This number pattern -1:5 ;x; 35 ; ...
Is a quadratic number pattern.
a) Calculate x
b) Hence, or otherwise, determine the nth term of the sequence.
This sequence 4;9; x; 37; .... is a quadratic sequence.
a) Calculate x
b) Hence, or otherwise, determine the nth term of the sequence.
Answers
Answer:
\(\textsf{a)} \quad x = 17\)
\(\textsf{b)} \quad T_n=3n^2-3n-1\)
\(\textsf{a)} \quad x = 20\)
\(\textsf{b)} \quad T_n=3n^2-4n+5\)
Step-by-step explanation:
Given quadratic number pattern:
-1, 5, x, 35, ...To find the equation for the nth term, we can use the general form of a quadratic equation:
\(\boxed{T_n=an^2 + bn + c}\)
where n is the position of the term.
Let's substitute the values of T₁, T₂ and T₄ into the quadratic equation: to create three equations:
\(\begin{aligned}T_1=a(1)^2+b(1)+c&=-1\\a+b+c&=-1\end{aligned}\)
\(\begin{aligned}T_2=a(2)^2+b(2)+c&=5\\4a+2b+c&=5\end{aligned}\)
\(\begin{aligned}T_4=a(4)^2+b(4)+c&=35\\16a+4b+c&=35\end{aligned}\)
Rearrange the first equation to isolate c:
\(c=-a-b-1\)
Substitute this into the second and third equations:
\(\begin{aligned}4a+2b+(-a-b-1)&=5\\3a+b&=6\end{ailgned}\)
\(\begin{aligned}16a+4b+(-a-b-1)&=35\\15a+3b&=36\end{ailgned}\)
Solve the equations simultaneously by rearranged the first equation to isolate b and substituting this into the second equation and solving for a:
\(b=-3a+6\)
\(\begin{aligned}15a+3(-3a+6)&=36 \\15a-9a+18&=36\\6a&=18\\a&=3 \end{aligned}\)
Substitute the found value of a into the equation for b and solve for b:
\(\begin{aligned}b&=-3a+6\\&=-3(3)+6\\&=-9+6\\&=-3\end{aligned}\)
Finally, substitute the found values of a and b into the equation for c and solve for c:
\(\begin{aligned}c&=-a-b-1\\&=-3-(-3)-1\\&=-3+3-1\\&=-1\end{aligned}\)
Therefore, the equation for the nth term is:
\(\boxed{T_n=3n^2-3n-1}\)
The value of x is the 3rd term. Therefore, to find the value of x, substitute n = 3 into the equation for the nth term:
\(\begin{aligned}T_3&=3(3)^2-3(3)-1\\&=3(9)-3(3)-1\\&=27-9-1\\&=18-1\\&=17\end{aligned}\)
Therefore, the value of x is 17.
\(\hrulefill\)
Given quadratic number pattern:
4, 9, x, 37, ...To find the equation for the nth term, we can use the general form of a quadratic equation:
\(\boxed{T_n=an^2 + bn + c}\)
where n is the position of the term.
Let's substitute the values of T₁, T₂ and T₄ into the quadratic equation: to create three equations:
\(\begin{aligned}T_1=a(1)^2+b(1)+c&=4\\a+b+c&=4\end{aligned}\)
\(\begin{aligned}T_2=a(2)^2+b(2)+c&=9\\4a+2b+c&=9\end{aligned}\)
\(\begin{aligned}T_4=a(4)^2+b(4)+c&=37\\16a+4b+c&=37\end{aligned}\)
Rearrange the first equation to isolate c:
\(c=-a-b+4\)
Substitute this into the second and third equations:
\(\begin{aligned}4a+2b+(-a-b+4)&=9\\3a+b&=5\end{ailgned}\)
\(\begin{aligned}16a+4b+(-a-b+4)&=37\\15a+3b&=33\end{ailgned}\)
Solve the equations simultaneously by rearranged the first equation to isolate b and substituting this into the second equation and solving for a:
\(b=-3a+5\)
\(\begin{aligned}15a+3(-3a+5)&=33 \\15a-9a+15&=33\\6a&=18\\a&=3 \end{aligned}\)
Substitute the found value of a into the equation for b and solve for b:
\(\begin{aligned}b&=-3a+5\\&=-3(3)+5\\&=-9+5\\&=-4\end{aligned}\)
Finally, substitute the found values of a and b into the equation for c and solve for c:
\(\begin{aligned}c&=-a-b+4\\&=-3-(-4)+4\\&=-3+4+4\\&=5\end{aligned}\)
Therefore, the equation for the nth term is:
\(\boxed{T_n=3n^2-4n+5}\)
The value of x is the 3rd term. Therefore, to find the value of x, substitute n = 3 into the equation for the nth term:
\(\begin{aligned}T_3&=3(3)^2-4(3)+5\\&=3(9)-4(3)+5\\&=27-12+5\\&=15+5\\&=20\end{aligned}\)
Therefore, the value of x is 20.
Related Questions
Your credit card has a balance of $5400 and an annual interest rate of 17%. You decide to pay off the balance over two years. If there are no further purchases charged to the card, you must pay $266.94 each month, and you will pay a total interest of $1006.56. Assume you decide to pay off the balance over one year rather than two. How much more must you pay each month and how much less will you pay in total interest?
Answers
Answer:
5400/12= 450 paid
1006.56/2=503.28 interest
total is 5,903.28
total for paid 491.94 for months
Step-by-step explanation:
Find the area of the shaded region.
Answers
Answer:
Step-by-step explanation:
512 sq. ft.
Answer:
512
Step-by-step explanation:
To start off with you can take the area of the the whole rectangle with the boxes inclosed to get (32+8) times (8+8) to get
40x16= 640ft
From their, find the areas of the two boxes inclosed in the rectangle
b1= 8x8= 64ft
b2= 8x8= 64ft
then you can subtract the two boxes areas from the larger rectangles area to get your answer of
640-64-64= 512ft
1. The Graduate Management Admission Test (GMAT) is a standardized exam used by many universities as part of the assessment for admission to graduate study in business. The average GMAT score is 547 (Magoosh website). Assume that GMAT scores are bell-shaped with a standard deviation of 100. What percentage of GMAT scores are 647 or higher
Answers
Answer:
16% of GMAT scores are 647 or higher.
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean \(\mu\) and standard deviation \(\sigma\), the z-score of a measure X is given by:
\(Z = \frac{X - \mu}{\sigma}\)
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
The average GMAT score is 547 (Magoosh website). Assume that GMAT scores are bell-shaped with a standard deviation of 100.
This means that \(\mu = 547, \sigma = 100\)
What percentage of GMAT scores are 647 or higher?
The proportion is 1 subtracted by the p-value of Z when X = 647. So
\(Z = \frac{X - \mu}{\sigma}\)
\(Z = \frac{647 - 547}{100}\)
\(Z = 1\)
\(Z = 1\) has a p-value of 0.84.
1 - 0.84 = 0.16
0.16*100% = 16%
16% of GMAT scores are 647 or higher.
I WILL GIVE 20 POINTS TO THOSE WHO ANSWER THIS QUESTION RIGHT NOOOO SCAMS AND EXPLAIN WHY THAT IS THE ANSWER
Answers
Answer:
A = 832 m²
Step-by-step explanation:
using the formula of a regular polygon with,
n = number of sides
s = Side length
a = apothem
Area = ½ × ans
Where n = 10, a = 16 and s = 10.4
A = ½ × 16 × 10 × 10.4
A = ½ × 1664
A = 832 m²
Answer:
area = 832 m²
Step-by-step explanation:
the area (A) is calculated as
A = \(\frac{1}{2}\) pa ( p is the perimeter and a the apothem )
a decagon has 10 sides , then
p = 10 × 10.4 = 104 m
A = \(\frac{1}{2}\) × 104 × 16 = 52 × 16 = 832 m²
Choose yes or no to tell whether the equation has the given solution 1/4×+3=3=4×+ 1,x=8
Answers
Answer:
\(\large\boxed{\tt No.}\)
Step-by-step explanation:
\(\textsf{We are asked to determine if the equation has a solution given a value.}\)
\(\textsf{Since x is given to us, we can use the \underline{Substitution Property of Equality} to evaluate}\)
\(\textsf{the equation.}\)
\(\large\underline{\textsf{What is the Substitution Property of Equality?}}\)
\(\textsf{The Substitution Property of Equality is a Property that allows us to substitute}\)
\(\textsf{a known term, or expression for an unknown variable, or some kind of placeholder.}\)
\(\textsf{After Substitution, we can prove that the expressions are still equal with this}\)
\(\textsf{property.}\)
\(\large\underline{\textsf{Solving;}}\)
\(\tt \frac{1}{4} x + 3 = " 3 = " 4x+1\)
\(\textsf{There's likely a typo in your equation given, hence I will fix it.}\)
\(\tt \frac{1}{4} x + 3 = 4x+1\)
\(\textsf{Substitute 8 for x in both sides of the equation using our property.}\)
\(\underline{\textsf{Use the Substitution Property of Equality;}}\)
\(\tt \frac{1}{4} (8) + 3 = 4(8)+1\)
\(\underline{\textsf{Follow PEMDAS, multiply first;}}\)
\(\tt 2 + 3 = 32+1\)
\(\underline{\textsf{Evaluate;}}\)
\(\tt 5 \neq 33\)
\(\textsf{If the "typo" was the actual equation;}\)
\(\tt 5 \neq 3 \neq 33\)
\(\large\boxed{\tt No.}\)
What is the formula for calculating the surface area of a sphere?
Answers
Answer:
Please give brainliest
Step-by-step explanation:
c
five less than a number is three
Answers
Answer: The number is 8.
Step-by-step explanation: Do the reverse operation and add 5 to 3, this gives us 8, so the number must be 8, to check, we can do 8 minus 5, it gives us 3.
Hope this helps.
Solve and determine if the equation has 1 solution, no solutions or
infinite solutions.
6p - 4 = -2(-3p+2)
Infinite Solutions
No Solutions
One Solution p = 4
One Solution p = 6
Answers
Answer:
Infinite Solutions
Eme is asked to find 15% of the number 60. If Eme knows that 10% is 6, how can Eme use that information to find 15% of 60?
Answers
Answer:
9
Step-by-step explanation:
15% of the number 60 is 9.
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
Given,
The number is 60
We know that 10% of 60 is 6.
By this information we have to find 15% of 60
15% we can write as sum of ten percentage and five percentage.
As we know that 10% of 60 is 6.
5% of 60 will be 3
10%+5%=15%
Now add 6 and 3 to get 15 percentage of 60.
6+3
9
Hence, 15% of the number 60 is 9.
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If the area of a certain square is 81 square inches or less, which set
describes the domain of the function?
F(s)=s^2
(0,81]
[0, 9]
(0,91
[0,81)
Answers
Answer:
(0, 9]
Step-by-step explanation:
√81 = 9
We must take positive numbers into consideration here.
You’ve a sponge that is 66 square inches. How many times would you use 3 inches and 1 inch length
Answers
write an equation that you can use to slove for x enter your answer in the box
Answers
The value of angle x is 133 degree
And the equation of line be of the form,
⇒ y - y₁ = 133(x - x₁)
In the given line,
one angle is of 47 degree
And other is x degree
To find the value of x,
Since we know that,
The angle of line is 180 degree.
Therefore,
⇒ x + 47 = 180
⇒ x = 133 degree
Therefore slope of this line be 133 degree
Now let this line is passing through (x₁, y₁)
Hence,
The equation of line be,
⇒ y - y₁ = (slope)(x - x₁)
⇒ y - y₁ = 133(x - x₁)
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find the slope of the line 6x + 2y=10
Answers
Answer:
y=-3x+5
Step-by-step explanation:
2y=10-6x
y=5-3x
y=-3x+5
Please help me with geometry
Answers
Answer:
Both distances are radii of the smaller circle and must be equal by the definition of a circle.
The following table shows the number and type of properties available in three cities.
City
Key West
Orlando
Miami
Write a matrix that represents the number of each type of property available in Key West.
Answers
[ 3 9 13 ] is the Matrix showing all types of property available in key west .
What is matrix ?A matrix is a rectangular array or table of numbers, symbols, or expressions arranged in rows and columns to represent a mathematical object or an attribute of such an entity in mathematics.
Calculationgiven in the table that how many types of property are there in the table
its a simple matrix which u can directly see
its a 3 x 1 matrix ...
[3 9 13] this matrix shows the required value
hope this helps...
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Answer: [3 9 13]
Step-by-step explanation:
Find the missing side lengths. Leave your answers and radicals in the simplest form.
Answers
Answer:
u = 12;
v = 6
Step-by-step explanation:
Use trigonometry:
\( \tan(60°) = \frac{6 \sqrt{3} }{v} \)
Use the property of proportion to find v:
\(v = \frac{6 \sqrt{3} }{ \tan(60°) } = \frac{6 \sqrt{3} }{ \sqrt{3} } = 6\)
Use the Pythagorean theorem to find u:
\( {u}^{2} = {v}^{2} + ( {6 \sqrt{3}) }^{2} \)
\( {u}^{2} = {6}^{2} + ( {6 \sqrt{3}) }^{2} = 36 + 36 \times 3 = 36 + 108 = 144\)
\(u > 0\)
\(u = \sqrt{144} = 12\)
4. Find the value of the missing angle (x).*
B
20
F
300
E
G
D
NOTE: Angles not necessarily drawn to scale.
Your answer
Answers
Answer:
hey, angle x:
it's 60 degree
8th grade math, please help.
I’ll give you brainliest if you want.
-Find the volume-
*links are reported*
Answers
Irving Manz works for Ben’s Food Mart. He is paid weekly on the basis of a 40-hour week at the rate of $8.95 an hour with time-and-a-half for overtime. During one week he works 49.5 hours. What was Irving’s time-and-a-half pay rate an hour?
Answers
Answer:
Irving earned about $363.00 during the week.
Step-by-step explanation:
Irving’s time-and-a-half pay rate an hour =$485.54
What is Unitary method?The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
Given:
Payment for one hour = $8.95
So, paid for 40 hours
=40*$8.95
= $358.00
Now for -a-half overtime
=$8.95*1.5
= $13.425
Now, for extra 9.5 hours
=$13.425*9.5
=$127.5375
Hence, Irving’s time-and-a-half pay rate an hour
=127.5375+358.00
=$485.54
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What is another way to write the compound inequality y + 3 ≥ 2 and y + 3 ≤ 6 ?
Answers
Another way to write the compound inequality is 2 ≤ y+3 < 6. The 1st option is the answer
How to write a compound inequality in another way?
An inequality is a relationship that makes a non-equal comparison between two numbers or other mathematical expressions e.g 2x > 4
Given: y + 3 ≥ 2 and y + 3 < 6
To write these in another way, change the inequality sign of one of the inequalities by rearranging. That is:
y + 3 ≥ 2 can be rewritten as 2 ≤ y+3. Thus, we have:
2 ≤ y+3 and y + 3 < 6
Combine the two:
2 ≤ y+3 < 6
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What values of x
and y
satisfy the system of equations {8x+9y=−36 x+7y=1}
Enter your answer as an ordered pair, like this: (42, 53)
If your answer includes one or more fractions, use the / symbol to separate numerators and denominators. For example, if your answer is (4253,6475),
enter it like this: (42/53, 64/75)
If there is no solution, enter "no"; if there are infinitely many solutions, enter "inf."
Answers
The solution to the system of equations is (x, y) = (-261/47, 44/47) as an ordered pair.
To solve the given system of equations:
Equation 1: 8x + 9y = -36
Equation 2: x + 7y = 1
We can use the method of substitution or elimination to find the values of x and y. Let's use the method of substitution:
From Equation 2, we can solve for x:
x = 1 - 7y
Substituting this value of x into Equation 1:
8(1 - 7y) + 9y = -36
8 - 56y + 9y = -36
-47y = -44
y = 44/47
Substituting the value of y back into Equation 2 to find x:
x + 7(44/47) = 1
x + 308/47 = 1
x = 1 - 308/47
x = (47 - 308)/47
x = -261/47
Therefore, as an ordered pair, the solution to the system of equations is (x, y) = (-261/47, 44/47).
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Solve for x. Please show your work. 2x + 6 = 3x - 2
Answers
Answer:
x=8
Step-by-step explanation:
\(2x + 6 = 3x - 2\)
then subtract the 6 from both sides of the equation
\(2x = 3x - 8\)
then subtract the 3x from both sides of the equation
\( - 1x = - 8\)
then divide each side by -1
\(x = 8\)
Please see screenshot.
Answers
Answer:
See below
Step-by-step explanation:
(x+1) (x-5)=16 formula cuadratica brainly
Answers
The calculated value of x in the equation (x + 1) (x - 5) = 16 is 7
Calculating the value of x in the equation
From the question, we have the following parameters that can be used in our computation:
(x + 1) (x - 5) = 16
The above expression is the product of two factors
(x + 1) and (x - 5)
And the result is 16
Express 16 as 8 * 2
So, we have
(x + 1) (x - 5) = 8 * 2
By comparison, we have
x + 1 = 8 and x - 5 = 2
When evaluated, we have
x = 7 and x = 7
This means that the value of x in the equation is 7
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review the simple linear graph what is the slope of the simple linear graph of Line c write the slope either as a integer or fraction NO decimals enter your answer in the box
Answers
Answer:
The answer is 1/4. Hope it helps.
Step-by-step explanation:
The digits 4, 5, 6, 7, and 8 are randomly arranged to form a five-digit number, Find the probability that the first and last digits of the number both are odd.
Answers
Answer:
5,4,6,7
Step-by-step explanation:
The digits 4, 5, 6, 7, and 8 are randomly arranged to form a five-digit number. Complete parts (a) and (b) below.
(a) Find the probability that the number is odd.
The probability that the number is odd
(Type an integer or a simplified fraction.)
(b) Find the probability that the first and last digits of the number both are odd.
The probability that the first and last digits of the number both are odd is
.
(Type an integer or a simplified fraction.)
if 4/5x =16, what is the value of -2x-15
Answers
Answer:
-55 I believe
Step-by-step explanation:
What is the equation of the line that is perpendicular to y = 3x + 3 and passes through the point (-6, 9)?
y=-1/3x+3
y=-1/3x+7
y=3x-33
y = 3x + 27
Answers
Answer:
y = - \(\frac{1}{3}\) x + 7
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = 3x + 3 ← is in slope- intercept form
with slope m = 3
given a line with slope m then the slope of a line perpendicular to it is
\(m_{perpendicular}\) = - \(\frac{1}{m}\) = - \(\frac{1}{3}\) , then
y = - \(\frac{1}{3}\) x + c ← is the partial equation
to find c substitute (- 6, 9 ) into the partial equation
9 = - \(\frac{1}{3}\) (-6) + c = 2 + c ( subtract 2 from both sides )
7 = c
y = - \(\frac{1}{3}\) x + 7 ← equation of perpendicular line
2.
Tom receives $18 from his father in a week. The ratio of the amount of
money he spends to the amount of money he saves in a week is 5 : 4.
(a) What is the difference between the amount of money spent and the
amount of money saved in a week?
B) How much does Tom save in a week?
Answers
Answer:
a= 2 and b= 8
Step-by-step explanation:
a=5/9×18=10
b=4/9×18=8, then a-b=10-8=2
b=4/9×18=8
the perimeter of a rectangular pool is 304 m. if the length of the pool is 81 m, what is its width?
Answers
Answer:
perimeter=2(L+W)
304=2(81+W)
Step-by-step explanation:
304=162+2W.2W=304-162.2W=142\2=71