2. What is the distance between points A and B?

A. -6 units
B. -1 unit
C. 5 units
D. 6 units

When we have a given function f(x), the rate of change in a given value x₀ is given by:

[tex]\frac{df(x_0)}{dx} = \lim_{h \to 0} \frac{f(x_0 + h) - f(x_0)}{h}[/tex]

We will find that the rate of change at t = 4s is:

r = -1/3

Now we can't do this if we do not have the function and we only have a text description of the graph, but what we can do is find the average rate of change.

For a function f(x), the average rate of change in an interval (a, b) such that a < b is given by:

[tex]r = \frac{f(b) - f(a)}{b - a}[/tex]

Something really nice is that the average rate of change is equal to the exact rate of change if f(x) is a linear equation.

If we want to find the rate of change at t = 4, then we need to find the smallest interval that contains t = 4.

Here we know that the graph passes through the points:

(3,1) to (6, 0)

Because of the statement "a line falling from (3, 1) to (6, 0)" we know that in this segment we have a line, which implies that the average rate of change will be equal to the exact rate of change.

Using the equation of the average rate of change we get:

[tex]r = \frac{d(6) - d(3)}{6 - 3} = \frac{0 - 1}{3} = - 1/3[/tex]

Then the rate of change in the distance at the time t = 4s is -1/3.

If you want to learn more, you can read:

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Answer: -6

Step-by-step explanation:

-18 - (-12)

= -6

none of them

it's actually-6.

Answer:

use the formula sn= n(a1+an)/2

Step-by-step explanation:

2982=28(228+an)/2

5964=28(228+an)

5964/28=228+an

213=228+an

an=-15(last term)

to find difference use formula

an = a+(n-1)d

-15=228+(28-1)d

-243=27d

d=-243/27

d=-9

arithmetic sequence  can be found be keep on subtracting 9 from 228

hence the arithmetic sequence is

228, 219, 210, 201, 192, 183, 174........-15

Answer:

54

Step-by-step explanation:

6x5=30

3x8=24

30+24=54

Answer:

(3,15)

Step-by-step explanation:

Rule 1

5x = y

Rule 2

x+12 = y

Set them equal

5x = x+12

Subtract x from each side

5x-x = x+12-x

4x= 12

Divide by 4

4x/4 = 12/4

x=3

5x=y

5*3 = y

15 = y

The solution is (3,15)

Given rules

Equate and solve

Opt ion B is correct as no other contains 3 as x

Step-by-step explanation:

find the area of the big semicircle and the small semicircle.minus the area of the small semicircle from the big semicircle.

now find the area of the other semicircle on top of the big semicircle.

add your results

area of semicircle=1/2(pir^2)

Answer:

False

Step-by-step explanation:

63 x 42= 2646

216 x 16= 3456

have a great day

Answer:

12:14

Step-by-step explanation:

Answer:

Try 0.17? I hope it's right

Answer:

2 10/15 or 2 2/3 (simplified)

Step-by-step explanation:

To Multiply we need to get the same denominator for each fraction:

2 x 5 =10

3 x 5 =15

10/15

4/15 x 10/15 (or) 4 x 10 = 40/15

40/15 (also) = 2 10/15

2 2/3 (simplified version of 2 10/15)

Hope This Helps! :)

Answer:

So for the sequence to work, the 5,3=18 would have to be changed to 5,3=23 in which it now fits and works to solve for x which is 4. There was a pattern of the numbers 4 and 5 that surfaced as the difference between each pairings sum total. The difference between each sum was alternating between the numbers 4 and 5, which equal 9 when added together. Which also helped me to form a chart of sorts that makes sense. My answer is typed above, that is the most stable conclusion that I could come to to make sense of the pairings that were listed.

Answer: A (if i have well corrected)

Step-by-step explanation:

[tex]f(x)=(x-6)(x^2+8x+16)\ i\ suppose)\\\\f(x)=(x-6)(x+4)^2\\Sol=\{6;-4\}\\Answer \ A[/tex]

Answer:

c

Step-by-step explanation:

The expression that gives my weight one year later is (180 pounds - x pounds). Hence the subtraction action that gives weight one year later.

Given that;

On my last birthday, I weighed 180 pounds.

And, One year later my weight decreased by x pounds.

Now the equation to represent the weighed after one year,

180 pounds - x pounds

Hence we can use the subtraction action that gives weight one year later.

Therefore, the correct option is C.

To learn more about subtraction visit:

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#SPJ3

Answer:

min | miles

———|———

1 | 3

2 | 6

3 | 9

4 | 12

5 | 15

6 | 18

Step-by-step explanation:

try putting this into a T-chart like I kind of did here or some other kind of other table.

Answer:

False

Brainliest, please!

Step-by-step explanation:

+ + = +

- - = +

+ - = -

- + = -

Answer:

False

Step-by-step explanation:

The question doesn't specify whether you are adding positive or negative integers. If you have add 2 positive integers, your answer will be positive. If you add 2 negative integers, the answer will be negative. Here is an example;

1 + 1 = 2

-1 + (-1) = -1 - 1 = -2

Best of Luck!

Answer:

[tex]y=\frac{1}{3} x+6[/tex]

Step-by-step explanation:

[tex](3,7)(-6,4)[/tex]

Step 1. Find the slope (by using the slope-formula)

m = slope

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

[tex]m=\frac{4-7}{-6-3}[/tex]

[tex]m=\frac{-3}{-9}[/tex]

[tex]m=\frac{3}{9}[/tex]

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

Step 2. Write the equation (using the slope and the points)

Here's how to do it:

Slope-intercept Formula [tex]y=mx+b[/tex] whrere m = slope and b = y-intercept

Plug in the slope into the Slope-intercept Formula

[tex]y=\frac{1}{3} x+b[/tex]

Find the y-intercept (b) by using a point and substituting their x and y values

[tex]y=\frac{1}{3} x+b[/tex]

Point: (3, 7)

[tex]7=\frac{1}{3} (3)+b[/tex]

[tex]7=1+b[/tex]

[tex]b=7-1[/tex]

[tex]b=6[/tex]

Step 3. Write the equation in Slope-intercept form

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

[tex]y=\frac{1}{3} x+6[/tex]

Answer:

a = 9

Step-by-step explanation:

7a = 63

Divide 7 on both sides,

=> 7a/7 = 63/7

=> a = 9

Answer:

3. Jaxson added the denominators instead of finding a common denominator and leaving it alone

Step-by-step explanation:

8 3/5 + 7 1/8 = 15 4/3

Get a common denominator

8 3/5 *8/8  + 7 1/8 *5/5

8 24/40 + 7 5/40

15 29/40

Answer:

Whenever the denom is 0, that's where it's undefined -- or in your case "restrictions"

So factoring 2x^2 + x - 21 gets you (x-3)(2x+7). That means 3 and -7/2 are the restricted values.

To simplify, I'm going to factor it. (Assuming what you wrote is 8x^2 for the numerator)

[(4x-7)(2x+7)] / (x-3)(2x+7)

You can cancel 2x+7 out,

so you get 4x-7/x-3

Perimeter = the sum of all the sides. In this case, we know the ratio but not what each would be multiplied by, hence the variable.

6x + 8x + 10x = 96

24x = 96

x = 4

6(4) = 24

8(4) = 32

10(4) = 40

Check:

24 + 32 + 40 = 96 cm

Area = (base * height) / 2

Base = 32

Height = 24

(The base and height are interchangeable here, as we just have to make sure we're multiplying the legs of the triangle together and avoiding the hypotenuse.)

(32 * 24) / 2

768 / 2

384

Area = 384 cm^2

Hope this helps!

Answer:

256

Step-by-step explanation:

4⁴

= 4 × 4 × 4 × 4

= 16 × 16

= 256

Answer:

Only Option III, IV, VI are correct

Step-by-step explanation:

Domain is the set of values of x at which the function is defined. f(x) has defined values from x>-3 to x<=4, so the domain is (-3,4). Incorrect.

Range of the function is the set of all defined values of it. Here all values with y=f(x)>-3 and y<=3 are defined. So the range is (-3, 3}.

Decreasing and increasing parts of the funtion are shown in the graph when the y value goes up (positive slope) and vice versa.

The negative part of the function should be (3,-2) and (2,4] since (4, 5] is not defined and there is no indication for its negative-ness.

Answer:

[tex] \frac{dy}{dx} = - \frac{ {x}^{3} }{ {y}^{3} } [/tex]

Step-by-step explanation:

Differentiate both sides of the equation (consider y as a function of x).

[tex] \frac{d}{dx} ( {x}^{4} + {y}^{4} (x)) = \frac{d}{dx} (16)[/tex]

the derivative of a sum/difference is the sum/difference of derivatives.

[tex]( \frac{d}{dx} ( {x}^{4} + {y}^{4} (x))[/tex]

[tex] = ( \frac{d}{dx} ( {x}^{4} ) + \frac{d}{dx} ( {y}^{4} (x)))[/tex]

the function of y^4(x) is the composition of f(g(x)) of the two functions.

the chain rule:

[tex] \frac{d}{dx} (f(g(x))) = \frac{d}{du} (f(u)) \frac{d}{dx} (g(x))[/tex]

[tex] = ( \frac{d}{du} ( {u}^{4} ) \frac{d}{dx} (y(x))) + \frac{d}{dx} ( {x}^{4} )[/tex]

apply the power rule:

[tex](4 {u}^{3} ) \frac{d}{dx} (y(x)) + \frac{d}{dx} ( {x}^{4} )[/tex]

return to the old variable:

[tex]4(y(x) {)}^{3} \frac{d}{dx} (y(x)) + \frac{d}{dx} ( {x}^{4} )[/tex]

apply the power rule once again:

[tex]4 {y}^{3} (x) \frac{d}{dx} (y(x)) + (4 {x}^{3} )[/tex]

simplify:

[tex]4 {x}^{3} + 4 {y}^{3} (x) \frac{d}{dx} (y(x))[/tex]

[tex] = 4( {x}^{3} + {y}^{3} (x) \frac{d}{dx} (y(x)))[/tex]

[tex] = \frac{d}{dx} ( {x}^{4} + {y}^{4} ))[/tex]

[tex] = 4( {x}^{3} + {y}^{3} (x) \frac{d}{dx}(y(x))) [/tex]

differentiate the equation:

[tex]( \frac{d}{dx} (16)) = (0)[/tex]

[tex] = \frac{d}{dx} (16) = 0[/tex]

derivative:

[tex]4 {x}^{3} + 4 {y}^{3} \frac{dy}{dx} = 0[/tex]

[tex] \frac{dy}{dx} = - \frac{ {x}^{3} }{ {y}^{3} } [/tex]

Answer:

They can all be simplified to 2/3

Answer:

Step-by-step explanation:

[tex]f(x,y)=arctan(xy)\\\\\dfrac{ \partial f}{ \partial x}=\dfrac{y}{1+x^2y^2} \\\\\dfrac{ \partial f}{ \partial y}=\dfrac{x}{1+x^2y^2} \\\\\dfrac{ \partial ^2 f}{ \partial x^2}=\dfrac{-2xy^3}{(1+x^2y^2)^2} \\\\\dfrac{ \partial ^2 f}{ \partial y^2}=\dfrac{-2x^3y}{(1+x^2y^2)^2} \\\\\dfrac{ \partial ^2 f}{ \partial x\ \partial y}=\dfrac{1-x^2y^2}{(1+x^2y^2)^2} \\[/tex]

[tex]f(x,y)= f(1,1)+(x-1)\dfrac{\partial f}{\partial x} (1,1)+(y-1)\dfrac{\partial f}{\partial y} (1,1)+\dfrac{(x-1)^2}{2} \dfrac{\partial^2 f}{\partial x^2} (1,1)+(x-1)(y-1)\dfrac{\partial^2 f}{\partial x\ \partial y} (1,1)+\dfrac{(y-1)^2}{2} \dfrac{\partial^2 f}{\partial y^2} (1,1)+...\\\\=\dfrac{\pi}{4}+\dfrac{(x-1)}{2} +\dfrac{(y-1)}{2} -\dfrac{(x-1)^2}{4} +(x-1)(y-1)*\dfrac{0}{4}-\dfrac{(y-1)^2}{4} \\\\[/tex]

[tex]\boxed{f(x,y)=\dfrac{\pi}{4}+\dfrac{(x-1)}{2} +\dfrac{(y-1)}{2} -\dfrac{(x-1)^2}{4} -\dfrac{(y-1)^2}{4} }\\\\[/tex]

Answer:

3²×5

Step-by-step explanation:

Product of its prime numbers its more like having the number in its simplest form by factorising it

Answer:

1/8

Step-by-step explanation:

There is a 1/2 probability for each of the three flips to result in the desired outcome. To get 3 desired outcomes in a row, we multiply each of the probabilities together

(1/2)³ = 1/8

Answer: it is D) 2/3