Is 10, 20, 40, 80... an arithmetic sequence?

Answer:

7

Step-by-step explanation:

I took the k12 quiz

Answer:

7

Step-by-step explanation:

I  took the quiz on K-12 the quiz name is 6.04 Quiz: Mean Absolute Deviation (MAD)

Answer:

B. 2.365

Step-by-step explanation:

Divide total distance by total people in order to get distance each person traveled.

28.375 miles / 12 = 2.36458333.......

If you round taht to nearest thousandth of a mile, the answer is: 2.365

Answer:

Step-by-step explanation:

In this question we have provided an equation that is 9 ( 3x - 16 ) + 15 = 6x - 24 . And we are asked to write the steps to solve the equation with explanation and to find the value of X .

Solution : -

[tex] \longmapsto \quad \: 9(3x - 16) + 15 = 6x - 24[/tex]

Step 1 : Solving parenthesis on left side using distributive property which means multiplying 9 with 3x as well as -16 :

[tex] \longmapsto \quad \:27x - \bold{144 }+ \bold{15 }= 6x - 24[/tex]

Step 2 : Solving like terms on left side that are -144 and 15 :

[tex] \longmapsto \quad \:27x -129 = 6x - 24[/tex]

Step 3 : Adding 129 on both sides :

[tex] \longmapsto \quad \:27x - \cancel{129} - \cancel{129} = 6x \bold{ - 24 } + \bold{129}[/tex]

Now on cancelling -129 with 129 on left side and solving the terms that are -24 and 129 on right side , We get :

[tex] \longmapsto \quad \:27x = 6x + 105[/tex]

Step 4 : Subtracting with 6x on both sides :

[tex] \longmapsto \quad \: \bold{27x} - \bold{6x} = \cancel{6x} +105 - \cancel{ 6x}[/tex]

On calculating further, We get :

[tex] \longmapsto \quad \:21x = 105[/tex]

Step 5 : Now we are Dividing with 21 on both sides so that we can isolate the variable that is x :

[tex] \longmapsto \quad \: \dfrac{ \cancel{21}x}{ \cancel{21}} = \dfrac{105}{ 21} [/tex]

Now , by cancelling 21 with 21 on left side , We get :

[tex] \longmapsto \quad \:x = \cancel{\dfrac{105}{21}} [/tex]

Step 6 : Now our final step is to simplify the value of x that is 105/21 . We know that 21 × 5 is equal to 105 . So :

[tex] \longmapsto \quad \: \purple{\underline{\boxed{\frak{ x = 5 }}}}[/tex]

Verifying : -

Now we are verifying our answer by substituting value of x in the given equation . So ,

Therefore, our value for x is correct that means it'll makes the equation true .

[tex]sin(2x) = 2sin(x) \\ 2sin(x)cos(x) = 2sin(x) \\ sin(x)cos(x) = sin(x) \\ sin(x)cos(x) - sin(x) = 0 \\ \sin(x) (cosx - 1) = 0 \\ \sin(x) = 0 \\ x = \pi \: or \: x = 0 \\ cos(x) = 1 \\ x = 0 \: or \: x = \pi \\ \\ s[/tex]

[tex]s = > {0 < = > \pi}[/tex]

Answer:

Linear expression

Step-by-step explanation:

The greateest exponent on a variable is 1 on x, so it is a linear expression,

Answer: Linear expression

[tex]\qquad\qquad\huge\underline{{\sf Answer}}[/tex]

[tex] \textbf{Let's calculate its volume :} [/tex]

[tex] \textbf{Volume if the prism is 52.5 ft³} [/tex]

Answer:

Step 1. Rewrite in the form of y=mx+b

Step 2. Find and plot 2 points (x and y-intercepts)

Step 3. Connect dots

y=mx+b

y - 5x = -2

y = 5x - 2

Find 2 points

y-intecept = (0, -2)

x-intercept = ?

0 = 5x - 2

2 = 5x

x = 2/5

x-intercept = (2/5, 0)

[tex]\text{Given that,} ~f(x) = 2x-4~~ \text{and}~~ g(x) = 2x+8\\\\ g(f(3))\\\\=g(2\cdot 3 -4)\\\\=g(2)\\\\=2(2)+8\\\\=4+8\\\\=12[/tex]

Answer:

Step-by-step explanation:

Its a linear function it goes throw the y-x Axis and is in a striaght line.

Answer:

y = [tex]\frac{5}{2}[/tex] x + 5

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

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

with (x₁, y₁ ) = (- 2, 0) and (x₂, y₂ ) = (0, 5) ← 2 points on the line

m = [tex]\frac{5-0}{0-(-2)}[/tex] = [tex]\frac{5}{0+2}[/tex] = [tex]\frac{5}{2}[/tex]

the line crosses the y- axis at (0, 5 ) ⇒ c = 5

y = [tex]\frac{5}{2}[/tex] x + 5 ← equation of line

Answer:

Step-by-step explanation:

Point P is marked in the expanded view on the 7th mark of the 10 marks between 5×10^-3 and 6×10^-3. That means it is representing ...

  (5 +7/10)×10^-3 = 5.7×10^-3 . . . . scientific notation

__

The -3 exponent of 10 means the multiplier of the value is 1 in the 3rd place to the right of the decimal point: 0.001. So, the standard form of the number is ...

  5.7×0.001 = 0.0057 . . . . . standard form

Answer:

a) 7000 x 1.06^t

b) 11156

Step-by-step explanation:

a) This is quite a case of compound interest where you begin with a value (7000) and every year (t) it goes up by a set amount (6%). To mathematically convert this you put 7000 at the start and you convert the 6% into 1.06 since 0.06 is the amount it increases by and the 1 adds the 0.06 to the previous value. The 't' makes it so each year the value increases so 1.06^t where t is 2 would mean 1.06 x 1.06 which is basically what happens every year.

b) Since it is 8 years later (2008 - 2000), you substitute t for 8 to find the range which is 7000 x 1.06^8 = 11156.9365 which rounds down to 11156 as that's what you do when talking with whole numbers as a new fox isn't quite there yet.

281.2 units³

volume of Prism: Base Area x Height

Here given:

Base Area: 38 units²

Height: 7.4 units

Solve for volume:

38 x 7.4

281.2 units³

Volume:-

Answer:

3:2

Step-by-step explanation:

If you are comparing one data point (A) to another data point (B), your formula would be A/B. This means you are dividing information A by information B. For example, if A is five and B is 10, your ratio will be 5/10.

for this problem we use 0.90 and 0.60, so our ratio is 0.90/0.60

using whole numbers can be converted now by actually dividing these data points and then multiplying to a whole number:

0.9/0.6 = 1.5

1.5 x 2 = 3

this gives 3/2 = 1.5

so we know that the ratio is 3:2 and this is the smallest whole number that it could be

Answer:

The perimeter of an equilateral traingle with height 42cm is 126cm.

Step-by-step explanation:

Given that the height or edge of an equilateral traingle is 42cm. With this information, we are asked to find the perimeter of an equilateral traingle.

The perimeter of equilateral traingle is defined as the three times of the length of edge. Mathematically;

→ Perimeter = 3a

By substituting the given values in the formula, we get the following results:

→ Perimeter = 3(42)

→ Perimeter = 126

Hence, the perimeter of an equilateral traingle with height 42cm is 126cm.

Additional information:

Step-by-step explanation:

problem 10 is function

but problem 9 is not

We can express the forcing function (the piecewise expression on the right side) in terms of the step function as [tex]e^{-t}(u(t) - u(t-1))[/tex] where

[tex]u(t) = \begin{cases}1&\text{for }t\ge0\\0&\text{otherwise}\end{cases}[/tex]

Let F(s) be the Laplace transform of a function f(t). Now recall the transform pair

[tex]f(t-c) u(t-c) \mapsto e^{-cs} F(s)[/tex]

This means

[tex]e^{-t} u(t) \mapsto \dfrac1{s+1}[/tex]

[tex]e^{-t} u(t-1) = \dfrac1e \times e^{-(t-1)} u(t-1) \mapsto  \dfrac{e^{-(s+1)}}{s+1}[/tex]

I assume you're familiar with the transform rule for derivatives of y(t). Now we're ready to take the transform of both sides of the ODE:

[tex]y'' + 3y' + 2y = e^{-t}(u(t) - u(t-1))[/tex]

[tex]\implies \left(s^2 Y(s) - s y(0) - y'(0)\right) + 3 \left(s Y(s) - y(0)\right) + 2 Y(s) = \dfrac{1 - e^{-(s+1)}}{s+1}[/tex]

Plug in the initial values and solve for Y(s) :

[tex]\left(s^2 Y(s) - s + 1\right) + 3 \left(s Y(s) + 1\right) + 2 Y(s) = \dfrac{1 - e^{-(s+1)}}{s+1}[/tex]

[tex](s^2 + 3s + 2) Y(s) - s + 4 = \dfrac{1 - e^{-(s+1)}}{s+1}[/tex]

[tex]Y(s) = \dfrac{1 - e^{-(s+1)} + (s-4)(s+1)}{(s+1)(s^2 + 3s + 2)}[/tex]

[tex]Y(s) = \dfrac{1 - e^{-(s+1)} + (s-4)(s+1)}{(s+1)^2 (s+2)}[/tex]

Consider the partial fraction expansion

[tex]\dfrac1{(s+1)^2(s+2)} = \dfrac a{s+1} + \dfrac b{(s+1)^2} + \dfrac c{s+2}[/tex]

Solve for the coefficients:

[tex]1 = a(s+1)(s+2) + b(s+2) + c(s+1)^2[/tex]

[tex]s = -1 \implies b = 1[/tex]

[tex]s = -2 \implies c = 1[/tex]

[tex]1 = (a+c)s^2 + \cdots \implies a+c = 0 \implies a = -1[/tex]

Hence we can expand Y(s) as

[tex]Y(s) = \dfrac1{(s+1)^2} + \dfrac1{s+2}  + \dfrac{e^{-(s+1)}}{s+1} - \dfrac{e^{-(s+1)}}{(s+1)^2} - \dfrac{e \times e^{-(s+2)}}{s+2}[/tex]

The last transform pair we need is

[tex]e^{ct} f(t) \mapsto F(s - c)[/tex]

Now, taking inverse transforms of everything yields

[tex]\dfrac1{(s+1)^2} \mapsto te^{-t}[/tex]

[tex]\dfrac1{s+2} \mapsto e^{-2t}[/tex]

[tex]\dfrac{e^{-(s+1)}}{s+1} \mapsto e^{-t} u(t-1)[/tex]

[tex]\dfrac{e^{-(s+1)}}{(s+1)^2} \mapsto e^{-t} (t-1) u(t-1)[/tex]

[tex]\dfrac{e \times e^{-(s+2)}}{s+2} \mapsto e^{-(2t-1)} u(t-1)[/tex]

and putting everything together gives the same solution as the one provided.

Answer:

12

Step-by-step explanation:

you add 92 with the 4 and get 96 then you divide the 8x with the 96 and get 12

Hope it helps <333

x = 12

Our goal is to find the value of x .

To find the value of x we need to get x by itself .

The first step is to move all numbers to the right . Luckily , there's only one number here : 4.

So we  add 4 on both sides :

8x=96

Now divide by 8 on both sides :

x = 12

[tex]\footnotesize\text{hope\:helpful~}[/tex]

Answer:

The answers are:x = ±7/4x = ±3/2x = ±11/8

yww:)

Answer:

Option A, [tex]x =[/tex] ± [tex]11/8[/tex]

Step-by-step explanation:

Step 1:  Add 144 to both sides

[tex]64x^2 - 144 = -23[/tex]

[tex]64x^2 - 144 + 144 = -23 + 144[/tex]

[tex]64x^2 = 121[/tex]

Step 2:  Divide both sides by 64

[tex]\frac{64x^2}{64} = \frac{121}{64}[/tex]

[tex]x^2 = 1.890625[/tex]

Step 3:  Square root both sides

[tex]\sqrt{x^2} = \sqrt{1.890625}[/tex]

[tex]x =[/tex] ± [tex]1.375[/tex]

[tex]x =[/tex] ± [tex]11/8[/tex]

Answer: Option A, [tex]x =[/tex] ± [tex]11/8[/tex]

Answer:

____________

3748 x 4 = (3000+700+40+8) x 4

(3000 x 4) + (700 x 4) + (40 x 4) + (8 x 4)

12000 + 2800 + 160 + 32

= 14992

Step-by-step explanation with answer:

3748x4 = (3000+700+40+8) x 4

= 3000x4 + 700x4 + 40x4 +8x4

=12000+2800+160+32

=14992

Answer:

  c.  3a^2b^11/2

Step-by-step explanation:

The applicable rule of exponents is ...

  (a^b)/(a^c) = a^(b-c)

__

 [tex]\dfrac{-18a^{-2}b^5}{-12a^{-4}b^{-6}}=\dfrac{-18}{-12}a^{-2-(-4)}b^{5-(-6)}=\boxed{\dfrac{3a^2b^{11}}{2}}[/tex]

Answer: t=2

Step-by-step explanation:

add the t's and calculate

Answer:

$31,500

Step-by-step explanation:

10% = 0.1

100% = 1

1 - 0.1 = 0.9

35,000 x 0.9 = 31,500

Answer:

24

Step-by-step explanation:

Lets start by working out 80% of 30

80% x 30=24

so the student answered 24 questions correctly

Answer:

Step-by-step explanation:

You are being asked to read the coordinates of several points from the graph. Each set of coordinates is an (x, y) pair, where the first coordinate is the horizontal distance to the right of the y-axis, and the second coordinate is the vertical distance above the x-axis. The distances are measured according to the scales marked on the x- and y-axes.

__

The vertex is the low point of the graph. The graph is horizontally symmetrical about this point. On this graph, the vertex is (3, -1).

The y-intercept is the point where the graph crosses the y-axis. On this graph, the y-intercept is (0, 8).

The x-intercepts are the points where the graph crosses the x-axis. You will notice they are symmetrically located about the vertex. On this graph, the x-intercepts are (2, 0) and (4, 0).

__

Additional comment

The reminder that these are "points" is to ensure that you write both coordinates as an ordered pair. We know the x-intercepts have a y-value of zero, for example, so there is a tendency to identify them simply as x=2 and x=4. This problem statement is telling you to write them as ordered pairs.

Answer:

51

Step-by-step explanation:

you plug in 3 for x.

5(3)^2 - 3 + 9

5(9) - 3 + 9

45-3+9

51

Answer: 5x^2+6

Step-by-step explanation: sorry if wrong

Answer:

Domain is all real numbers

Range is (3, ∞) or y > 3

Step-by-step explanation: