Does the table below represent a function?

Answer:

Step-by-step explanation:

The [tex]nth[/tex] term rule of the quadratic sequence will be [tex]n^2+5n+2[/tex] .

Quadratic sequences are sequences that include  [tex]nth[/tex]  term. They can be identified by the fact that the differences between the terms are not equal, but the second differences between terms are equal.

Quadratic sequence [tex]=an^2+bn+c[/tex]

Here [tex]a,b,c[/tex] are constant and [tex]n[/tex] is the position of term.

First difference [tex]= 3a+b[/tex]

Second difference [tex]=2a[/tex]

We have,

Quadratic sequence [tex]8,16,26,38,52,68,86,....[/tex]

Quadratic sequence [tex]=an^2+bn+c[/tex]

so,

For [tex]n=1[/tex];

[tex]8=an^2+bn+c[/tex]

[tex]8=a+b+c[/tex]   [tex]........(i)[/tex]

For [tex]n=2[/tex];

[tex]16=4a+2b+c[/tex]    [tex]........(ii)[/tex]

For [tex]n=3[/tex];

[tex]26=9a+3b+c[/tex]    [tex]........(iii)[/tex]

Now,

Subtract equation [tex](i)[/tex] from [tex](ii)[/tex]

we get,

[tex]8=3a+b[/tex]    [tex]........(iv)[/tex]

Subtract equation [tex](ii)[/tex] from [tex](iii)[/tex] we get,

[tex]10=5a+b[/tex]    [tex]........(v)[/tex]

Subtract equation [tex](iv)[/tex] from [tex](v)[/tex] we get,

[tex]2=2a[/tex]  (This is second difference mentioned above)

[tex]a=1[/tex]

Putting [tex]a=1[/tex]  in [tex](iv)[/tex]

⇒[tex]b=5[/tex]

Now putting values of [tex]a[/tex] and [tex]b[/tex] in equation [tex](i)[/tex]

[tex]8=1+5+c[/tex]

[tex]c=2[/tex]

Now, putting values of [tex]a[/tex] , [tex]b[/tex] and [tex]c[/tex] in,

Quadratic sequence [tex]=an^2+bn+c[/tex]

we get,

[tex]nth[/tex] term rule [tex]=n^2+5n+2[/tex]

Hence, we can say that the [tex]nth[/tex] term rule of the quadratic sequence will be [tex]n^2+5n+2[/tex].

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Answer:

d.

took the test

Step-by-step explanation

Answer:

Here,

3

,

(

−

6

)

,

12

,

(

−

24

)

,

...

is the geometric sequn.

w

h

e

r

e

,

1

s

t

t

e

r

m

=

a

1

=

3

and

common ratio

r

=

−

6

3

=

12

−

6

=

−

24

12

=

−

2

and

S

9

=

?

⇒

n

=

9

We know that,

The sum of first n term of Geometric series is :

S

n

=

a

1

(

r

n

−

1

)

r

−

1

Putting ,

a

1

=

3

,

r

=

−

2

and

n

=

9

S

9

=

3

[

(

−

2

)

9

−

1

]

(

−

2

)

−

1

∴

S

9

=

3

[

−

512

−

1

]

−

3

⇒

S

9

=

3

(

−

513

)

−

3

⇒

S

9

=

513

Step-by-step explanation:

Answer:

Step-by-step explanation:

c.r. r=-6/3=-2

[tex]S_{n}=3\frac{(-2)^n-1}{-2-1} =-(-2)^n+1\\let~n\rightarrow \infty\\then S_{\infty} \rightarrow \infty~or~ -\infty[/tex]

Answer:

how watched 3/4 of the movie

Step-by-step explanation:

I know this because 2 is more then half of 3 and 3 is more then half of 4 so you can come to a conclusion that he watched a total of 3/4 and 2/4 at night.

P.S when ever using a fraction when typing like 1/4 instead of doing

1

4

do 1/4

-(m+n)+2(m-3n)

-m+n+2m-6n

-m+2m+n-6n

m-5n

Answer:

m -7n

Step-by-step explanation:

-(m+n)+2 (m-3n)​, distribute in the first parenthesis the -1 and in the second parentheses the 2

-m -n + 2m -6n , group like terms

-m + 2m -n -6n , combine like terms

     m     -7n

Step-by-step explanation:

756000000 = 7.56×10⁸.

hope this helps you.

Answer:

7.56   x10^8

.......................................

Answer:

27

Step-by-step explanation:

Note : -

That square like symbol at the intersection of two lines is 90°.

( 4x - 18 )° and 90° are corresponding angles.

Corresponding angles are equal since lines

a & b are parallel.

4x - 18 = 90

4x = 90 + 18

4x = 108

x = 108 / 4

x = 27

Compute 2²⁰¹⁷ modulo 100.

From the given table,

2²² ≡ 2⁴² ≡ 2⁶² ≡ 4 (mod 100)

and we have

2017 = 32 • 62 + 33

62 = 1 • 42 + 20

Then

2²⁰¹⁷ ≡ (2⁶²)³² • 2³³ (mod 100)

2²⁰¹⁷ ≡ 4³² • 2³³ (mod 100)

2²⁰¹⁷ ≡ (2²)³² • 2³³ (mod 100)

2²⁰¹⁷ ≡ 2⁶⁴ • 2³³ (mod 100)

2²⁰¹⁷ ≡ 2⁶² • 2²² • 2¹³ (mod 100)

2²⁰¹⁷ ≡ 4² • 2¹³ (mod 100)

2²⁰¹⁷ ≡ (2²)² • 2¹³ (mod 100)

2²⁰¹⁷ ≡ 2⁴ • 2¹³ (mod 100)

2²⁰¹⁷ ≡ 2¹⁷ (mod 100)

and from the table, we get

2²⁰¹⁷ ≡ 2¹⁷ ≡ 72 (mod 100)

Answer:

-34

Step-by-step explanation:

r^2 - 8r - 22  ( R = 6)

6^2 =36   (8r = 8*6=48)

36 - 48 =  -12

-12 - 22 = -34

Answer:

you can find the answer in this link bit.3ckFc

Step-by-step explanation:

no real solution ig

Answer:

Step-by-step explanation:

The system is not given to give exact answer.

Possible solution is:

A. (2,7), because this point is true for both equations

B. (4, -6), because this point lies only on one of the two lines

C. (4, -6), because this point makes both equations true

D. (2,7), because the lines intersect the x-axis at these points

Answer:

Step-by-step explanation:

Line A:

Mark two points in line A.

(1,3) & ( 2 , 5)

[tex]Gradient =\dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}\\\\\\=\dfrac{5-3}{2-1}=\dfrac{2}{1}\\\\\\= 2[/tex]

Line B:

(0,5) ; (5,0)

[tex]Gradient = \dfrac{0-5}{5-0}=\dfrac{-5}{5}=-1[/tex]

Answer:

The interest is $0.03

Step-by-step explanation:

($720*0.014)/365

The first day's interest will be $10.15 if Janine opens a savings account with a deposit of $720. The account pays 1.4% interest, compounded daily.

It is defined as the interest on the principal value or deposit and the interest which is gained on the principal value in the previous year.

We can calculate the compound interest using the below formula:

[tex]\rm A = P(1+\dfrac{r}{n})^{nt}[/tex]

Where A = Final amount

          P = Principal amount

          r  = annual rate of interest

          n = how many times interest is compounded per year

          t = How long the money is deposited or borrowed (in years)

It is given that:

Janine opens a savings account with a deposit of $720. The account pays 1.4% interest, compounded daily.

P =$720

r = 1.4% = 0.014

n = 365

t = 1 day

[tex]\rm A = 720(1+\dfrac{0.014}{365})^{365\times1}[/tex]

After solving:

A = $730.15

The interest I = A - P

I = $730.15 - 720

I = $10.15

Thus, the first day's interest will be $10.15 if Janine opens a savings account with a deposit of $720. The account pays 1.4% interest, compounded daily.

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Answer:

Can you explain what this is then I can help

Answer:

Step-by-step explanation:

Given a = -2.9

Simplify the fraction:

Now substitute the value of a:

Answer:

First divide 3 on both sides to get x by itself, now you have x < -2.

Step-by-step explanation:

Hope this helps :)

Answer:

25896

Step-by-step explanation:

Answer:

x = 0

Step-by-step explanation:

Answer:

Step-by-step explanation:

Lol hi

Step-by-step explanation:

x = -2 and x = -5

x + 2 = 0 and x + 5 = 0

(x + 2)(x + 5) = 0

x² + 5x + 2x + 10 = 0

x² + 7x + 10 = 0

f(x) = x² + 7x + 10

The  quadratic equation is x² + 7x + 10.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

We have the zeroes of Quadratic Equation as -2 and -5.

So, the factors of the equation is (x +2 ) and (x + 5).

Then, the Quadratic equation is

= (x+5)(x+2)

= x² + 5x +2x + 10

= x² + 7x + 10

Thus, the quadratic equation is x² + 7x + 10.

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Answer:

-2.43 then -2 2/3 then 2.045 then 2 5/9 that is from least to greatest :) hope this helps

Step-by-step explanation:

i am positive :)

just to make sure you got it i put this in your comments too !

Answer:

8 ft. 5 in.

Step-by-step explanation:

First, let's change everything to inches

[] 3 ft. 8 in -> 3 * 12 = 36, 36 + 8 = 44 inches

[] 4 ft. 9 in -> 4 * 12 = 48, 48 + 9 = 57 inches

Now, we can add

44 + 57 = 101 inches

Last, we will simplify

101 -> 8 feet and 5 inches

Have a nice day!

     I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly. (ノ^∇^)

- Heather

Answer: Leah made more money by 1,996 dollars more than Gemma,

Step-by-step explanation: 1484 is how much Gemma made and 3480 is how much Leah made all you had to do is multiply the total amount of necklaces they sold and the price of each so Leah made more money by 1996 dollars

Answer:

1) 25

2) 32,768

3) 729

4) 16 or 2^4

5) 117,649 or 7^6

6) 5.29 or 2.3^2

Not sure what 7-12 mean

13) 1 mile 64-63=1

14) Mali bought a new car. She drove 63 miles the first month and 100 the second month. How much further did she drive the second month? Explain each step. 37 miles 100-63=37

15) An exponet is a number raised to a power, which means that number times itself that many times. It is used because it's alot easier to go 7^6 than 7x7x7x7x7x7.

16) 8^5= 32,768  6^6= 46,656  5^7= 78,125  5^5= 3,125  4^10= 1,048,576

Step-by-step explanation:

Answer:

40°

Step-by-step explanation:

We know that a triangle is equal to 180°

Since one angle is 50° we can figure out that the rest of the angles are equal to 130° (180° - 50°)

If we use 40° then 2·(40°) = 80°

and the second angle is 40° + 10° = 50°

if we add all the angles (80° + 50° + 50°) we get 180° which is correct.

Answer:

final answer: 58xy

Step-by-step explanation:

24xy + 4xy - 2y + 42xy - 12xy + 2y

(24xy + 4xy + 42xy - 2xy) + ( - 2y + 2y)

(24 + 4 + 42 - 12)x xy + ( - 2 + 2)xy

58xy + ( - 2 + 2)xy

58xy + 0y

58xy

Answer:

1st one is 11

2nd one is -4

3rd one is 0

Step-by-step explanation:

no need

you can trust me :)

Answer:

[tex]\frac{1}{108}[/tex]

Step-by-step explanation:

Using the rules of exponents

[tex]a^{\frac{m}{n} }[/tex] = [tex]\sqrt[n]{a^m}[/tex]

[tex]a^{-m}[/tex] = [tex]\frac{1}{a^m}[/tex]

[tex]a^{\frac{1}{3} }[/tex] × [tex]b^{-\frac{3}{2} }[/tex] ← substitute a = 8 and b = 36

= [tex]8^{\frac{1}{3} }[/tex] × [tex]36^{-\frac{3}{2} }[/tex]

= [tex]\sqrt[3]{8}[/tex] × [tex]\frac{1}{36^{\frac{3}{2} } }[/tex]

= 2 × [tex]\frac{1}{(\sqrt{36})^3 }[/tex]

= 2 [tex]\frac{1}{6^3}[/tex]

= 2 × [tex]\frac{1}{216}[/tex]

= [tex]\frac{1}{108}[/tex]