Answers
Answer:
D is true, E is true, F is true
Step-by-step explanation:
Hello,
n is an odd number it means that n = 2a+1 where a is integer
A
[tex]n^2-1=(2a+1)^2-1=4a^2+4a+1-1=4a(a+1)[/tex]
this is not an odd number
B
[tex]n(n-1)=(2a+1)2a[/tex]
this is not an odd number
C
[tex](n-1)^2=(2a+1-1)^2=4a^2[/tex]
this is not an odd number
D
[tex]n^2+2=(2a+1)^2+2=4a^2+4a+1+2=4a^2+4a+3= 2(2a^2+2a+1)+1[/tex]
so this is an odd number
E
[tex]n(n-2)=(2a+1)(2a-1)=4a^2-1=4a^2-2+1=2(2a^2-1)+1[/tex]
so this is an odd number
F
[tex](n-2)^2=(2a+1-2)^2=(2a-1)^2=4a^2-4a+1 = 2(2a^2-2a)+1[/tex]
this is an odd number
hope this helps
Related Questions
Let p, q be the solutions of the quadratic equation x^2 − 2mx − 5n = 0 and let m, n be the solutions of x^2 − 2px − 5q = 0. If p,q,m and n are real and non-equal, then the value of p + q + m + n is ....
(A) 15
(B) 30
(C) 75
(D) 150
(E) 225
Answers
Answer:
The correct option is;
(B) 30
Step-by-step explanation:
The equations are;
x² - 2·m·x - 5·n = 0.............(1)
Solution = p, q
x² - 2·p·x - 5·q = 0..............(2)
Solution = m, n
For equation (1), we have;
x² - 2·m·x - 5·n = 0 = (x - p)·(x - q)
x² - 2·m·x - 5·n = x² -x·p - x·q + q·p = x² -x·(p + q) + q·p
2·m = p + q..............(3)
5·n = -q·p..............(4)
Given the similarity between equation (1) and (2), we have;
2·p = m + n..............(5)
5·q = -m·n..............(6)
Therefore;
m = (p + q)/2
n = -q·p/5
Substituting the value of m and n in equation (5) and (6), we have;
2·p = (p + q)/2 - q·p/5.............(7)
5·q = (p + q)/2·q·p/5.............(8)
Making q the subject of equation (7) gives;
[tex]q = \dfrac{-7.5 \cdot p}{p -2.5}[/tex]
Substituting the value of q above in equation (8) gives;
[tex]-\dfrac{75\cdot p}{2\cdot p-5}=-\dfrac{3\cdot p^{4}-30\cdot p^{3}}{4\cdot p^{2}-20\cdot p+25}[/tex]
By cross multiplying and collecting like terms we have;
6·p⁵ -75·p⁴-150·p³+1500·p²-1875·p = 0
Which gives
(p+0)(p-1.91)(p-2.5)(p+5)(p-13.1)
p = 1.91 or 2.5 or -5 or 13.1
q = 24.27 or undef or -5 or -9.27
m = 13.09 or undef or -5 or 1.95
n = -9.27 or undef or -5 or -24.29
Therefore, p + q + m + n = 1.91 + 24.27 + 13.09 + (-9.27) = 30
The correct option is (B) 30
I need help on this question
Answers
Answer:
c
Step-by-step explanation:
Isaac applied the steps below to find the product of (4.2)(-5.4).
.
Step 1: (4.2)(-5.4) = (-5.4)(4.2)
Step 2:
= (-5.4)(4) + (-5.4)(0.2)
Step 3:
= (-21.6) + (-1.08)
Step 4:
=-22.68
Which step shows where Isaac applied the distributive property?
Step 1
0 0
Step 2
Step 3
Step 4
Answers
The answer is step 2. hope it helps.
Answer:
step 2
Step-by-step explanation:
How can a triangular prism have a greater volume than a rectangular prism?
Answers
Answer:
Step-by-step explanation:
Assume that the two prisms have bases of equal area.
Then the volume of the rectangular prism is V = (base area)(height).
The volume of the triangular prism is V = (1/3)(base area)(height)
We could compare the two volumes by creating the ratio inequality
(1/3) (base area)(t-height)
------------------------------------------
(base area)(r-height)
The triangular prism will have the greater volume for (1/3)((t-height) > r-height.
Jorden is cutting a 2 m by 1 1/4 m piece of rectangular paper into two pieces along its diagonal
Answers
Answer:
2.36 =C or your diagonal side
Step-by-step explanation:
You have rectangle that is
2 by 1.25
2² + 1.25² =C²
4 + 1.5625=C²
5.5625 = C²
2.36 =C
if 15% of a number is 100, find 4% of the number
Answers
Answer:
26.6667
Step-by-step explanation:
.15x=100
Divide each side by .15.
x=666.6667
.04(666.6667)=26.6667
Answer:
26(approx.)
Step-by-step explanation:
15/100 times x = 100
3/20 times x = 100
3x/20 = 100
3x = 2000
X= 666 2/3
So,
4/100 x 666.67
1/25 x 666.67 = 26
Decrease £248 by 30%
Answers
Answer:
173.6
Step-by-step explanation:
0.7(248)
173.6
Answer:
£ 173.6
Step-by-step explanation:
£248 *0.30= 74.4
£248 -74.4 =173.6
A sequence is defined by the explicit formula an=3n+4 Which recursive formula represents the same sequence of numbers?
Answers
Answer:
Option (3)
Step-by-step explanation:
Explicit formula of the sequence is,
[tex]a_n=3^n+4[/tex]
From this explicit formula,
First term of the sequence will be,
[tex]a_1=(3^1)+4[/tex]
[tex]a_1=7[/tex]
Second term of the sequence,
[tex]a_2=(3^2)+4[/tex]
[tex]a_2[/tex] = 13
3rd term of the sequence,
[tex]a_{3}=(3^3)+4[/tex]
= 31
Sequence formed,
7, 13, 31 ..........
From the given options,
Recursive formula,
[tex]a_n=3a_{n-1}-8[/tex]
[tex]a_2=3(a_1)-8[/tex]
[tex]a_2=3(7)-8[/tex]
[tex]a_2=21-8[/tex] = 13
[tex]a_3=3a_2-8[/tex]
[tex]a_3=3a_2-8[/tex]
[tex]a_3=3(13)-8[/tex]
= 39 - 8
= 31
Sequence formed from this recursive formula will be,
7, 13, 31........
Therefore, Option (3) will be the answer.
Answer:
C
Step-by-step explanation:
i took the test
x square + 4 x - 12 all over x squared - 2x
Answers
Answer:
[tex]\frac{x+6}{x}[/tex]
Step-by-step explanation:
=> [tex]\frac{x^2+4x-12}{x^2-2x}[/tex]
=> [tex]\frac{x^2+6x-2x-12}{x(x-2)}[/tex]
=> [tex]\frac{x(x+6)-2(x+6)}{x(x-2)}[/tex]
=> [tex]\frac{(x-2)(x+6)}{x(x-2)}[/tex]
Cancelling (x-2)
=> [tex]\frac{x+6}{x}[/tex]
I will mark you brainliest!!!! Which ordered pair is the best approximation of the solution?
Answers
Answer:
D
Step-by-step explanation:
We can substitute y = 2x + 1 in the second equation
2x + 1 = -7x + 8
Add 7x to both sides
9x + 1 = 8
Subtact 1 from both sides
9x = 7
x = 7/9
Substituing x in the first equation
y = 14/9 + 1
x rounds to 0.8
y rounds to 2.5
5. A man sells his house for
$295,000 at a
profit of 18% . What is the cast price of the house?
Answers
Answer:
$250000Solution
Selling price(SP)=$295000
profit percent=18%
Cost price(CP)=?
Now,
[tex]cp = \frac{sp \times 100}{100 + profit \: percent} \\ \: \: \: \: = \frac{295000 \times 100}{100 + 18} \\ = \frac{29500000}{118} \\ = 250000[/tex]
hope this helps...
Good luck on your assignment...
Let x be a constant. The 5th term of an arithmetic sequence is a5=16x+11. The 9th term of the sequence is a9=28x+19. Find the first term of the sequence. Write your answer in simplest form
Answers
19
Step-by-step explanation:
The first term of the arithmetic sequence is 4x+3.
What is arithmetic sequence?An ordered group of numbers with a shared difference between each successive term is known as an arithmetic sequence.
The formula to find the nth term of an arithmetic sequence is,
aₙ= a+(n-1)d
Where a is the 1st term and d is the common difference.
Let the first term of sequence is a and the common difference is d.
Given that,
The 5th term of the arithmetic sequence = 16x+11,
⇒ a+4d= 16x+11 (1)
And the 9th term of the arithmetic sequence = 28x+19,
⇒ a+8d= 28x+19 (2)
To find the first term of the sequence, multiply equation (1) with 2 and subtract equation (2) from it.
(2a+8d)-(a+8d) = (32x+22) - (28x+19)
a = 4x+3
The first term of the arithmetic sequence is 4x+3.
To know more about Arithmetic sequence on :
https://brainly.com/question/1452631
#SPJ2
The snail moved 6 inches in 120 minutes. What was the average speed of the snail in inches per minute
20 of an inch per minute
1
O z of an inch per minute
O2 inches per minute
O 20 inches per minute
Answers
Answer:
The answer is; the snail moved 1 inch every 20 minutes.
Step-by-step explanation:
120 divided by 6 is 20
Answer:
A) 1 Over 20 of an inch per minute
Step-by-step explanation:
I took this test and got 100
Work of the size of one exterior angle
Answers
Answer:
<x = 36°
Step-by-step explanation:
In a regular decagon, Every interior angles is equal to 144.
So,
<x + 144 = 180 [Angles on a straight line]
<x = 180-144
<x = 36°
Calculate 85% of 2 500m
Answers
Answer:
Step-by-step explanation:
85% of 2500 m
= 85/100 × 2500 = 2125 m
hope this helps
plz mark it as brainliest!!!!!!
Answer:
2125
Step-by-step explanation:
85% times 2500
Mrs. Hudson has made another assignment that Karen and Dakota are excited to try. To conduct your own experiment, you will need dice and a place to record your results. In this assignment, you will first calculate the theoretical probability for rolling a sum of 7. Then, you will roll the dice and add the numbers shown, recording your results as you go. Calculate the experimental probability for rolling a 7 after the 1st, 10th, and 100th rolls. Compare these results with the theoretical probability of rolling a sum of 7. How does this comparison change as the number of trials increase? 1. List out the sample space for the experiment and then calculate the theoretical probability. _______________________________________________________________ _______________________________________________________________ _______________________________________________________________ _______________________________________________________________ _______________________________________________________________ _______________________________________________________________ _______________________________________________________________ _______________________________________________________________
Answers
I belive,
The experimental probability could be more, the same or less than the theoretical probability of rolling a 1 (which is 1/6).
The larger your sample (i. e., as you go beyond 60 tosses), the closer the two different probabilities are likely to be. (Think: Law of Large Numbers).
Answer:
Step-by-step explanation:
Jsiehsjsndj im here to get you a brainliest
Please answer asap thanks
Answers
Answer:
V = 200 pi units ^3
Step-by-step explanation:
The volume of a cone is given by
V = 1/3 pi r^2 h
V = 1/3 pi ( 10 ^2) (6)
V = 1/3 pi (100) *6
V = 200 pi
straight line graphs: find the equation of the lines shown
Answers
Answer:
1. y = -2n + 9
2. y = (1/2)x + 1/2
Step-by-step explanation:
1.
The equation of a line is denoted by y = mx + b, where m is the slope and b is the y-intercept.
Slope is calculated by taking two coordinates and dividing the difference of the y-coordinates by the difference of the x-coordinates. The y-intercept is where the line intersects the y-axis.
Let's choose any two points on the line: (4, 1) and (3, 3). Then:
slope = m = (3 - 1) / (3 - 4) = 2 / (-1) = -2
Now, we can also see that at the point (0, 9), the line intersects the y-axis, so that means b = 9.
The equation is thus y = -2n + 9.
2.
Let's again choose any two points to find the slope: (1, 1) and (3, 2). Then:
slope = m = (2 - 1) / (3 - 1) = 1/2
We can see that the line crosses the y-axis at the point (0, 1/2), so that means b = 1/2.
The equation is thus y = (1/2)x + 1/2.
~ an aesthetics lover
Answer:
1. y = -2x + 9
2. y = (1/2)x + 1/2
Step-by-step explanation:
There was a mistake on the last one so I would like to correct it it is
y= -2x+9
The other one said -2n its -2x
What is the units digit of $7^7$ when expressed as an integer?
Answers
Answer:
3
Step-by-step explanation:
Answer:
3
Step-by-step explanation:
Just stick it into a calculator lol
The cost in dollars C(x), where x is the number of miles driven, of renting a car for a day is C(x)=1.95x+32. What is the independent variable and its units? ______ (dollars, miles, miles per dollar, or dollars per mile) - select the correct units What is the dependent variable and its units? ______ (miles or dollars) - select the correct units
Answers
Answer:
the independent variable is 32 (price of the car in dollars) as it stands alone without a variable and 1.95 is the dependent (cost per mile)
Please help :)
James paid $3.40 for lunch using a total of 16 nickels and quarters. How many of each coin did he have?
A. 5 nickels 11 quarters
B. 13 nickels 3 quarters
C. 3 nickels 13 quarters
D. 1 nickel 15 quarters
Answers
Answer:
3 nickels, and 13 quarters.
Step-by-step explanation:
0.05n+0.25q=3.40
n+q=16
q=16-n
0.05n+0.25(16-n)=3.40
0.05n+4-0.25n=3.40
-0.2n=-0.6
n=3
3+q=16
q=13
A bookstore has marked down the price for all the books in a certain series by 15%. How much is the discount on a book that normally costs $18.00? After the discount, how much would the book cost?
Answers
Answer:
just multiply 18.00 by 15 and than divide 100
Answer:
Discount = $2.70
Price = 18 - 2.70 = $15.30
Step-by-step explanation:
18 x 0.15 = 2.7
Solve x^4 -3x^2 +2=0 using substitution. U=
Answers
Answer:
U = x^2
hope this helped!
Answer:
x^2
Step-by-step explanation:
The person above me is spitting mad facts and da TRUTH and also UNUS ANNUS
Anyone know this ? Please help
Answers
Answer:
3018
Step-by-step explanation:
an = a1 + (n-1)d
a1 is the first term in the sequence = 24
n is the term number which is 500
d is the common difference
Take the second term and subtract the first term to find the common difference
d = 30-24 = 6
a500 = 24 + (500-1) *6
=24+ 499*6
=24 + 2994
=3018
Answer:
3018 is the correct answer.
Solve the system of equations. 6x-5y=-32, -7x+8y=46
Answers
Answer:
x = -2
y = 4
Step-by-step explanation:
6x-5y=-32
-7x+8y=46
Solve for x in the first equation.
6x = -32 + 5y
x = (-32 + 5y) /6
x = 5/6y - 16/3
Put x as 5/6y - 16/3 in the second equation and solve for y.
-7(5/6y - 16/3) +8y = 46
-35/6y+112/3 +8y = 46
13/6y + 112/3 = 46
13/6y = 46 - 112/3
13/6y = 26/3
y = 26/3 × 6/13
y = 4
Put y as 4 in the first equation and solve for x.
6x-5(4)=-32
6x-20 = -32
6x = -32+20
6x = -12
x = -12/6
x = -2
8(4-x)=7x+2 solve for X
Answers
Answer: x= 2
Step-by-step explanation:
(8 X 4)+[8 X (-x)]= 7x+2
32- 8x = 7x+2
-8x-7x =2-32
-15x = -30
x= 2
Answer:
x=2
Step-by-step explanation:
[tex]8(4-x)=7x+2[/tex] Original equation
[tex]32-8x=7x+2[/tex] Distributive property on left
[tex]30=15x[/tex] Combine like terms and isolate the variable (x)
[tex]2=x[/tex] Divide both sides by 15 (Division Property of Equality)
20 POINTS + BRAINLIEST ||| Which of these scale factors will result in a reduction? A. 0 B. 1/2 C. 1 D. 5
Answers
Answer:
B
Step-by-step explanation:
When you dilate by a factor of 0, this doesn't really make sense because the length of each side is multiplied by 0, and the shape basically doesn't exist anymore. When you multiply by a scale factor of 1, the figure does not change in size at all. When you dilate by a scale factor of 5, each side length gets 5 times larger, meaning that this is not a reduction. Hope this helps!
PLEASE HELP! Use a graphing calculator to find an equation of the line of best fit for the data in the table. Round the slope and y-intercept to the nearest tenth. Then Identify and interpret the correlation coefficient.
X- 10.1 9.8 9.7 9.4 8.9 8.7 8.4 8.1
Y- 4.3 4.8 5.3 5.2 5.6 5.8 6.1 6.3
The equation of the line of best fit is y=
To the nearest thousandth, the correlation coefficient is r=
Answers
Answer:
ŷ = -0.895X + 13.600
Slope = -0.9
Intercept = 13.6
r = - 0.964
Step-by-step explanation:
Given the data:
X- 10.1 9.8 9.7 9.4 8.9 8.7 8.4 8.1
Y- 4.3 4.8 5.3 5.2 5.6 5.8 6.1 6.3
Inputting the data given into the online regression calculator :
The equation of line of best fit :
ŷ = -0.895X + 13.600
Slope = - 0.9(to the nearest tenth)
Intercept = 13.6 (to the nearest tenth)
The correlation Coefficient 'r' of the data supplied is - 0.9643, which implies that a strong negative correlation exists between the dependent and independent variables.
r = - 0.964 (to the nearest thousandth)
Inputting the data into the STAT then Fit Data function of the HP 50g
Graphing Calculator.
The equation of the line of best fit is; y ≈ 13.6 - 0.9·xThe correlation coefficient is r ≈ -0.964The meaning of the strong negative correlation is that the x-values
of the data is decreasing, while the corresponding y-values of the data
increasing.
Reasons:
The least squares regression line equation is the best fit line for the data
The formula for the least squares regression line is [tex]\hat Y = b \cdot X + a[/tex]
Where;
[tex]b = \dfrac{n \cdot \sum X \cdot Y - \left (\sum X \right )\left (\sum Y \right )}{n \cdot \sum X^{2} - \left (\sum X \right )^{2}}[/tex]
[tex]a = \dfrac{\sum Y - b \cdot \sum X}{n}[/tex]
n = The sample size
Inputting the given data into the function Fit Data on a graphing calculator,
by editing ∑DAT.
The left column, represent the x-values, and right column represent the y-
values as follows;
[tex]\begin{array}{|c|cc|} \mathbf{Column \ 1}&&\mathbf{Column \ 2}\\10.1&&4.3\\9.8&&4.8\\9.7&&5.3\\9.4&&5.2\\8.9&&5.6\\8.7&&5.8\\8.4&&6.1\\8.1&&6.3\end{array}\right][/tex]
After inputting the data as above, press enter.
Move the pointer to the Model options line, select choose to choose the
Linear Fit model by selecting OK.
Select OK again for the calculator to do the calculations.
The least squares regression line equation given by the calculator is
presented as follows;
y = 13.5998272884 - 0.894645941278·x
The slope and the y-intercept rounded to the nearest tenth gives;
y = 13.6 - 0.9·xThe slope = -0.9The y-intercept = 13.6Correlation coefficient:
The correlation coefficient is given from the data using the following
formula;
[tex]r = \dfrac{n \cdot \sum X \cdot Y - \left (\sum X \right ) \cdot \left (\sum Y \right )}{\sqrt{n \cdot \sum X^{2} - \left (\sum X \right )^{2}\times n \cdot \sum Y^{2} - \left (\sum Y \right )^{2}}}[/tex]
From the graphing calculator, we have the correlation coefficient, given as
follows;
Correlation: (-0.964276229529)
Therefore, to the nearest thousandth;
The correlation coefficient, r ≈ -0.964The high negative value of the correlation coefficient indicates a strong
and near perfect relationship between the variables, x, and y, such that we
have;
A decrease in the value of x leads to a proportional increase in the value of y.Learn more here:
https://brainly.com/question/24848242
Brainliest will be given i need answer ASAP please.
Simplify 84,375/325 to its lowest multiple Example 16/4 = 4/1
Answers
Answer:
3375/13
Step-by-step explanation:
it's found though this equation [tex]\frac{84375/25}{325/25}[/tex]
Answer:
[tex]3375/13[/tex]
Step-by-step explanation:
[tex]84,375/325[/tex]
Divide the numerator and denominator by 25.
[tex]3375/13[/tex]
[tex]=259.615385[/tex]
can someone help me with this and explain me how to do it please :) ^
Answers
Answer:
x= 4
[tex]perpendicular (p) = \sqrt{x} + 1[/tex]
[tex]base(b) = 2 \sqrt{x} [/tex]
[tex]hypotenuse(h) = 2 \sqrt{x} + 1[/tex]
According to the Pythagoras Theoram,
p²+b²= h²
[tex] {( \sqrt{x } + 1) }^{2} + {(2 \sqrt{x} )}^{2} = {(2 \sqrt{x} + 1)}^{2} [/tex]
=>x+2√x+1+4x = 4x +4√x +1=> x = 4x - 4x +4√x- 2√x+ 1- 1=>x= 2√x=> x/√x = 2=> √x = 2Therefore, x= (√x)² = (2)² = 4Answer:
4
Step-by-step explanation:
2√x, √x + 1, 2√x + 1 sides of triangle
√x= y
2y, y+1, 2y+1
(2y)²+(y+1)²= (2y+1)²
4y²+y²+2y+1= 4y²+4y+1
y²-2y=0
y=0 (discarded as side can't be zero) or y= 2
so √x=2 ⇒ x= 4