A rectangular prism is shown below. What is the lateral surface area?

Answer:

28.137 sq. units.

Step-by-step explanation:

Area of a regular hexagon is

\(A=\dfrac{3\sqrt{3}}{2}a^2\)

where, a is the side length.

It is given that the side length of the regular hexagon is \(1.9\sqrt{3}\).

Substitute \(a=1.9\sqrt{3}\) in the above formula.

\(A=\dfrac{3\sqrt{3}}{2}(1.9\sqrt{3})^2\)

\(A=(1.5\sqrt{3})(10.83)\)

\(A=16.245\sqrt{3}\)

\(A=28.137\)

Therefore, the area of regular hexagon is 28.137 sq. units.

Answer:

y = -2/3x + 20

Step-by-step explanation:

Two things we notice about the graph :

According to the options, feature 1 is incorrect in options 1 and 4, and feature 2 is incorrect in option 3.

Hence, the correct option is :

y = -2/3x + 20

Answer:

all of the abpve

Step-by-step explanation:

Answer:y=mx+b

Step-by-step explanation:

Answer: 8

Step-by-step explanation: Speed is distance/time

18/3 = 6 miles per hour running

18/2 = 9 miles per hour biking

3 hour bike = 27 miles

1.50 hour run (0.50 because 30 minutes is half of an hour) = 9 miles

27 + 9/3 + 1.50 = 36/4.5 or 8

Answer:

501.57g  

Step-by-step explanation:

g=1.06×473.176

Answer: probably c

Step-by-step explanation:

i divided it and got 401.063963

Answer:

C.

Step-by-step explanation:

trust -.-

Answer:

y=-5x+4

Step-by-step explanation:

y=mx+b is slope-intercept form.

Plug in -5 for m and 4 for b.

The equation we're left with is y=-5x+4

Answer:

5 gallons

31.05 dollars

jon

free shipping

Answer:

So do I

Step-by-step explanation:

I rate this a 4/5. The reason is that not all problems are perfect. Other than that its pretty good!

Answer:

7.65

Step-by-step explanation:

Answer: $6.11

Step-by-step explanation:

10.77+3.12=13.89

20-13.89=11

Answer:

To find the scalar value, simply choose one side of D and one did of D’ and divide them to find the scalar. We can verify that we have the correct scalar by performing this division on each related edge. Below I will do D to D’ represented like D/D’:

4.8 / 1.2 = 4

5.2 / 1.3 = 4

3.6 / x = 4

Knowing that the scaling for each edge is 4, we can solve for x.

3.6 / 3 = x

1.2=x

So we know the edges for D are 4.8, 5.2, and 3.6 respectively to D’ scaled by 1/4. So we can determine that the edges for D’ are 1.2, 1.3, and 1.2 respectively to D scaled by 4.

So if we go D’ to D, we scale by 4. If we go D to D’, we scale by 1/4.

Answer:

1/4 (*^▽^*)

Step-by-step explanation:

Answer:

To find the first four terms of the series, we can substitute the values of n from 1 to 4 in the given formula and simplify:

n=1: -4(2/3)^0 = -4(1) = -4

n=2: -4(2/3)^1 = -4(2/3) = -8/3

n=3: -4(2/3)^2 = -4(4/9) = -16/9

n=4: -4(2/3)^3 = -4(8/27) = -32/27

So the first four terms of the series are -4, -8/3, -16/9, -32/27.

To determine if the series converges or diverges, we need to find the common ratio r, which is the ratio of any term to its preceding term:

r = (-4(2/3)^n) / (-4(2/3)^(n-1)) = 2/3

Since the absolute value of the common ratio is less than 1, the series converges.

To find the sum of the series, we can use the formula for the sum of an infinite geometric series:

S = a / (1 - r)

where a is the first term and r is the common ratio. Substituting the values we found:

S = -4 / (1 - 2/3) = -4 / (1/3) = -12

So the sum of the infinite geometric series is -12.

Answer:

a)  The first four terms of the series are:

    -4, -8/3, -16/9, -32/27

b)  The series converges.

c)  The sum of the infinite geometric series is -12.

Step-by-step explanation:

Given infinite geometric series:

\(\displaystyle \sum^{\infty}_{n=1} -4 \left(\dfrac{2}{3}\right)^{n-1}\)

Therefore, the formula for the nth term of the sequence is:

\(a_n=-4 \left(\dfrac{2}{3}\right)^{n-1}\)

where:

Calculate the first four terms of the series by substituting the n-values 1 through 4 into the nth term formula.

\(a_1 = -4 \left(\dfrac{2}{3}\right)^{1-1} = -4 \left(\dfrac{2}{3}\right)^{0}=-4\)

\(a_2 = -4 \left(\dfrac{2}{3}\right)^{2-1}= -4 \left(\dfrac{2}{3}\right)^{1}=-\dfrac{8}{3}\)

\(a_3 = -4 \left(\dfrac{2}{3}\right)^{3-1}= -4 \left(\dfrac{2}{3}\right)^{2}=-4 \left(\dfrac{4}{9}\right)=-\dfrac{16}{9}\)

\(a_4 = -4 \left(\dfrac{2}{3}\right)^{4-1}= -4 \left(\dfrac{2}{3}\right)^{3}= -4 \left(\dfrac{8}{27}\right)=-\dfrac{32}{27}\)

A geometric series converges if the absolute value of its common ratio is less than 1. As r = 2/3 and |2/3| < 1, the series converges.

Use the infinite geometric series sum formula to find sum of the infinite series.

\(\boxed{\begin{minipage}{5.5 cm}\underline{Sum of an infinite geometric series}\\\\$S_{\infty}=\dfrac{a}{1-r}$,\;\;for\;$|r| < 1$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the first term. \\ \phantom{ww}$\bullet$ $r$ is the common ratio.\\\end{minipage}}\)

Substitute a = -4 and r = 2/3 into the formula to find the sum of the infinite series:

\(\begin{aligned}\implies S_{\infty}&=\dfrac{-4}{1-\frac{2}{3}}\\\\ &=\dfrac{-4}{\frac{1}{3}}\\\\&=-4 \cdot \dfrac{3}{1}\\\\&=-\dfrac{12}{1}\\\\&=-12\end{aligned}\)

Therefore, the sum of the given infinite geometric series is -12.

Answer:

photo 1: D. a + b = 180

photo 2:

a. interior angles of a triangle

b. vertical angles

c. complementary angles

d. supplementary angles

photo 3:

a. 82

b. 82

photo 4:

a. 51

b. 129

photo 5: x = 60

Step-by-step explanation:

The interior angles of a triangle are the angles that are inside the triangle and are formed by the intersection of two sides of the triangle. In a triangle, there are always three interior angles.

The sum of the interior angles of a triangle is always 180 degrees. This is because the interior angles of a triangle are supplementary, meaning that they add up to 180 degrees.

Vertical angles are two angles that are opposite each other and are formed by two intersecting lines. The lines that intersect to form the vertical angles are called "arms" of the angles.

Vertical angles are always congruent, which means that they have the same measure

Complementary angles are two angles whose measures add up to 90 degrees. In other words, if two angles are complementary, then one angle is the complement of the other.

Supplementary angles are two angles whose measures add up to 180 degrees. In other words, if two angles are supplementary, then one angle is the supplement of the other.

Answer:1  i think

Step-by-step explanation:

Answer: 1)The median number of hours spent on Math was about 3.

Answer:

y = 21

x = 8

Step-by-step explanation:

AB = 180

27 + 3y = 90°

-27           -27

-----------------------

3y = 63

÷3     ÷3

--------------

y = 21

x + 27 + 3y + 8x + 18 = 180

9x + 45 + 3(21) = 180

9x + 45 + 63 = 180

9x + 108 = 180

      -108   -108

-----------------------

9x = 72

÷9    ÷9

----------------

x = 8

I hope this helps!

Answer:

You could use a dice.

Step-by-step explanation:

This then shows that if there 1 meal you want, it shows a 1 in 6 chance to get but not always. For example you could roll the dice and it hit the 1st meal prize three times and not the 5th meal prize once.    

Answer:

Juan rode more slowly

Step-by-step explanation:

Have a nice day

Answer:

Tracey has lost $60

Step-by-step explanation:

>Tracey gives $5 every missed class

>She has missed 12 classes

>5(12) is 60

>Tracey owes $60

3 x 4 = 12

12 x 5 = 60 dollars

Answer:

40.63% to the nearest whole percent is 41

Step-by-step explanation:

(45 - 32) / 32) * 100 = 40.63 %

To round 40.63 to the nearest whole number consider the tenths’ value of 40.63, which is 6 and equal to or more than 5. Therefore, we have to round up: the whole number part of 40.63, 40, increases by 1 to 41, and the decimal point and all digits (.63) are removed...

40.63 rounded to the nearest whole number = 41