8x+6y=18
Put the following equation of a line into slope-intercept form, simplifying all fractions.

-(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

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].

To know more about quadratic sequence click here

https://brainly.com/question/22412845

#SPJ3

Answer:

A    y - 1 = -4(x + 2)

Step-by-step explanation:

point-slope form: [tex]y - y_{1} = m(x -x_{1} )[/tex]

y - 1 = -4(x -(-2) )

y - 1 = -4(x + 2)

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:

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.

Learn more about Quadratic Equation here:

https://brainly.com/question/30098550

#SPJ1

Answer:

Side length = 4.80 cm

Step-by-step explanation:

Given the perimeter of an equilateral triangle, 14.4 cm:

An equilateral triangle has three congruent sides.

Perimeter of an equilateral triangle = side + side + side = 3(side)  

Perimeter = 14.4 cm

[tex]\displaystyle\mathsf{side=\frac{14.4\:cm}{3}=4.80\:cm}[/tex]

Therefore, the length of each side of an equilateral triangle is:  4.80 cm.

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:

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.

Learn more about the compound interest here:

brainly.com/question/26457073

#SPJ2

Answer: 25% or B

Step-by-step explanation:

1. Money in November - Money in October

2. 50 - 40 = 10 dollars increased

3. 10/40 = 0.25 or 25%

Answer:

y is the value of 1

Step-by-step explanation:

no need for one

Answer:

y = - 2

Step-by-step explanation:

Substitute x = 5y - 1 into the other equation

3(5y - 1) + 5y = - 43 ← distribute parenthesis and simplify left side

15y - 3 + 5y = - 43

20y - 3 = - 43 ( add 3 to both sides )

20y = - 40 ( divide both sides by 20 )

y = - 2

Answer:

Step-by-step explanation:

Lol hi

Answer:

-6

Step-by-step explanation:

Because 2×(-6) is - 12

Answer:

-24

Step-by-step explanation:

[tex]\pink{Answer}[/tex]

[tex]\\ \sf\longmapsto2x + 3x + 4x = 180 \\ [/tex]

[tex]\\ \sf\longmapsto9x = 180 = > x = 20[/tex]

[tex]\\ \sf\longmapsto \: a = 2x = 2 \times 2 0 = 4 0 [/tex]

[tex]\\ \sf\longmapsto \: b \: = 3x = 3 \times 20 = 60[/tex]

[tex]\\ \sf\longmapsto \: c = 4x = 4 \times 20 = 80[/tex]

hence , angles of the triangle are 40 , 60 and 80

The angles of a triangle are in the ratio 2 : 3 : 4 . find the angles of the triangle .

40° , 60° and 80°

We know that sum of all the angles of a triangle adds to 180° .

Let the angles be 2x , 3x and 4x

Now,

=> 2x + 3x + 4x = 180°

=> 9x = 180°

=> x = 180/9

=> x = 20°

(The value of x is 20)

Answer:

1.5

1.5

Step-by-step explanation:

The steps are in the image above

The slope of the line through these two data points is 1.5.

A linear equation is in the form:

y = mx + b

where y, x are variables, m is the rate of change and b is the initial value of y.

x represents the time and y represents the temperature in degrees Fahrenheit.

temperature of –2°F at 8 a.m. Hence:

-2 = 8m + b   (1)

it was 4°F at 12:00 p.m. Hence:

4 = 12m + b  (2)

Solving equations 1 and 2 simultaneously gives:

m = 1.5, b = -14

The slope of the line through these two data points is 1.5.

Find out more on linear equation at: https://brainly.com/question/14323743

Answer:

d.

took the test

Step-by-step explanation

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

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:

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:

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:

k

Step-by-step explanation:

3k-2k=1k

1k=k so this is the answer

Answer: $15.90/hr

Step-by-step explanation:

We need to add 6% to her $15/hr current pay.  This can be calculated with:

$15/hr *(1+0.06) = $15.90/hr

The "(1+0.06)" represents a) 1  the current salary, and b) the 6% raise.

Answer:

See answer below.

Step-by-step explanation:

LA = π rl

1st find l    

The radius is 5" and the height is 12"  l = ?

  h and the r is the two legs in the right triangle when drawn in a cone.

Use a²  + b² = c²     ⇔ h² + r² = l²

                                    12² + 5²  = l²

                                   144 + 25 = l²

                                     169 = l²

                                    [tex]\sqrt{169} = l[/tex]

                                        13 = l

Formula for LA = π r l

                  LA = 3.14 × 5 ×13  or with a calculator   LA = π × 5 × 13

                   LA = 204.1  sq.in                                   LA  = 204.2035225 sq. in

I use 3.14 = for π  but you know what the teacher uses in class.

Answer:

The area of the triangle is equal to half of the base times the height: A = b x h x 1/2 You could find the area of a triangle with base length of 4 inches and height of 3 inches as follows: A = 4 inches x 3 inches x 1/2 = 6 square inches

Step-by-step explanation:

The corresponding height is the length of a perpendicular segment from the base to the vertex opposite of it. The opposite vertex is the vertex that is not an endpoint of the base.

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

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)