What's the recursive formula of the geometric sequence below?
2, 6, 18, 54, 162, 486,...
O ay = 3; an = an-1 · (2)n-1 for n 2 2
a1 = 2; an = an-1 . (3) for n 2 2
O a1 = 2; an = an-1 • (3)n-1 for n 2 1
ay = 2; an = an-1. (2) for n 2 1

Answer:

The solution set is therefore {-10, 2}

Step-by-step explanation:

The absolute value equation |3x + 12| = 18 has two distinct solutions.

|3x + 12| = 18 may be rewritten as

3x + 12 = 18 and

-(3x + 12) = 18

The first equation immediately above becomes 3x = 6 after we subtract 12 from both sides.  Therefore, x = 6/3, or x = 2.

Simplifying the second equation yields -3x - 12 = 18.  To solve this for x, we add 12 to both sides, obtaining -3x = 30.

Dividing both sides by -3 yields x = -10.

The solution set is therefore {-10, 2}

Answer:

1. b.  2. a.  3. a.

Step-by-step explanation:

1. (f + g)x = f(x) + g(x)

= x^2 + 2x + 4

(f + g)(-1) =  (f + g)(x)  where x = 1 so it is

(-1)^2 + 2(-1) + 4

=  1 - 2 + 4

= 3.

2.  We find (f o g)(x) by replacing the x in f(x) by g(x):

= √(x + 1) and

(f o g)(3) =  √(3 + 1)

= √4

= 2.

3. (f/g) c  = f(x) / g(x)

= (x - 3)/(x + 1)

The domain is the values of x which give real values of (f/g).

x cannot be - 1 because the denominator x + 1 = -1+1 = 0 and dividing by zero is undefined. So x can be all real values of x except x = -1.

The domain is (-∞, -1) U (-1, ∞)

Answer:

1 state

Step-by-step explanation:

You can see this by the state increases by 1, from 14-15, in the graph above.

Also, can you please give me the brainliest answer thing. :)

Answer:

[tex]\boxed{x = 40}[/tex]

Step-by-step explanation:

Hey there!

Well angles like 142 and 2x + 22 equal each other because they are across from each other.

So we can set up the following,

142 = 3x + 22

Single out x

-22 to both sides

120 = 3x

Divide both sides by 3

x = 40

Hope this helps :)

Answer:

x=40

Step-by-step explanation:

142=3x+22

3x+22-22=142-22

3x=120

120/3=40

Answer:

a 0,1 and b 1,0

Step-by-step explanation:

exam took

Answer:

The other answer is incorrect the answer is

D) The locations of A' and B' are A' (0, 6) and B' (6, 0); lines f and f' are parallel.

Since ∠COA and ∠BOD are vertical angles, they are congruent.

You are also given that ∠ACO ≅ ∠DBO and BO ≅ CO.

By ASA (Angle-Side-Angle) congruency, you know that △ACO ≅ △DBO

The proof is shown below:

If the three angles and the three sides of a triangle are equal to the corresponding angles and the corresponding sides of another triangle, then both the triangles are said to be congruent.

In Δ PQR and ΔXYZ, as shown below, we can identify that PQ = XY, PR = XZ, and QR = YZ and ∠P = ∠X, ∠Q = ∠Y and ∠R = ∠Z. Then we can say that Δ PQR ≅ ΔXYZ.

ASA criterion stands for Angle-Side-Angle criterion. Under the ASA criterion, two triangles are congruent if any two angles and the side included between them of one triangle are equal to the corresponding angles and the included side of the other triangle.

Given:

∠ACO ≅ ∠DBO, and BO ≅ CO

as, ∠COA =∠BOD (vertically opposite angles)

∠ACO ≅ ∠DBO ( given)

BO ≅ CO ( given)

So, By ASA (Angle-Side-Angle) congruency,  △ACO ≅ △DBO

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Answer:

k=-6

Step-by-step explanation:

Answer:

[tex]\Large \boxed{k=-6}}[/tex]

Step-by-step explanation:

35 = -5(2k+5)

Expand brackets.

35 = -10k - 25

Add 25 on both sides.

60 = -10k

Divide both sides by -10.

-6 = k

Answer: 14 1-cent stamps (in case anyone else still needs)

Step-by-step explanation:

1-cent stamps=x

8-cent stamps=x-4

12-cent stamp=.5x

x+x-4+.5x=31

2.5x-4=31

2.5x=35

x=14

You can use the $1.78 to double check:

(1*14)+(8*10)+(12*7)

14+80+84=178 cents (or $1.78)

Answer:

(7, -5.5)

Step-by-step explanation:

is seen below on this graph (7, -5.5) shows x = 7 and y = -5.5

The required ways of the combination to display the flowers on the dinner is  20.

There are 6 flowers in vases in your kitchen. You want to put 3 of them on the dining room table for dinner tonight. Order isn’t important. How many ways can you display the flowers for dinner to determiined.

In arithmetic, combination and permutation are two different ways of grouping elements of a set into subsets. In a combination, the components of the subset can be recorded in any order. In a permutation, the components of the subset are listed in a distinctive order.

Examples of permutation and combination, Managing people, numbers, numerals, alphabets, letters , and colors are examples of permutations. Choosing of menu, foodstuffs, dresses, matters, and the group are examples of combinations.

Since, the total number of flower in vases is 6
3 of them to be selected for the dinner table tonight.
The combination is given as.
= C( 6 , 3)
= 6!/3!(6 - 3)!
= 6!/3!3!
= 20

Thus, the required ways of combination to display the flowers on dinner is  20.

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Answer:

5/6, 0.23, -5 3/8

Step-by-step explanation:

Answer Step one x=16/9 =1.778

Last step is x²=0

Hope I helped you

Answer:

the roots are {0, 0, 16/9}

Step-by-step explanation:

The trick to solving this is to factor out x^2 from both terms on the left:

x^2*9*x - 16x^2=0, or

x^2(9x - 16) = 0

Then, either x^2 = 0 or (9x - 16) = 0.

Thus, the roots are {0, 0, 16/9}

Answer:

27

Step-by-step explanation:

By the theorem of intersecting secant and tangent out side of a circle, we have:

[tex] {60}^{2} = 48 \times (48 + x) \\ 3600 = 48 \times (48 + x) \\ \frac{3600}{48} = 48 + x \\ 75 = 48 + x \\ 75 - 48 = x \\ x = 27 \\ [/tex]

Sry i couldn't find the answer

Answer:

(2) 42°

Step-by-step explanation:

Copy of the given problem:

4. Multiple-Choice

1. Two complementary angles measure (12r - 18)° and (5x + 23)°. What

is the measure of the smaller angle?

(1) 5°

(2) 42°

(3) 48°

(4) 90°

Solution:

The sum of the measures of complementary angles is 90 deg.

12r - 18 + 5x + 23 = 90

We have 1 equation with two different variables, so we cannot solve the equation to find unique values of the variables.

I assume the above is an error, and both variables should be the same.

12r - 18 + 5r + 23 = 90

Combine like terms on the left side. Terms with r are combined. Terms with no variable are combined.

12r + 5r - 18 + 23 = 90

17r + 5 = 90

Subtract 5 from both sides.

17r = 85

Divide both sides by 5.

r = 5

The measures of the angles are:

12r - 18 = 12(5) - 18 = 60 - 18 = 42

5r + 23 = 5(5) + 23 = 25 + 23 = 48

The measures of the two angles are 42°  and 48°.

The smaller angle measures 42°

Answer: (2) 42°

The construction that you can use to prove the Pythagorean Theorem based on similarity of triangles is 2nd construction. Please see the attached file.

Two triangles are similar triangles of their corresponding angles are equal corresponding sides are in equal ratios.

The Pythagorean theorem, also known as Pythagoras's theorem, is a fundamental relation in Euclidean geometry among the three sides of a right triangle. It mentions that the sum of the squares of the other two sides is equal to the square of the hypotenuse (the side opposite the right angle).

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260 units2 is the answer

Basically the first three items are true, with the rest false.

=========================================================

Explanation:

Let's go through each answer choice one by one to see if it is true or false.

---------------------

A. The quadratic equation is in standard form.  

This is true. Standard form for quadratics is y = ax^2+bx+c. In this case, a = 2, b = 0, c = 3. It might help to write the equation as y = 2x^2+0x+3.

---------------------

B. Using substitution, the system of equations can be rewritten as 2x2 – x – 3 = 0.  

This is true. Start with y-x = 6. Replace y with 2x^2+3 and we get

2x^2+3-x = 6

From here we subtract 6 from both sides

2x^2+3-x-6 = 6-6

2x^2-x-3 = 0

---------------------

C. There are two real number solutions.  

This is true. When you graph the two equations (I recommend GeoGebra but Desmos is another good tool), you'll see they intersect at two different locations. Each location is a solution in the form (x,y).

---------------------

D. There are no real number solutions.  

This is false. It contradicts choice C.

---------------------

E. A solution of the system of equations is (–1, 1.5).

This is false. The two solutions are (-1, 5) and (1.5, 7.5) which is where the two graphs intersect.

Another way to check is to plug x = -1 into either equation. You'll find the result to both is y = 5 instead of y = 1.5

Answer:

its ABC

Step-by-step explanation:

[tex]\dfrac{x}{4}=\dfrac{x+9}{4+12}\\\\16x=4(x+9)\\16x=4x+36\\12x=36\\x=3[/tex]

Explanation : If 66 is a factor of this unknown value, then 22 must be as well considering that 22 is a factor off 66. Let's say that this large value is 330. It is a multiple of 66, as 66 [tex]*[/tex] 5 = 330. At the same time 22 [tex]*[/tex] 15 = 330, so 330 is a multiple of 22 as well - or vice versa, 12 is a factor of 330.

We can also tell that 15, 22 fit into 330 through another approach. 22 [tex]*[/tex] 3 = 66, and 66 [tex]*[/tex] 5 = 330, so 5 [tex]*[/tex] 3 = 15 - the same value. This proves that 22 will always be a factor of a value that is the factor of 66.

Answer:

7/6

Step-by-step explanation:

We can find the slope by using the slope formula

m = (y2-y1)/(x2-x1)

    = ( -3 -4)/(5 -11)

  -7/-6

  =7/6

Answer:

7/6

Step-by-step explanation:

m = (y2 - y1)/(x2 - x1)

m = (-3 - 4)/(5 - 11)

m = -7/(-6)

m = 7/6

Answer:

The least number of steps she takes to reach 20 m is 118 steps

Step-by-step explanation:

For Laura, the length of a walking step = 50 cm = 0.5 m

The repeating number of steps she takes = Two steps forward one step backwards

The number of forward steps it would take for her to reach 20 m = (20 m)/(0.5 m) = 40 steps

Given that she always takes two steps forward and one step backwards, we have;

The number of steps forward every three steps = 2 step forward + (-1) step (backward)

The number of steps forward every three steps = 2 - 1 = 1 step forward

To reach 39 steps forward, she would need 39 × 3 =  117 steps

To get to the 40 steps she needs just a step forward, making the total number of steps to reach 40 steps = 117 + 1 = 118 steps

Therefore, the least number of steps she takes to reach 20 m = 118 steps.

Answer: 24

Step-by-step explanation:

R= 3

You can find this using simple algebra

The measure of RA is 24 units after using the concept of congruent triangle option (A) 24 is correct.

Congruent triangles are those that are exactly the same size and shape. Congruent is represented by the symbol ≅ When the three sides and three angles of one triangle match the dimensions of the three sides and three angles of another triangle, they are said to be congruent.

We have a triangle shown in the picture.

It is required to find the measure of the RA

To find the measure of the RA we can apply the concept of congruent triangle:

In the triangle LRU and triangle LAU

LU = LU (common side)

LR = LA (equal sides)

Angle RLU = Angle ALU (equal)

The triangles are congruent.

RU = UA

18 - 2r = 4r

6r  = 18

r = 18/6 = 3

The measure of the RA = 18 - 2r + 4r = 18 + 2r

The measure of the RA = 18 + 2(3) = 18+6 = 24 units

Thus, the measure of RA is 24 units after using the concept of congruent triangle option (A) 24 is correct.

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Answer:

[tex] 2w^2(w + 2)(4w - 3) [/tex]

Step-by-step explanation:

[tex] 8w^4 + 10w^3 − 12w^2 = [/tex]

First, factor out the GCF of all terms, 2w^2:

[tex] = 2w^2(4w^2 + 5w - 6) [/tex]

Now we work on the trinomial.

Think of ax^2 + bx + c.

Multiply ac

ac = 4 * (-6) = -24

Now we need two numbers whose product is -24 and whose sum is 5.

They are -3 and 8.

We break up the middle term, 5w, into a sum using these two numbers.

5w = 8x - 3w

[tex] = 2w^2(4w^2 + 8w - 3w - 6) [/tex]

Now we factor by parts. We factor a common factor out of the first two terms, and we factor a common factor out of the last two terms.

[tex] = 2w^2[4w(w + 2) - 3(w + 2)] [/tex]

[tex] = 2w^2(w + 2)(4w - 3) [/tex]

Answer:

Step-by-step explanation:

To find the side adjacent to the 50° angle we use tan

[tex] \tan( \alpha ) = \frac{opposite}{adjacent} [/tex]

From the question

The opposite is 6m

The adjacent is ?

So we have

[tex] \tan(50) = \frac{6}{?} [/tex]

[tex]? \tan(50) = 6[/tex]

[tex]? = 6 \times \frac{1}{ \tan(50) } [/tex]

But

[tex] \frac{1}{ \tan(x) } = \cot(x) [/tex]

So we have

[tex] \frac{1}{ \tan(50) } = \cot(50) [/tex]

Substitute it into the expression

That's

We have the final answer as

[tex]? = 6 \cot(50) [/tex]

Hope this helps you

=====================================================

Explanation:

We're given an opposite side and an adjacent side. The tangent rule ties these two sides together. "tangent" is nowhere to be found in any of the answer choices, but cotangent is. Recall that

cot = 1/tan

which means

tan = opposite/adjacent

cot = adjacent/opposite

one is the reciprocal of the other

-----------

This means

cot(angle) = adjacent/opposite

cot(50) = x/6

6*cot(50) = x

x = 6*cot(50)

Answer:

Yes, that is correct.

Step-by-step explanation:

W = x

L = ?

A = x^2 + 12x

(x^2 + 12x)/x = x + 12

L = x + 12

Subbing in 10 for each X, we get:

Perimeter: 64

2(10) + 2(10 + 12) = 20 + 44 = 64

Area: 220

10 * 22 = 220

Part A looks perfect. You've shown that x^2+12x factors into x(x+12) indicating that x is the width and x+12 is the length. Convention usually has the length be longer than the width, but to be honest, the order doesn't really matter (since we can multiply in any order we want).

----------------

Part B is a bit hazy. You show that 10 * 22 = 220 is the area, so you imply that the rectangle has width 10 and length 22. However, you don't directly mention the dimensions of the rectangle.

You can pick either x^2+12x or x(x+12). I prefer x(x+12) as its easier in my opinion. You don't need to do both.

All you really need to do is say that if x is the width and x = 10, then the width is 10. Furthermore, if x+12 is the length then x+12 = 10+12 = 22 is the length.

Answer:

[tex]3 + 3^2 + 3^3 ...+ 3^n = \frac{3(3^n - 1)}{2}[/tex]

Step-by-step explanation:

Given

[tex]3 + 3^2 + 3^3 ...+ 3^n[/tex]

Required

Show that the sum of the series is [tex]\frac{3(3^{n}-1)}{2}[/tex]

The above shows the sum of a geometric series and this will be calculated as shown below;

[tex]S_n = \frac{a(r^n - 1)}{r - 1}[/tex]

Where

a = First term;

[tex]a = 3[/tex]

r = common ratio

[tex]r = \frac{3^2}{3} = \frac{3^3}{3^2}[/tex]

[tex]r = 3[/tex]

Substitute 3 for r and 3 for a in the formula above;

[tex]S_n = \frac{a(r^n - 1)}{r - 1}[/tex] becomes

[tex]S_n = \frac{3(3^n - 1)}{3 - 1}[/tex]

[tex]S_n = \frac{3(3^n - 1)}{2}[/tex]

Hence;

[tex]3 + 3^2 + 3^3 ...+ 3^n = \frac{3(3^n - 1)}{2}[/tex]

Answer:

2. it stays the same even if the angles in the triangle change

a. the angles must add up to 180º. a straight line is equal to 180º, so as long as the angles add up to 180º, it will be a straight line.

5. it represents the sum of the measures of the interior angles of the triangle

a. Kellianne lined up the interior angles of the triangle. if added they equal 180º which is the measure of the straight line.

7. it combines the three interior angles of the triangle to form a straight line

a. same answers as previous

8. it is a straight line with a measure of 180º

a. refer to above

hope this helps :)

Answer:

B E H

Step-by-step explanation:

Answer:

Hey there!

What we know:

What we would like to know:

First, let's find AB.

Sine 58= AB/65

Solving for AB, we see that it is about 55.12 m.

Next, let's find BD.

Sine 42= BD/55.12

Solving for BD, we see that it is about 36.88 m.

Let me know if this helps :)

Answer:

6/8 of a mile,

Step-by-step explanation:

if one furlong is 1/8 of a mile, the 6 shall be 1/8 added to itself 6 times, therefore it shall be 6/8.

Answer:

3/4 of a mile

Step-by-step explanation:

1 furlong = 1/8 mile

========     ====

6 forlongs = x

cross multiply

1*x = 6 * (1/8)

x = 6/8

reduce 6/8. Divide top and bottom by 2

x = 3/4