Find the area of a regular

polygon with 8 sides that has a

the side length of 4 inches and an

apothem of 5 inches.


Area = [?]in2

Answer:

D) [tex]22\:\text{m/s}^2[/tex]

Step-by-step explanation:

Acceleration is the derivative of velocity, which is the derivative of position, so we must differentiate the function twice:

Position of Particle: [tex]s(t)=t^3-4t^2+2t+8[/tex]

Velocity of Particle: [tex]v(t)=3t^2-8t+2[/tex]

Acceleration of Particle: [tex]a(t)=6t-8[/tex]

After [tex]t=5[/tex] seconds, the acceleration of the particle is [tex]a(5)=6(5)-8=30-8=22\:\text{m/s}^2[/tex]

The acceleration of the particle after 5 seconds is 38 m/s².

Acceleration is the rate of change of velocity or the slope of velocity.

We know that the first derivative of motion or speed is velocity and the second derivative of motion or speed is acceleration.

∴ We have to take the derivative of s = t³ + 4t² + 2t + 8 twice to obtain the equation of acceleration and replace t with 5 to get the acceleration value after 5 seconds.

Now, s = t³ + 4t² + 2t + 8 meters.

ds/dt = 3t² + 8t + 2 m/s.

d²s/dt² = 6t + 8m/s²

Now, at t = 5 seconds d²s/dt² = 6t + 8 is,

d²s/dt² = 6(5) + 8 m/s².

d²s/dt² = 38 m/s².

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Answer:

you're right

Step-by-step explanation:

the answer is false because side AD and sides AE are not the same length, so AB/BD does not equal AC/CE

The length and width of the piece of​ metal are 20 and 30 inches respectively.

The term “volume” refers to the amount of three-dimensional space taken up by an item or a closed surface. It is denoted by V and its SI unit is in cubic cm.

Dimension of the rectangle;

Width(w)

Length,L= 10 + w

volume of the box = length  * width * height

Dimension of the box;

length of box, (x + 10) - 4  = x + 6

width of box,(x - 4)

height of box =  2

The volume of the box is 1102 in³;

⇒V=lwh

⇒V=2 (x -4)( x + 6) =

⇒1102 in³ = 2x² + 4x - 48

⇒2x² + 4x - 880 = 0

⇒x  + 2x - 440 = 0

⇒(x + 22)(x - 20) = 0

⇒x = 20

⇒x=-22 (value of the dimesion will not be negative.

The width of an original piece of metal is;

Width,w=20 inches

length,l= 30 inches

Hence. the length and width of the piece of​ metal are 20 and 30 inches respectively.

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Answer:

Step-by-step explanation:

If x = 3

then

5x² = 5×(3)² = 5 × 9 = 45

and 45 > 40

Therefore

3 is not a solution to the inequality 5x² < 40.

Hi Student!

This question is fairly simply and the main goal of this question is to determine whether x = 3 is a solution of the expression that was provided or not.  The first step that we take is to plug in all of the values or in this case we input the value 3 for everywhere we see x in the equation.  The next step is to simplify the expression on both sides and finally compare the expression to see if it evaluates to true.  If it evaluates to true then x = 3 is a solution but if it evaluates to false then x = 3 isn't a solution.

Plug in the values

Simplify the expression

Looking at the final expression that was simplified, we can see that it states that 45 is less than 40 when we know that is not the case.  Therefore, this would evaluate to the expression being false and x = 3 not being a solution of the expression that was given in the problem statement.

Answer:

[tex]\frac{1}{13}[/tex]

Step-by-step explanation:

The total number of cards in a standard deck of cards is 52, in which there:

King: 4 cards <----------

Queens: 4 cards

Jack: 4 cards

Ace: 4 cards

Club/Diamond/Heart/Spade: 13 cards

Moreover, 26 of the 52 cards are red, and the remainder 26 are of black.

So the probability that a "king" card will be picked is [tex]\frac{4}{52}[/tex], which can be further simplified [tex]\frac{1}{13}[/tex]

Answer: x-axis

Explanation:

Hope that helps!

The region [tex]D[/tex] is essentially parameterized in three dimensions by

[tex]\Phi(u,v) = (u^2, u+v, 0)[/tex]

with [tex]1\le u\le8[/tex] and [tex]0\le v\le6[/tex].

The normal vector to [tex]D[/tex] is

[tex]\vec n = \dfrac{\partial\Phi}{\partial u} \times \dfrac{\partial\Phi}{\partial v} = (0,0,2u)[/tex]

with norm [tex]\|\vec n\| = 2u[/tex].

Then the surface integral is

[tex]\displaystyle \iint_D y \, dA = 2 \int_0^6 \int_1^8 (u+v)u \, du \, dv \\\\ = 2 \int_0^6 \left(\frac{1022}3 + 63 v\right) \, dv = \boxed{3178}[/tex]

Answer:

[tex]log_2(10)[/tex]

Simplify the equation using logarithms.

[tex]2^3x=10[/tex]

[tex]log_1_0(2^3x)=log_1_0(10)[/tex]

log rule ⇩

[tex]log_a(x^y)=y*log_a(x)[/tex]

move exponent out of log.

[tex]x*log_1_0(2)=log_1_0(10)[/tex]

isolate variable further

[tex]x*log_1_0(2)=log_1_0(10)[/tex]

[tex]x=\frac{log_{10}(10)}{log_{10}(2)}[/tex]

formula for combining logs. ⇩

[tex]\frac {log_b(x)}{log_b(a)}=log_a(x)[/tex]

the result ⇩

[tex]x=log_2(10)[/tex]

7-digit:9999999

9-digit: 1000000

Answer:

  68 texts per day

Step-by-step explanation:

The description of the variables in the equation tells you that you want to find t (texts sent per day) for the given value of 'a' (age in years).

__

Substitute the number (15) for the variable (a) and do the arithmetic:

  t = -1.63a +92.14

  t = -1.63(15) +92.14 = -24.45 +92.14

  t = 67.69

Keiko's trend line estimates a 15-year-old would send about 68 texts per day.

Resolviendo un sistema de ecuaciones veremos que se vendieron 900 boletos de $15 y 3600 boletos de $10.

Primero definamos las variables:

Sabemos que se vendieron 4500 boletos, entonces:

x + y = 4500

Y se recaudo un total de $49,500, entonces:

x*$10 + y*$15 = $49,500

Entonces tenemos un sistema de ecuaciones:

Para resolver esto, primero debemos aislar una de las variables en la primer ecuación, voy a aislar x:

x = 4500 - y

Ahora reemplazamos esto en la otra ecuación:

(4,500 - y)*$10 + y*$15 = $49,500

Ahora debemos resolver estoy para y.

$45,000 - y*$10 + y*$15 = $49,500

y*$5 = $49,500 - $45,000 = $4,500

y = ( $4,500)/$5 = 900

Entonces:

x = 4500 - 900 = 3600

Se vendieron 900 boletos de $15 y 3600 boletos de $10.

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[tex](\stackrel{x_1}{0}~,~\stackrel{y_1}{1})\qquad (\stackrel{x_2}{1}~,~\stackrel{y_2}{-2}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-2}-\stackrel{y1}{1}}}{\underset{run} {\underset{x_2}{1}-\underset{x_1}{0}}} \implies \cfrac{-2 -1}{1 +0} \implies \cfrac{ -3 }{ 1 }\implies -3[/tex]

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{1}=\stackrel{m}{-3}(x-\stackrel{x_1}{0}) \\\\\\ y-1=-3x\implies y=-3x+1[/tex]

Answer:

Calculator soup can help just search for whatever your learning and add a calculator at the end

Considering it's volume of 113 cm³, the approximate radius of the sphere is given by:

A. 3 cm

The volume of an sphere of radius r is given by:

[tex]V = \frac{4\pi r^3}{3}[/tex]

In this problem, we have that V = 113 cm³, hence the radius in cm is given as follows:

[tex]V = \frac{4\pi r^3}{3}[/tex]

[tex]113 = \frac{4\pi r^3}{3}[/tex]

[tex]r^3 = \frac{113 \times 3}{4\pi}[/tex]

[tex]r = \sqrt[3]{\frac{113 \times 3}{4\pi}}[/tex]

r = 3 cm.

Hence option A is correct.

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Answer:

is 3 cm

Step-by-step explanation:

Answer:

Step-by-step explanation:

Formula:

Let b be the base (circle) of the cone

and h be the height of the cone

[tex]\text{volume of the cone} =\frac{1}{3} \times b\times h[/tex]

……………………………………………

→ b = π × r²

  = π × 6²

  = (22÷7) × 36

  = 113.142857142857 cm²

→ h = 7

[tex]\text{volume of the cone} =\frac{1}{3} \times b\times h[/tex]

The volume = (1÷3)×(113,142857142857)×(7)

                    = 264 cm³

===================

 METHOD 2 :

Volume = (1÷3)×(22÷7)×36×7

             = (1÷3)×22×36

             = 22×12

             = 264

Answer:

IUOIUJUIYIYIYUYUYUYIYUYUY

Since diagonals bisect each other, both halves of a diagonal have the  same length.

[tex]5y-5=y+23\\4y=28\\y=7\\\\2x-0=x+2\\x=2[/tex]

Therefore b)

Answer:

Decimal = 0.05

Percentage = 5%

Explanation:

Total count : 20

Sarah count : 1

probability = favorable outcomes/total outcomes

                   =     1/20

                   =     0.05

Answer:

d

Step-by-step explanation:

Answer:

A=l*w

Step-by-step explanation:

so We Derive Their Formula

L=A/w

Answer:

0.1235

Step-by-step explanation:

I'm not exactly sure what you mean, but I'm guessing that it's how much is needed to get 10 as the whole number. In that case, you just do 10-9.8765 to get 0.1235. So, 9.8765+0.1235=10. Hope this helped!

The inequalities are; 5¹/₄ tons = 10500 pounds; 1/2 ton + 3/4 ton > 2800 pounds; 2 tons > 60000 pounces; 1¹/₄tons > 20000 ounces

1) 5¹/₄ tons when converted to pounds is 10500 pounds.

Thus; 5¹/₄ tons = 10500 pounds.

2) 1/2 ton + 3/4 ton = 5/4 tons

Converting 1.25 to tons gives 2500 tons. Thus;

1/2 ton + 3/4 ton > 2800 pounds

3) Converting 2 tons to Ounces gives 64000 ounces. Thus;

2 tons > 60000 pounces.

4) 1¹/₄tons - ¹/₂ton = ³/₄ tons

Converting to ounces gives 24000 ounces

Thus; 1¹/₄tons > 20000 ounces

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Answer: The save $1134.48

Step-by-step explanation:

3912 x 0.29 = 1134.48

The amount of money that the family saves in a month will be $1,017.12.

The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates to one hundred percent. It is symbolized by the character '%'.

The percentage is given as,

Percentage (P) = [Final value - Initial value] / Initial value x 100

The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.

A family has a month-to-month payment of $3912. Their month-to-month uses are displayed in the diagram underneath.

Rent 21%

Food 24%

Transportation 11%

Other Expenses 18%

Savings 26%

Then the amount of money that the family saves in a month is calculated as,

⇒ $3,912 x 0.26

⇒ $1,017.12

The amount of money that the family saves in a month will be $1,017.12.

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Answer:

b

Step-by-step explanation:

answer is b

Answer: g(x)

Step-by-step explanation:

Answer:

There were 67 coins in the bag, 36 of which were 50-cent coins and 31 of which were 20-cent coins.

Let x be the number of 50-cent coins in the bag,

And y be the number of 20-cent coins.

From the problem,

we know that y = x - 5,

Since there were 5 fewer 20-cent coins than 50-cent coins.

We can also set up an equation for the total value of the coins in the bag,

⇒ 0.5x + 0.2y = 24.20

Now we can substitute y = x - 5 into the equation,

⇒ 0.5x + 0.2(x - 5) = 24.20

Simplifying, we get,

⇒ 0.7x - 1 = 24.20

⇒ 0.7x = 25.20

⇒ x = 36

So there were 36 50-cent coins in the bag.

Using y = x - 5,

We can find that there were 31 20-cent coins.

Therefore, there were a total of 67 coins in the bag (36 + 31 = 67).

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Since, Maxwell wants to know how much space his globes occupies he has to find its volume.

Volume is the amount of space an object or substance occupies.

Every three dimensional object occupies a space.

Volume is measured in cubic units.

Therefore, the three dimensional object that has a width, length and height will have its volume as follows;

volume = lwh

where

Therefore, the space occupied by the globe is the volume of the globe.

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