Answer:
10,26,74,218,650
Explanation:
Each number is 4 less then 3 times than previous number.
The list of number is bounded by a set of rules that guide the creation of the set of numbers. The first 5 terms are: 10, 26, 74, 218, 650
Represent the number of terms with n.
So, the nth term is: [tex]T_n[/tex]
The start of the build is 10 means:
[tex]T_1 = 10[/tex]
The rule to generate the next terms is:
[tex]T_{n+1} = 3 \times T_n - 4[/tex] ---- i.e. 4 less than 3 times the previous term
So, the next terms till the 5th are:
[tex]T_{2} = 3 \times 10 - 4 = 26[/tex]
[tex]T_{3} = 3 \times 26- 4 = 74[/tex]
[tex]T_{4} = 3 \times 74- 4 = 218[/tex]
[tex]T_{5} = 3 \times 218- 4 = 650[/tex]
So, the first 5 terms are: 10, 26, 74, 218, 650
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If 2x3 – 4x2 + kx + 10 is divided by (x + 2), the remainder is 4. Find the value of k using remainder theorem. Please help :)
The polynomial remainder theorem states that the remainder of the division of a polynomial [tex]P(x)[/tex] by [tex]x-a[/tex] is equal to [tex]P(a)[/tex].
Therefore
[tex]P(-2)=4\\2\cdot(-2)^3 - 4\cdot(-2)^2 + k\cdot(-2) + 10=4\\-16-16-2k=-6\\-2k=26\\k=-13[/tex]
3.1x^3-2.4x² +6x – 3 = 4x² + 3x +2
solving problem
Answer:
The roots of the equation, 3.1·x³ - 2.4·x²+ 6·x - 3 = 4·x² + 3·x + 2, are;
x = 1.986, x = 0.0392 - 0.9·i, x = 0.0392 + 0.9·i
Step-by-step explanation:
The given equation is 3.1·x³ - 2.4·x²+ 6·x - 3 = 4·x² + 3·x + 2
Which gives;
3.1·x³ - 2.4·x²+ 6·x - 3 - 4·x² - 3·x - 2 = 0
3.1·x³ - 6.4·x²+ 3·x - 5 = 0
Factorizing online, we get;
3.1·x³ - 6.4·x²+ 6·x + 3·x - 5 = 3.1·(x - 1.986)·(x² - 0.0784·x + 0.812) = 0
Therefore, the possible solutions are;
x - 1.986= 0 or x² - 0.0784·x + 0.812 = 0
The roots of the equation are x² - 0.0784·x + 0.812 = 0 are;
x = 0.0392 - 0.9·i, x = 0.0392 + 0.9·i
Therefore, the roots of the equation, 3.1·x³ - 2.4·x²+ 6·x - 3 = 4·x² + 3·x + 2, are;
x = 1.986, x = 0.0392 - 0.9·i, x = 0.0392 + 0.9·i.
Find the area of the shape shown below.
12
5
5
units
Answer:
42.5 units²
Explenation:
The area of the square on the left is 5×5=25.
At the top you do 12-5=7 to find the length of the tringle.
Than it is 7×5=35 than this divided by two, so 17.5.
You add both areas 25+17.5=42.5
Answer:
42.5 square units
Step-by-step explanation:
Separate shape into a square and a triangle
Calculate the area of the square (5*5=25 square units)
Calculate the are of the triangle (7*5/2=35/2= 17.5 square units)
Add together (17.5+25=42.5 square units)
m +2p; use m = 2, and p = 4
Answer:
10
Step-by-step explanation:
m + 2p
2 + 2(4)
= 2 + 8
= 10
Answer:
10
Step-by-step explanation:
m +2p;
let m = 2, and p = 4
2+2*4
2+8
10
I NEED HELP PLEASE ! I GIVE 5 STARS !
Answer:
2
Step-by-step explanation:
Remember, a radical is the same thing as an exponent, but as a fraction. Therefore, instead of taking the 12th of the root, you can put [tex]8^4[/tex] to the 12th power like this: [tex](8^4)^{\frac{1}{12} }[/tex]
The two exponents can multiply together, so now it'll be [tex]8^{\frac{4}{12} }[/tex] which is [tex]8^{\frac{1}{3} }[/tex] when reduced
[tex]8^{\frac{1}{3} }[/tex] is the same thing as [tex]\sqrt[3]{8}[/tex]
Now, think about which number, when multiplied by itself 3 times is equal to 8... that number is 2--your answer
Answer:
2
Step-by-step explanation:
make it simple.. use a scientific calculator.
= ¹²√8⁴
= ¹²√4096
= 2
Rank the total mass of each stack
Answer:
Stack A (12M) > Stack D (9M) > Stack E (8M) > Stack B (6M) and Stack C (6M)
Step-by-step explanation:
Stack A has [tex] 6M + 2M + 4M = 12M [/tex]
Stack B has [tex] 2M + 2M + 2M = 6M [/tex]
Stack C has [tex] M + 5M = 6M [/tex]
Stack D has [tex] M + 3M + 5M = 9M [/tex]
Stack E has [tex] 5M + 3M = 8M [/tex]
The total mass of each stack from the highest to the least can be ranked as follows:
Stack A (12M) > Stack D (9M) > Stack E (8M) > Stack B (6M) and Stack C (6M)
Which translation maps the graph of the function f(x) = x2 onto the function g(x) = x2 − 6x + 6? left 3 units, down 3 units right 3 units, down 3 units left 6 units, down 1 unit right 6 units, down 1 unit
Answer:
its not 1, its the second one (B)
Step-by-step explanation:
Answer:
I know I'm 1 year late but B is the correct answer choice. I just did it on edge 2021.
I'm just big brain.What is the value of "c" in the quadratic equation 3x^2 + 5x + 7 = 0?
Answer:
c = 7
Step-by-step explanation:
ax^2 + bx + c = 0
3x^2 + 5x + 7 = 0
c = 7
Need help and will mark brainlist and thank You
In a circle whose center is O, arc AB contaisn 100 degrees. Find the number of degrees in angle ABO?
Answer:
40
Step-by-step explanation:
Angles ABO, BAO, and AOB are the angles of isosceles triangle AOB. The angles at A and B are equal, so we have ...
AOB +2ABO = 180° . . . . . sum of angles in the triangle
100° +2ABO = 180° . . . . . . use the given value
50° +ABO = 90° . . . . . . . . divide by 2; next, subtract 50°
∠ABO = 40°
A group of 6 people planned to spend $10.00 each to
rent a boat for an outing. At the last minute, 1 person
could not go on the outing. The others then paid
equally for the boat. How much did each pay?
Answer:
the ansser is $12
Step-by-step explanation:
becases 10 *6 is equal to 60 so if 1 person can not pay then you divide 60 by the remaineing 5 to get 12
A group of 6 people planned to spend $10.00 each to rent a boat for an outing. Each person have to pay 12 dollars.
How to calculate unit price of something?Unit means 'single entity', the fundamental constructing block. Usually, it is 1 in mathematics and science.
Thus, unit price of something is price of 1 thing.
Thus, suppose we're taking about price of mangoes, then unit price will denote the price of 1 mango.
A group of 6 people planned to spend $10.00 each to rent a boat for an outing. At the last minute, 1 person could not go on the outing.
10 x 6 = 60
So if 1 person can not pay then
We will divide 60 by the remaining 5
60/ 5 = 12
Therefore, Each person have to pay 12 dollars.
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Factorise : x^2+x-72 Step by Step
Answer:
(x + 9)(x - 8)
Step-by-step explanation:
f(x) = x^2 + x - 72
= x^2 - 8x + 9x - 72
= (x^2 - 8x) + (9x - 72)
= x(x - 8) + 9(x - 8)
= (x + 9)(x - 8)
Answer:
x² + x - 72 = (x + 9)(x - 8)
Step-by-step explanation:
[tex]x^2+x-72\quad \implies\quad a=1\,,\quad b=1\,,\quad c=-72\\\\x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\x=\dfrac{-1\pm\sqrt{1^2-4\cdot1\cdot(-72)}}{2\cdot1}=\dfrac{-1\pm\sqrt{1+288}}{2}=\dfrac{17\pm\sqrt{289}}{2}\\\\x_1=\dfrac{-1-17}{2}=-9\quad,\qquad x_2=\dfrac{-1+17}{2}=8\\\\\\x^2+x-72=(x-(-9))(x-8)=(x+9)(x-8)[/tex]
or:
x² + x - 72 =
= x² + 9x - 8x - 72 =
= x(x + 9) - 8(x + 9) =
= (x + 9)(x - 8)
31y+12y= combine like terms
Answer:
43y
Step-by-step explanation:
31y+12y
combine like terms
Factor out y
y( 31+12)
y (43)
43y
Since we are dealing with two numbers with the same variable (y), all we need to do is combine like terms.
31y + 12y = 43y
Best of Luck!
19 x97 find the product using suitable properties
Answer:
19 x 97 = 1843
Helppp 100pts
A television network is about to telecast a new television show. Before a show is launched, the network airs a pilot episode and receives a report assessing favorable or unfavorable viewer response. In the past, 60% of the network's shows have received a favorable response from viewers, and 40% have received an unfavorable response. If 50% of the network’s shows have received a favorable response and have been successful, and 30% of the network’s shows have received an unfavorable response and have been successful, what is the probability that this new show will be successful if it receives a favorable response? A. 0.41 B. 0.53 C. 0.67 D. 0.70 E. 0.83
Answer:
.83
Step-by-step explanation:
If you take 100 shows 60 shows got favorable response and in that 50 shows were successful.
So probability for a show to be successful if it got a favorable response is = 50/60 = 0.83
Answer:
Ty for the free points
Step-by-step explanation:
✊✊✊
Write the equation of a circle with a center at (12, 6) and a radius of 6.
Answer:
(x-12)² + (y-6)² = 36 (Option C)
Step-by-step explanation:
use circle formula
(x-h)² + (y-k)²= r²
h= 12 and k= 6 and r= 6
(x-12)² + (y-6)² = 6²
6 squared = 36 (6·6)
(x-12)² + (y-6)² = 36
Please Help, I can't figure out this problem
Find the distance between the points (9,-7) and (5, -4).
A.
[tex] \sqrt{137} [/tex]
B.
5
C.
[tex] \sqrt{7} [/tex]
D.
25
Answer:
The answer is 5 unitsStep-by-step explanation:
The distance between two points can be found by using the formula
[tex]d = \sqrt{ ({x1 - x2})^{2} + ({y1 - y2})^{2} } \\ [/tex]
where
(x1 , y1) and (x2 , y2) are the points
From the question
The points are (9,-7) and (5, -4)
The distance between them is
[tex]d = \sqrt{ ({9 - 5})^{2} + ({ - 7 + 4})^{2} } \\ = \sqrt{ {4}^{2} + ({ - 3})^{2} } \\ = \sqrt{16 + 9} \\ = \sqrt{25} [/tex]
We have the final answer as
5 unitsHope this helps you
In Exercises 22 describe how the change affects
the surface area of the right prism or right cylinder. Thank you!!
Step-by-step explanation:
Total Surface Area of original cylinder
= (2×(22/7)×9)(9+24)
=18×22/7×33
=1,866.8
Total Surface Area of new cylinder
=(2×(22/7)×9/3)(9/3+24/3)
=(2×(22/7)×3)(3+8)
=6×22/7×11
=207.4
Change or Ratio of org. cylinder to new cylinder
=1,866.8/207.4
=9.0009
11. House Prices In 1985, the median selling price of an
existing single-family home in Atlanta, Georgia, was
$66,200. Between 1985 and 1990, the average price in-
creased by 30%. Between 1990 and 2005, the average
price increased again, this time by 15%. What was the
median house price in Atlanta in 2005? -
Answer:
$98,969Step-by-step explanation:
$66,200 - the median selling price of a home in 1985
and the price increased by 30%:
66,200•30% = 66,200•0.3 = 19,860
66,200 + 19,860 = 86,060
$86,060 - the median selling price of a home in 1990
and the price increased by 15%
86,060•15% = 86,060•0.15 = 12,909
86,060 + 12,909 = 98,969
$98,969 - the median house price in Atlanta in 2005
Mikayla has $32 in her piggy bank. Her sister, Jessica, has $21. Mikayla earns $10 a week by doing chores for her grandparents, while Jessica earns $12 a week by mowing lawns. Which expressions give how much more or less money Mikayla has compared to Jessica after x weeks? Check all that apply. 11 – 2x ,2x – 11, 11 + 22x ,32 + 10x – (21 + 12x) 32 – 21 + 10x – 12x
Answer:
Hey There!! The answer to this is: 32+10x-(21+12x) We are given that:
Amount MIkayla has in here piggy bank initially = $32
Money earned by Mikayla per week = $10
Money earned by Mikayla in x weeks = 10x
Total money MIkayla has after x weeks = 32+10x
Amount Jessica has in here piggy bank initially = $21
Money earned by Jessica per week = $12
Money earned by Jessica in x weeks = 12x
Total money Jessica has after x weeks = 21+12x
Comparing,
In order to compare, we subtract the money earned by Jessica from that earned by MIkalya,
The final expression would be:
32+10x-(21+12x
Hope It Helped!~ ♡
ItsNobody~ ☆
Answer:
1
4
5
Step-by-step explanation:
my age is 13 and i was born in 2006 and my brother was born in 2004 how old he.is
how do you solve 2m-10=44+8m
Answer:
m = -9
Step-by-step explanation:
2m-10=44+8m
Subtract 2m from each side
2m-2m-10=44+8m-2m
-10 = 44+6m
Subtract 44 from each side
-10-44 = 44-44+6m
-54 = 6m
Divide by 6
-54/6 = 6m/6
-9 = m
Answer:
solve by solving the salvation for equation don't be a slave get educated from what's gave
What rational number, when multiplied by an irrational number, has a product that is a rational number? (1 point)
оооо
Answer:
It's 0Step-by-step explanation:
Why?
Because if you multiplied any irrational number by 0 will be equal to 0 and 0 is rational number.
For example, 5.6371...... x 0 = 0
What is the product? One-fourth times three and two-thirds
Answer:
11/12
Step-by-step explanation:
The product of One-fourth times three and two-thirds will be 1 / 2.
What is multiplication?Multiplication is the process of determining the product of two or more numbers in mathematics. A product, or an expression that specifies factors to be multiplied, is what happens when you multiply two numbers in mathematics.
Given that, the numbers are one-fourth times three and two-thirds. The product of the numbers will be calculated as,
Product = ( 1 / 4 ) x ( 3 ) x ( 2 / 3 )
Product = 6 / 12
Product = 1 / 2
Therefore, the product of One-fourth times three and two-thirds will be 1 / 2.
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simpily 2^3×3^2=6^5
Answer:
2^3×3^2=6^5 equation is wrong because
2×2×2×3×3=72
6^5=6×6×6×6×6=36×36×6=7776
the two numbers are not equal
Mate, I think your question is wrong ! ;(
[tex]Corrected \\ Question...\\[/tex] (2^3)^2*(3^2)^3=6^5
243 as a power of 3
Answer:
243 as a power of 3
= 3^5
=243
Follow the process of completing the square to solve x2 = -4x + 3
Answer:
x1 = 0.64575
x2 = -4.64574
Step-by-step explanation:
Step 1: We want to rearrange the equation so all the variables are on one side
0 = -x² - 4x + 3
Step 2: We take out -1 in the first 2 terms so a = 1
0 = -(x² + 4x) + 3
Step 3: Force a square, take the 'b' value and divide it by 2 and square the result. Add it and subtract it from the inside of the brackets
b = 4
4/2 = 2
2² = 4
0 = -(x² + 4x + 4 - 4) + 3
Step 4: Move the -4 out remembering to apply the -
= -(x² + 4x + 4) + 4 + 3
Step 5: We notice is inside the brackets is a perfect square
0 = -(x + 2)² + 7
Therefore the vertex form of the equation is
y = -(x + 2)² + 7
Step 6: We want to solve the equation (find the x intercepts) so we set y to 0 and solve for x
0 = -(x + 2)² + 7
-7 = -(x + 2)²
7 = (x + 2)²
[tex] \sqrt{7 } = x + 2 [/tex]
[tex]x = \sqrt{7} - 2[/tex]
1st Solution:
x = +2.64575 - 2
x = 0.64575
2nd Solution:
x = -2.64575 - 2
x = -4.64574
What is the square root of 100?
Answer:
10
Step-by-step explanation:
Square root of 100 is 10
Answer:
10
Step-by-step explanation:
The square root of 100 is written as 2√100=√100=±10.
So it is 10. Also, 10 times 10 equals 100, so it checks out.
A square root is just two of the same numbers added together to equal a specific number.
Maths!
1) Calculate the variance and standard division of the set of the data
2) If each value is added by 2, calculate the new standard deviation of the set
3) What is the effect on the measure of dispersion if each value is changed uniformly
Answer:
(1) Variance = 4.5 and Standard deviation = 2.121.
(2) Variance = 4.5 and Standard deviation = 2.121.
(3) The effect on the measure of dispersion if each value is changed uniformly is that it remains unchanged.
Step-by-step explanation:
We are given with the following set of data below;
X [tex]X-\bar X[/tex] [tex](X-\bar X)^{2}[/tex]
5 5 - 8 = -3 9
5 5 - 8 = -3 9
8 8 - 8 = 0 0
10 10 - 8 = 2 4
10 10 - 8 = 2 4
10 10 - 8 = 2 4
9 9 - 8 = 1 1
9 9 - 8 = 1 1
6 6 - 8 = -2 4
Total 72 36
Firstly, the mean of the above data is given by;
Mean, [tex]\bar X[/tex] = [tex]\frac{\sum X}{n}[/tex]
= [tex]\frac{72}{9}[/tex] = 8
(1)Now, the variance of the given data is;
Variance = [tex]\frac{\sum (X-\bar X)^{2} }{n-1}[/tex]
= [tex]\frac{36}{9-1}[/tex] = 4.5
So, the standard deviation, (S.D.) = [tex]\sqrt{\text{Variance}}[/tex]
= [tex]\sqrt{4.5}[/tex] = 2.12
(2) Now, each value is added by 2; so the new data set is given by;
X [tex]X-\bar X[/tex] [tex](X-\bar X)^{2}[/tex]
7 7 - 10 = -3 9
7 7 - 10 = -3 9
10 10 - 10 = 0 0
12 12 - 10 = 2 4
12 12 - 10 = 2 4
12 12 - 10 = 2 4
11 11 - 10 = 1 1
11 11 - 10 = 1 1
8 8 - 10 = -2 4
Total 90 36
Firstly, the mean of the above data is given by;
Mean, [tex]\bar X[/tex] = [tex]\frac{\sum X}{n}[/tex]
= [tex]\frac{90}{9}[/tex] = 10
(1)Now, the variance of the given data is;
Variance = [tex]\frac{\sum (X-\bar X)^{2} }{n-1}[/tex]
= [tex]\frac{36}{9-1}[/tex] = 4.5
So, the new standard deviation, (S.D.) = [tex]\sqrt{\text{Variance}}[/tex]
= [tex]\sqrt{4.5}[/tex] = 2.12
(3) The effect on the measure of dispersion if each value is changed uniformly is that it remains unchanged as we see in the case of variance or standard deviation.
the school bought a sandbox that measures 50 meters long 25 meters wide and 5 meters tall how many cubic meters if sand would you need to buy if each cubic meter of sand cost $1.50 how much money would it cost to fill the sandbox
Answer:
Cost of sandbox = $9,375
Step-by-step explanation:
Given:
Height of sandbox = 5 m
Length of sandbox = 50 m
Width of sandbox = 25 m
Cost of 1 cubic meter = $1.50
Find:
Cost of sandbox
Computation:
Volume of sandbox = (50)(25)(5)
Volume of sandbox = 6,250 m³
Cost of sandbox = 6,250 × $1.50
Cost of sandbox = $9,375
5/6 = b/12 help please
Answer:
[tex]b = 10[/tex]
Step-by-step explanation:
We can use the cross products property and solve for b.
[tex]\frac{5}{6} = \frac{b}{12}\\\\\\b=(12\cdot5)\div6\\b=60\div6\\b=10[/tex]
Hope this helped!
Answer:
The answer is b=10
Step-by-step explanation:
All you need to do is think 12/6 is what, the answer would be 2, then you would multiply the numerator by 2, which would be 5*2 which is 10.
Thank you, Hope this helps you.
