Find the 12th term in the arithmetic sequence an = 3 − 6(n − 1)

Answers

Answer 1

Answer:

-63

Step-by-step explanation:

3 - 6(12 - 1) = 3 - 6(11) = 3 - 66 = -63

Answer 2
Answer: -63

Step-by-Step Solution:

=> an = 3 - 6(n - 1)

Hence,
=> a = 3
=> d = -6
=> n = 12

Therefore,
an = 3 - 6(n - 1)
a12 = 3 - 6(12 - 1)
a12 = 3 - 6(11)
a12 = 3 - 66
=> a12 = -63

12th Term of this A.P is -63

Related Questions

Work out the value of (2^3)^2

Answers

Answer:

2⁶

Step-by-step explanation:

law of indices states multiplication of powers in and out of bracket 3×2=6

[tex]\text{Let's work out:: 2 to the power of 3 to the power of 2 }\\\text{We can start by raising 2 to the power of 3:: 2*2*2=8, then raising that}\\\text{to the power of 2:: 8*8=64}[/tex]

[tex]\rule{300}{1.7}[/tex]

[tex]\text{The value is 64}[/tex]

Name the property of equality or congruence that justifies going from the first statement to the second statement.

3x+x+7=23

4x+7=23

Answers

Answer:

Reflexive Property

A random sample is taken and the sample size is 25. the sample is normally distributed, the sample mean is 80, and the standard deviation is 5.5. find a 90% confidence interval for the population mean.

Answers

The 90% confidence interval for the population mean is 78.1905<x<81.8095

Confidence interval

The formula for calculating the confidence interval is expressed as:

CI = x ± z*s/√n

Given the following parameters

mean "x" = 80

z = 1.645

s = 5.5

n = 25

Substitute

CI = 80 ± 1.645*5.5/√25

CI = 80 ± 1.8095

CI = {78.1905, 81.8095}

Hence the 90% confidence interval for the population mean is 78.1905<x<81.8095

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Graph the result of the following transformation on f(x)​

Answers

The graph would be the normal parent function of f(x) but all points would be 6 units up.

There's an upward vertical shift of 6. To graph this, you need to graph the function f(x) and then add 6 units to all the y values.

What is the area of the shaded sector of the circle? 9pi units squared 27pi units squared 81pi units squared 162pi units squared

Answers

Answer:

27

Step-by-step explanation:

i promise :)

Answer:

27π units^2

Step-by-step explanation:

There are 130 people in a
sport centre.
73 people use the
gym.
62 people use the swimming pool.
58 people use the track.
22 people use the gym and the pool.
29 people use the pool and the track.
25 people use the gym and the track.
11 people use all three facilities.
A person is selected at random.
What is the probability that this
person doesn't use any facility?

Answers

Answer:

If 11 people use all three facilities, this means:

22 − 11 or 11 are using the gym and the pool but no the track,

29 − 11 or 18 are using the pool and the track but no the gym,

25 − 11 or 14 are using the gym and the track but no the pool.

How many people use the gym only?

130 − (14 + 11 + 11) = 94

How many people use the pool only?

62 − (18 + 11 + 11) = 22

How many people use the track only?

58 − (14 + 11 + 18) = 15

How many people go in for sports?

94 + 22 + 15 + 11 + 14 + 18 + 11 = 185

How many people use exactly one of the facilities?

94 + 22 + 15 = 131

What is the probability that the person uses exactly one of the facilities?

= 131/185 ≈ 0.7081

Step-by-step explanation:

its a bit confusing

Hope It Helps !!!!

The directrix and vertex of a parabola are shown on the graph. What is the vertex form of the equation for the associated parabola?

Answers

Considering the directrix and vertex given in the graph, the equation of the parabola is:

B. [tex]x = -\frac{1}{4}(y + 2)^2 - 2[/tex]

What is the equation of a parabola given it’s vertex?

The equation of a quadratic function, of vertex (h,k), is given by:

(y - k)² = 4p(x - h).

In which the directrix is the line x = h - p.

Looking at the graph, we have that:

The vertex is (-2,-2), hence h = k = -2.The directrix is x = -1, hence -1 = -2 - p -> p = -1.

Thus the equation is:

(y + 2)² = -4(x + 2).

Writing x as a function of y:

B. [tex]x = -\frac{1}{4}(y + 2)^2 - 2[/tex]

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Calculate the cost of the number of units used

Answers

Step-by-step explanation:

calculated the cost of numbers of units usex

Find cos (330°). Your answer MUST be in radical form.

Answers

Step-by-step explanation:

square root 3 divided by

2

A game requires players to throw a ball into a target. The table below shows values from the function that represents one path of a thrown ball, where x represents the horizontal distance the ball travels in feet and f(x) represents the height of the ball in feet.



If the ball enters the target at the highest point in its path, based on the table, what is the height of the target?

1.5 feet
4 feet
28 feet
29 feet

Answers

The height of the target is 29 feet.

The correct option is (D)

What is function?

An expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

The given table path of the thrown ball,

where x represents the horizontal distance and f(x) represents the height of the ball.

Now,

when x = 1.25 feet horizontally, the height will be maximum.

also, the height of the ball at  distance x = 1.25 feet is

f(1.25) = 29 feet.

Hence, height of the target is 29 feet.

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Answer:

D. 29 feet

Step-by-step explanation:

lateral surface for a triangular prism l=8 w=4 h=6

Answers

Answer:

? i need help

Step-by-step explanation:

4x^{4}-x^{2} -12x-36

Answers

Answer:

(x-2)(4x³+8x²+15x+18)

The nth term of a sequence is -2n - 4. Work out the 50th term of the sequence.

Answers

Answer:

-104

Step-by-step explanation:

1) Substitute 50 into n.

-2(50) - 4

-100 - 4

-104

4 2/3 ÷ 2 1/3 ? what is the quotient?​

Answers

Answer: 42/21 or 2

Step-by-step explanation:

you first convert them to improper fractions, which is 14/3 and 7/3. Then, you multiply the reciprocal and get 14/3x3/7, and get 42/21. Simplify, and you get 2.

PLSS HELP WIT 4 QUESTIONNN

Answers

Answer:

1. Statement C is not true.

2. Option B is correct

3. Option C is correct

4.Option C is correct

Step-by-step explanation:

1. There are 5 Platonic solids : The tetrahedron, cube

,octahedron, dodecahedron ,icosahedron.

The faces of cube and dodecahedron are not triangles.

therefore statement C is incorrect.

2. Polyhedron formula : Vertices - Edges + Faces = 2

now put the values

12 - 18 + F= 2

F = 8.

3. Polyhedron formula : Vertices - Edges + Faces = 2

now put the values

V - 30 + 12 = 2

V = 20.

4. Probability is the number of favourable or unfavourable event divided by total events.

therefore denominator always greater than numinator.

so [tex]\frac{8}{7}[/tex] cannot represent the probability

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Pls help quickly!!!

Find the coordinates of the vertex of the graph of the function.
y=3x^2-4x+3

Answers

Answer:

vertex = ( [tex]\frac{2}{3}[/tex], [tex]\frac{8}{3}[/tex] )

Step-by-step explanation:

given the equation of a parabola in standard form

y = ax² + bx + c ( a ≠ 0 )

then the x- coordinate of the vertex is

x = - [tex]\frac{b}{2a}[/tex]

y = 3x² - 4x + 3 ← is in standard form

with a = 3 , b = - 4 , then

x = - [tex]\frac{-4}{6}[/tex] = [tex]\frac{2}{3}[/tex]

substitute x = [tex]\frac{2}{3}[/tex] into the equation for corresponding y- coordinate of vertex

y = 3([tex]\frac{2}{3}[/tex] )² - 4([tex]\frac{2}{3}[/tex] ) + 3

  = 3([tex]\frac{4}{9}[/tex] ) - [tex]\frac{8}{3}[/tex] + 3

  = [tex]\frac{4}{3}[/tex] - [tex]\frac{8}{3}[/tex] + [tex]\frac{12}{3}[/tex]

  = [tex]\frac{8}{3}[/tex]

vertex = ( [tex]\frac{2}{3}[/tex], [tex]\frac{8}{3}[/tex] )

Vertex ( 2/3 , 8/3 )

A rectangle has perimeter 16 m. Express the area A (in m2) of the rectangle as a function of the length, L, of one of its sides.

Answers

The area A of the rectangle as a function of the length, L of one of its sides is A = 8L - L²

What is the perimeter of a rectangle?

The perimeter of a rectangle is P = 2(L + W) where

L = length of the rectangle and W = width of the rectangle

Given that P = 16 m,

P = 2(L + W)

16 = 2(L + W)

16/2 = L + W

L + W = 8

So, W = 8 - L

What is the area of the rectangle?

The area of the rectangle, A = LW where

L = length of the rectangle and W = width of the rectangle

Since W = 8 - L, substituting W into the equation for A, we have

A = LW

A = L(8 - L)

A = 8L - L²

So, the area A of the rectangle as a function of the length, L of one of its sides is A = 8L - L²

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Please help me with this question!

Answers

The diameter of the sphere is 14 cm.

What is a sphere ?

Sphere is a three dimensional object , it has no edges or vertices and is round in shape.

The surface area of the sphere is given by 4πr²

As radius = diameter /2

Surface area =  4π r²

196 π = 4π *(d/2)²

196/4 = d²/4

49 *4 = d²

d = 14 cm

Therefore the diameter of the sphere is 14 cm.

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Hii! I need some help, would anyone mind helping me?
Find the center of this hyperbola.
[tex]\boldsymbol{x^2-25y^2-14x+100y-76=0}[/tex]
[tex]\stackrel\bigstar{\boldsymbol{\underbrace{Thankyou!!}}}[/tex]

Answers

Step-by-step explanation:

[tex] {x}^{2} - 14x - 25 {y}^{2} + 100y = 76[/tex]

Factor by grouping,

[tex]( {x}^{2} - 14x) - (25 {y}^{2} - 100y) = 76[/tex]

Complete the square, with the x variables,

[tex]( {x}^{2} - 14x + 49) - (25 {y}^{2} - 100y) = 125[/tex]

Factor out 25 for the y variables

[tex]( {x}^{2} - 14x + 49) - 25( {y}^{2} - 4y) = 125[/tex]

Complete the square

[tex]( {x}^{2} - 14x + 49) - 25( {y}^{2} - 4y + 4) = 25[/tex]

Simplify the perfect square trinomial

[tex](x - 7) {}^{2} - 25(y - 2) {}^{2} = 25[/tex]

Make the right side be 1 so divide everything by 25.

[tex] \frac{(x - 7) {}^{2} }{25} - (y - 2) {}^{2} = 1[/tex]

Here our center is (7,2).



What are the solutions to the quadratic equation below in factored form?
(10x + 5)(11x - 44) = 0
= ½, x = 4
0x=
0 x = 2, x = -4
0x = 2, x = 4
○ x = − ½, x = 4

Answers

Answer:

D.) x = − ½, x = 4

Explanation:

[tex]\rightarrow \sf (10x + 5)(11x - 44) = 0[/tex]

set the factors to zero

[tex]\rightarrow \sf 10x + 5 = 0, \ 11x - 44 = 0[/tex]

exchange the sides

[tex]\rightarrow \sf 10x = -5, \ 11x = 44[/tex]

exchange the sides

[tex]\rightarrow \sf x = -\dfrac{5}{10} , \ x = \dfrac{44}{11}[/tex]

simplify the following

[tex]\rightarrow \sf x = -\dfrac{1}{2} , \ x =4[/tex]

(10x+5)(11x-44)=010x(11x-44)+5(11x-44)=0110x²-440x+55x-220=0110x²-385x-220=0

On solving

x=-1/2 or x=4

Could someone do this question for me? Thanks

Answers

Answer:

20 counters/box

Step-by-step explanation:

Missing counters(m)= 8

Total number of counters available (t-m)= 132

Required number of counters(t):

=(t-m) + m

= 132 + 8 = 140

Total number of boxes(tB) = 7( 6 full and one with eight missing)

Total Counters/Boxes= t/tB

= 140/7

= 20

Need to know asap thanks

Answers

Answer:

[tex]\large \boxed{\sf 16}[/tex]

Explanation:

[tex]\Rightarrow \sf \sqrt{121} + \sqrt[3]{125}[/tex]

[tex]\Rightarrow \sf{ \sqrt{11 \ x \ 11} + \sqrt[3] {\sf5 \ x \ 5 \ x \ 5}[/tex]

[tex]\Rightarrow \sf{ \sqrt{11^2} + \sqrt[\sf 3] {\sf 5^3}[/tex]

[tex]\Rightarrow \sf 11 + 5[/tex]

[tex]\Rightarrow \sf 16[/tex]

I hope this help you . the concept of sure and cube roo

Which type of geometry best describes the following statement?
The boundaries of an arc are considered to be at infinity.

A. spherical geometry
B. Euclidean geometry
C. hyperbolic geometry
D. non-euclidean geometry

Answers

Answer:

B=hyperbolic geometry

pls help me with this question

Answers

Answer:

D, C

Step-by-step explanation:

for part a, there is a negative slope with the graph shifted two units upwards

for part b, if you plug in C, you get an answer that works

Can you answer the question

Answers

well if its asking for an exponent then its (-5)⁴

The correct answer would be (-5)^4.

Explanation : (-5) to the power of 4, or, 625.

Bao says: "i can prove this using the fact that opposite sides in a parallelogram are congruent, and by establishing the congruence of a single pair of triangles." which pair of triangles is bao referring to, and which criterion should he use for establishing congruence?

Answers

The pair of triangle formed are congruent using the side-side-side congruency theorem.

What are congruent triangles?

Two triangles are said to be congruent if they have the same shape and their corresponding sides are congruent.

Since the opposite sides of a parallelogram are congruent, if the parallelogram is cut through the diagonal, the pair of triangle formed are congruent using the side-side-side congruency theorem.

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w = -5?
w2 + 3w − 11

Answers

The value of an expression will be equal to -1.

The complete question is given below:-

If the value of w is -5 then find the value of the expression w² + 3w -11.

What is an expression?

Expression in maths is defined as the collection of numbers, variables, and functions using signs like addition, subtraction, multiplication and division.

The given expression will be solved as follows:-

E = w² + 3w -11.

E = ( -5 )²  + ( 3 x -5 ) -11

E = 25 - -15 - 11

E = 25 - 26

E = -1

Therefore the value of an expression will be equal to -1.

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If the diagonal of the rectangle is 10.5 inches and the length of the rectangle is 7.25, what is the width of the rectangle?

Answers

Answer:

w≈7.6in

Step-by-step explanation:

L= 7.25

D= 10.5

Using the formula    [tex]d=\sqrt{w^{2} + l^{2} } \\[/tex]Solving for w          [tex]w=\sqrt{d^{2} -l^{2} }[/tex]                                    [tex]\sqrt{10.52^{2}-7.25^{2} } = 7.59523in[/tex]

Answer:-

The width of this rectangle is = 7.59

Given:-

In this question, it is given that -

The diagonal of this rectangle is = 10.5

the length of this rectangle is = 7.25

To find:-

We have to find the width of this rectangle.

Solution:-

We can easily solve this problem using the Pythagorean theorem.

In this problem, it is given that the length of this rectangle is = 7.25 and the diagonal is =10.5

so by the Pythagorean theorem, we can get-

(length)² + (width)² = (diagonal)²

or, (7.25)² + (width)² = (10.5)²

or, (width)² = (10.5)² - (7.25)²

= 17.75 × 3.25

= 57.6875

or, width = 7.59

So, the width of the rectangle is 7.59.

Find the equation of the parabola with its focus at (6, 2) and its directrix y = 0

Answers

Answer:

y= 1/4 x-62+1

Step-by-step explanation:

Use the commutative property to simplify the expression 4/3 + 3/4 + 2/3

Answers

The simplified expression using  the commutative property is : [tex]\frac{6}{3}[/tex] + [tex]\frac{3}{4}[/tex]

Meaning of commutative property

commutative property can be defined as a mathematics attribute that is possessed by a mathematical equation, that enables the objects undergoing addition or multiplication to change position.

In conclusion, The simplified expression using  the commutative property is : [tex]\frac{6}{3}[/tex] + [tex]\frac{3}{4}[/tex]

Analysis

4/3 + 3/4 + 2/3 =  ( [tex]\frac{4}{3}[/tex] +  [tex]\frac{2}{3}[/tex] ) +  [tex]\frac{3}{4}[/tex]  =   [tex]\frac{6}{3}[/tex] + [tex]\frac{3}{4}[/tex]

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