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
can anyone help me ?
Find the missing angle measure.
Answer:
x° = 99°
Step-by-step explanation:
The polygon is a hexagon and the sum of its internal angles is:
[tex]180(n-2)=180(6-2)=180(4)=720^{0}[/tex]
subtract the 5 known angles:
[tex]x^{0} =720-145-164-59-132-121=99^{0}[/tex]
Hope this helps
Fill in the blank.
The
is the intersection of the three medians in a triangle.
O centroid
O incenter
O orthocenter
O circumcenter
O centroid
Step-by-step explanation:
In geometry, a median of a triangle is a line segment joining a vertex to the midpoint of the opposite side, thus bisecting that side. Every triangle has three medians, one from each vertex, and they all intersect each other at the triangle's centroid.
In parallelogram HIJK, the measure of angle H is 45∘.
Find the measure of angle J. Explain how you know.
Find the measure of angle K. Explain how you know.
Answer:
The angle diagonal to angle H = 45
The other two angles equal 135
Step-by-step explanation:
A line equals 180. So 45+135 = 180
I'm sorry that I couldn't list names of the angles. I would need a picture. I hope this made since and could help. God bless!
The measure of angle J is 45 degrees and The measure of angle K is also 45 degree. In a parallelogram, opposite angles are congruent, meaning they have the same measure.
Given that angle H measures 45 degrees, we can use this property to find the measures of angles J and K.
Measure of Angle J:
Since angle J is opposite to angle H in parallelogram HIJK, angle J will also measure 45 degrees. This is because opposite angles in a parallelogram are equal.
Measure of Angle K:
Similarly, angle K is opposite to angle I in parallelogram HIJK. Since the opposite angles are congruent, angle K will also have a measure of 45 degrees.
In summary, the measure of angle J in parallelogram HIJK is 45 degrees, and the measure of angle K is also 45 degrees. This is a property of parallelograms where opposite angles are congruent.
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Find Algebraically, the coordinates of P.
Answer:
x =2.5 and y=5.5
Step-by-step explanation:
using elimination method
An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
The point of intersection is (2.4, 5.5).
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example:
2x + 4 = 5 is an equation.
3x + 4y = 5 is an equation.
We have,
Two equations.
3x - y = 2 ____(1)
x + 3y = 19 _____(2)
The point of intersection can be calculated as,
From (1) we get,
3x = 2 + y
x = (2 + y) / 3 _____(3)
From (2) we get,
x = 19 - 3y ______(4)
From (3) and (4) we get,
(2 + y)/3 = 19 - 3y
2 + y = 57 - 9y
y + 9y = 57 - 2
10y = 55
y = 55/10
y = 5.5
Now,
From (3) we get,
x = 19 - 3y
x = 19 - 3 x 5.5
x = 19 - 16.6
x = 2.4
Thus,
The point of intersection is (2.4, 5.5).
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If 43 liters of water are enough to water 25 of the plants in the house, how much water is necessary to water all the plants in the house? Write a multiplication equation and a division equation for the situation, then answer the question. Show your reasoning.
what is -18 1/2 plus 27 3/5?
Step-by-step explanation:
so if I did it wrong
Rewrite the following equation in slope-intercept form. 20x − 11y = –17
Answer:
y = 20/11x +17/11
Step-by-step explanation:
Slope-intercept for: y=mx+b
20x -11y = -17
-11y = -20x -17 Subtract 20x on both sides
y = 20/11x + 17/11 Divide both sides by -11
The difference between two times a number and eight is twenty two. What is twice the number?
Answer: 30
Step-by-step explanation:
2x -8 = 22
2x = 22 + 8
2x = 30
Divide both sides by 2
X = 15
Twice of x
2 x X = 2 x 15 = 30
help me with this please and thank you
Answer:
a. 2x +5
b. Pic attached
c. f(4) = 2•4 +5
f(4) = 8 +5
f(4) = 13
d. Domain: all the real numbers
Range: all the real numbers
what number x 9 is 57
6×9=57
Step-by-step explanation:
get a multiplication chart and find the answer
Answer:
6.33
Step-by-step explanation:
6.33 x 9 = ~57
the quick brown fox jumped over the lazy dog.
help ? yes ? no ? maybe
haha 6 days of history, 3 weeks of math, and 1 week of english all to do tn. It's currently 9:27. oh well who cares aha kinda funny tho
Answer:
Good Luck - You can do it!!!!!!!
Step-by-step explanation:
I once had 3 months of math to do in one night, but I was able to complete it through online videos. Never Give Up!
Answer:
Sorry about that
Step-by-step explanation:
I hope you finished it all
80 POINTS!!! HELP ASAP!!!!
Select the correct answer.
Which statement is true about the effects of the transformations on the graph of function f to obtain the graph of function g.
g(x) = f(x − 3) + 4
A.
The graph of function f is shifted right 3 units and down 4 units.
B.
The graph of function f is shifted right 3 units and up 4 units.
C.
The graph of function f is shifted left 3 units and down 4 units.
D.
The graph of function f is shifted left 3 units and up 4 units.
Answer:
its c
Step-by-step explanation:
Answer:
The answer is B
Step-by-step explanation: shifted right 3 units and up 4 units.
Please help! ):
For the functions f(x)=3x−4 and g(x)=6x^2+5, find (g∘f)(x).
Answer:
(g°f)(x) = 54x^2 - 144x + 101
Step-by-step explanation:
(g°f)(x)= g(f(x)) = g(3x-4) = 6(9x^2 - 24x + 16)+5 = 54x^2 - 144x + 101
Classify the following polynomial by degree and the number of terms.
3x² - 7
Answer:
A.) Quadratic binomial
Step-by-step explanation:
The degree of 2 (x²) makes the polynomial quadratic. It is binomial because it contains 2 terms.
The polynomial is:
↬ quadratic binomialSolution:
We classify polynomials based on the number of terms and the degree,
No. of Termsmonomial - 1 term
binomial - 2 terms
trinomial - 3 terms
polynomial - 4 terms or more
Degree (highest exponent)first
second (quadratic)
third (cubic)
fourth (quartic)
and so on.
[tex]\pmb{3x^2-7}[/tex] has 2 terms. Its highest exponent is 2, so clearly, we have a quadratic binomial.
Hence, 3x² - 7 is a quadratic binomial.
Ivan finished Four-fifths of his math homework problems and all 3 problems for his science homework before dinner. If he finished a total of 43 problems before dinner, what is the total number of math homework problems he was assigned?
Answer:
Step-by-step explanation:
Since we know that Ivan finished all his science problems (3) we know that there are only math problems remaining
substract the science problems from the total 43-3=40
And now we can determine the amount of math problems
4/5 = 40/x where x is the total amount of math problems Ivan was assigned
cross multiply
4x = 5*40
4x=200
isolate the variable
4x/4 = 200/4
x=50
So Ivan was assigned a total of 50 math problems
(Note*) since there are 40 math problems finished 40/50 is equal to 4/5. Just a tip if you don't want to do the whole calculation
Hope this helps!
how can i solve this
Answer: Ill show you some not everything so u can try
Step-by-step explanation: for example 8+y=92
you can make a new problem...
move the 92...
92
subtract
92-
subtract the other number which isnt the variable
92-8
subtract and you get your answer!
Step-by-step explanation:
an equation means that whatever is on one side of the "=" sign is truly equal to whatever is on the other side.
it is like a balance.
you can change the content on one side of the balance, but then you have to make the same change on the other side of the balance. otherwise the balanced relation between both sides is destroyed. and it is no longer an equation.
for the same reason, you can perform any mathematical operation on an equation, as long as you do it simultaneously on both sides.
all these equations are equations with one variable.
so, if we find a way to bring all terms with the variable to one side, and everything else (typically constant numbers) to the other side, while still maintaining the equation relation, then we can solve this by saying "this is only an equation, if the variable has this is that value".
and that is the whole trick.
so, for e.g. t + 3 = 5, how can we get only the variable on one side ? well, the "+ 3" is disturbing, so we subtract 3.
and to keep the balance, we need to subtract 3 on both sides.
that gives us then
t + 3 - 3 = 5 - 3
t = 2
and boom ! the equation has solved itself right in front of our eyes.
and the same thing for all the other equations.
find what is the disturbing additional term on the side of the variable, then get rid of it (and repeat that exact action on the other side) and see what is left on the other side. and you have solved the equation.
that works in every direction like
n + 22 = 5
n + 22 - 22 = 5 - 22
n = -17
12.5 = 7.4 + z
12.5 - 7.4 = 7.4 - 7.4 + z
5.1 = z or
z = 5.1
remember, it is an equation like a balance. you can switch the balance bowls from left to right and right to left, and still they are in balance.
If Susan can type 72 words per minute, how long will it take her to type her 360 word essay?
Answer:
5 minutes
Step-by-step explanation:
72/1 = 360/5
write the equation of the line in fully simplified slope-intercept form
Answer:
y = 3/5x+1
Step-by-step explanation:
y intercept - (0,1), so b=1
Slope = rise/run = 3/5, so m = 3/5
Our Answer is y = 3/5x+1
pleaseeeeeeee HELPPPPPPP
A park is rectangular with a length of 1/2 miles. If the area of the park is 6/8 square miles, what is its width? Input your answer as a fraction.
Answer:
3/2 miles, or 1 1/2 miles
Step-by-step explanation:
Area = Length times Width
So Width is Area / Length
Calculate the problem, (6/8) / (1/2) = (6/8) * (2/1) = 3/2 miles.
Answer:
Area of Park = Length * Width
Therefore Width = Area / Length
= (6/8) / (1/2) = (6/8) * (2/1) = 3/2 miles.
PLZZ MARK BRAINLY
easy one - giving brainly if correct - show work.
Answer:
51,000
Step-by-step explanation:
50,000
20% raise is
50,000 + 50,000 * 20/100
= 50,000 + 10,000
= 60,000
15% tax is
60,000 * 15/100
= 9000
so total money is 60000 - 9000
= 51000
I NEED HELP AS SOON AS POSSIBLE Which of the following describes the location of the opposite of the number that R represents on this line? vertical number line from negative 6 to positive 6 in increments of 2 is shown. Only the whole even numbers are labeled. A point labeled R is placed on the 2nd tick mark below the 0. At a distance of 4 tick marks above 0 At a distance of 4 tick marks below 0 At a distance of 2 tick marks below 0 At a distance of 2 tick marks above 0
Answer:
At a distance of 4 tick marks above 0
Step-by-step explanation:
plz help for brainliest
Answer:
Yes it is an isosceles triangle
Step-by-step explanation:
We just need to see if the distance between two points is the same as the distance with two others
Distance between AB = (4 -(-1))² + (7 - 2)² = c²
5² + 5² = c²
25 + 25 = c²
c = √50
Distance between AC = (11-(-1))² + (8 - 2)² = c²
12² + 6² = c²
144 + 36 = c²
180 = c²
c = √180
Distance between CB = (11-4)² + (8 - 7)² = c²
7² + 1² = c²
49 + 1 = c²
50 = c²
c = √50
Hence, this is an isosceles triangle because AB and CB are congruent in length.
-Chetan K
We need to verify if any of two sides are equal then it is an isosceles triangle.
Refer to the attachment now
A survey was given to a random sample of 80 residents of a town to determine
whether they support a new plan to raise taxes in order to increase education
spending. Of those surveyed, 40 respondents said they were in favor of the plan.
Answer:
sorry i dont quite understand your question .
Ratio would be 1/2 or 50:100 in terms to 40:80
Step-by-step explanation:
if this was more or less of a GOVT question for history or law class then the answer would be " If no candidate for president receives an absolute majority of the electoral votes, pursuant to the 12th Amendment, the House of Representatives is required to go into session immediately to choose a president from among the three candidates who received the most electoral votes. "
Graph the line with slope -3 and y-Intercept -1
I need a line
write a function g whose graph represents the indicated transformation of the graph of f. f(x)=|x+1|-3; horizontal stretch by a factor of 9.
Answer:
f(x) = |[tex]\frac{1}{9}[/tex](x+1)|-3
Step-by-step explanation:
The value representing the horizontal scaling must be placed inside the absolute value, and we need to put () around x - 1 to change the horizontal shift as well. And remember that we must use the reciprocal in the function, so instead of writing y = |9(x+1)|-3, we need to write y = |[tex]\frac{1}{9}[/tex](x+1)|-3.
graph the following features: slope= -3/2 y intercept = 2
Using the given information the equation of the line is y = -3/2x + 2
Now replace x with any number and solve for y. Do this twice to get to points to plot on the graph:
Using X = 0:
y = -3/2(0) + 2, y = 2
First point is (0,2)
Now X = 4:
y = -3/2(4) + 2 = -6 + 2 = -4
Second point = (4,-4)
See attached image with plotted line:
HELP!!!!What is 1/4 turned into a decimal I REALLY NEED HELP BEFORE MY TEACHER GIVES ME A BAD GRADE
Answer:
0.25
Step-by-step explanation:
Answer:
→1/4 as a decimal is 0.25
(I hope you get this answer correct, and also hope you have a great day or night! :)).
Marty can dig a 10 ft trench in 90 minutes. Chris can dig a 10 ft trench in 110
minutes. If they work together, how quickly could they dig the trench?
A)100 minutes
B)42.6 minutes
C)49.5 minutes
D)155 minutes
Answer:
"minutes" (and any subsequent words) was ignored because we limit queries to 32 words.
Step-by-step explanation:
b. po
If they work together, they need 47 minutes to dig the trench.
What is the equation?An equation is a statement that two expressions, which include variables and/or numbers, are equal. In essence, equations are questions, and efforts to systematically find solutions to these questions have been the driving forces behind the creation of mathematics.
It is given that, Marty can dig a 10 ft trench in 90 minutes. Chris can dig a 10 ft trench in 110 minutes.
Marty can dig a 10 ft trench in 90 minutes, and in one minute
10 ft = 90
1 ft = 90/10
1ft = 9 minuted
If Chris can dig a 10 ft trench in 110 minutes, and in one minute
10 ft = 100 minute
1 ft = 100/10
1 ft = 10 minute
If they worked together x minute needed to dig 1 ft,
1/x =1/9+1/10
1/x=1/9+1/10
1=19/90 x
90x=19
x=90/19
x=4.7 minute
For 10 feet,
x = 47 minute
Thus, if they work together, they need 47 minutes to dig the trench.
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pls help asap! i will mark brainliest!
Answer:
AB would be 18 or the first choice.
Since BD is the median that means from A to D and from D to C are equal. We set this up as an equation and solve it.
x + 8 = 2x - 17
+ 17 +17
x + 25 = 2x
-x -x
25 = x
This gives us our first bit of the answer. Then we plug this into our equation for the length of AB to get 18.
Step-by-step explanation:
hope this helps. . . <3
good luck! uωu