The [tex]nth[/tex] term rule of the quadratic sequence will be [tex]n^2+5n+2[/tex] .
What is quadratic sequence ?Quadratic sequences are sequences that include [tex]nth[/tex] term. They can be identified by the fact that the differences between the terms are not equal, but the second differences between terms are equal.
Quadratic sequence [tex]=an^2+bn+c[/tex]
Here [tex]a,b,c[/tex] are constant and [tex]n[/tex] is the position of term.
First difference [tex]= 3a+b[/tex]
Second difference [tex]=2a[/tex]
We have,
Quadratic sequence [tex]8,16,26,38,52,68,86,....[/tex]
Quadratic sequence [tex]=an^2+bn+c[/tex]
so,
For [tex]n=1[/tex];
[tex]8=an^2+bn+c[/tex]
[tex]8=a+b+c[/tex] [tex]........(i)[/tex]
For [tex]n=2[/tex];
[tex]16=4a+2b+c[/tex] [tex]........(ii)[/tex]
For [tex]n=3[/tex];
[tex]26=9a+3b+c[/tex] [tex]........(iii)[/tex]
Now,
Subtract equation [tex](i)[/tex] from [tex](ii)[/tex]
we get,
[tex]8=3a+b[/tex] [tex]........(iv)[/tex]
Subtract equation [tex](ii)[/tex] from [tex](iii)[/tex] we get,
[tex]10=5a+b[/tex] [tex]........(v)[/tex]
Subtract equation [tex](iv)[/tex] from [tex](v)[/tex] we get,
[tex]2=2a[/tex] (This is second difference mentioned above)
[tex]a=1[/tex]
Putting [tex]a=1[/tex] in [tex](iv)[/tex]
⇒[tex]b=5[/tex]
Now putting values of [tex]a[/tex] and [tex]b[/tex] in equation [tex](i)[/tex]
[tex]8=1+5+c[/tex]
[tex]c=2[/tex]
Now, putting values of [tex]a[/tex] , [tex]b[/tex] and [tex]c[/tex] in,
Quadratic sequence [tex]=an^2+bn+c[/tex]
we get,
[tex]nth[/tex] term rule [tex]=n^2+5n+2[/tex]
Hence, we can say that the [tex]nth[/tex] term rule of the quadratic sequence will be [tex]n^2+5n+2[/tex].
To know more about quadratic sequence click here
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please I need help solving the equation, -2/5c < 9
Answer:
c > -22 1/2
Step-by-step explanation:
Step 1: Multiply both sides by -5/2 and flip the sign.
[tex]-\frac{2}{5}c * -\frac{5}{2} < 9 * -\frac{5}{2}[/tex] [tex]c > -\frac{45}{2}[/tex] [tex]c > -22\frac{1}{2}[/tex]Therefore, the answer is c > -22 1/2.
Help!! (Question in picture)
Answer:
A, B, C are perfect squares. Their roots are 22, 66, 89.
D is not a perfect square. The root is about 94.995
Step-by-step explanation:
Your calculator can help. The integer is a perfect square if its square root is an integer.
A. √484 = 22 . . . . 484 is a perfect square
B. √4356 = 66 . . . . 4356 is a perfect square
C. √7921 = 89 . . . . 7921 is a perfect square
D. √9024 ≈ 94.9947... . . . . not a perfect square
__
Additional comment
When you compute the square root using the "long division" method, the first step is to divide the radicand into groups of 2 digits. The most significant digit of the root will be the root of the largest square less than the leftmost group.
For example, the first step in finding the root of 4356 is to divide it into the groups 43'56'. The most significant digit of the root will be 6, because 36 = 6² is the largest square less than or equal to 43.
If the number is a perfect square, the least-significant digit of the radicand will be the least-significant digit of the square of the least-significant digit of the root. Here, the least digit of 43'56' is 6, which can only be the least-significant digit of 4² = 16 or 6² = 36. No other single digits have a square ending in 6.
So, if the number 4356 is a perfect square, it must be the square of 64 or 66. It is the square of 66. (If you're familiar with powers of 2, you know 64²=4096.)
X=
A. 30
B. 70
C. 110
D. 130
Answer:
Step-by-step explanation:
the answer is D)130 hope it helps
!!!!5 step plan!!!!!
The width of a rectangle is 5 cm more than twice the length the perimeter is 56 cm find the dimensions of the rectangle
Answer: W = 20 1/3, L = 7 2/3 cm
Step-by-step explanation:
Width, W, is 5 cm more than twice the length of the perimeter.
Perimeter = 2W + 2L
W = 2L+5
Perimeter is 56cm:
56 cm = 2W + 2L
Substitute W = 2L + 5 for W:
56 cm = 2W + 2L
56 cm = 2(2L+5) + 2L
56 cm = 4L + 10 + 2L
6L = 46 cm
L = 7 2/3 cm
Since W = 2L + 5
W = 2(7 2/3) + 5
W = 2 (23/3) + 5
W = 46/3 + 5
W = 15 1/3 + 5
W = 20 1/3
2W + 2L = P?
2(20 1/3) + 2(7 2/3) =56 ?
40 2/3 + 15 1/3 = 56?
56 = 56 YES
Translate to an algebraic expression
1. double a number increased by one is seventeen
2. Three less than a number is twelve
3. Triple a number is the same as double the number increased by five
4. Double a number increased by two is the same as the sum of the number and eight
Answer:
1) 2n + 1 = 17
2) n - 3 = 12
3) 3n = 2n + 5
4) 2n + 2 = n + 8
Step-by-step explanation:
Use "n" to represent the unknown number.
For question one:
we double the number → 2n
then we increase (add) by one → + 1
is (equal) to seventeen → = 17
For question two:
three less (minus) than a number is (equals) twelve → n - 3 = 12
Question three:
triple (times 3) a number is the same (equal) as double (times 2) the number increased (add) by five → 3n = 2n + 5
Question four:
double (times two) a number increased (add) by two is (equals) the same as the sum (add) of the number and eight → 2n + 2 = n + 8
evaluate 10-(5-(4-(8-2))
=》The answer is 3.
Steps are in the attachment.
______
Hope it helps :)) ⚜
Answer:
The answer is 3
Step-by-step explanation:
By using PEMDAS, calculate the parenthesis first.
10-(5-(4-(8-2))
10-(5-(4-6)
10-(5-(-2)
10-7
= 3
please help me in questions 16 and 17 only and i’ll mark you as brainliest i promise
Answer:
16. Domain: [-3,5] and range : [-5,3]
17. Domain: [0,4] and range: [0,4]
7,200 divided by 10 to the power of 2
Answer:
51840
[tex] 51840[/tex]
Answer:
518400
Step-by-step explanation:
7200 ÷ 10 is just the zero less:
= 720
Then
720 × 720 =
+1440
+5040
=518400
Given that E is the midpoint of AD and BC, which of the following proves that AB∥CD?
HELP ASAP!
The proof that shows that AB∥CD in the diagram given is:
1. E is the midpoint of AD --> Given
2. [tex]\overline{AE} \cong \overline{ED}[/tex] ---> Definition of midpoint
3. E is the midpoint of BC --> Given
4. [tex]\overline{BE} \cong \overline{EC}[/tex] ---> Definition of midpoint
5. ∠AEB ≅ ∠CED --> Vertical Angles Theorem
6. ΔABE ≅ ΔDCE ---> SAS Congruence Theorem
7. AB∥CD ---> CPCTC Theorem.
The given figure showing ΔABE ≅ ΔDCE is in the image attached below.
We know that:
E is the midpoint of AD. Therefore, AE ≅ ED by the definition of midpoint.
E is the midpoint of BC. Therefore, BE ≅ EC by the definition of midpoint.
∠AEB and ∠CED are vertical angles, therefore, ∠AEB ≅ ∠CED by the vertical angles theorem.
This means that ΔAEB and ΔDEC have:
two pairs of congruent sides - AE ≅ ED and BE ≅ EC
one pair of congruent included side - ∠AEB ≅ ∠CED
Hence, ΔABE ≅ ΔDCE by the SAS Congruence Theorem.
If both triangles are congruent, it implies that all corresponding sides and angles of ΔAEB will be congruent to that of ΔDEC.
Therefore, AB∥CD by the CPCTC Theorem.
Thus, the proof that shows that AB∥CD in the diagram given is:
1. E is the midpoint of AD --> Given
2. [tex]\overline{AE} \cong \overline{ED}[/tex] ---> Definition of midpoint
3. E is the midpoint of BC --> Given
4. [tex]\overline{BE} \cong \overline{EC}[/tex] ---> Definition of midpoint
5. ∠AEB ≅ ∠CED --> Vertical Angles Theorem
6. ΔABE ≅ ΔDCE ---> SAS Congruence Theorem
7. AB∥CD ---> CPCTC Theorem.
Learn more about the CPCTC Theorem on:
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The two lines graphed below are not parallel. How many solutions are there to the system of equations? 5 3 O A. Two O B. Zero O C. Infinitely many O D.One
pls help ill give brainliest to whoever gets it right
Answer:
D
Step-by-step explanation:
Is that the correct answer for it please help me. I want to past my ecam
Answer:
No answer is be 28%
5+9+7+4=25
7/25 + .28 =28%
Step-by-step explanation:
Find the area of the shaded portion.
6
120
Answer:
A = 36√3 - 12π
Step-by-step explanation:
Make 2 identical 30-60-90 triangles out of the "wedge"
For each 30-60-90 triangle:
Since the short leg is 6 the long leg is 6√3
short leg is the base and long leg is the height
a = (1/2)bh
a = (1/2)(6)(6√3)
a = 3(6√3)
a = 18√3
Since there are 2 triangles
a = 36√3
--------------------------------
Then subtract off the area of the 120º sector
a = (120/360)πr^2
a = (1/3)π(6^2)
a = (1/3)π(36)
a = 12π
Shaded area
a = 36√3 - 12π
Step-by-step explanation:
we have the areas of 2 right-angled triangles minus 1/3 the area of the circle (because the 120 degree segment of the circle is 1/3 of the whole 360 degree circle).
since the answer is asking for a square root, we need to aim for the result of a Pythagoras calculation.
basically, the area of a triangle is
1/2 × b×c × sin(A)
A being the angle between the 2 sides b and c. for any 2 sides of the triangle.
one triangle is from the outmost left point to the center of the circle and up to the 90 degree angle. the other triangle is then down to the second right angle.
we know all angles in such a triangle : 90, 120/2 = 60, 180-90-60 = 30.
remember, the sum of all angles in a triangle is 180 degrees.
so, via the law of sines we can then calculate all sides :
a/sin(A) = b/sin(B) = c/sin(C)
with the angles being opposite of the sides.
6/sin(30) = baseline/sin(90)
6/0.5 = baseline/1
12 = baseline
top side² + 6² = 12²
top side² = 12² - 6² = 144 - 36 = 108
top side = sqrt(108) = sqrt(36×3) = 6×sqrt(3)
we pick then top side and 6 as the 2 sides, so that we can use sin(90)=1 in the formula.
the area of the 2 triangles is then
6×sqrt(3)×6×sin(90) = 36×sqrt(3)
and the circle segment to be deducted is
pi×r²/3 = pi×6²/3 = pi×36/3 = pi×12
so, the complete answer is
A = 36×sqrt(3) - 12×pi
its urgent please. my assignment is due in like 30 minutes
Answer:
( iii)
a-x/a+x =b
a-x=b(a+x)
a-x=ab+ax
a-ab=ax+x
a-ab=x(a+1)
a-ab/a+1=x(a+1)/a+1
x=a-ab/a+1
x=a(1-b)/a+1
Is the point (3,2) a solution of the equation?
Step-by-step explanation:
no cause 3/2 can't be changed
Solve the equation for X:
4x2 + 15x = 4
Answer:
15x=-4
Step-by-step explanation:
Find the radius of the button.
A circular button with a diameter of 5 centimeters.
Answer:
r = 2.5 cm
Step-by-step explanation:
The radius is 1/2 of the diameter
r = 1/2 (d)
r = 1/2 (5)
r = 2.5 cm
solve pls brainliest
Answer:
76%
Step-by-step explanation:
to make this a percentage we need to make the denominator 100. luckily 25*4=100, so multiply 19/25 by 4/4 to get 76/100. so our percentage is 76
Answer:
76%
Step-by-step explanation:
percent is out of 100, so 19*4/25*4=76/100=76%
I'm stuck on question 6 + (-20.5)
Answer:
Step-by-step explanation:
First you put the negative sign away for the end and then you switch the problem to 20.5 - 6. Then you put the 0.5 away for later too. 20 - 6 is equal to 14. Then you add the 0.5 back to the number. So it is equal 14.5 and the you put the negative sign back on to get the final answer of -14.5.
Find values of x and y
Answer:
x=15
y= 21
Step-by-step explanation:
6x-11+x+5+81=180
6x+x+86-11=180
7x+75=180
-75. -75
7x=105
--- ----
7. 7
x=15
substitute the x value we just got into the following equation to find y
4y-18+y+14+6x-11=180
4y-18+y+14+6(15)-11=180
4y+y+14+79-18=180
5y+75=180
-75 -75
5y=105
---- -----
5. 5
y=21
If -2 is a zero of P(x) = 2x²- 3x( 5k+4) then k = ____.
Brainly Challange for high level user.
Answer:
k = - [tex]\frac{16}{15}[/tex]
Step-by-step explanation:
Since x = - 2 is a zero , then p(- 2) = 0 , that is
2(- 2)² - 3(- 2)(5k + 4) = 0
2(4) + 6(5k + 4) = 0 ← distribute parenthesis
8 + 30k + 24 = 0
30k + 32 = 0 ( subtract 32 from both sides )
30k = - 32 ( divide both sides by 30 )
k = [tex]\frac{-32}{30}[/tex] = - [tex]\frac{16}{15}[/tex]
Given Polynomial P(x) = 2x^2-3x(5k+4)
Zero = -2
We know that
If -2 is zero of the Polynomial then it satisfies the given Polynomial
⇛P(-2) = 0
⇛ 2(-2)^2-3(-2)(5k+4)=0
⇛ 2(4)+6(5k+4) = 0
⇛ 8+30k+24 = 0
⇛ 30k+32 = 0
⇛ 30 k = -32
⇛ k = -32/30
⇛ k = -16/15
Answer:- The value of k = -16/15.
Read more:
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BRAINLIEST
please help me ty
You can just do two questions or even just one but I would appreciate all
Answer:
Some answers for #4 I think!
a = 36
b = 90
c = 36
d = 90
e = 54
Sorry if they are wrong I tried my bestest!
what is 6/2(1+2)=?give with expiation
Step-by-step explanation:
6/2 (1+2) = 3(3) = 9.
hope this helps you.
Answer:
9
Step-by-step explanation:
First you need to multiply 6/2 or 3 by the numbers in the ( ) 6/2 x 1 and 6/2 x 2. You will get 3 and 6. 3+6= 9
a string 27.2 meters long is cut into shorter pieces, each measuring 3.4 meters long. How many pieces were cut from the 27.2-metres string ?
Answer:
There are 8 pieces of string cut
Explanation:
27.2 ÷ 3.4 = 8
Researchers will conduct a study of the television-viewing habits of children. They will select a simple random sample of children and record the number of hours of television the children watch per week. The researchers will report the sample mean as a point estimate for the population mean. Which of the following statements is correct for the sample mean as a point estimator?
(A) A sample of size 25 will produce more variability of the estimator than a sample of size 50.
(B) A sample of size 25 will produce less variability of the estimator than a sample of size 50.
(C) A sample of size 25 will produce a biased estimator, but a sample size of 50 will produce an unbiased estimator.
(D) A sample of size 25 will produce a more biased estimator than a sample of size 50.
(E) A sample of size 25 will produce a less biased estimator than a sample of size 50.
Using the Central Limit Theorem, it is found that the correct option is:
(A) A sample of size 25 will produce more variability of the estimator than a sample of size 50.
By the Central Limit Theorem, for a distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], considering the sampling distribution of sample means of size n, the measure of variability is the standard error, which is given by:
[tex]s = \frac{\sigma}{\sqrt{n}}[/tex]
Hence, the higher the sample size, the lower the variability, and option A is correct.A similar problem is given at https://brainly.com/question/24663213
answer this
help me with this question.
Answer:
i cant read the handwriting
Step-by-step explanation:
2.5(10x +8) + 3x distributive property
Answer:
23/25
Step-by-step explanation:
(25x+20)/25x+3x/25x
20+3/25=23/25
28x+20
Step-by-step explanation:
[tex]2.5(10x + 8) + 3x \\ 25x + 20 + 3x \\ 28x + 20[/tex]
the 120 grams powdered milk make 12 cups of milk. how many kilograms of powdered milk can produce 60 cups of milk. how many liters is 60 cups of milk?
Answer: 0.6 Liters of powdered milk can produce 60 cups of milk.
Explanation: 120 grams of powdered milk makes 12 cups of milk. 120 divided by 12 is 10. 60 times 10 is 600. So 600 grams of powdered milk to make 60 cups of milk. That is equal to 0.6 kilograms and that is equal to 0.6 liters.
please explain this got a final tomorrow
Answer:
9/9=(1/2x+2)/x_2x_2=1/2x+21/2x=4x=8Guys need help with c,f,g,j
Answer:
Step-by-step explanation:
Javad had a mix of yellow and red jelly beans are shown on the graph if there are 42 jelly beans in his bag how many are red?
Answer:
there is no graph though