What is the greatest common factor of 6 and 8

Answer:

[tex]a_8=-128x^8-384x^7[/tex]

Step-by-step explanation:

The terms of the sequence are:

[tex]x+3,-2x^2-6x,4x^3+12x^2,...[/tex]

We can rewrite the terms in factored form to get;

[tex]x+3,-2x(x+3),4x^2(x+3),...[/tex]

We can see that the subsequent terms are obtained by multiplying the previous term by [tex]-2x[/tex]. This is called the common ratio.

Therefore the first term of this geometric sequence is [tex]a_1=x+3[/tex] and the common ratio is [tex]r=-2x[/tex].

The nth term of a geometric sequence is given by: [tex]a_n=a_1(r^{n-1})[/tex].

Let us substitute the first term, the common ratio, and [tex]n=8[/tex] to obtain:

[tex]a_8=(x+3)(-2x)^{8-1}[/tex]

[tex]a_8=(x+3)(-2x)^{7}[/tex]

[tex]a_8=-128x^7(x+3)[/tex]

[tex]a_8=-128x^8-384x^7[/tex]

Answer:

the answer is x=0,-(3/7)

Step-by-step explanation:

Answer:

x = { - [tex]\frac{3}{7}[/tex], 0 }

Step-by-step explanation:

Given

7x² + 3x = 0 ← factor out x from each term

x(7x + 3) = 0

Equate each factor to zero and solve for x

x = 0

7x + 3 = 0 ⇒ 7x = - 3 ⇒ x = - [tex]\frac{3}{7}[/tex]

Answer:

Step-by-step explanation:

[tex]f(n+1)=f(n)-2\\\\f(1)=10\\f(2)=f(1)-2=10-2=8\\f(3)=f(2)-2=8-2=6[/tex]

Answer:

B) 6

Step-by-step explanation:

Answer:

7

Step-by-step explanation:

Givens

x = 4

y = 2

z =-3

equation

xy - z^y

Solution

(4)(2) - (-3)^2     be sure and add the brackets. Otherwise it won't come out correctly.

16 - (9) = 7

Answer:

A. concave hexagon

Step-by-step explanation:

It has 6 sides, so it's a hexagon. (A heptagon has 7 sides.)

If all interior angles are less than 180 deg, then it is convex. There is one interior angle on the left side that is more than 180 deg, so it is concave.

Answer: concave hexagon

Answer:

The number line should look like this;

<---- -3 -------- 0 ------- 3 ----->

It must have both 3 and -3 shown

Step-by-step explanation:

Step-by-step explanation:how do you feguire this out because the left of a number line is always negative and the right is always posittive easy right i hope it helped you just like when i learned it it helped me.

Answer:

5

Step-by-step explanation:

dot

[tex]\bf 3x^3+27x^2-15x\div 3x\implies \cfrac{3x^3+27x^2-15x}{3x}\implies \stackrel{\textit{distributing the denominator}}{\cfrac{3x^3}{3x}+\cfrac{27x^2}{3x}-\cfrac{15x}{3x}} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill x^2+9x-5~\hfill[/tex]

63-5x

So you do PEMDAS

There aren’t any parenthesis

There aren’t any exponents

So you multiply 3*3 and get 9

Multiply 27 by 2 and get 54

And divide 15x by 3x

Now moving on to addition/subtraction

The equation is now 9+54-5x

9+54 is 63

So the answer is 63+5x

Answer:

h= 12

Step-by-step explanation:

Given

66 = [tex]\frac{1}{2}[/tex] h(5 + 6)

Multiply both sides by 2 to eliminate the fraction

132 = h(5 + 6)

132 = 11h ( divide both sides by 11 )

12 = h

Answer:

[tex]\large\boxed{\dfrac{2s-6}{s+3}}[/tex]

Step-by-step explanation:

[tex]s^2-9=s^2-3^2\qquad\text{use}\ a^2-b^2=(a-b)(a+b)\\=(s-3)(s+3)\\\\s^2+6s+9=s^2+2(s)(3)+3^2\qquad\text{use}\ (a+b)^2=a^2+2ab+b^2\\=(s+3)^2[/tex]

[tex]\dfrac{s^2-9}{2s}\div\dfrac{s^2+6s+9}{4s}=\dfrac{s^2-9}{2s\!\!\!\!\diagup_1}\cdot\dfrac{4s}{s^2+6s+9}\\\\=\dfrac{(s-3)(s+3)}{2s\!\!\!\!\!\diagup_{_1}}\cdot\dfrac{4s\!\!\!\!\!\diagup^{^2}}{(s+3)^2}=\dfrac{2(s-3)(s+3)}{(s+3)(s+3)}\qquad\text{cancel}\ (s+3)\\\\=\dfrac{2(s-3)}{s+3}=\dfrac{2s-6}{s+3}[/tex]

Answer:

C(w) = 6w + 9

Step-by-step explanation:

Anytime 0 is given somewhere, it should be given close scrutiny. In an equation whose general form is

y = mx + b

0 will determine the y intercept immediately.

So when x = 0, y will equal

y = 0*m + 9

So b = 9

y = mx + 9 Now we need to find m

I should start using your variables.

C(w) = m*w + 9

when w = 3 then C(3) = 27

27= 3m +9

27-9 =3m + 9 -9

18 = 3m

18/3 = 3m/3

x = 6

So the complete equation is

C(w) = 6w + 9

Answer:

[tex]P(w)=6w+9[/tex]

Step-by-step explanation:

To find the linear equation, first we need to calculate the slope of that line, we is defined as

[tex]m=\frac{y_{2}-y_{1} }{x_{2} -x_{1} }[/tex]

Where we need to use two points from the table: (0,9) and (4,33).

Replacing these points, we have

[tex]m=\frac{33-9}{4-0}=\frac{24}{4} =6[/tex]

Now, we use the point-slope formula to find the equation

[tex]y-y_{1} =m(x-x_{1} )\\y-9=6(x-0)\\y=6x+9[/tex]

Let's call [tex]y=P(w)[/tex] and [tex]x=w[/tex].

The equation that models the given table is

[tex]P(w)=6w+9[/tex]

Answer:

P = 4 / 6 = 2/3 = 0.66 = 66%

Step-by-step explanation:

Assuming the die is numbered 1 to 6.

To answer the question, we first need to know many prime numbers can be represented on the die.  What are the prime numbers equal to 6 or lower?

We have 2, 3 and 5.  (since 4 and 6 are not prime numbers).  So we have 3 prime numbers, plus the number 1... so there are 4 possibilities valid for rolling a 1 or a prime number: 1,2,3 and 5.

4 possibilities out of 6 total possible outcomes, so...

P = 4 / 6 = 2/3 = 0.66 = 66%

Answer:

The probability of rolling a 6 sided die and getting a 1 or a prime number = 2/3

Step-by-step explanation:

The numbers on the die are 1, 2, 3, 4, 5 and 6

To find the probability

Total outcomes of rolling a die = 6

Prime numbers less than 6 are 2, 3 and 5

Possible outcomes(getting 1 or a prime number) =  1, 2, 3 and 5

Probability of getting 1 or prime number when rolling a die = 4/6 = 2/3

Let us check each Option :

[tex]\mathsf{First\;Option : \left(\dfrac{m + 9}{m - 9}\right)\left(\dfrac{m + 9}{m - 9}\right)}[/tex]

[tex]\mathsf{\implies \left(\dfrac{m + 9}{m - 9}\right)^2\;\neq\;1}[/tex]

[tex]\mathsf{Second\;Option : \left(\dfrac{m + 9}{m - 9}\right)\left(\dfrac{m - 9}{m + 9}\right)}[/tex]

[tex]\mathsf{\implies 1}[/tex]

[tex]\mathsf{Third\;Option : \left(\dfrac{m + 9}{m - 9}\right)\left(\dfrac{9 + m}{9 - m}\right)}[/tex]

[tex]\mathsf{\implies \left(\dfrac{m + 9}{m - 9}\right)\left(\dfrac{m + 9}{-(m - 9)}\right)}[/tex]

[tex]\mathsf{\implies-\left(\dfrac{m + 9}{m - 9}\right)\left(\dfrac{m + 9}{m - 9}\right)}[/tex]

[tex]\mathsf{\implies-\left(\dfrac{m + 9}{m - 9}\right)^2\;\neq\;1}[/tex]

[tex]\mathsf{Fourth\;Option : \left(\dfrac{m + 9}{m - 9}\right)\left(\dfrac{9 - m}{9 + m}\right)}[/tex]

[tex]\mathsf{\implies \left(\dfrac{m + 9}{m - 9}\right)\left(\dfrac{-(m - 9)}{9 + m}\right)}[/tex]

[tex]\mathsf{\implies -\left(\dfrac{m + 9}{m - 9}\right)\left(\dfrac{m - 9}{9 + m}\right)}[/tex]

[tex]\mathsf{\implies -1\;\neq\;1}[/tex]

Answer : Option (2)

Answer:

B.⁽[tex](\frac{m}{m}\frac{+9}{-9} ) (\frac{m}{m} \frac{- 9}{+ 9} )[/tex]

Step-by-step explanation:

Answer: B and F

Hope it helps!!!

Answer: OPTION B AND OPTION D.

Step-by-step explanation:

Analyze  the triangle provided.

You can observe that the lenghts of its sides are: 10.9, 15, 14

Then the lenghts of its sides are not equal.

 By definition, when all sides of a triangle are different this is called: "Scalene".

You can notice that the measures of its angles are: 63°, 44° and 73°

Then, all its angles are less than 90 degrees.

By definition if all three angles of a triangle are less than 90 degrees, then is called: "Acute".

Answer:

x=42

Step-by-step explanation:

Add by 26 from both sides of equation.

6x-26+26=58+4x+26

Simplify.

6x=4x+84

Subtract by 4x from both sides of equation.

6x-4x=4x+84-4x

Simplify.

2x=84

Divide by 2 from both sides of equation.

2x/2=84/2

Simplify, to find the answer.

84/2=42

x=42 is the correct answer.

I hope this helps you, and have a wonderful day!

For this case we have the following functions:

[tex]f (x) = 7x + 1\\g (x) = x ^ 2[/tex]

We must find[tex](g_ {0} f) (x).[/tex]

By definition of composition of functions we have to:

[tex](g_ {0} f) (x) = g (f (x))[/tex]

So:

[tex](g_ {0} f) (x) = g (f (x)) = (7x + 1) ^ 2 = 49x ^ 2 + 2 (7x) (1) + 1 = 49x ^ 2 + 14x + 1[/tex]

ANswer:

[tex](7x + 1) ^ 2 = 49x ^ 2 + 14x + 1[/tex]

Answer:

Option C is correct.

Step-by-step explanation:

The x-intercepts of the function (x − 1)(x − 4)(x + 7) can be found by putting this function equal to zero

(x − 1)(x − 4)(x + 7) = 0

Now,

x-1 = 0

x-4 = 0

and x+7 = 0

Now finding the values of x

x-1 = 0 + 1

x - 1 + 1 = 1

=> x = 1

or (1,0)

x - 4 = 0

x -4 + 4 = 0 + 4

x = 4

or (4,0)

x + 7 = 0

x +7 -7 = 0 -7

x = -7

or (-7,0)

SO, the x-intercepts of the function (x − 1)(x − 4)(x + 7) are (1,0),(4,0) and (-7,0)

Option C is correct.

Answer:

+ 1  + 4   -7

Step-by-step explanation:

when they ask for x intercepts you simply have to set the function to 0 and then solve for x or in other words just reverse the number for example. here we have -1 -4 and +7 so just reverse the negative and positive signs

Answer:

no solution

Step-by-step explanation:

The solution to a system of equations given graphically is at the point of intersection of the 2 graphs.

The given lines are parallel ( both have a slope = 2 )

Hence the lines never intersect thus there is no solution.

Answer

AAS

Step-by-step explanation:

Answer:

D. 7.46  

Hope this helps and have a nice day!!

If I'm wrong pleaseeee tell me

Step-by-step explanation:

Step-by-step explanation:

Write the prime factorization for each:

22a² = 2×11×a²

32a = 2⁵×a

So the greatest common factor is 2a.

Answer:

B 9/10

Step-by-step explanation:

3/5 ÷2/3

Copy dot flip

3/5 * 3/2

9/10

Answer:

C, D,F

Step-by-step explanation:

Answer:

Its C

Step-by-step explanation:

[tex]\bf \textit{area of a circle}\\\\ A=\pi r^2~~ \begin{cases} r=radius\\ \cline{1-1} A=452\frac{4}{7} \end{cases}\implies 452\frac{4}{7}=\pi r^2\implies \cfrac{3168}{7}=\pi r^2 \implies \cfrac{3168}{7\pi }=r^2 \\\\\\ \stackrel{\pi =\frac{22}{7}}{\cfrac{3168}{7\cdot \frac{22}{7}}}=r^2\implies \cfrac{3168}{22}=r^2\implies 144=r^2\implies \sqrt{144}=r\implies 12=r \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill \stackrel{diameter=2r}{d=24}~\hfill[/tex]

Answer:

see below

Step-by-step explanation:

2/3 ÷ 4

We use copy dot flip

The flip means make a reciprocal of the second number

2/3 * 1/4

Multiply the numerators

2*1 = 2

Multiply the denominators

3*4 =12

Put the numerator over the denominator

2/12

Simplify

1/6

To use equivalent fractions to find the quotient of \( \frac{2}{3} \) ÷ 4, follow these steps:

### Step 1: Understand the Operation
Division of fractions can be thought of as multiplying by the reciprocal. The reciprocal of a number a is simply \( \frac{1}{a} \).

### Step 2: Find the Reciprocal of the Divisor
The divisor here is the whole number 4. Its reciprocal is \( \frac{1}{4} \).

### Step 3: Multiply the Dividend by the Reciprocal of the Divisor
Instead of dividing \( \frac{2}{3} \) by 4, you can multiply \( \frac{2}{3} \) by \( \frac{1}{4} \).

### Step 4: Perform the Multiplication
Now, multiply the two fractions:

\[ \frac{2}{3} \times \frac{1}{4} = \frac{2 \cdot 1}{3 \cdot 4} \]

This results in a new fraction:

\[ \frac{2}{12} \]

### Step 5: Simplify the Resulting Fraction
Finally, you need to simplify the fraction to its simplest form. To do that, find the greatest common factor (GCF) of the numerator and the denominator and divide both by this number.

For \( \frac{2}{12} \), the greatest common factor is 2. So we divide both the numerator and the denominator by 2:

\[ \frac{2 \div 2}{12 \div 2} = \frac{1}{6} \]

### Conclusion
Therefore, the quotient of \( \frac{2}{3} \) ÷ 4 is \( \frac{1}{6} \). This is the simplest form of the fraction you obtain when \( \frac{2}{3} \) is divided by 4.

Answer:

[tex]\frac{3}{2}[/tex]

Step-by-step explanation:

Using the addition formulae for cosine

cos(x ± y) = cosxcosy ∓ sinxsiny

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

cos(120 + x) = cos120cosx - sin120sinx

                   = - cos60cosx - sin60sinx

                   = - [tex]\frac{1}{2}[/tex] cosx - [tex]\frac{\sqrt{3} }{2}[/tex] sinx

squaring to obtain cos² (120 + x)

= [tex]\frac{1}{4}[/tex]cos²x + [tex]\frac{\sqrt{3} }{2}[/tex]sinxcosx + [tex]\frac{3}{4}[/tex]sin²x

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

cos(120 - x) = cos120cosx + sin120sinx

                   = -cos60cosx + sin60sinx

                   = - [tex]\frac{1}{2}[/tex]cosx + [tex]\frac{\sqrt{3} }{2}[/tex]sinx

squaring to obtain cos²(120 - x)

= [tex]\frac{1}{4}[/tex]cos²x - [tex]\frac{\sqrt{3} }{2}[/tex]sinxcosx + [tex]\frac{3}{4}[/tex]sin²x

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

Putting it all together

cos²x + [tex]\frac{1}{4}[/tex]cos²x + [tex]\frac{\sqrt{3} }{2}[/tex]sinxcosx + [tex]\frac{3}{4}[/tex]sin²x + [tex]\frac{1}{4}[/tex]cos²x - [tex]\frac{\sqrt{3} }{2}[/tex]sinxcosx + [tex]\frac{3}{4}[/tex]sin²x

= cos²x + [tex]\frac{1}{2}[/tex]cos²x + [tex]\frac{3}{2}[/tex]sin²x

= [tex]\frac{3}{2}[/tex]cos²x + [tex]\frac{3}{2}[/tex]sin²x

= [tex]\frac{3}{2}[/tex](cos²x + sin²x) = [tex]\frac{3}{2}[/tex]

Answer:

Isosceles and obtuse

Step-by-step explanation:

It is not a scalene triangle because it has two same lengths 41 degrees and 41 degrees.

It is a Isosceles triangle because two of the sides have the same lengths 41 degrees and 41 degrees

It is an obtuse triangle because it has on obtuse angle which is 98 and two acute angles that are 41 degrees

It is not an equilateral because not all of the sides are the same lengths

It is not a right triangle because there are 90 degree angles

It is not an acute triangle because not all the angles are acute angles

A triangle can be classified based on its angles and sides. A Trigonal Bipyramidal triangle has angles of 90 degrees or 120 degrees, and atoms can be positioned equatorially (in the plane of the triangle) or axially (above or below the plane). Always remember that the sum of all interior angles of a triangle is 180°.

The classification of a triangle depends on its angles and sides. If you have a triangle like a Trigonal Bipyramidal, the angles of such a triangle can be 90 degrees or 120 degrees. This relates to a three-dimensional trigonal bipyramidal molecular geometry where three atoms or groups of atoms are positioned in a flat triangle around a central atom, symmetrically positioned with 120° angles between each pair.

Another element you mentioned is the position of an attached atom in a triangle. This can be either equatorial (in the plane of the triangle) or axial (above or below that plane).

For detailed classification, always keep in mind that the sum of all interior angles of a triangle is always 180°. A triangle with one angle measuring 90° is a right triangle. An equilateral triangle has all angles measuring 60°. In the trigonal planar case, all atoms are in one plane, and bond angles are 120°.

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Answer:

A'(-4,4)

B'(-2,11)

Step-by-step explanation:

6 unit up and 3 unit left

A (-1,-2) : 6 unit up → (-1,4) → 3 unit left → (-4,4)

A'(-4,4)

B (1,5) : 6 unit up → (1,11) → 3 unit left → (-2,11)

B'(-2,11)

Answer:

a

Step-by-step explanation:

You're trying to find the distance between D and E so u use the distance formula.

sqrt (a+b-b^2)+(c-c)^2=sqrt a^2=a

Answer:

a

Step-by-step explanation:

We are given that

D is the mid-point of AB and E is the mid-point of AC.

We have to find the missing information in given proof of DE is equal to half of BC.

Proof:

D is the mid-point of AB and E is the mid-point of AC.

The coordinates of A are (2b,2c)

The coordinates of D are (b,c)

The coordinates of E are (a+b,c)

The coordinates of  B are (0,0)

The coordinates of  C are (2a,0)

Distance formula:[tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Using the formula

Length of BC=[tex]\sqrt{(2a)^2+(0-0)^2}=2a[/tex] units

Length of DE=[tex]\sqrt{(a+b-b)^2+(c-c)^2}=a[/tex] units

[tex]BC=2a=2\times DE[/tex]

[tex]DE=\frac{1}{2}BC[/tex]

Hence, proved.

Option A is true.