Determine the equation of the line given by the graph.
A)y = -2/7x+2/5
B)y = -2/7x+5/2
C)y = -7/2x+2/5
D)y = -7/2x+5/2

Starting from

[tex]f(x)=\dfrac14(x+1)^{\frac83}-4(x+1)^{\frac23}[/tex]

take the first derivative using the power and chain rules:

[tex]f'(x)=\dfrac83\cdot\dfrac14(x+1)^{\frac83-1}-\dfrac23\cdot4(x+1)^{\frac23-1}[/tex]

[tex]f'(x)=\dfrac23(x+1)^{\frac53}-\dfrac83(x+1)^{-\frac13}[/tex]

Now take the second derivative:

[tex]f''(x)=\dfrac53\cdot\dfrac23(x+1)^{\frac53-1}-\left(-\dfrac13\right)\cdot\dfrac83(x+1)^{-\frac13-1}[/tex]

[tex]f''(x)=\boxed{\dfrac{10}9(x+1)^{\frac23}+\dfrac89(x+1)^{-\frac43}}[/tex]

Optionally, you can condense the second derivative a bit by factoring out [tex]\frac89(x+1)^{-\frac43}[/tex], which gives

[tex]f''(x)=\dfrac89 (x+1)^{-\frac43} \left(80(x+1)^{\frac63}+1\right)[/tex]

[tex]f''(x)=\dfrac89 (x+1)^{-\frac43} \left(80(x+1)^2+1\right)[/tex]

[tex]f''(x)=\dfrac89 (x+1)^{-\frac43} \left(80x^2+160x+81\right)[/tex]

The decay of 277 mg of an isotope is described by the function

A(t)= 277e-0.019t,

where t is time in years.

To find the amount left after 64 years,

We substitute t = 64 in the expression.

A(t=64)= 277e-0.019(64)

or A(t=64) = 277 * e-1.216

                = 277 * 0.29

                = 82 mg

Answer:

The measure of the largest angle is 72º.

Step-by-step explanation:

We will first solve for x. We know that the sum of the interior angles of a triangle is 180º, so 15x + 21x + 24x is equal to 180º. This means that 60x = 180º, so x = 3º. The largest angle is 24x, which is 72º.

Answer:

b, d, e

Step-by-step explanation:

Answer:

Table (4)

Step-by-step explanation:

If data in the given tables show the proportional relation then they will follow the rule,

y = kx

k = [tex]\frac{y}{x}[/tex]

where 'k' = proportionality constant

From table (1),

k = [tex]\frac{2}{1}[/tex] = 2

k = [tex]\frac{3}{2}=1.5[/tex]

But 2 ≠ 1.5

So the data in the table (1) is not proportional.

Table (2)

k = [tex]\frac{0}{2}=0[/tex]

k = [tex]\frac{2}{4}=0.5[/tex]

Therefore, data in the table is not proportional.

Table (3)

k = [tex]\frac{1}{0}[/tex] = Not defined

k = [tex]\frac{3}{2}=1.5[/tex]

Data is not proportional.

Table (4)

k = [tex]\frac{y}{x}=\frac{-6}{-2}[/tex]

  = 3

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

3 = 3

Therefore, data given in table (4) represents the proportional relationship.

Answer: it is less then 5

Step-by-step explanation:

Because 10 lies between two consecutive perfect squares (in increasing order) 10 is located between the square roots of these two numbers. This means that 10 is located between 10 is less than 5.

Answer:

less than

Step-by-step explanation:

finding the square root of 10 is a bit complicated because the number 10 is not a perfect square which has a number 0 at it's unit Place. Finding the square root of a number is the reverse process of squaring the number. we can find the square root of 10 using two methods one method is to find the root value using unit places and another method is with the help of long division method.

Answer:

The answer is that it decreased 24f.

Answer:

the next point will be 4, 6

Step-by-step explanation:

if you follow the dots in the line that they make, the next on will be 4, 6

Answer:

I can’t see the picture!

Step-by-step explanation:

Answer:

0.008 meters

Step-by-step explanation:

Answer:

0.008 meters

Step-by-step explanation:

Hope this helps!     :3

plz mark as brainliest!

Answer: pretty sure it's -1,1

M ( 3 , 1 )

Step-by-step explanation:

Answer:

J ( -1 , 1 )

M ( 3 , 1 )

Explanation:

When moving coordinates left = subtract from previous X position

When moving coordinates right = add from previous X position

When moving coordinates up = add from previous Y position

When moving coordinates down = subtract from previous Y position

Answer:

[tex]Average = 2.073[/tex]

Step-by-step explanation:

Given:

Time: 2.15, 2.05, 2.02

Required

Determine the average

Average is calculated as thus:

[tex]Average = \frac{\sum x}{n}[/tex]

In this case:

[tex]\sum x = 2.15+2.05+2.02[/tex]

and

[tex]n = 3[/tex]

[tex]Average = \frac{\sum x}{n}[/tex] becomes

[tex]Average = \frac{2.15+2.05+2.02}{3}[/tex]

[tex]Average = \frac{6.22}{3}[/tex]

[tex]Average = 2.073[/tex]

Answer:

2.07

Step-by-step explanation:

I took the Lab and got it right

the answer for the next two questions are

The average time to the first quarter checkpoint is

2.07

seconds.

The average time to the second quarter checkpoint is

3.16

seconds.

The average time to the third quarter checkpoint is

4.11

seconds.

The average time to the finish line is

4.92

seconds.

Have a good day and good luck with the rest of your school :D

Answer:

x=30

Step-by-step explanation:

Let's solve your equation step-by-step.

35=1.5x−10

Step 1: Flip the equation.

1.5x−10=35

Step 2: Add 10 to both sides.

1.5x−10+10=35+10

1.5x=45

Step 3: Divide both sides by 1.5.

1.5x÷1.5=45÷1.5

x=30

Answer:

[tex]\frac{8}{14} = \frac{14}{x+2}[/tex]  (since they're similar, set them up as a proportion to find x)

14*14 = 8(x+2) (cross multiply, solve the left side, and distribute the right side)

196 = 8x +16 (subtract 16 from both sides)

180 = 8x (divide both sides by 8)

x= 22.5 (is your answer, or C)

Step-by-step explanation:

Answer:

a $2

Step-by-step explanation:

One of the ordered pairs were (1, 2) which meant that at 1 bag of candy, the total cost in dollars is 2 based on the labelling of the x- and y-axis. Thus, the cost of one bag of candy is $2.

Answer:

[tex]p(1) - p(-1) =8[/tex]

Step-by-step explanation:

Given

[tex]p(m) = 4m^3 + 3[/tex]

Required

[tex]p(1) - p(-1)[/tex]

First, we calculate p(1)

Substitute 1 for m in [tex]p(m) = 4m^3 + 3[/tex]

[tex]p(1) = 4(1)^3 + 3[/tex]

[tex]p(1) = 4*1 + 3[/tex]

[tex]p(1) = 4 + 3[/tex]

[tex]p(1) = 7[/tex]

Next, we calculate p(-1)

Substitute -1 for m in [tex]p(m) = 4m^3 + 3[/tex]

[tex]p(-1) = 4(-1)^3 + 3[/tex]

[tex]p(-1) = 4*-1 + 3[/tex]

[tex]p(-1) = -4 + 3[/tex]

[tex]p(-1) = -1[/tex]

[tex]p(1) - p(-1)[/tex] is then calculated as:

[tex]p(1) - p(-1) = 7 - (-1)[/tex]

[tex]p(1) - p(-1) = 7+1[/tex]

[tex]p(1) - p(-1) =8[/tex]

Answer:

[tex]m=3[/tex]

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Step-by-step explanation:

Step 1: Define

Point (-1, 7)

Point (-3, 1)

Step 2: Solve for x

Answer:

80?

Step-by-step explanation:

Answer:

(8+4)x5

Step-by-step explanation:

Answer: 70%

Step-by-step explanation:

2 quarters and 2 dimes is 70 cents. 100 cents total in a dollar so no need for further calculation. 70%

Answer:

-7/5

Step-by-step explanation:

Answer:

Me please

Step-by-step explanation:

I like ice cream :D

Answer:

I do!!! Please may I get it? If someone else asked and you chose them that's fine!

Step-by-step explanation:

(The upcoming and this sentence is pre-written and copy and pasted in every brainly question or comment I write or answer.) If this answer helped you please consider giving it brainliest.

- •Trix•

( Yes I know my - •Trix• thingy is not my user but its what I would change it to if I could but I can't, please address me as Trix while commenting or talking to me here.)

Answer:

13

Step-by-step explanation:

Answer:

running a two year contract is the best i have to do with my life in this world and it has a great way to go through the

Answer:

The 2nd one

Step-by-step explanation:

Answer:

10...............................

Answer:

2.54 x 6.3 = 16.00200

Step-by-step explanation:

hope this helped!

Answer:

i think the product (multiplication) of 2.54 and 6.3 is 16.002

Answer: D= 0.72

Step-by-step explanation: Because 0.18 times 4 is 0.72 miles.

Answer:

D. 0.72 miles

Step-by-step explanation:

Since David swam 4 times as far is Yvonne, he swam 4 times more than 0.18.  0.18 times 4 is 0.72.  If you want/need to do it in your head, just imagine 0.18 as 18, and that multiplied by 4 is 72.  then move the decimal point back over before the 7, to get your answer.  

Two of the other choices are clearly wrong because the actual answer is way less than the other choices (except for B).  One way to quickly figure out which two (or sometimes three) are wrong is by rounding 0.18 up to 0.2.  You can try this quickly because 0.2 is barely bigger than 0.18, and 0.2 is easy to multiply by 4.  The answer you would get from multiplying 0.2 is not exactly correct, but gives you a general idea.