Answer:
The nth term = n^2 - 2n - 3.
Step-by-step explanation:
Here, we will be finding the nth term of a quadratic number sequence. A quadratic number sequence has nth term = an² + bn + c
Example 1
Write down the nth term of this quadratic number sequence.
-3, 8, 23, 42, 65...
Step 1: Confirm the sequence is quadratic. This is done by finding the second difference.
Sequence = -3, 8, 23, 42, 65
1st difference = 11,15,19,23
2nd difference = 4,4,4,4
Step 2: If you divide the second difference by 2, you will get the value of a.
4 ÷ 2 = 2
So the first term of the nth term is 2n²
Step 3: Next, substitute the number 1 to 5 into 2n².
n = 1,2,3,4,5
2n² = 2,8,18,32,50
Step 4: Now, take these values (2n²) from the numbers in the original number sequence and work out the nth term of these numbers that form a linear sequence.
n = 1,2,3,4,5
2n² = 2,8,18,32,50
Differences = -5,0,5,10,15
Now the nth term of these differences (-5,0,5,10,15) is 5n -10.
So b = 5 and c = -10.
Step 5: Write down your final answer in the form an² + bn + c.
2n² + 5n -10
Example 2
Write down the nth term of this quadratic number sequence.
9, 28, 57, 96, 145...
Step 1: Confirm if the sequence is quadratic. This is done by finding the second difference.
Sequence = 9, 28, 57, 96, 145...
1st differences = 19,29,39,49
2nd differences = 10,10,10
Step 2: If you divide the second difference by 2, you will get the value of a.
10 ÷ 2 = 5
So the first term of the nth term is 5n²
Step 3: Next, substitute the number 1 to 5 into 5n².
n = 1,2,3,4,5
5n² = 5,20,45,80,125
Step 4: Now, take these values (5n²) from the numbers in the original number sequence and work out the nth term of these numbers that form a linear sequence.
n = 1,2,3,4,5
5n² = 5,20,45,80,125
Differences = 4,8,12,16,20
Now the nth term of these differences (4,8,12,16,20) is 4n. So b = 4 and c = 0.
Step 5: Write down your final answer in the form an² + bn + c.
5n² + 4n
1) An airplane is at 10,000 feet above the ground. It needs to fly higher to reach the regular flying height. It increases its height at a constant rate of 2,000 feet per minute. How high will the plane be in 10 minutes?
Answer:
20000
Step-by-step explanation:
Answer: 30,000 feet
Step-by-step explanation: We start with the 10,000 feet original height. From there, we can take 2,000 feet per minute and multiply it by 10 minutes. That gets us 20,000 feet. Add 20,000 to our original 10,000 and we get 30,000.
Which ordered pairs in the form (x, y) are solutions to the equation 3x−4y=21? select each correct answer. (−1, −6) (7, 0) (11, 3) (−3, 3).
Answer:
(-1, -6), (7, 0) , and (11, 3)
Step-by-step explanation:
3x - 4y = 21 Solve the equation for y
3x - 21 = 4y
(3x - 21)/4 = y
Now use the ordered pair and find the true ordered pair
(-1, -6) [ (3)(-1) - 21]/ 4 ; (-3 -21)/4 ; (-24)/4 = -6 True
(7, 0) [(3)(7) -21]/4 ; (21 - 21)/4; 0/4 = 0 True
(11, 3) [(3)(11) - 21]/4; (33 - 21)/4; 12/4 = 3 True
(-3 ,3) [(3)(-3) - 21]/4 (-9 -21)/4 ; -30/4 = -7.5 No
Will mark brainiest if right Is this function linear or nonlinear?
y=3x−5
Answer: This function is linear because it forms a straight line when graphed.
Would appreciate brainly <3
please answer this for me!!
Answer:
x = 40
y = 8
Step-by-step explanation:
3x-9 = 2x+31
3x-2x = 31+9
x = 40
4y+5 = 2y+21
4y-2y = 21-5
2y=16
y=8
15 metres at a speed of 20 cm/s (answer in seconds) a
Here's the perfect answer.
PLEASE MARK ME BRAINLIEST
how many solutions does  3x+9=25x+14 have?
Answer:
one solution
Step-by-step explanation:
3x + 9 = 25x + 14
-3x -3x
9 = 22x + 14
-14 - 14
-5 = 22x
Select the choice that translates the following verbal phrase correctly to algebra: (1 point)
the product of 12 and y increased by 11
12(y + 11)
12y + 11
12 + 11y
12(11y)
Answer:
[tex]⟼12(y + 11)[/tex]
Please help and no links!!!!
Answer: 18
Step-by-step explanation:
. A triangle has an angle that measures 85°. The other two angles are in a ratio of 6:13. What are the measures of those two angles?
AND EXPLAIN THE STEPS
Answer:
Smaller angle : 30 degrees
Bigger Angle : 65 degrees
Step-by-step explanation:
85+6x+13x=180, 85+19x=180,19x=95,x=5
Smaller angle : 30
Bigger Angle : 65
Evaluate g(x)=4−3x when x=−3, 0, and 5
Answer:
13, 4, and -11
Step-by-step explanation:
g(-3)=4+9=13
g(0)=4+0=4
g(5)=4-15=-11
What are the solutions of y=x^2+5x-7
Answer:
You have two variables, and only one condition. It means you have infinite solutions of the form [tex](t; t^2+5t-7)[/tex]. Technically correct, probably not what you want to know.
If you wanted to know if and where the RHS crosses the x axis, the points are the solution to
[tex]x^2+5x-7= 0 \rightarrow x=\frac12(-5\pm\sqrt{25+28})\\x_1= \frac12(\sqrt{53}-5); x_2=-\frac12(\sqrt{53}+5)[/tex]
If you wanted the graph it's a parabola passing through the two points we just found, (0;-7), and with an axis of equation [tex]x=-\frac52[/tex].
. Write the equation of a line passing through the points (3,-1) and (6,7).
(Hint - Use the Calculator)
Step-by-step explanation:
the most usual firm of line equation is
y = ax + b
a is the slope of the line and is expressed as the ratio
y coordinate change / x coordinate change
when going from one point to the other.
b is the y-interception (the bake of y when x = 0).
once we have the slope, we get b by using the coordinates of one of the given points as x and y in the equation and solve for b.
the slope a :
x changes by +3 (from 3 to 6)
y changes by +8 (from -1 to 7)
so, the slope is +8/+3 = 8/3
our line equation now looks like
y = (8/3)x + b
let's simply use the first point
-1 = (8/3)×3 + b
-1 = 24/3 + b = 8 + b
-9 = b
and the full line equation is
y = (8/3)x - 9
Is this graph proportional or non-proportional? How do you know?
Answer:
It is a proportional graph.
Step-by-step explanation:
By definition, a proportional graph is a graph which goes through the origin (O), in this picture the graph appears to indeed go through the origin, and is thus proportional.
y+5 = -3/2(x-2) in slope intercept form
Answer:
y = -3/2x -2
Step-by-step explanation:
Solve for y:
y +5 = -3/2x +3 . . . . . eliminate parentheses
y = -3/2x -2 . . . . . . . . subtract 5
The slope-intercept form of the equation is ...
y = -3/2x -2
Answer:
[tex]y = -\frac{3}{2} x -2[/tex]
Step-by-step explanation:
[tex]y+5=-\frac{3}{2} (x-2)[/tex]
The slope-intercept form is [tex]y =mx+b[/tex], where [tex]m[/tex] is the slope and [tex]b[/tex] is the [tex]y[/tex]-intercept.
[tex]\mathrm{Simplify}: -\frac{3}{2} \cdot(x-2)[/tex]
[tex]\mathrm{Move\: all\: terms\: not\: containing}\:\bold{y}\: \mathrm{to\: the\: right\: side\: of\: the\: equation.}[/tex]
[tex]\sf{Then,\:rewrite\: in\: slope-intercept\: form.[/tex]
how do you subtract fractions with like numerators
Answer:
Step-by-step explanation:
To SUBTRACT fractions with like or the same denominator, just subtract the numerators then copy the common denominator. Always reduce your final answer to its lowest term.
Find the slope for the table.
Answer:
2
Step-by-step explanation:
as x increases by 2, y increases by 4, slope= rise/run, so the slope= 4/2=2
Expand & simplify 4 ( p + 3 ) + 4 ( p − 6 )
Answer:
8p -12Step-by-step explanation:
Expand & simplify 4 ( p + 3 ) + 4 ( p − 6 )
4(p + 3) +4(p - 6) =
4p + 12 + 4p - 24 =
8p -12
can someone help me with this please:)
Answer:
A
Step-by-step explanation:
[tex]2 \sqrt{3} + \sqrt{9} \times \sqrt{ - 1} = 2 \sqrt{3} + 3i[/tex]
Solve for c.
c= -9 - 8c
c=-9-8c
+8c
9c=-9
c=-1
Hope this helps:D!!
The letter C is equal to negative one.
c = -1
Hope this helps!
____x0.01 = 180.4932
what's the answer?
A polyhedron has 6 faces and 7 vertices, how many edges does it have explain your answer
Indeed it in 5mins hurry plsssss
Answer: 12
Step-by-step explanation:
what does coplanar mean?
Answer:
Step-by-step explanation:
Co-planer
When points are in the same plane it means that the points are co-planer.
Answer:
In geometry, a set of points in space are coplanar if there exists a geometric plane that contains them all.
HELP THIS IS VERY IMPAORTANT
Answer:
The answer is the second option
Step-by-step explanation:
All you have to do is replace x with the data given.
Example: f(x) = 3[tex]x^{2}[/tex] - 6
x = 0 => f(x) = 3 x [tex]0^{2}[/tex] - 6 = 3 x 0 - 6 = -6
x = 1 => f(x) = 3 x [tex]1^{2}[/tex] - 6 = 3 x 1 - 6 = 3 - 6 = -3
x = 2 => f(x) = 3 x [tex]2^{2}[/tex] - 6 = 3 x 4 - 6 = 12 - 6 = 6
Use the model to find the missing number in the pair of equivalent expressions.
15 + 9 = ?(5 + 3)
What number is missing from the expression?
Answer:
3
Reasoning:
[tex]3(5+3)=15+9[/tex]
Distribute three to the numbers to get 15+9.
There are 22 tables in the cafeteria. Each table can seat 8 students.There are 4 lunch periods each day.How many students can the cafeteria seat each day?
Answer:
704 students can fit in the cafeteria a day
in the equation 3(x-1)=2x+c for what value of c will x=3? explain your reasoning.
Answer:
0
Step-by-step explanation:
if x is 3 then;
3(3-1)=2×3+c
c=0
so if c=0 then
x=3
the point (-2,6) is on a line with a slope of 3/4. If the point -8,k) is also on the same line what is the value of k
For a point with a slope 3/4 and which passes through the points (-2, 6) and (-8, k), the value of k is 1.5
The line passes through the points (-2, 6) and (-8, k)
That is, [tex]x_1=-2, y_1=6, x_2=-8, y_2=k[/tex]
The slope of the line, m = 3/4
The formula for calculating the slope of a line is given as:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Substitute [tex]x_1=-2, y_1=6, x_2=-8, y_2=k, m = \frac{3}{4}[/tex] into the formula above
[tex]\frac{3}{4} = \frac{k-6}{-8-(-2)} \\\\\frac{3}{4} = \frac{k-6}{-8+2}\\\\\frac{3}{4} = \frac{k-6}{-6}\\\\-6(3)=4(k-6)\\\\-18=4k-24\\\\4k=-18+24\\\\4k=6\\\\k=\frac{6}{4} \\\\k=1.5[/tex]
Therefore, the value of k is 1.5
Learn more here: https://brainly.com/question/25613656
Please help! WILL MARK BRAINLIEST
Answer:
50
Step-by-step explanation:
If x = − 6, which number line shows the value of |x|?
Answer:
I would say the one that has the blue dot. bc, the absolute value of -6 is 6.
Answer:
The second one -6[------------]0 with 6 on top.
Step-by-step explanation:
What is meaning of irrational exponents.
Answer:
Here
Step-by-step explanation:
Irrational exponents are non repeating or infinite decimals while rational exponents are rational numbers. The value of an irrational exponent when calculated is approximate in nature while the value of rational exponent is exact.
