a reindeer leaves the north pole flying east at 20mph. Another reindeer leaves the north pole at the same time flying west at 15mph. How long will it take them to be 700miles apart?​

Answer:

The cubic function is f(x) = (27/32)·x  - 3/32·x³ - -9/32·x² - 9/32

Step-by-step explanation:

The given function is f(x) = a·x³ + b·x² + c·x + d

By differentiation, we have;

3·a·x² + 2·b·x + c = 0

3·a·(-3)² + 2·b·(-3) + c = 0

3·a·9 - 6·b + c = 0

27·a - 6·b + c = 0

3·a·(1)² + 2·b·(1) + c = 0

3·a + 2·b + c = 0

a·(-3)³ + b·(-3)² + c·(-3) + d = -3

-27·a + 9·b - 3·c + d = -3...(1)

a + b + c + d = 0...(2)

Subtracting equation (1) from equation (2) gives;

28·a - 8·b + 4·c = 3

Therefore, we have;

27·a - 6·b + c = 0

3·a + 2·b + c = 0

28·a - 8·b + 4·c = 0

Solving the system of equations using an Wolfram Alpha gives;

a = -3/32, b = -9/32, c = 27/32 from which we have;

a + b + c + d = 0 3 × (-3/32) + 2 × (-9/32) + (27/32) + d = 0

d = 0 - (0 3 × (-3/32) + 2 × (-9/32) + (27/32)) = -9/32

The cubic function is therefore f(x) = (-3/32)·x³ + (-9/32)·x² + (27/32)·x + (-9/32).

Answer:

The interest rate r = 0.02 or 2%

Step-by-step explanation:

Given

P = $600

I = $12

t = 1 year

To determine

Interest rate = r

Using the formula

I=Prt

r = I / Pt

substituting I = 12, P = 600, t = 1

r = (12) / (600 × 1)

r = 12/600

r = 0.02

Thus, the interest rate r = 0.02 or 2%

Answer:

(-8,-5)

Step-by-step explanation:

Well, if we divide the square root of M by the hypotenuse due to the activation of the square root of A, then we can achieve the absolute equilibrium between both statements as we bring the oven to about 220 degrees Farenheit, the brownies will look great.

Answer:

Ummmmm ehhhhhh

I need points for a hw

Answer:

a. Juan

b. J(t) = A(t) at t = 7 minutes

c. J(t) > A(t) for the interval 0 ≤ t ≤ 7

Step-by-step explanation:

a. From the graph, Juan completes the 4-mile bike race in 13 minutes while Antonio completes the 4-mile bike race in 15 minutes, therefore, Juan completes the distance first and wins the race

b. From the graph, the line of the graph of the functions J(t) and A(t) are equal at the time t = 7 minutes

Therefore;

J(t) = A(t) at t = 7 minutes

c. The value of the function, and the line of the graph of the function, J(t) is larger than and above the value and the line of the graph of the function A(t) for the interval 0 ≤ t ≤ 7

Answer:

2

Step-by-step explanation:

8 + 10 = 18

18/9 = 2

Answer:

Step-by-step explanation:

Answer: 80 - 94

Step-by-step explanation:

Answer: 1.55%

Step-by-step explanation:

p = Principal = $40000

r = Interest rate = 1.55% = 0.0155

n = Number of periods = 365

APY = [1 + (r/n)^n - 1]

= [1 + (0.0155/365)^365 - 1]

= [1 + 0.000042)^365 - 1]

= [1.000042]^365 - 1

= 1.015448 - 1

= 1.55%

Answer:

it is 0

Step-by-step explanation:

Answer:

0

Step-by-step explanation:

Once you simplify the equation, you get 40-64+24. When you use 40+24, you get 64 which cancles out the other 64

Answer: 36

Step-by-step explanation:

First one

Answer:

see below

Step-by-step explanation:

36.196

tens ones. tenths  hundredths thousandths

The greatest places is the tens place.  We look one place to the right to the ones place.  The number in the ones place is 5 or greater so the tens place goes up one place and the ones place becomes a zero

40

Answer:

Option 4

Step-by-step explanation:

Coordinances for a three-dimensional coordinate system are (x, y, z).

The letter labeling each axis is always on the positive side.

The fourth option is correct because you move 3 units away from the 'x', 1 unit away from the 'y', then 2 units toward the 'z'.

Answer:

+7 -8 = -1

lost yard

lost yard by 1 yard

Step-by-step explanation:

Answer:

(2x – 4) dollars

Step-by-step explanation:

Answer:

I will explain the equation

in a graph, the slope will look like this

The Y Intercept is -1, and the slope is -3, as in it will go downward

For every 1x, the slope will go downward by 3.

Answer:

7. A

8. D

9. C

10. D

13. D

Step-by-step explanation:

Hope that helps :)

Answer:

4.8 hours

Step-by-step explanation:

Step one:

given data

The total distance= 220 miles

The velocity of the train= 3/4 mile per minute

Required

The time of travel

Step two:

we know that

velocity= distance/time

velocity= 220/3/4

let us multiply the numerator (220) by the inverse of the denominator(4/3)

velocity =220*4/3

velocity= 880/3

velocity= 293.3 minutes

in hours

= 293.3/60

= 4.8 hours

The correct format of the question is

At the end of 2006, the population of Riverside was 400 people. The population for this small town can be modeled by the equation below, where t represents the number of years since the end of 2006 and P represents the number of people. [tex]P = 400 ( 1.2 )^ t[/tex] Based on this model, approximately what was the increase in the population of Riverside at the end of 2009 compared to the end of 2006?

(A) 291

(B) 691

(C) 1040

(D) 1440

Answer:

The increase in the population at the end of 2009 is 291 people

Step-by-step explanation:

We are given the equation as [tex]P = 400 ( 1.2 )^ t[/tex]

where

P = No of People

t= No of Years

it is given that in the year 2006 the population is 400

this will only happen when we take t= 0

so for

Year    value of t

2006-    t = 0

2007-    t  = 1

2008-    t = 2

2009     t = 3

No of people in 2009 will be

[tex]P = 400(1.2)^3[/tex]

     = 400*1.728

   P  = 691.2

Since the equation represents no of people so it can't be in decimals, Therefore the population will be 691

Increase = P(2009) - P(2006)

               = 691 - 400

                = 291

The increase in the population at the end of 2009 is 291 people.

Note: You missed to add some basic information of the perpendicular line or missed the answer options, hence I am solving using a sample equation but it would clear your concept.

Answer:

Please check the attached graph.

Step-by-step explanation:

We know the slope-intercept form of line equation is

[tex]y = mx+b[/tex]

where m is the slope and b is the y-intercept

Given the points

Finding the slope between F(1, 8) and G(-3, -4)

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

[tex]\left(x_1,\:y_1\right)=\left(1,\:8\right),\:\left(x_2,\:y_2\right)=\left(-3,\:-4\right)[/tex]

[tex]m=\frac{-4-8}{-3-1}[/tex]

[tex]m=3[/tex]

Thus, the slope of the line FG = m = 3

From the given line, we can also determine the y-intercept 'b' by setting x = 0 and checking the corresponding y value.

i.e. at x = 0, y = 5

Thus, y-intercept b = 5

so substituting m = 3 and b = 5 in the slope-intercept form

y = mx+b

y = 3x+5

Therefore, the equation of line FG will be:

Please check the attached diagram, where the red line represents the line y=3x+5

We know that a line perpendicular to another line contains a slope that is the negative reciprocal of the slope of the other line.

Slope of Perpendicular line = -1/m = -1/3

Thus, any line with the slope m = -1/3 would be the line that will be perpendicular to line FG​

Let say the line with the slope m = -1/3 and y-intercept 2

y = -1/3x + 5

Please check the attached graph, the blue line is representing the perpendicular line y =  -1/3x + 5 to line FG

The graph of both lines is clearly representing that the line y = -1/3x + 5 is perpendicular to line FG.

Answer:

Step-by-step explanation:

Answer:

I think it is 5 + 2x

Step-by-step explanation:

Answer:

x=6

Step-by-step explanation:

x-10=-4      (Distribute)

x=6             (Inverse operations {Add 10 on both sides} )

X=6

Answer:

47 days

Step-by-step explanation:

Since the patch of pads doubles in size every day, the lake would be half covered just one day before it was covered entirely.

Answer:

she would be 16 years old

Step-by-step explanation:

hope this helps!! :D

From the given information we found out that age of Mia is 16 years.

A linear equation is an algebraic equation of degree one. In general, the variable or the variables(in the case of a linear equation in two variables) the variables are x and y.

Given, Mia discovered that if she takes half her age and adds 3,

Assuming Mia's age to be x years.

∴ (1/2)x + 3...(i)

It produces the same result as taking one-fourth of her age and adding 7,

∴ (1/4)x + 7...(ii)

So, (1/2)x + 3 = (1/4)x + 7.

(1/2)x - (1/4)x = 7 - 3.

(1/4)x = 4.

x = 4×4/1.

x = 16.

So, Age of Mia is 16 years.

learn more about linear equations here :

https://brainly.com/question/19549073

#SPJ2

Answer: 120 sq in.

Step-by-step explanation:

full answer hope it helps please like and comment if you have some doubts

Answer:

D

Step-by-step explanation:

Cory is 5 times as far as kira. that makes it 5 times 5. tina is 5 times as far as cory. that makes it 5 times 5 times 5

Answer:

The first one

Step-by-step explanation:

Credit report does NOT state whether borrower will pay loan on time ...though it may give an INDICATION of this