Find the equation of the line which has slope 7 and y-intercept 2. Give your answer in the form y=mx+b

Answer:

Step-by-step explanation:

I will ASSUME that your equation is

s(t) = 3t⁴ - 40t³ + 126t² - 9

1) velocity is the derivative of position

v(t) = s'(t) = 12t³ - 120t² + 252t

2) changing what? position? velocity? acceleration? gender? color?

position No   the plot is continuous

velocity Yes  both magnitude and direction. Zeros at t = 0, 3, and 7 s

acceleration Yes, both magnitude and direction. Zeros at approx. t = 1.306 and 5.361 s

gender? who knows

color? probably.

3) velocity is positive (moving to the right on a standard number line) for

0 < t < 3 and t > 7

Moves to the left for

t < 0 and 3 < t < 7

1. the velocity of the object at any time "t" is v(t) = 12t³ - 120t² + 252t.

2. the object stops changing at t = 6 and t = 3.5.

3. the object is moving to the right in the interval 0 < t < 3.5 and moving to the left in the interval t > 6.

To determine the velocity of the object at any time "t," we need to find the derivative of the position function "s(t)" with respect to "t."

1. Velocity of the object at any time "t":

The velocity is the rate of change of position with respect to time, which is given by the derivative of the position function, s(t).

s(t) = 3t⁴ - 40t³ + 126t² - 9

To find the velocity function, we take the derivative of s(t) with respect to t:

v(t) = d/dt (3t⁴ - 40t³ + 126t²- 9)

v(t) = 12t³ - 120t² + 252t

So, the velocity of the object at any time "t" is v(t) = 12t³ - 120t² + 252t.

2. Does the object ever stop changing?

The object stops changing when its velocity becomes zero. To find when the velocity is zero, we need to solve the equation v(t) = 0.

12t³ - 120t² + 252t = 0

Now, we can factor out common terms:

t(12t² - 120t + 252) = 0

Now, set each factor equal to zero and solve for "t":

1st factor: t = 0

2nd factor: 12t² - 120t + 252 = 0

To solve the quadratic equation, we can either factor it further or use the quadratic formula. Factoring the quadratic equation gives us:

(t - 6)(12t - 42) = 0

Setting each factor to zero:

1. t - 6 = 0

t = 6

2. 12t - 42 = 0

12t = 42

t = 3.5

So, the object stops changing at t = 6 and t = 3.5.

3. When is the object moving to the right and when is the object moving to the left?

The object is moving to the right when its velocity (v(t)) is positive, and it is moving to the left when its velocity (v(t)) is negative.

Let's analyze the velocity function

v(t) = 12t³ - 120t² + 252t

To find the intervals where the object is moving to the right or left, we need to determine when v(t) is positive or negative.

1. Find critical points by setting v(t) = 0 and solving for "t":

12t³ - 120t² + 252t = 0

As we already found earlier, the critical points are t = 6 and t = 3.5.

2. Test each interval created by these critical points using test points to determine the sign of v(t) in those intervals.

Pick a value of "t" in each of these intervals:

- When t < 3.5 (e.g., t = 0),

- When 3.5 < t < 6 (e.g., t = 4),

- When t > 6 (e.g., t = 7).

Now, substitute these test values into the velocity function v(t):

- v(0) = 12(0)³ - 120(0)² + 252(0) = 0

- v(4) = 12(4)³ - 120(4)² + 252(4) = 192

- v(7) = 12(7)³ - 120(7)² + 252(7) = -588

Based on the test points, we can conclude:

- The object is moving to the right when 0 < t < 3.5 (positive velocity).

- The object is moving to the left when t > 6 (negative velocity).

Therefore, the object is moving to the right in the interval 0 < t < 3.5 and moving to the left in the interval t > 6.

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Answer:

60

Step-by-step explanation:

using the bodmas

multiply 4 by -3

then multiply with 5

Answer:

Hello! I know I am a bit late but for those who come here in the future,

This is the order (Least to Greatest)

1) 1,500 at 8% simple interest for 6 years

2) 1,500 at 6% simple interest for 10 years

3) 1,500 at 8% simple interest for 10 years

Hope this helps!

In situation 3, a person will earn the least simple interest in situation 1, a person will earn the most simple interest.

It is defined as the interest based on the principal amount, it does not include the compounded amount. The interest calculates on the initial amount or borrowed amount.

It is given for the three cases as,

P =$1500, R=8% , T = 10 years

P =$1500, R=8% , T = 6 years

P =$1500, R=6% , T = 10 years

The formula for the simple interest is,

Case 1,

SI = (P×R×T) / 100

SI = (1500×8×10)/100

SI = $ 1200

Case 2,

SI = (P×R×T) / 100

SI = (1500×6×10)/100

SI = $ 900

Case 3,

SI = (P×R×T) / 100

SI = (1500×8×6)/100

SI = $ 720

The simple interest for cases 1, 2, and 3 will be $ 1200, $ 900, and $ 720.

Thus, in situation 3, a person will earn the least simple interest in situation 1, a person will earn the most simple interest.

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Answer:

∠A = 98

Step-by-step explanation:

total sum of angles in a quadrilateral is 360

∠A + ∠B + ∠C +∠D = 360

∠A + 59 + 103 + 100 = 360

∠A + 262 = 360

∠A = 360- 262

∠A = 98

The solution to the equation f(x) = g(x) is any x-value that makes the equation true.  In terms of using graphs, the solutions are the x-coordinates of any point of intersection.  

So if the graphs intersect at (1,5), then the solution is x=1.

This checks, because f(1) = 5 and g(1) = 5, so f(1) = g(1).

Answer:

x + 2 ( x - 20 )( 4 ) = -70

Step-by-step explanation:

hope this helps. . .<3

Answer:

5,000 yoyos per day

Step-by-step explanation:

80 x 1.25 = 100

4,000 x 1.25 = 5,000

Answer:

The negatives are at the bottom and the positives are at the top, if you need help with the (x,y) let me know!!!

Step-by-step explanation:

Answer:

right and above side of graph are positive

and

left and bottom side of graph are negative

Answer:

Step-by-step explanation:

c = children

a = adults

2200 people enter the zoo mean :

c + a = 2200

$4,550.00 is collected mean :

1.5 c + 4 a = 4550

Now you must solve system:

c + a = 2200

1.5 c + 4 a = 4550

c + a = 2200 Subtract c to both sides

c + a - c = 2200 - c

a = 2200 - c

1.5 c + 4 a = 4550

1.5 c + 4 ( 2200 - c ) = 4550

1.5 * c + 4 * 2200 - 4 c = 4550

1.5 * c + 8800 - 4 c = 4550

- 2.5 c + 8800 = 4550 Subtract 8800 to both sides

- 2.5 c + 8800 - 8800 = 4550 - 8800

- 2.5 c = - 4250 Divide both sides by - 2.5

c = - 4250 / - 2.5

c = 1700

a = 2200 - c = 2200 - 1700 = 500

1700 children and 500 adults

Proof :

c + a = 1700 = 2200

$ 1.5 * c + $ 4 * a =

$ 1.5 * 1700 + $ 4 * 500 =

$ 2550 + $ 2000 = $ 4550

The number of children and the number of adults are 1600 and 800, respectively.

The allocation of weights to the relevant variables that produce the calculation's optimum is referred to as a direct consequence.

A nearby zoo charges $1.50 for kids and $3.00 for adults to enter. 2400 persons visit the zoo on a certain day, and $4,800.00 is gathered.

Let x be the number of children and y be the number of adults. Then the equation is written as,

x + y = 2400           ...1

1.5x + 3y = 4800

x + 2y = 3200    ...2

Subtract equation 1 from equation 1, then

2y - y = 3200 - 2400

y = 800

Then the value of x is calculated as,

x + 800 = 2400

x = 2400 - 800

x = 1600

The number of children and the number of adults are 1600 and 800, respectively.

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Answer:

  D.  126 cm³

Step-by-step explanation:

The formula for the volume of a cylinder in terms of its diameter can be written as ...

 V = (π/4)d²h

The difference between the volume of the overall cylinder and the volume of the hole is ...

  V = V2 -V1 = (π/4)(d2²)h -(π/4)d1²)h = (π/4)(d2² -d1²)h

  V = (π/4)((6 cm)² -(2 cm)²)(5 cm) = (π/4)(36 -4)(5) cm³ = 40π cm³ ≈ 126 cm³

The volume of the solid cylinder with a hole in it is about 126 cm³.

Answer:

Step-by-step explanation:

C

Answer:

rational

Step-by-step explanation:

Answer:

width = 6

Step-by-step explanation:

We can think of the width as x and the height as 3x-6. the perimeter formula is (width + height)*2, since we have x as width and 3x-6 as height, we can put it in the formula, which will get you (x + 3x-6)*2 = 36, if we devide both sides by 2, we'll get (x + 3x - 6) = 18, when we simplify it, we will get 4x-6 = 18, which can then be simplified into 4x = 24, which will get you that x = 6

Hope it helped :)

Answer:

The answer is 14

Step-by-step explanation:

c - 4 = 10

c = 10 + 4

c = 14

Answer: c = 14

Step-by-step explanation:

14 - 4 = 10

Answer:

0.48£

Step-by-step explanation:

(3x8)/50=0.48£

Answer:

it is 1.5

Step-by-step explanation:

if u do 4.50÷3 you will get 1.5 so the cost per jar is 1.5

After doing some quick calculations, we can determine that X = −35.9

I hope this helps! :)

Answer:

x = -35.9

Step-by-step explanation:

Subtract both sides by 11.2                                                                                                 11.2 - 11.2 equals zero leaving x on one side.

x = - 24.7 - 11.2

A negative minus another negative number is a larger negative number.

x= -24.7 - 11.2 = -35.9

x = -35.9

Answer:

58

Step-by-step explanation:

Step-by-step explanation:

-1728 y'all i do by using calculator and it is correct

Answer:

its -1728

Step-by-step explanation:

i worked it out right.

a. There are 26 letters in the English alphabet, with two cases for each letter; 10 numerical characters in the range 0-9; and 5 special characters; thus a total of 26•2 + 10 + 5 = 67 characters.

Any character can be used more than once, so there are

67⁶ + 67⁷ + 67⁸ + 67⁹

or 27,618,753,243,839,080 total possible passwords.

b. If we require at least 1 special character, then there are 62 choices for each ordinary character we use and 5 for each special character.

Suppose we use a password of length 6. Then there are

62⁵•5¹ + 62⁴•5² + 62³•5³ + 62²•5⁴ + 62¹•5⁵ + 62⁰•5⁶

or

[tex]\displaystyle \sum_{k=1}^6 62^{6-k}\cdot5^k[/tex]

We count the longer passwords in a similar fashion:

[tex]\displaystyle \sum_{m=6}^9 \left(\sum_{k=1}^m 62^{m-k}\cdot5^k\right)[/tex]

or 1,206,930,268,794,100 total passwords

c. 1 second (s) is equal to 10⁶ microseconds (μs). If it takes 1 μs to try 1 password, then it would take

(1,206,930,268,794,100 passwords) • (1 μs / password) • (1 s / 10⁶ μs)

= 1,206,930,268.7941 s

= (1,206,930,268.7941 s) • (1 min / 60 s)

≈ 20,115,504.4799 min

≈ (20,115,504.4799 min) • (1 h / 60 min)

≈ 335,258.408 h

≈ (335,258.408 h) • (1 day / 24 h)

≈ 13,969.1003 days

≈ (13,969.1003 days) • (1 year / 365 days)

≈ 38.2715 years

Answer:

1724

Step-by-step explanation:

first find the nth term = -19n+5

then do -19×91+5= 1724

Answer:

Step-by-step explanation:

The geometric mean is the average of the 5 numbers

8 + 6 + 3 + 5 + 4                 Just add.

Total = 26

There are 5 elements, so the average = 26/5 = 5.2

Answer:

X-intercept: [tex](\frac{14}{3}, 0)[/tex].

Y-intercept: (0, 7) ⇒ Option B.

Step-by-step explanation:

I'm not certain whether the question asks for either the x-intercept or the y-intercept, but I will provide the answers for both since none of the given options matches the coordinates of the x-intercept.  

The x-intercept is the point on the graph where it crosses the x-axis, with coordinates of (a, 0).  The x-intercept is the value of x when y = 0.

Given the linear equation in standard form, 3x + 2y = 14, set y = 0 to solve for the x-intercept:

3x + 2y = 14

3x + 2(0) = 14

3x + 0 = 14

3x = 14

Divide both sides by 3 to solve for x:

[tex]\frac{3x}{3} = \frac{14}{3}[/tex]

[tex]x = \frac{14}{3}[/tex]

Therefore, the x-intercept is [tex](\frac{14}{3}, 0)[/tex].   None of the given option matches the value of the x-intercept.

The y-intercept is the point on the graph where it crosses the y-axis, and has coordinates of (0, b). It is the value of y when x = 0.

Set x = 0, and substitute into the given equation.

3x + 2y = 14

3(0) + 2y = 14

0 + 2y = 14

2y = 14

Divide both sides by 2 to solve for y:

[tex]\frac{2y}{2} = \frac{14}{2}[/tex]

y = 7

Therefore, the y-intercept is (0, 7), which matches Option B.

    [] 3, 7, 11, 15, 19, 23

4 is being added

    [] 4, 8, 16, 32, 64, 128

They are being multipled by 2

    [] 9, 16, 25, 36, 49, 64

It is increasing the addition by 2s, first one is adding 7, then 9, then 11, etc

    [] 256, 64, 16, 4, 1, 1/4

It is being divided by 4

    [] 50, 45, 34, 26, ____, _____

I am currently unsure on this one, if I figure it out I will edit my answer to reflect that!

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:

[tex]\huge\boxed{-0.001a^{n+1}}[/tex]

Step-by-step explanation:

[tex]-0.001a^{3n+3}=-0.001a^{3(n+1)}=(-0.001a^{n+1})^3\\\\\text{Used}\\\\a(b+c)=ab+ac\qquad\text{distributive property}\\\\(a^n)^m=a^{n\cdot m}[/tex]