In an arithmetic sequence Sn=n^2SN=N^2-2N .USE formula (Tn=Sn-Sn-1) to determine the value of Tn
Answer:
[tex]T_n = 2n -3[/tex]
Step-by-step explanation:
Given
[tex]S_n = n^2- 2n[/tex]
[tex]T_n = S_n - S_{n-1[/tex]
Required
Find [tex]T_n[/tex]
[tex]S_n = n^2- 2n[/tex]
Calculate [tex]S_{n-1[/tex]
[tex]S_{n-1} = (n-1)^2- 2(n-1)[/tex]
[tex]S_{n-1} = n^2-2n+1- 2n+2[/tex]
[tex]S_{n-1} = n^2-2n- 2n+1+2[/tex]
[tex]S_{n-1} = n^2-4n+3[/tex]
[tex]T_n = S_n - S_{n-1[/tex] becomes
[tex]T_n = n^2 - 2n - (n^2 - 4n +3)[/tex]
[tex]T_n = n^2 - 2n - n^2 + 4n -3[/tex]
[tex]T_n = n^2 - n^2- 2n + 4n -3[/tex]
[tex]T_n = 2n -3[/tex]
two cars drive on the same highway in the same direction the graphs show the distance d of each one as a function of time t which car drives faster explain how you know
Answer:
lol dont know
Step-by-step explanation:
In the figure below,
Answer:
m<GLK = 58°
Step-by-step explanation:
Given:
m<GLH = 2x + 6
m<HLJ = x
Required:
m<GLK
Solution:
First, find the value of x
m<GLH + m<HLJ = 180° => Linear Pair Theorem
Substitute
2x + 6 + x = 180
Add like terms
3x + 6 = 180
3x + 6 - 6 = 180 - 6
3x = 174
3x/3 = 174/3
x = 58
m<HLJ = x = 58°
Thus, m<HLJ and m<GLK are Vertical angles.
Therefore:
m<GLK = m<HLJ (Vertical angles theorem)
m<GLK = 58° (Substitution)
If a(x) = -9 - 2x, what is an equation for a-'(x)?
O A. a-1
= -x - 7
O
B. a-'(x) = 2 - 9
d
C.
1
a
(2)
1
-9 - 2:3
о
D.
1
-
9
a
=
2
Answer:
The answer should be A..
If Sam's present age is x years, what will be his age in years after 20 years from now?
31 x + 20
x - 20
20x
x/20
Help please!!!!!!!!!!
Answer:
6/8,
12/16,
24/32
48/64
96/128
192/256
384/512
Step-by-step explanation:
Factorise the following.
Answer:
Q.1 14x³ by 42x²
= 14x³/42x²
= x/3
Q.2 11xy²z³ by 55xyz
= 11xy²z³/55xyz
= 1/5yz²
A college basketball player makes 5/6 of his free throws. Assuming free throws are independent, the probability that makes exactly three of his next four free throws if
Answer:
if he got hops
Step-by-step explanation:
Solve for the unknown in the following diagram. Round the answer to two decimal places.
degrees
Answer:
x° ≈ 71.69°
Step-by-step explanation:
HURRY AND ANDWER ASAP PLZ answer with work plz and thanks
A cap and a shirt together costs 22.52. If the shirt costs three times as much as the cap how much did each item cost?
Find the volume please help
(Multiple choice)
Answer:
A. 72 mi³C. 261.8 mi³Step-by-step explanation:
Volume formula:
V = 1/3Bh, B- base area, h- heightQ1
V = 1/3*6²*6 = 72 mi³Correct choice is AQ2
V = 1/3*(π*5²)*10 = 261.8 mi³ (rounded)Correct choice is CHELP DONT UNDERSTAND THIS
Given:
A diagram of two triangles.
To find:
Check whether the triangles are similar or not.
Solution:
In triangle ABC and triangle UVT,
[tex]\angle A\cong \angle U[/tex]
[tex]\angle B\cong \angle V[/tex]
Two corresponding angles of the triangles are congruent. So,
[tex]\Delta ABC\sim \Delta UVT[/tex] (AA property of similarity)
Therefore, the given triangles are similar by AA property of similarity.
Make a the subject of formula b=a^2/(a+c)^2
Answer:
[tex] \orange { \bold{a = \frac{c \sqrt{b} }{(1 - \sqrt{b}) } }}[/tex]
Step-by-step explanation:
[tex]b = \frac{ {a}^{2} }{ {(a + c)}^{2} } \\ \\ b = \bigg(\frac{ {a} }{ {a + c}} \bigg)^{2} \\ \\ \sqrt{b} = \frac{a}{a + c} \\ \\ (a + c) \sqrt{b} = a \\ \\ a \sqrt{b} + c \sqrt{b} = a \\ \\ a \sqrt{b} - a = - c \sqrt{b} \\ \\ a( \sqrt{b} - 1) = - c \sqrt{b} \\ \\ a = \frac{ - c \sqrt{b} }{( \sqrt{b} - 1)} \\ \\ \purple{ \bold{a = \frac{c \sqrt{b} }{(1 - \sqrt{b}) } }}[/tex]
m = 4 b = 3 slope form
Answer:
y=4x+3
Step-by-step explanation:
Slope form is y=mx+b so using your data points the slope form is
y=4x+3
Help please asap. Also please teach how to do this type of problem
Answer:
[tex]64m^{2}[/tex]
Step-by-step explanation:
TSA (total surface area) of cuboid= 2(lw+wh+hl)and the problem said one small cube with 1m width that means it also has 1m length and height
so lets count the cubes for the height, length and width
Height contains 4 cubes (4m)Length contains 4 cubes also (4m)Width contains 2 cubes (2m)Now lets put the givens we got from the figure in the formula of TSA
2*(4*2+4*2+4*4)=64
Divide. Write the quotient in lowest terms, 1 1/3 divided by 1 3/4. Please give a thorough explanation as i need help to figure out how to solve problems of this caliber.
Answer:
Step-by-step explanation:
convert mixed fractions to improper fractions
rule=a b/c=(ac+b)/c
(1 1/3)/(1 3/4)
(4/3)/(7/4)
rule for dividing fractions=(a/b)/(c/d)=(a/b)(d/c)
(4/3)(4/7) then you can multiply the numerators and denominators
16/21
What is the value of 3n-1 when n 20?
Answer:
59
Step-by-step explanation:
3*20-1=59
Solve showing all the steps
Answer:
Step-by-step explanation:
Is the second exponent 6, or 6x ?
If it is 6x, then x = -½
decide which of the following sets of points.
Answer:
Im pretty sure that the answer would be choice f.
Step-by-step explanation:
(a) {T, P, E}: Neither. These points are not collinear because they do not lie on the same line, and they are not coplanar because they are not contained within the same plane.
(b) {A, B, D, M}: Coplanar. These points lie on the same plane since they are contained within the drawing.
(c) {B, K, C}: Collinear. These points lie on the same line within the drawing.
(d) {A, K, E}: Neither. These points are not collinear because they do not lie on the same line, and they are not coplanar because they are not contained within the same plane.
(e) {M, K, T}: Neither. These points are not collinear because they do not lie on the same line, and they are not coplanar because they are not contained within the same plane.
(f) {A, Q, P, D}: Coplanar. These points lie on the same plane since they are contained within the drawing.
EM, P, B: Neither. These points are not collinear because they do not lie on the same line, and they are not coplanar because they are not contained within the same plane.
EM, P, B: Neither. These points are not collinear because they do not lie on the same line, and they are not coplanar because they are not contained within the same plane.
To know more about "Coplanar." here
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1) Ms. Bonanno goes to the gym every 2 days. Ms. Zabo goes to the gym every
3 days. They both went to the gym on May 1. What is the next day Ms.
Bonanno and Ms. Zabo will be at the gym at the same day?
Answer:
may 6th
Step-by-step explanation:
2+3=5 so if they when on the 1st and 2 +3=5 1+5=6
Determine the vertex of the function f(x) = 3x2 – 6x + 13
Identify the values of a and b
Find the x-coordinate of the vertex.
Find the y-coordinate by evaluating the function at the x-value found in
the previous step.
Find the volume of the composite figure. First, find the volume of the triangular prism. 4 cm Triangular prism Volume = [?] cm 5 cm 5 cm 6 cm Rectangular prism Volume = [ ] cm? 10 cm Total Volume of Composite Figure = [ ]cm 8 cm Enter
Answer: See attached image.
The total volume of the composite figure is 530 cm³.
To find the volume of the composite figure, we need to calculate the volumes of the individual prisms and then add them together.
Triangular Prism:
The volume of a triangular prism is given by the formula:
Volume = base area × height
The base of the triangular prism is a triangle with a base of 5 cm and a height of 5 cm.
Therefore, the base area is:
Base area = (1/2) × base × height = (1/2) × 5 cm × 5 cm = 12.5 cm².
Now, we can calculate the volume of the triangular prism:
Triangular prism volume = base area × height = 12.5 cm² × 4 cm = 50 cm³.
So, the volume of the triangular prism is 50 cm³.
Rectangular Prism:
The volume of a rectangular prism is given by the formula:
Volume = length × width × height.
Given the dimensions of the rectangular prism as length = 6 cm, width = 10 cm, and height = 8 cm, we can calculate its volume:
Rectangular prism volume = length × width × height = 6 cm × 10 cm × 8 cm = 480 cm³.
So, the volume of the rectangular prism is 480 cm³.
Total Volume of Composite Figure:
To find the total volume of the composite figure, we add the volumes of the individual prisms:
Total Volume = Triangular prism volume + Rectangular prism volume = 50 cm³ + 480 cm³ = 530 cm³.
Therefore, the total volume of the composite figure is 530 cm³.
Learn more about composite figure click;
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A boat travels 20 miles in 5 hours
(with a constant speed). How far can it
travel in 53 hours (with the same
speed)?
Answer:
212 miles
Step-by-step explanation:
the boat is going 4mph so in 53 hours it would be 212mi
4. A savings account is started with $10,000. Calculate the
current value of the account in 5 years for both of the
following scenarios.
(a) Interest is earned at a rate of 2.3% and is compounded
monthly,
Answer:
$1217.50Step-by-step explanation:
Given:
Principal P = $10000Interest rate r = 2.3% = 0.023Compound number n = 12Time t = 5 yearsInterest amount is:
I = P(1+ r/n)^(nt) - PI = 10000(1 + 0.023/12)^60 - 10000 = $1217.50Explain why the denominator does not change when you are counting by the
unit fraction 1
··4
to reach 3
··4 .
Answer:
Yes, when dividing a whole number by a unit fraction, multiplying the whole number by the unit fraction's denominator always works! a divided by (1/b) = a times (b/1) = (a/1) times (b/1) = ab/1 = ab. Have a blessed, wonderful day! Comment on Ian Pulizzotto's post “Yes, when dividing a whole number by a unit fracti...”
Quadratic formula 3x^2 - 2x + 5 = 0
Step-by-step explanation:
The given quadratic equation is :
[tex]3x^2 - 2x + 5 = 0[/tex]
We need to solve the given equation. The formula used to solve a quadratic equation is :
[tex]x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
We have, a = 3, b = -2 and c = 5
So,
[tex]x=\dfrac{-(-2)\pm \sqrt{(-2)^2-4(3)(5)}}{2(3)}\\\\x=0.333,4.667[/tex]
Hence, this is the required solution.
Which group contains triangles that are similar. im having a hard time
Answer:
1st group contains triangles that are similar
Step-by-step explanation:
since its opposite corresponding angle are equal.
Is this correct if not can someone give me the answer I will mark u brilliant
Answer: the first one is 735.75
the second one is 69
Step-by-step explanation:
THEY ARE BOTH CORRECT!
Answer: They are both correct. Good job! :)
Step-by-step explanation:
HELP it's Geometry HW I WILL GIVE BRAIN LIST AND 5 STARS
CAN SOMEONE ANSWER THIS! Find the lateral surface area of the cylinder. Round your answer to the nearest hundredth. A) 315.04 in2 B) 370.62 in2 C) 395.84 in2 D) 408.92 in2
Answer:
C) 395.84 in^2
Step-by-step explanation:
I took the test
