 \sqrt{3} - 6 \sqrt{3} + 20 \sqrt{3} \\ \\ \sf\longmapsto (10 - 6 + 20) \sqrt{3} \\ \\ \sf\longmapsto 24 \sqrt{3} [/tex]
Answer:
24aprtment3
Step-by-step explanation:
pls I'll mark u BRAINLIEST
(B−A)∪C=(B∪C)−(A−C)
Answer:
(I don't have the complement sign of sets, so I've used "©" to denote compliment)
L.H.S.
(B-A)∪C
= (B∩A©)∪C
= (B∪C)∩(A©∪C)
= (B∪C)∩(A-C)©
= (B∪C)-(A-C) = R.H.S.
(Proved)
which of the following represents x= 1/2 y written in general form?
2x-y = 0
=============================================
Work Shown:
x = (1/2)y
2x = y ... multiply both sides by 2
2x-y = 0 ... subtract y from both sides
This is in standard form Ax+By = C, where A,B,C are integers. In this case, A = 2, B = -1, C = 0.
what is 1680 mm in feet
5.51181102 feet (5 feet 6 9⁄64 inches)
QUESTION 2 Write the slope-intercept form of the equation of the line through the gran point micia the grea slope through: (5,-2), siope--1 Oay=-2=6 Oby=-2-3 O cy=-x=3 Ody=-z-6
Answer:
y = -x+3
Step-by-step explanation:
Slope intercept form of a line is
y = mx+b where m is the slope and b is the y intercept
y = -1x +b
Using the point for x and y we can calculate b
-2 = -1(5)+b
-2 = -5+b
Add 5 to each side
-2+5 = b
3 = b
y = -x+3
Which label on the cone below represents the vertex?
D
B
А.
С
ОА
D
Mark this and stum
Save and Exit
ANSWER QUICK !!
Yuri is participating in a tund-raiser at school. She will receive donations from 2 people. A cousin will donate $0.40 for every 1/8 mile that Yuri walks.
A friend will give Yuri a one-time donation of $30
What is the minimum number of miles Yuri needs to walk to raise at least $507 Enter the answer in the box,
507 - 30 = 477
477 / 0.4 = 1192.5
1192.4 / 8 = 149.0625 miles or 150 miles
i don't know if this is right cause the answer seems so absurd
given that f(m) = m/2, find m
Answer:
let f(m) = u
multipling both sides by 2
We have 2f(m)=m
therefore m=2
kendra is 3 times her dauters age plus 7 years kendra is 49 years old. write an equation to find he duaghters age?
Answer:
3x+ 7 =49
Step-by-step explanation:
49-7= 42
42 divided by 3 = 14
her daughter is 14 years old
I truly hope this helped, it makes sense to me. I wasn't sure whether or not you needed a more detailed equation, but that's one.
have a great day!
Daisy (5,9,2,6,14,3)
Milkweed (10,8,22,12,12,9)
Coneflower (3,7,2,10,16,7)
A biology class took a field trip. The students counted the number of daisy, milkweed, and coneflower plants in six different locations. The data sets are shown above. What is the overall range in the number of plants for all three types of plants?
Answer:
The overall range is 20
Step-by-step explanation:
Given
The above dataset
Required
The overall range
Range is calculated as
[tex]Range = Highest - Lowest[/tex]
The highest of the dataset is 22, and it can be found in Milkweed.
The lowest of the dataset is 2, and it can be found in Daisy
So, the range is:
[tex]Range = 22 - 2[/tex]
[tex]Range = 20[/tex]
1.) You plan to cut a board into 3 pieces to repair part of a railing. You are going to cut the two ends of the board off into two equal pieces that are 1.4 feet long, if the remaining piece needs to be 1.17 times longer than the each of the first two cuts what length board should you buy? Round to the nearest tenth.
The board length that will be bought is 4.438 feet
Since the board will be cut into 3 pieces. From the information given in the question, the lengths of the board will be:
= 1.4 feet + 1.4 feet + (1.17 × 1.4 feet)
= 1.4 feet + 1.4 feet + 1.638 feet
= 4.438 feet
In conclusion, the board length that should be bought is 4.438 feet.
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Within 9 hours, the number of stars seen went from 190 to 33 as the sun started to rise. Find out how many stars are getting hidden by the sunlight each hour.
Answer:
Approximately 17 stars
Pat’s Pizza Shack offers customers two choices of crust, three choices of sauce, and four choices of toppings shown below. If a 1-topping pizza is selected at random, what is the probability that it will be deep dish crust, with traditional sauce and green peppers?
Answer:
1/24 (fraction form)
hope this helps
A 16-ounce package of frozen peas costs
85¢. Give the unit price in cents per ounce. Round to the nearest tenth of a cent.
The peas cost ___ cents per ounce.
Note: Rounding to the nearest tenth of a cent is the same as rounding to the nearest thousandth of a dollar.
Answer:
5.3 cents
Step-by-step explanation:
85/16
because all 16 ounces cost 85 cents
Answer:
5.3 cents.
Step-by-step explanation:
HELP ASAP
A bowl contains 5 pieces of red candy, 6 pieces of green candy, and 11 pieces of blue candy. Two pieces of candy are drawn and then replaced back into the bowl. What is the probability of drawing from the bowl a piece of red and green candy?
Red Candy = 5
Green Candy = 6
Blue Candy = 11
Total Candies = 22
Probability = Possible Outcomes/Total Outcomes
Red + Green = 11
Total outcomes = 22
Probability = 11/22
= 1/2
Must click thanks and mark brainliest
There is 6.19% chance of drawing a red and green candy from the bowl.
Probability is a branch of mathematics that deals with the likelihood of an event occurring. In this case, we are interested in finding the probability of drawing a piece of red and green candy from a bowl containing red, green, and blue candies. To calculate this probability, we will use the concept of independent events and the formula for probability.
We have a bowl with a total of 5 red candies, 6 green candies, and 11 blue candies. The total number of candies in the bowl is 5 + 6 + 11 = 22.
We are drawing two candies from the bowl, and after each draw, we replace the candy back into the bowl. This means that the number of candies remains the same for each draw.
To calculate the probability of drawing a red and green candy, we need to determine the number of favorable outcomes and the total number of possible outcomes.
The number of favorable outcomes is the number of ways we can draw one red candy and one green candy.
We can draw a red candy in 5 ways (since there are 5 red candies), and we can draw a green candy in 6 ways (since there are 6 green candies). Therefore, the number of favorable outcomes is 5 * 6 = 30.
The total number of possible outcomes is the total number of ways we can draw two candies from the bowl. Since we are replacing the candies after each draw, the total number of possible outcomes for each draw is equal to the total number of candies in the bowl, which is 22. Since we have two draws, the total number of possible outcomes is 22 * 22 = 484.
Now, we can calculate the probability of drawing a red and green candy by dividing the number of favorable outcomes by the total number of possible outcomes:
Probability = Number of favorable outcomes / Total number of possible outcomes
Probability = 30 / 484
Probability ≈ 0.0619
Therefore, the probability of drawing a piece of red and green candy from the bowl is approximately 0.0619 or 6.19%.
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What is 51809 rounded to 1,2 and 3 significant figures?
PLSS HELP
Answer:
1 significant figure: 50,000 2 significant figures: 52,000 3 significant figures: 51,800
Step-by-step explanation:
FIrst, a significant figure is basically a non-zero digit (at least in your case). Basically, the 1 significant figure in your case would be to the nearest 10 thousand, which would be 50,000. Now, for 2 significant figures. This would be the nearest thousand, 52,000. Finally, 3 significant figures is to the nearest hundred, aka 51,800. Note: If you find a problem like this again 0 in between two digits that aren't 0 is a significant digit, aka the 0 in 51809. Hope this helped!
