The nth terms of sequence 1 ; 5 ; 11 ; 19 is n² + n + -1 and the nth terms of sequence -2;-3; -6;-11; is -n² + 2n -3 .
What is quadratic sequence?The differences (referred to as first differences) between every two successive terms are the same, then it is called an arithmetic sequence (which is also known as a linear sequence). But if the first differences are NOT same, and instead, the second differences are the same, then the sequence is known as a quadratic sequence.
According to the question
The sequence 1 , 5 , 11 , 19
First difference : 4 6 8
Second difference: 2 2
1.1.1>
Now, expression for the nth term of the sequence.
Quadratic equation
ax² + bx + c
at n= 1
a + b + c = 1 -----------------(1)
At n = 2
4a + 2b + c = 5 ------------------(2)
At n = 3
9a + 3b + c = 11 -------------------(3)
solving equation
Subtracting equation (3) from (2)
9a + 3b + c = 11
-4a - 2b - c = -5
5a + b = 6 ----------------------(4)
Subtracting equation (2) from (1)
4a + 2b + c = 5
-a - b - c = -1
3a + b = 4 ---------------------------- (5)
Subtracting equation (5) from (4)
5a + b = 6
-3a - b = -4
2a = 2
a = 1
Putting value in equation (5)
3a + b = 4
3*1 + b = 4
b = 1
Substituting the value in equation (1)
a + b + c = 1
1 + 1 + c = 1
c = -1
Substituting the value in the quadratic equation
x² + x + -1
For nth term
n² + n + -1
1.1.2>
Term of the sequence is 2549
Now,
using the nth term
n² + n + -1 = 2549
n (n+1) = 2550
n (n+1) = 50 * 51
n = 50
1.2> sequence of numbers is given: -2 ,-3 ,-6 ,-11
First difference = -1 -3 -5
Second difference = -2 -2
1.2.1 >
Now , expression for the nth term of the sequence.
Quadratic equation
ax² + bx + c
at n= 1
a + b + c = -2 -----------------(1)
At n = 2
4a + 2b + c = -3 ------------------(2)
At n = 3
9a + 3b + c = -6 -------------------(3)
solving equations
Subtracting equation (3) and (2)
9a + 3b + c = -6
-4a - 2b - c = 3
5a +b = -3 ----------------(4)
Subtracting equation (2) and (1)
4a + 2b + c = -3
-a - b - c = 2
3a + b = -1 -------------------(5)
Now,
Subtracting equation (5) and (4)
5a +b = -3
-3a - b = 1
2a = -2
a = -1
Putting value of a in equation (5)
3*-1 + b = -1
b = 2
Substituting values in equation (1)
-1 + 2 + c = -2
c = -3
nth term
-n² + 2n -3
1.2.2>the sequence of numbers will never contain a positive term.
because its first term is -ve and difference between consecutive term is always -ve. or as per nth term n² is a -ve term .
Hence, the nth terms of sequence 1 ; 5 ; 11 ; 19 is n² + n + -1 and the nth terms of sequence -2;-3; -6;-11; is -n² + 2n -3 .
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Write the equation of a line with a slope of 4 that passes through the point (-3,5) in slope intercept form
What is the equation
Answer:
[tex]y = 4x+17[/tex]
Step-by-step explanation:
1) First, write the equation of the line in point-slope form. From there, we can convert it to slope-intercept form. Use the point-slope formula [tex]y-y_1 = m (x-x_1)[/tex] and substitute values for [tex]m[/tex], [tex]x_1[/tex], and [tex]y_1[/tex].
[tex]m[/tex] represents the x and y values of one point the line intersects, so substitute 4 in its place. [tex]x_1[/tex] and [tex]y_1[/tex] represent the x and y values of one point the line intersects, so substitute -3 for [tex]x_1[/tex] and 5 for [tex]y_1[/tex]. This gives the following equation in point-slope form:
[tex]y-5 = 4(x+3)[/tex]
2) Now, put it in [tex]y =mx + b[/tex] format, or slope-intercept form by isolating the y:
[tex]y-5 = 4(x+3)\\y-5 = 4x + 12\\y = 4x+17[/tex]
The equation of a line with a slope of 4 that passes through the point (-3,5) in slope intercept form is,y=4x+17.
What is the slope?A numerical assessment of a line's angle relative to the ground is known as the slope.
The inclination of any line, ray, or line segment is the fraction of the perpendicular to the horizontal distance between any two positions on it.
The line's equation in point-slope form is;
y = mx+c
We may then transform it to a slope-intercept form. Substitute values in the point-slope formula as;
y-y₁=m(x-x₁)
y-5=4(x-(-3)
y-5=4(x+3)
y--5=4x+12
y-4x+17
Hence,the equation of a line with a slope of 4 that passes through the point (-3,5) in slope intercept form is,y=4x+17.
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Using 3.14 for , what is the volume of the cylinder?
O A. 21.771 cubic meters
O B. 32.656 cubic meters
O C. 65.312 cubic meters
O D. 169.811 cubic meters
In how many ways can a starting team of 5 players be chosen from a team of 14
Answer:
There are thousands of different combinations possible.
Step-by-step explanation:
2,057,328 to the nearest 100,000
Answer:
2,100,000
Step-by-step explanation:
Just round
I need help with angles
Answer:
1. ∠CFD = 28°
2. ∠RPQ = 53°
Step-by-step explanation:
For the first one:
∠CFD and ∠DFE are angles on a straight line
Angles on a straight line add up to equal 180
That being said we can find the missing angle (∠CFD) by subtracting the given angle measure (152°) from 180
so ∠CFD = 180 - 152
180 - 152 = 28
Hence, ∠CFD = 28°
For the second one:
Complementary angles have a sum of 90°
If ∠RPQ and ∠SPR are complementary angles we can find the missing angle ( ∠RPQ in this case ) by subtract the given angle measure ( 37° ) from 90
so ∠RPQ = 90 - 37
90 - 37 = 53
Hence , ∠RPQ = 53°
look at pic 10 pts will mark brainilest
Answer:
48
Step-by-step explanation:
6x8=48
6 baked a cake for the 8
--------48-------
A standard bathtub holds 60 gallons of water. A full tub drains 12 gallons per minute. Which of the following tables best represents the situation?
J.
x represents the minutes and y shows how many gallons over that time.
The correct table for best represents the situation is shown in Table J.
What is Equation of line?The equation of line in point-slope form passing through the points
(x₁ , y₁) and (x₂, y₂) with slope m is defined as;
⇒ y - y₁ = m (x - x₁)
Where, m = (y₂ - y₁) / (x₂ - x₁)
Given that;
A standard bathtub holds 60 gallons of water.
And, A full tub drains 12 gallons per minute.
Now, From table J;
Rate of change is,
⇒ (24 - 12) / (2 - 1)
⇒ 12 / 1
⇒ 12 gallons per minutes
Which is given in situation.
Thus, The correct table for best represents the situation is shown in Table J.
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Whats the area of number 10 ? Help please, help me do it and explain if you can! BTW THIS IS COMPOSITE SHAPES
Answer:
10. Area = 72 units²
Step-by-step explanation:
10. The shape in number 10 is a trapezoid.
Area of trapezoid = ½(a + b)*h
Where,
a = 6
b = 12
h = 8
Area = ½(6 + 12) * 8
Area = ½(18)8
Area = 72 units²
at a football game, every person is either a fan of the home team or of the visiting team. omar observes that the ratio of fans of the home team to fans of the visiting team is 7:2. omar states that the total number of fans at the game must be an odd number because 7 + 2 = 9 and 9 is an odd number.
Determine a number of fans of the home team and a number of fans of the visiting team that show omar statement is false.
the first question is, enter a number of fans of the home team that would show Omar's statement is false.
the second question, enter a number of fans of the visiting team that would show omar statement is false.
pls I need help!!!!!!
Change the statement from standard form to slope-intercept form. Identify the slope and y-intercept.
9x + 2y = 4
slope (m)
y -intercept
9
a.
b.
C.
9
2
d. 2
e. -4
PREVIOUS
00:35:13
Answer: 2 is the y intercept
Step-by-step explanation:
Slope is rise over run and in this problem our y intercept is 2 because it is defined as the y. Negate your 9 and put it over the y intercept to make into a fraction to represent slope. This makes it y = mx + b form now.
y = - 9/2x + 2
-4r + 1 = -2r - 17
a. 9
b. 11
c. -18
d. -16
¿Cuál es la diferencia entre
una cadena lineal saturada
y una insaturada?
Los alcanos son un ejemplo de compuestos saturados. ... Un compuesto no saturado o un compuesto insaturado es un compuesto químico que contiene enlaces carbono-carbono dobles o triples, como los que se encuentran en los alquenos o alquinos, respectivamente.
Answer:
Can you do it in english? I can't read in spanish sorry.
Anyone I need this please
i’m literally over here crying bc i can’t figure this out. if i don’t turn it in before an hour i get an F. PLEASE HELP. the question is “the diameter of the semicircle below is 12 yards. find the area and perimeter” you don’t have to do both numbers just pls let me know what one you solve. you can even only do area. i just rlly need help.
Answer:
Area = 346.2yd²
Perimeter = 72.1yd
Step-by-step explanation:
AREA
Split it into three shapes: (1) the semi-circle, (2) the triangle, and (3) the rectangle. Find the area of each and then add them together for the area of the whole shape.
Area₁ = πr² = (6²)π = 36π = 113.1 yd²
Area₂ = (1/2)bh = (1/2)(11.3)(14) = 79.1 yd²
Area₃ = lw = (11)(14) = 154 yd²
154 + 79.1 + 113.1=346.2yd²
PERIMETER
The perimeter consists of the length of the curve on the semi-circle, the top , the right side, the bottom, and the slanted line.
length of the curve on the semi-circle = half the cicumference of circle with radius 6 = (2π(6))/2 = 6π = 18.8
the top = 22.3
the right side = 14
the bottom = 11
the slanted line = the hypotenuse of triangle(2) - the diameter of circle(1) = (√(11.3²+14²))-12= (√(323.69))-12=18-12=6
18.8+22.3+14+11+6=72.1yd
use a long method division to calculate 145 413 by 321
Answer:
i dont know because you have not really explained it
Step-by-step explanation:
The quotient of the division of 145413 by 321 is 453.
What is Division?Division is one of the operation in mathematics where number is divideD into equal parts as that of a definite number.
We are using long division method here.
For that dividend is 145413 and divisor is 321.
First take the first some digits of dividend which is greater than 321.
That is the first four digits, 1454.
The multiple of 321 closest to 1454 is 1284 which is equal to 4 × 321
So the first digit of quotient is 4.
1454 - 1284 = 170
Now 170 is less than 321.
Add the next digit of the dividend to 170.
It becomes 1701.
Multiple of 321 closest to 1701 is 1605 which is equal to 5 × 321.
The next digit of the quotient is 5.
1701 - 1605 = 96
Again since 96 less than 321, take the next digit of the dividend and the number becomes 963.
Now 963 is a multiple of 321, where 963 = 3 × 321
So the next digit of the quotient is 3.
Quotient = 453
Hence the quotient of the given division is 453.
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giving brainliest !!! *easy*
Answer: 600 sq cm
Step-by-step explanation: Each side is 100 cm^2, and there are a total of 6 sides. 100•6=600.
Hope this helps!
Answer:
SA = 600
Step-by-step explanation:
A cube has six sides.
The formula to find the SA of a cube is 6a^2
6 x 10^2 = 6 x 100 = 600
Find the surface area of the prism. 5cm 7cm 4cm
Determine whether the series -3 + 9 - 27+ .... is convergent or divergent.
Answer:
divergent
Step-by-step explanation:
just took it
Hurrry dont be bots A bag of marbles has 5 blue marbles, 3 red marbles, and 6 yellow marbles A marble is drawn from the bag at
random. How many possible outcomes are there?
BI
03
O 5
06
O 14
Answer:
14
Step-by-step explanation:
im so sorry that the other people's comments are making you feel uncomfortable :(
there are 14 marbles in total since:
5 marbles+3 marbles+6 marbles = 14 marbles
each marble has one chance of being pulled out, therefore, there are 14 different outcomes.
Find the value of x.
PLEASE HELP
20 points! Please help
A population has a standard deviation of 7.89. What is the approximate standard error of the mean for a sample size of 300?
A.
0.026
B.
0.46
C.
17.32
D.
2.20
Using the Central Limit Theorem, it is found that the approximate standard error of the mean for a sample size of 300 is given by:
B. 0.46
What does the Central Limit Theorem State?It states that the sampling distribution of sample means of size n from a population with standard deviation [tex]\sigma[/tex] has standard error [tex]s = \frac{\sigma}{\sqrt{n}}[/tex]
In this problem, we have that the parameters are [tex]\sigma = 7.89, n = 300[/tex], hence the standard error is given by:
[tex]s = \frac{7.89}{\sqrt{300}} = 0.46[/tex]
Hence option B is correct.
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1. Which equation represents the line that passes through the points (1,1) and (-2,7)?
a. y=-2x + 9
b. y=-2x + 3
c. y=-1/2x + 8
d. y=-1/2x + 6
Answer:
B
Step-by-step explanation:
find slope which is -2 then plug into equation y=mx+b to find constant of 3
A bike wheel has a diameter of 21 in. What is the circumference of
the tire? Use 22/7 for π
Answer:
66 in
Step-by-step explanation:
Find the measure of 46.
46 = [?]
24°
46
Answer:
Solution given:
<6+24=180[co- interior angle]
<6=180-24=156°
<6=156°
Mt. Lincoln In Colorado Is Fourteen Thousand, Two Hundred Eighty Six Feet High.
How Is This Number Written Using Digits?
Answer:
The hight written in digital is 14286
PLEASE HELP !! ILL GIVE 40 POINTS ; PLUS BRAINLIEST !! DONT SKIP ANSWER.
Victoria purchased 0.6lbs of deli ham for $4.71. What is the cost of ham per pound?
Answer:
$7.85
Step-by-step explanation:
Per pound = 1
Ratios:
[tex]\frac{4.71}{0.6} =\frac{x}{1} \\\\0.6x=4.71\\x=7.85[/tex]
HELP! WILL GIVE BRANLIEST!
Answer:
x = 7
z = 85
Step-by-step explanation:
For x:
8x + 39 = 95
8x = 56
x = 7
For z:
95 + 95 + z + z = 360
190 + 2z = 360
2z = 170
z = 85
Check work:
DOES 85 + 85 + 95 + 95 = 360 ? Yes. Answer is correct.
I would appreciate Brainliest, but no worries.
7th grade math help plssss
Answer:
Radius: R = 12 in
Diameter: D = 24 in
Circumference: C = 75.4in
Area: A = 452.39 in²
Step-by-step explanation:
Solutions:
Diameter d= 2r
D = 2 × 12
D = 24
Circumference
C = 2πr
C = 2 × π × 12
C = 24π
C = 75.3982237
Area:
A = πr²
A = π × 12²
A = 144π
A = 452.389342
which one is it? asking for my kid
Answer:
QUESTION:
which one is it?
ANSWER:
Okay, so everyone knows that a straight angle/ full triangle equals up to the sum of 180°, right?
So you take the 180° and subtract the 51°. And you should be getting 129°.
But, since this is a right triangle all I did was subtract 51° from 90° (a right triangle). In the end, the final answer is 39°
Step-by-step explanation:
Hope that this helps you out! :)
If you have any questions please put them in the comment section below this answer.
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