The constant of proportionality (k) tells you how steep the graph of a proportional relationship is. TRUE or FALSE

Okay, suppose your income is about $100.

You might spend $70 & save $30.

Now, suppose your income remains constant at $100 but your expenses go up to, say, $90. You can see that your savings will reduce or decrease. Now, you'll only have about $10 to save.

=》 So, if your income is constant, then your savings will 'decrease' when your expenses increase.

_______

RainbowSalt2222 ☔

Answer: 4

Step-by-step explanation:

It crosses on the y axis at the point (0,4)

Answer:

4

Step-by-step explanation:

The y-intercept of the line shown is 4.

Hope this helps :)

Answer: f(-9)

Step-by-step explanation:

A function is described in the form of f(x)

Therefore, if this is how a function is stated we have x as the input.

Here, the x is equal to -9

So now:

f(-9) after substitution.

Answer:

25

Step-by-step explanation:

turn 68% into a decimal (or keep as a percentage, your choice) and divide

17 divided by 0.68 (68% as a decimal) = 25

Hi how u doin ?

[tex] log( \frac{x}{x + 1} ) = \\ [/tex]

[tex] log(x) - log(x + 1) [/tex]

Have a great day ❤

Answer:

x = 29

Step-by-step explanation:

These angles are vertical angles which mean that they're equal to each other:

2x - 24 = x + 5

2x - x = 5 + 24

x = 29

Answer:

24 meters cubed

HOPE THIS HELPS

- Todo ❤️

Step-by-step explanation:

V=Bh

V=6*4

V=24

Answer:

Volume = 24 m³

Units is either cubic meters, m³ or something like that

BTW, am I a pro hacker know?

Step-by-step explanation:

Volume = B x h

Base = B = 6 m²

Height = h = 4 m

Volume = 6 m² * 4 m

Volume = 24 m³

-Chetan K (aka pro hacker)

Answer:

F =672

Step-by-step explanation:

joint variation is of the form

F = k *q1 * q2

Inversly means divide

F = k * q1 * q2

     -------------------

              d^2

We know  F=8 when q1=2, q2=8, and d=4  so we can solve for k

8 = k * 2*8

    -----------------

          4^2

8 = 16k

     ----

     16

8 = k

Substituting

F = 8 * q1 * q2

     -------------------

              d^2

Let q1=28, q2=12, and d=2

F = 8 * 28 * 12

   ----------------

    2^2

F = 2688

      -------

         4

F =672

We are given:

F varies jointly (directly) with q1 and q2, which means that F is proportional to both q1 and q2. also,

F varies inversely with d², so F is inversely proportional to the square to d

Finding a mathemetical experssion:

using the above information, we can say that:

F ∝ q₁

F ∝ q₂

F ∝ 1/(d²)

joining these together, we get:

F ∝ q₁q₂ / d²

let's say that 'k' is the constant of proportionality in this case,

F = k (q₁q₂ / d²)

First case:

F = 8, q₁ = 2, q₂ = 8, d = 4

we can use these values in our expression to find k

[tex]8 = k\frac{2*8}{4^2}[/tex]

[tex]8 = k\frac{16}{16}[/tex]

k = 8

Finding F in the second case:

q₁ = 28, q₂ = 12, d = 2, k = 8

[tex]F = k\frac{q_{1}*q_{2}}{d^2}[/tex]

[tex]F = 8(\frac{28*12}{2^2})[/tex]

[tex]F = 8(\frac{336}{4})[/tex]

[tex]F = 2(336)[/tex]

F = 672 N

Answer:

Option B) 13 is correct

Step-by-step explanation:

0.70 ft

Step-by-step explanation:

The volume V of a cone is given by

[tex]V = \dfrac{\pi}{3}r^2h[/tex]

where r is the radius of the base and h is the height of the cone. Since the radius is half the diameter D, we can rewrite V as

[tex]V = \dfrac{\pi}{3}\left(\dfrac{D}{2}\right)^2h = \dfrac{\pi}{12}D^2h[/tex]

But since the base diameter D is always equal to the cone's height, we can write the volume in terms of the height h as

[tex]V = \dfrac{\pi}{12}h^3[/tex]

Now gravel is being added to the conical pile at a rate of 35 cubic ft per minute so to find the rate at which the height of the pile is increasing, we are going to take the derivative of V with respect to time:

[tex]\dfrac{dV}{dt} = \dfrac{d}{dt}\left(\dfrac{\pi}{12}h^3\right)[/tex]

[tex]\:\:\:\:\:\:\:= \dfrac{\pi}{12}\cdot 3h^2\dfrac{dh}{dt} = \dfrac{\pi}{4}h^2\dfrac{dh}{dt}[/tex]

Rearranging the variables and solving for dh/dt, we get

[tex]\dfrac{dh}{dt} = \dfrac{4}{\pi h^2}\dfrac{dV}{dt}[/tex]

[tex]\:\:\:\:\:\:\:\:= \dfrac{4}{\pi(8\:\text{ft})^2}(35\:\text{ft}^3\text{min})[/tex]

[tex]\:\:\:\:\:\:\:=0.70\:\text{ft/min}[/tex]

Percentage decrease is the amount by which a given number is decreased expressed as a percentage.

Reasons:

The percentage by which the number was decreased = 10%

The number is decreased by 10%

Let x represent the number, we have;

New remainder after first decrease = x -  10% × x = x - 0.1·x = 0.9·x

Decreasing the new number by 10% gives;

Second new number = 0.9·x - 0.09·x = 0.81·x

The percentage by which the number is decreased = x - 0.81·x = 0.19·x

The percentage by which the number is decreased = 19%

Learn more here:

https://brainly.com/question/18569053

Answer:

1

Step-by-step explanation:

2/7+5/7=7/7=1 because 7/7 would be a 1 whole

Answer:

35/7

Step-by-step explanation:

4 = 28/7

28/7 + 2/7 + 5/7 = 35/7

Answer:

what

Step-by-step explanation:

Answer:

Appologies but Why do you have pOn open?

Step-by-step explanation:

umm that is inapropriate but idrc

Answer:

under

Step-by-step explanation:

B D E

Answer:

y = - 1/7x - 7

Step-by-step explanation:

Given equation ,

=> y = -1/7 - 2

On comparing to slope intercept form of the line we get the slope as -1/7

Now as we know that the slope of two parallel lines are same . So the slope of parallel line will be -1/7 .

Using point slope form ,

=> y - 6 = -1/7( x -7)

=> y -6 = -1/7x +1

=> y -7 = -1/7x

=> y = -1/7x -7

Answer:

  x = 6

Step-by-step explanation:

12(x -2) +3x = 1/3(x +12) +10x

12x -24 +3x = 1/3x +4 +10x . . . . . eliminate parentheses

15x = (10 1/3)x +28 . . . . . . . . . . add 24, collect terms

(4 2/3)x = 28 . . . . . . . . . . . . . subtract 10 1/3

x = (3/14)(28) = 6 . . . . . . . . multiply by 1/(4 2/3) = 3/14

The value x=6 satisfies the equation.

Answer:

The volume of a 3-dimensional unit cube is 1 cubic unit, and its total surface area is 6 square units.

Answer:

-15

Step-by-step explanation:

5 * -3 = -15

x = -3

5x = 5(-3)

5(-3) = -15

Answer:

[tex]\displaystyle \int {2 \tan (2x + \pi)} \, dx = - \ln \big| \cos (2x + \pi) \big| + C[/tex]

General Formulas and Concepts:

Calculus

Differentiation

Derivative Property [Multiplied Constant]:                                                           [tex]\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)[/tex]

Derivative Property [Addition/Subtraction]:                                                         [tex]\displaystyle \frac{d}{dx}[f(x) + g(x)] = \frac{d}{dx}[f(x)] + \frac{d}{dx}[g(x)][/tex]

Basic Power Rule:

Integration

Integration Property [Multiplied Constant]:                                                         [tex]\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx[/tex]

U-Substitution

Trigonometric Integration

Step-by-step explanation:

Step 1: Define

Identify.

[tex]\displaystyle \int {2 \tan (2x + \pi)} \, dx[/tex]

Step 2: Integrate Pt. 1

Step 3: Integrate Pt. 2

Identify variables for u-substitution.

Step 4: Integrate Pt. 3

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Integration

Answer:

multiply them by a a number that allows the denominators to be the same

Step-by-step explanation:

example

1/2-1/6

I would multiply 1/2 by 3 to get 3/6 which i could then subtract from 1/6

3/6-1/6 = 2/6

Answer:

it is a b and c

Step-by-step explanation:

Step-by-step explanation: −913−(−113)

=−913−(−113)

=−913+113

=−800

Answer:

[tex](10x - 14) = (7x - 8) \\ \\ 10x - 7x = 14 - 8 \\ \\ 3x = 6 \\ \\ x\frac{6}{3} \\ \\ x = 2[/tex]

it was equal to each other

Step-by-step explanation:

Thereafter,

Distance :-

Time :-

Average Speed :-