The rule of the following sequence is k = 3n − 1. What is the tenth term of the sequence?
2, 5, 8, 11, ...
b. Analyze What pattern do you recognize in this sequence?

Answer:

3

Step-by-step explanation:

Easy pythagorean theorum question.

The law states that "A squared plus B squared, equals C squared."

A and B are the two sides that border the 90 degree mark.

C is the hypotenuse or the longest side/diagonal.

Since we know C and A (I chose to use A because why not) we can fill in the equation with what we know

2^2 + ?^2 = [tex]\sqrt{13^{2} }[/tex]

So

4 + ?^2 = [tex]\sqrt{13^{2} }[/tex]

Since the 13 is already squared in side of a root, it stays as 13

4 + x^2 = 13

4 - 4 + x^2 = 13 - 4

x^2 = 9

x^2 root = root of 9

x = 3

The missing side is 3.

Or you could use an online calculator xD

Answer:

I think the correct answer is F. y = 6x

We will see that the line equation is y = 6*x

A general linear equation is written as:

y = a*x + b

Where a is the slope and b is the y-intercept.

If we know that the line passes through two points (x₁, y₁) and (x₂, y₂) then we can write the slope as:

[tex]a = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

In this case, the line passes through the points: (0, 0) and (-1/2, -3)

Then the slope is:

[tex]a = \frac{0 - (-3)}{0 - (-1/2)} = 6[/tex]

Then the line is of the form y = 6*x + b

To find the value of b, we use the fact that the line passes through the point (0, 0), then we have:

0 = 6*0 + b

0 = b

We can conclude that the line is y = 6*x

If you want to learn more about linear equations, you can read:

https://brainly.com/question/4074386

Answer:

common difference is 0.5

first term is 5

Step-by-step explanation:

use the formula for the nth term of an ap Tn=a+(n-1)d

T12=10.5

T18=13.5

therefore come up with two equations

T12=a+(12-1)d

10.5=a+11d(1st equation)

T18=a+(18-1)d

13.5=a+17d(2nd equation)

then solve both as a simultaneous equation

a+11d=10.5

a+17d=13.5

-6d/-6=-3/-6

d=0.5

use one of the equations to find the first term

a+11(0.5)=10.5

a+5.5=10.5

a=10.5-5.5

a=5

I hope this helps

please mark as brainliest

Answer:

C' (-1,-2)

V' (-2,2)

N' (2,0)

Answered by GAUTHMATH

Answer:

[tex]( - 11.7)[/tex]

Range 18

Step-by-step explanation:

Twice the amplitude.

Answer: 16x^2 + 24x + 9

Step-by-step explanation:

Simplified version: (4x+3)^2

Answer:

[tex]a = \frac{1}{2} \\ b = - 3 \\ c = - 2[/tex]

Step-by-step explanation:

The explanation is in the picture!

Step-by-step explanation:

x/3 = 5/6

cross multiply

6x=15

x=2.5

Answer:

x=5/2

Step-by-step explanation:

The type of transformation in this situation is refelction on the x-axis.

It cannot possibly be translated or rotated around the origin.

Hope this helps!

Have a wonderful day!

Answer:

Step-by-step explanation:

I graphed this on my calculator to get the region of feasibility. You should learn how to use your calculator to help you do things like this. You should know by now how to graph by hand, which is tedious, so now it's time to use your calculator to sweat the small stuff and learn to do some useful things.

When you graph this inequality on your calculator, you can see the points of intersection which in turn translate to the vertices of the feasible region. They are located at:

(-14, -6), (-9, -11), (6, 4)

You could then use those vertices to maximize the profit equation or production equation or whatever it is this system pertains to.

Option C

Corresponding angles along parrellel lines are conguerent.

Answered by Gauthmath must click thanks and mark brainliest

Let

ATQ

[tex]\\ \qquad\quad\sf{:}\twoheadrightarrow 40x+50x=45000[/tex]

[tex]\\ \qquad\quad\sf{:}\twoheadrightarrow 90x=45000[/tex]

[tex]\\ \qquad\quad\sf{:}\twoheadrightarrow x=\dfrac{45000}{90}[/tex]

[tex]\\ \qquad\quad\sf{:}\twoheadrightarrow x=500[/tex]

Now

[tex]\\ \qquad\quad\sf{:}\twoheadrightarrow Rita=50x=50(500)=25000[/tex]

[tex]\\ \qquad\quad\sf{:}\twoheadrightarrow Mina=40x=40(500)=20000[/tex]

Answer:

No symmetry

Step-by-step explanation:

The shape cannot be folded over any line to be equally matched up to the other side

Answer:  [tex]\log_{2}\left(\frac{q^2\sqrt{m}}{n^3}\right)[/tex]

We have something in the form log(x/y) where x = q^2*sqrt(m) and y = n^3. The log is base 2.

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

Explanation:

It seems strange how the first two logs you wrote are base 2, but the third one is not. I'll assume that you meant to say it's also base 2. Because base 2 is fundamental to computing, logs of this nature are often referred to as binary logarithms.

I'm going to use these three log rules, which apply to any base.

From there, we can then say the following:

[tex]\frac{1}{2}\log_{2}\left(m\right)-3\log_{2}\left(n\right)+2\log_{2}\left(q\right)\\\\\log_{2}\left(m^{1/2}\right)-\log_{2}\left(n^3\right)+\log_{2}\left(q^2\right) \ \text{ .... use log rule 3}\\\\\log_{2}\left(\sqrt{m}\right)+\log_{2}\left(q^2\right)-\log_{2}\left(n^3\right)\\\\\log_{2}\left(\sqrt{m}*q^2\right)-\log_{2}\left(n^3\right) \ \text{ .... use log rule 1}\\\\\log_{2}\left(\frac{q^2\sqrt{m}}{n^3}\right) \ \text{ .... use log rule 2}[/tex]

Step-by-step explanation:

you're just going to switch x and y and then solve for y

Answer:

Hello,

Step-by-step explanation:

The problem is that the inverse function is not a function but

an union of 2 functions.

[tex]y=(x+6)^2+1\ is\ the\ orignal\ function\ f(x).\\\\Inverting\ x\ and\ y\ gives: \ x=(y+6)^2+1\\\\(y+6)^2=x-1 \ nota\ bene\ x-1\geq 0 \\(y+6)^2-(x-1)=0\\\\((y+6)-\sqrt{x-1} ) * ((y+6)+\sqrt{x-1}) =0\\\\y=-6+\sqrt{x-1}-6\ or\ y=-6-\sqrt{x-1}\\[/tex]

For the fun

,[tex]f_1(x)= (x+6)^2+1=0\ if\ x<6\\f_1^{-1}(x)=-6-\sqrt{x-1} =0\ if\ x<6\\\\f_2(x)=(x+6)^2+1=0\ if\ x \geq 6\\\\f_2^{-1}(x)=-6+\sqrt{x-1} =0\ if\ x\geq 6\\[/tex]

Answer:

(3x + 1)(x + 6)

3x^2 + 19x + 6

3x^2 + 18x + x + 6

3x^2 + 18x + x + 6

3x(x + 6) + x + 6

3x(x + 6) + x + 6

(3x + 1)(x + 6)

Haven't done this in a pretty long time so I might be wrong

Answer:

1/9

Step-by-step explanation:

The vertex form is

y =a(x-h)^2 +k where (h,k) is the vertex

The vertex is (-2,-3)

y =a(x--2)^2 +-3

y =a(x+2)^2 -3

Substitute the point into the equation

-2 = a(-5+2)^2 -3

-2=a(-3)^2-3

Add 3 to each side

-2+3 = a(9)

1 = 9a

1/9 =a

y =1/9(x+2)^2 -3

The coefficient of the x^2 is 1/9

Answer:

[tex]\frac{1}{9}[/tex]

Step-by-step explanation:

The equation of a parabola in vertex form is

y = a(x - h)² + k

where (h, k) are the coordinates of the vertex and a is a multiplier

Here (h, k ) = (- 2, - 3) , then

y = a(x + 2)² - 3

To find a substitute (- 5, - 2 ) into the equation

- 2 = a(- 5 + 3)² - 3 ( add 3 to both sides )

1 = a(- 3)² = 9a ( divide both sides by 9 )

[tex]\frac{1}{9}[/tex] = a

y = [tex]\frac{1}{9}[/tex] (x + 2)² - 3

The coefficient of the x² term is therefore [tex]\frac{1}{9}[/tex]

ill add you if you follow my t i k t o k(:

Answer:

56 cm^2

Step-by-step explanation:

The area of a triangle is

A = 1/2 bh where b is the base and h is the height

A = 1/2 (14) (8)

A = 56 cm^2

Answer:

(√366 - 3)/24

Step-by-step explanation:

Given the following:

cos∝ = √3/8 and sinβ = √3/3

Sin(∝-β) = sin∝cosβ - cos∝sinβ

Get sin∝

Since cos∝ = √3/8

adj = √3

hyp = 8

opp = √8² - (√3)²

opp = √64 - 3

opp = √61

Recall that sin∝ = opp/hyp  

sin∝ = √61/8

Get cosβ

Since sinβ =  √3/3

opp = √3

hyp = 3

adj =√3² - (√3)²

adj = √9-3

adj = √6

Recall that cosβ = adj/hyp

cosβ = √6/3

Substitute the gotten values into the formula

Sin(∝-β) = sin∝cosβ - cos∝sinβ

Sin(∝-β) = ( √61/8)(√6/3)- (√3/8)(√3/3)

Sin(∝-β) = √366/24 - √9/24

Sin(∝-β) = (√366 - 3)/24

Answer:

0.48 is ......

[tex]0.48 < 2.1[/tex]

The unknown sides are 60.81cm and 51.57cm while the unknown angle is 58degrees

4a) Given the following

Opposite side = 38cm (side facing the given angle)

Required

Adjacent and hypotenuse side

According to SOH CAH TOA

[tex]tan \theta = \frac{opp}{hyp}\\tan 32=\frac{38}{hyp}\\hyp=\frac{38}{tan 32}\\hyp=\frac{38}{0.6249}\\hyp= 60.81cm[/tex]

Next is to get the adjacent

[tex]Cos 32=\frac{adj}{60.81}\\adj=60.81cos32\\adj=60.81(0.8480)\\adj= 51.57cm[/tex]

Next is to get the missing angle

Since sum of angle in the triangle is 180degrees

32 + 90 + x = 180

122 + x = 180

x = 180 - 122

x = 58degrees

The unknown sides are 60.81cm and 51.57cm while the unknown angle is 58degrees.

Learn more about the properties of triangles here: https://brainly.com/question/16908652

Answer:

3.398

Step-by-step explanation:

log(2500)=log(25)+log(100)=2+2*0.699=3.398

Answer:

-10k×2+7

= -20k+7

Step-by-step explanation:

is the answer

Answer:

y = 4/3x+2/3

Step-by-step explanation:

the 2 coordinates provided are: (4,6) and (-5,-6)

y=mx+c

m= (y1-y2)/(x1-x2) = (-6-6)/(-5-4) = 4/3

sub x = 4, y = 6

6 = 4/3 * 4 + c

c = 2/3

Answer:

y = 4/3x+2/3

Step-by-step explanation:

Pick two points on the line to find the slope

(-5,-6) and (4,6)

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

m = ( 6 - -6)/( 4 - -5)

   = ( 6+6)/(4+5)

   = 12/9

  = 4/3

The slope intercept form of a line is y =mx+b where m is the slope and b is the y intercept

y = 4/3x+b

Substitute a point into the equation

6 = 4/3(4)+b

6 = 16/3+b

Subtract 16/3 from each side

18/3 - 16/3 =b

2/3 = b

y = 4/3x+2/3