Determine if the sequence below is arithmetic or geometric and determine the
common difference / ratio in simplest form.
12, 9, 6, ...

Answer:

[tex]y=\frac{1}{6}x+6[/tex]

Step-by-step explanation:

Let [tex](x_1,y_1)\rightarrow(-6,5)[/tex] and [tex](x_2,y_2)\rightarrow(6,7)[/tex]

Determine slope

[tex]m=\frac{y_2-y_1}{x_2-x_1}\\ \\m=\frac{7-5}{6-(-6)}\\ \\m=\frac{2}{6+6}\\ \\m=\frac{2}{12}\\ \\m=\frac{1}{6}[/tex]

Use either ordered pair to find the y-intercept

[tex]y=mx+b\\\\7=\frac{1}{6}(6)+b\\\\7=1+b\\\\6=b[/tex]

Final equation

[tex]y=\frac{1}{6}x+6[/tex]

Answer:

13.5m/s

Step-by-step explanation:

formula is v=u + at

as given:

u=3m/s

a=1.5m/s²

t=7secs

v=3+1.5(7)

v=3 + 10.5

v = 13.5m/s

The unit for velocity is m/s

Answer:

a) 87

b) 13.5

Step-by-step explanation:

for the first question we've been given the equation and the parameters needed

so we just input the parameters

3a+4b when a is 17 and b is 9

therefore the answer is 3*17 + 4*9

51+36=87

second question

that's an equation of motion and we've been given all the parameters we also need so we just input the parameters In the equation

v=u+at

v=3+1.5*7

v= 3+10.5

v=13.5

Answer:

-2, 0, d

refer the image attached

Answer:

d > -2

Graph :

Answer:

30

Step-by-step explanation:

(3+3³)

3+27

30

Answer:

[tex]30[/tex]

Step-by-step explanation:

[tex]3\cdot(1+3^2)\\\\3\cdot(1+9)\\\\3\cdot(10)\\\\30[/tex]

Remember to follow PEMDAS

Answer:

x²

Step-by-step explanation:

4x²-14x+6

x²-7x²+12x

=2×2×x×x-2×7×x+2×3

x×x×x-7×x×x+2×2×3

= -2+2

x×x

the 2s cancle each other

= x²

Answer:

Just add the 2 fractions that were mentioned

Step-by-step explanation:

turn 6 1/2 into an improper fraction and then add it to 5/8 by finding a common denominator

so it would be like -

13/2 + 5/8    =      52/8 + 5/8   =   57/8   =   7  1/8

Answer:

6 1/2 + 5/8 = 57/8 = 7 1/8 = 7.125

Step-by-step explanation:

Conversion a mixed number 6 1/2

to a improper fraction: 6 1/2 = 6 1/2 = 6 · 2 + 1/2 = 12 + 1/2 = 13/2

To find a new numerator:

a) Multiply the whole number 6 by the denominator 2. Whole number 6 equally 6 * 2/2 = 12/2

b) Add the answer from previous step 12 to the numerator 1. New numerator is 12 + 1 = 13

c) Write a previous answer (new numerator 13) over the denominator 2.

Six and one half is thirteen halfs

Add: 13/2 + 5/8 = 13 · 4/2 · 4 + 5/8 = 52/8 + 5/8 = 52 + 5/8= 57/8

For adding, subtracting, and comparing fractions, it is suitable to adjust both fractions to a common (equal, identical) denominator. The common denominator you can calculate as the least common multiple of both denominators - LCM(2, 8) = 8. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 2 × 8 = 16. In the following intermediate step, it cannot further simplify the fraction result by canceling.

In other words - thirteen halves plus five-eighths = fifty-seven eighths.

Answer:

Slope intercept: y = -3/2x + 1

Point slope: y + 2 = -3/2 * (x - 2) [Forgot to add the work for this, I will add it if you need it, feel free to ask.]

Step-by-step explanation:

m = (change in y)/change in x)

But also

m = y_2 - y_1/x_2 - x_1

So lets substitute

m = 1 - (-2)/0 - (2)

Lets find the slope

m = 3/0 - (2)

m = 3/-2

m = -3/2 (Moved the negative)

Now we find the value of b using the equation of a line.

y = mx + b

y = (-3/2) * x + b

y = (-3/2) * (2) + b

-2 = (-3/2) * (2) + b

Now we find the value of b

Lets rewrite

-3/2 * 2 + b = -2

Cancel the CF of 2

-3 + b = -2

Move the terms without b to the right

b = -2 + 3

b = 1

Now we substitute our values of the slope and y-int into y = mx + b to find the equation.

y = -3/2x + 1

Answer:

[tex]y=\frac{-3}{2}x-1[/tex]

Step-by-step explanation:

Given the two points, we can use the slope formula to get the slope of our equation.

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

Plug in what we know

[tex]\frac{(1)-(-2)}{0-2}=m[/tex]

[tex]m=\frac{-3}{2}[/tex]

[tex]y=\frac{-3}{2}x-b[/tex]

Plug in one of the points given and solve to find our y-intercept [b]

[tex]-2=\frac{-3}{2}(2)-b[/tex]

[tex]b=1[/tex]

(we already know our y-intercept since we're given what y is when x is 0 [hence (0,1)], but this is how it is done if we did not know it initially)

Final equation

[tex]y=\frac{-3}{2}x-1[/tex]

Answer:

  sin(x) = ±(√357)/29 ≈ ±0.651533

Step-by-step explanation:

The relation between sine and cosine is ...

  sin(x) = ±√(1 -cos(x)^2)

  sin(x) = ±√(1 -(-22/29)^2) = √(1 -484/841) = √(357/841)

  sin(x) = ±(√357)/29

_____

Additional comment

The sign of the cosine is negative, which places the angle in quadrant II or III. In quadrant II, the sine is positive; in quadrant III, the sine is negative. That is, we cannot tell which sign to apply from the information given.

(20, 21, 29) is a Pythagorean triple. We suspect a typo in the question: 22 is used where 20 or 21 is likely intended.

Answer:a hope this helps

Step-by-step explanation:

Answer:

[1] [tex]\frac{3}{22}[/tex]

[2] [tex]\frac{4}{9}[/tex]

[3] [tex]\frac{1}{8}[/tex]

[4] [tex]\frac{9}{25}[/tex]

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

[6] [tex]\frac{1}{5}[/tex]

Step-by-step explanation:

[1] Using the given fractions,

3/8×4/11

Applying the fractions formula for multiplication,

=3×4/8×11

=12/88

Simplifying 12/88, the answer is

=3/22

ˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋ

[2] Using the given fractions,

8/15×5/6

Applying the fractions formula for multiplication,

=8×5/15×6

=40/90

Simplifying 40/90, the answer is

=4/9

ˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊ

[3] Using the given fractions,

7/12×3/14

Applying the fractions formula for multiplication,

=7×3/12×14

=21/168

Simplifying 21/168, the answer is

=1/8

ˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊ

[4] Using the given fractions,

9/20×4/5

Applying the fractions formula for multiplication,

=9×4/20×5

=36/100

Simplifying 36/100, the answer is

=9/25

ˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊ

[5] Using the given fractions,

7/10×20/21

Applying the fractions formula for multiplication,

=7×20/10×21

=140/210

Simplifying 140/210, the answer is

=2/3

ˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊ

[6] First:

Reduce fractions where possible.

Then your initial equation becomes:

4/9×9/20

Applying the fractions formula for multiplication,

=4×9/9×20

=36/180

Simplifying 36/180, the answer is

=1/5

[RevyBreeze]

Your most trustful answer

Answer:

y = 4x - 2

Step-by-step explanation:

slope = (10 - 2)/(3 - 1) = 8/2 = 4

Let the equation be y = 4x + b

Sub (1, 2) into it,

2 = 4*1 + b

so b = 2 - 4 = -2

The equation is y = 4x - 2

Answer:

it was 200

Step-by-step explanation:

srry if its wrong

Answer:

26400

Step-by-step explanation:

1 mi=1760 yd

5mi=8800yd

1yd=3ft

8800yd=26400ft

If Heather jogged 5 miles in terms of feet he jogged 26400 feet.

A unitary method is a mathematical way of obtaining the value of a single unit and then deriving any no. of given units by multiplying it with the single unit.

Given, Heather jogged 5 miles.

Also given that 1 mi = 1760 yd and 1 yd = 3 ft.

Therefore, If Heather jogged 5 miles then he jogged 5×1760 yards and

5×1760×3 feet which is,

= 26400 feet.

learn more about the unitary method here :

https://brainly.com/question/28276953

#SPJ2

Answer:

x > -6  or  x > 4

Answer: B. x = –8

Step-by-step explanation:

Answer: $1.44

Step-by-step explanation:

Answer: The new number is 1.44% smaller than the original.

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

Explanation:

To increase by 12%, we involve the multiplier 1.12

Think of 1.12 as 100% + 12% = 1 + 0.12 = 1.12

We go from x to 1.12x

To decrease by 12%, we will use the multiplier 0.88 because 1 - 0.12 = 0.88

Think of it like a discount. If you save 12%, then you pay the remaining 88%

So 0.88*1.12x = 0.9856x

The value 0.9856 is smaller than 1, meaning that overall we have a net discount going on.

The discount rate is 1 - 0.9856 = 0.0144 = 1.44%

In other words, x ultimately goes down by exactly 1.44%

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

If you want to use an actual number to see an example, let's go for x = 100

Increasing 100 by 12% means we increase by 0.12*100 = 12

We go from 100 to 112

Then decreasing by 12% means the value goes down by 0.12*112 = 13.44 and drops to 112-13.44 = 98.56

The original value 100 becomes the final value 98.56

This is a percent decrease of (100-98.56)/100 = 0.0144 = 1.44%

Answer:

0.025

Step-by-step explanation:

The solution is in the attached file

Answer:

the awnser is 19,500

Step-by-step explanation:

you multiply 325 × 2=650 then you multiply 30×650=19,500

Answer:1(2x3)-4= 3

2x3= 6 -4=2+1=3

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

2x3=6

1+6=7

7-4=3

The value of E(Y) and Var(Y) are 50 and 178/5 respectively

Given the formula for temperature conversion expressed as:

Y = (9/5)*X + 32

where:

X stands for a temperature in degrees Celsius,

Y the same temperature in degrees

If E(X) = 10, then;

Y = (9/5) * 10 + 32

Y = (9*2) + 32

Y = 18 + 32

Y = 50

Hence E(Y) = 50

If Var(X) = 2

Y = (9/5) * 2 + 32

Y = 18/5 + 32

Y =  178/5

Hence Var(Y) = 50

The value of E(Y) and Var(Y) are 50 and 178/5 respectively

Learn more on temperature here: https://brainly.com/question/894531

Answer:

(Q.1) No solution

(Q.2) True

(Q.3)  x = 4 - 2y

(Q.4) True

Step-by-step explanation:

(Q.1) As shown in the first attached figure.

By graphing.   x + 2y = 8   &   x + 2y = -4

The two lines are parallel, there is no intersection points between the lines.

So, there is no solution to the system of equations.

Also, we should note the parallel lines have the same slope

to find it make the equation similar to y = mx + c where m is the slope

at this situation m = -1/2

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

(Q.2) As shown in the second attached figure.

By graphing the system of inequalities  y> -3x+2  &  y<2x+1

The Shaded area represents the solution of the system of inequalities

And the point (4,2) is inside the shaded area

So, The ordered pair (4,2) is a solution to the system of inequalities.

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

(Q.3) solving the system { x+2y=4  &  2x+2y=6 } by substitution

From the first equation x + 2y = 4

we will find x in terms of y then plug it into the second equation

So, x + 2y = 4 ⇒  x = 4 - 2y

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

(Q.4) As shown in the third attached figure.

By graphing.   2x + 4y = 8  &  x + 2y = 6

The two lines are parallel, there is no intersection points between the lines.

So, there is no solution to the system of equations.

Also, we should note the parallel lines have the same slope

to find it make the equation similar to y = mx + c where m is the slope

at this situation m = -1/2

Answer:

a) odd

b) even

Step-by-step explanation:

a) It is an odd symmetry because it is symmetric about the origin, meaning if you rotate an odd function 180° around the origin, you will have the same function you started with.

b) It is an even symmetry because it reflects over the y-axis. The left and right looks the same.

Answer:

Step-by-step explanation:

Let's replace Ram with r and Sudha with s.

(r = 3s) + 3 = (r = 2s)

(r = 2x) = ( r = 3s - 3)

3s - 3 = 2x

3s - 1x = 2x

s = 3

If r = 3s and s = 3, then r = 3 x 3 = 9.

Ram is 9 years old and Sudha is 3 years old.

Answer:

age of ram = 9 years

and the age of sudha is 3 years

Step-by-step explanation:

let the present age of ram be x

and his sister sudha's present age be y

Ram is three times as old as his sister Sudha

so, x = 3y ----i)

After three years, he will be twice as old as Sudha.

so , x+3 =(y+3)2

=> x+3 = 2y+6 ----ii)

now putting the value of x in equation ii)

=> 3y+3 = 2y+6

=> 3y-2y = 6-3

=> y = 3 { the present age of sudha is 3 year}

now the age of ram = x = 3y

=> x = 3(3)

=> x = 9

Answer:

6. 8.2g

7. 3800 ml

8. 560 L

9. 6300 ml

10. 30.48cm

11. 21120 ft

12. 487.48cm

Step-by-step explanation:

820 ÷ 100

3.8 × 1000

56000 ÷ 100

63 × 100

12 × 2.54

4 × 5280

16 × 30.48

Please mark me as brainliest

Answer:

5000 meters

Step-by-step explanation:

kilometers to meters=1km to 1000m

so 5km to 5000m

The total meters did ed hike and swim on Saturday and Sunday 5000 meters.

We have given,

Ed hiked 3 kilometers on Saturday and

Swam 2 kilometers on Sunday.

Kilometers to meters

1km = 1000m

We have to find the total distance Ed hiked and swam on Sunday and Saturday,

Total distance=3km +2km

=3km +2km

=5km

1km=1000m.

So 5km to 5000m.

To learn more about the distance visit:

https://brainly.com/question/17273444

Answer:

[tex]\frac{2}{9\pi}ft^3/min[/tex]

Step-by-step explanation:

Given

[tex]\frac{dV}{dt}=2ft^3/min\\ \\\frac{dh}{dt}=?\\ \\V_{cone}=\frac{1}{3}\pi r^2h\\\\d=2r=3h\\\\\frac{d}{2}=r=\frac{3}{2}h\\\\h=2[/tex]

Calculation

[tex]V=\frac{1}{3}\pi r^2h\\ \\V=\frac{1}{3}\pi(\frac{3}{2}h) ^2h\\\\V=\frac{1}{3}\pi(\frac{9}{4}h^2)h\\ \\V=\frac{9}{12}\pi h^3\\ \\V=\frac{3\pi}{4}h^3\\ \\\frac{dV}{dt}=\frac{9\pi}{4}h^2\frac{dh}{dt}\\ \\2=\frac{9\pi}{4}(2)^2\frac{dh}{dt}\\ \\ 2=9\pi\frac{dh}{dt}\\ \\ \frac{2}{9\pi} =\frac{dh}{dt}[/tex]

Therefore, the rate that the height of the pile is changing when the pile is 2 feet high is [tex]\frac{2}{9\pi}ft^3/min[/tex].

Answer:

Step-by-step explanation:

An exponent is a number that makes another number multiply itself.

If it's on a fraction, then we need to do this:

It can be confusing.

Remember,

We are not adding.

Answer:

1 5/8

Step-by-step explanation:

Answer:

The General Sherman Tree is the world's largest tree, measured by volume. It stands 275 feet (83 m) tall and is over 36 feet (11 m) in diameter at the base. Sequoia trunks remain wide high up. Sixty feet above the base, the Sherman Tree is 17.5 feet (5.3 m) in diameter.

Step-by-step explanation: