Two numbers are graphed on the line below. Consider the inequality t

The rate of change of the area of the trapezoid at that instant is 5 square kilometers per second and this can be determined by differentiating the area of the trapezoid with respect to time 't'.

Given :

First, determine the area of a trapezoid, that is:

[tex]\rm A = \dfrac{b_1+b_2}{2}\times h[/tex]

[tex]\rm \dfrac{2A}{h}=b_1+b_2[/tex]

[tex]\rm b_2 = \dfrac{2A}{h}-b_1[/tex]

Now, differentiate the above expression with respect to 't'.

[tex]\rm \dfrac{db_2}{dt} = -\dfrac{2A}{h^2}\dfrac{dh}{dt}-\dfrac{db_1}{dt}[/tex]

Now. substitute the values of the known terms in the above formula.

[tex]\rm \dfrac{db_2}{dt} = -\dfrac{2\times (16)}{2^2}\times (5)-(-8)[/tex]

[tex]\rm \dfrac{db_2}{dt} = -32\;km/sec[/tex]

So, the area is decreasing at the rate of 5.

For more information, refer to the link given below:

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Answer:

$3,715.30

Step-by-step explanation:

Total P+I (A): $3,715.30

Principal (P): $2,000

Compound (n): Continuously

Time (t in years): 15 years

By plugging this into an interest rate calculator, the amount settles to be approximently $3,715.30

Hope this helps!

Answer:

$15500

Step-by-step explanation:

10^3 x 12 = 12,000

10^2 x 35 = 3,500

12,000 + 3,500 = 15,500

Answer:

$32.10

Step-by-step explanation:

do 5.35 but six times and then add that all up then it will be 32.10

Answer:

C

Step-by-step explanation:

its c because 5.35 times 6 is C

Answer:

Step-by-step explanation:

[tex](a^{m})^{n} = a^{m*n}\\\\\frac{a^{m}}{a^{n}}=a^{m-n}\\\\\\\frac{w^{30}}{(w^{3})^{2}} = \frac{w^{30}}{w^{3*2}}[/tex]

        [tex]= \frac{w^{30}}{w^{6}}\\\\=w^{30-6}\\\\= w^{24}[/tex]

Answer:

w^24

You would simplify the expression by first finding the product of (w^3)^2 which is w^6. Next you would divide w^30 and w^6 which would get you your answer which is w^24. Hope this helps!

im just answering for free points

Step-by-step explanation:

Answer:

x=2

Step-by-step explanation:

-5=-3x+1

-1         -1

-6=-3x

divide both sides by -3

x=2

The value of x when f(x) = - 5, In the function f(x) = - 3x + 1 is 2.

A function can be defined as the outputs for a given set of inputs.

The inputs of a function are known as the independent variable and the outputs of a function are known as the dependent variable.

Given, A function f(x) = - 3x + 1.

Now, when f(x) = - 5 the equation would be,

- 5 = - 3x + 1.

- 5 - 1 = - 3x.

- 6 = - 3x.

3x = 6.

x = 2.

learn more about functions here :

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#SPJ2

Answer:

hey can you give us the buying price of the ticket so we can find the increase? thanks :)

Step-by-step explanation:

Answer:

14 + 3x

Step-by-step explanation:

6x2= 12

12 + 3x + 2

=14 + 3x

Answer:

y =-6(x-1/4)^2+19/8

Step-by-step explanation:

I hope this helps I don't have an explanation I just got it right on EDG 2021

God Bless You!!!!!

Answer:

1) $283.50

2) 65.21 meters.

Step-by-step explanation:

Part 1)

We know that a spool of ribbon holds 6.75 meters.

A craft club buys 21 spools.

So, the total length of ribbon bought is:

[tex]T=21(6.75)=141.75\text{ meters}[/tex]

Each meter costs $2. So, the total cost will be:

[tex]141.75(2)=\$ 283.50[/tex]

Part 2)

A spool holds 6.75 meters.

We bought 21 of them, so that total length we have is 141.75 meters.

The club used 76.54 meters.

So, the amount of ribbon that is left is represented by:

[tex]141.75-76.54[/tex]

Subtract:

[tex]=65.21\text{ meters}[/tex]

So, 65.21 meters of ribbon will be left.

Answer:

1. $283.5

2. 11

Step-by-step explanation:

1. 6.75*21 = 141.75

                = 141.75 * 2

                = 283.5

Answer:

2 solutions cuz

2 variable are there

Answer:

9x9x9 because if you multiply themyou get 729

Step-by-step explanation:

Answer:

Yes this represents additive inverse,

Step-by-step explanation:

Since you are subtracting the same number 4 to get to zero.

Answer:

Jeremy has 5 1/4 cups of all purpose flour after preparing his recipe.

Step-by-step explanation:

Since the recipe for whole wheat pizza crust calls for 1 1/2 cups of all purpose flour, 1.5 cups of that product is required to create the meal in question.

Now, since Jeremy has 5 7/4 of all purpose flour, it can be stated that he has 6.75 cups of it (7/4 = 1.75).

Therefore, to determine the amount of flour that Jeremy will have left over after preparing the recipe, it is necessary to perform the following calculation:

6.75 - 1.5 = X

5.25 = X

So since 0.25 is equal to 1/4, Jeremy has 5 1/4 cups of all purpose flour after preparing his recipe.

Answer:

Revenue: $46

Profit: $6

Answer:

$6.82 per foot

Step-by-step explanation:

To find the unit rate, divide.

150 / 22 ≈ 6.82

Best of Luck!

Answer:

it is -2

Step-by-step explanation:

because 13-2=11-2=9-2=7-2=5-2=3-2=1

Answer:

500 boxes an hour?

Step-by-step explanation:

Answer:

The machine can pack 500 boxes in one hour

You can add +500 in case for more hours

Step-by-step explanation:

2,500 divided by 5 is 500.

Answer:

m  (parallel)  = 3 /4

Step-by-step explanation:

on the graph Y will start on two

Answer:

three boys to 1 girl

Step-by-step explanation:

a

By direct evaluation, we will see that the pair (8,2) is not a solution of the system of equations.

A given point is a solution of a system of equations if and only if it is a solution for both equations, then to see if (8, 2) is a solution of the given system, we need to replace the values in both equations and see if it is a solution of each one.

For the first one we have:

x - y = 6

8 - 2 = 6

6 = 6

So (8, 2) is a solution of the first equation.

For the second one we have:

2x - 10y = 4

2*8 - 10*2 = 4

16 - 20 = 4

-4 = 4

Note that this equation is false, then the point (8, 2) is not a solution for the second equation, then the point is not a solution for the system of equations.

If you want to learn more about systems of equations, you can read:

https://brainly.com/question/14323743

Answer: Quadrant IV

Step-by-step explanation: Pic attached.

I found the x and y using substitution (isolating one variable and plugging it into the other). There was probably an easier way but I couldn't think of it at that moment.

From there, you have the point ( 133/36 , -23/18), or a (+, -).

Find Which quadrant has positive x and negative y.

In this case, this would be Quadrant IV or 4.

Hope this helps! Sorry if too complicated lol.

Answer:

C

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

5t-3=3t+9

5t-3-3t=3t+9-3t

2t-3=9

2t-3+3=9+3

2t=12

2t/2 =12/2

t=6

Answer:

The distance between the two points is six units.

Step-by-step explanation:

We are given two coordinate pairs:

With these, we can find the distance between the two using the distance formula. The distance formula is:

[tex]\displaystyle d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}, \ \text{where d is the distance.}[/tex]

Additionally, we need to label our coordinates. In math, coordinates are labeled as (x₁, y₁) and (x₂, y₂).

Therefore, our coordinate pairs can be labeled in this format.

(-8, 4)

(-8, -2)

Now, we can substitute these values into the formula and solve for d.

[tex]\displaystyle d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\\\d = \sqrt{(-8 - -8)^2 + (-2 - 4)^2}\\\\d = \sqrt{(0)^2+(-6)^2}\\\\d = \sqrt{0 + 36}\\\\d = \sqrt{36}\\\\d = 6[/tex]

Therefore, the distance between the two points is six units.

Answer:

7,9

Step-by-step explanation:

Let two consecutive odd integer=X and (X+1)

The difference of the squares of two positive consecutive odd integers is 32.

So(X+2)^2-x^2=32

(x^2+4+4x)-x^2=32

x^2+4+4x-x^2=32

4x=32-4

4x=28

X=28/4

X=7

So first integer=7

Second integer=7+2

=9.

Answer:

The right response is "0.0085". A further explanation is given below.

Step-by-step explanation:

Let,

P (across each pair, this same null hypothesis would be wrongly rejected) be "a".

Therefore,

⇒ [tex]P=1-P(no \ time \ rejected)[/tex]

⇒ [tex]1-(1-a)^6 =0.05[/tex]

⇒ [tex]1-a=0.95^{(\frac{1}{6} )}[/tex]

⇒ [tex]a=1-0.95^{(\frac{1}{6} )}[/tex]

⇒ [tex]0.0085[/tex]

Answer:

a= 10/3

Step-by-step explanation:

multiply both sides by 2

get 6a +8 =28

subtract 8 from both sides

you get 6a=20

divide 6 both sides and 10/3.