The area and the perimeter of a square are equal. Find the side
length of the square.

please help me

The expression that represents the volume of the prism, in cubic centimetres is [tex]28.476(2x+1) \: \rm cm^3[/tex] approx

If the prism is such that if we slice it horizontally at any height smaller or equal to its original height, the cross section is same as its base, then its volume is:

[tex]V = B \times h[/tex]
where h is the height of that prism and B is the area of the base of that prism.

For this case, we are provided a prism which has pentagon as its cross sections, and its height is [tex]2x + 1[/tex] units.

Let B be the area of those pentagons, then:
Volume of the prism = [tex]B(2x + 1) \: \rm cm^3[/tex]

It is provided that the apothem of the pentagon is 2.8 cm.

An n sided regular polygon has internal angles' sum as 180(n-2)°

Thus, each internal angle would be of  180(n-2)/n°

For n = 5, this comes as 108°

Since the line AO is bisecting the internal angle, the angle OAB is o of 108/2 = 54°

Using the tangent ratio, we get:

[tex]\tan(54^\circ) = \dfrac{|OD|}{|AD|}\\\\|AD| = \dfrac{2.8}{\tan(54^\circ)} \approx 2.034 \: \rm cm[/tex]

Thus, area of the triangle AOD = [tex]\dfrac{1}{2} \times |AD| \times |OD| \approx \dfrac{1}{2} \times 2.034\times 2.8 = 2.8476 \: \rm cm^2[/tex]

There are 10 such triangles, all congruent, thus:

Area of pentagon = [tex]B \approx 10 \times 2.8476= 28.476 \: \rm cm^2[/tex]

Thus, volume of the pentagonal prism is:

[tex]V = B \times h \approx 28.476(2x+1) cm^3[/tex]

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Answer:

14x^2+7x

B

Step-by-step explanation:

I did the test.

Answer:

Here is your answer

Step-by-step explanation:

Solution,

here,

Base is 75 cm

Height is 12 cm

Now,

Area of triangle=1/2×b×h

=1/2×75×12

= 900/2

=450. ans

Answer:

(2, -1)

Step-by-step explanation:

x = 2, y = −1

Answer:

To find the volume of this figure, we must find the base area(pentagon) and multiply it by the figure's height.

Formula for area of a pentagon:-

A = 1/2 x p x a

Where 'p' represents the perimeter, and 'a' represents the apothem.

First, let's figure out the perimeter of the base pentagon.

One side of this pentagon is 10cm, and there are 5 side lengths of 10cm to this pentagon. So it'll result in (5 x 10) = 50cm altogether.

The apothem is given, 6.9cm.

So, we plug these into our formula:-

A = 1/2 x p x a

A = 1/2 x 50 x 6.9

A = 50/2 x 6.9

A = 25 x 6.9

A = 172.5cm, is the area of the pentagon.

Now we find the height of this figure and multiply it by the base area we've found(pentagon).

Our height is 17cm.

172.5(17)

= 2,932.5 cubic centimetres, is our volume.

Answer:

ok so this is a system of equations

x+32=y

x*y=-256

so lets just make y x+32

x^2+32=-256

-32

x^2=-288

find root

this can't be solved since negitive numbers don't have roots

Hope This Helps!!!

The distance between the two buildings is 844.23 feet apart, we go this answer by simply applying the SOH CAH TOA method

Given Data

Applying the SOH CAH TOA Approach we have

Tan  θ = Opp/Adj

Substituting our given data we have

Tan 35 = 400/x

0.4738 = 400/x

make x subject of the formula we have

x = 400/0.4738

x = 844.23 feet

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Answer:

5a - 4b

Step-by-step explanation:

= 8a - 6b - 3a +2b

= 8a - 3a - 6b + 2b

= 5a - 4b

Hope it helps :)

Answer:

5a - 4b

Step-by-step explanation:

- 6/17 = (-6) / 17 (2nde solution)

         = - (6/17) (4th solution)

         = 6/(-17) (last solution)

Answer:

no increase

Step-by-step explanation:

the range is the difference between the largest and smallest values in the data set.

largest value = 9 and smallest value = 3 , then

range = 9 - 3 = 6

replacing 8 by 5 has no effect on the above 2 values , so no change

Answer:

The range would stay the same.

Step-by-step explanation:

The old set is 6 9 3 6 8 6 3

- range is 9-3 = 6.

The new set is  6 9 3 6 5 6 3

which has a range of 9 - 3 = 6.

Given -

ie, length of the mirror, L = 4 feet and breadth of the mirror, B = 7 feet .

To find -

Solution -

As we know to find the area of rectangle we use the formula, Area = L × B

Hence, we will be doing the same.

Area = 4 × 7

Area = 28 square feet

Answer:

28 sq. feet

Step-by-step explanation:

Given:-

To find:-

Solution:-

Area of rectangular bathroom mirror:- L × B

putting the values ,

Area :- 4 × 7 sq. feet

Area:- 28 sq. feet

Answer:

y = m x + b     is the standard form of a straight line

m = (y2 - y1) / (x2 - x1) = (10 - (-8)) / (-3 - 0) = 18 / -3 = -6

When x = 0 y = b from the equation for a line

y = - 8

So our equation is  

y = -6 x - 8

As a check let x = -2 then

y = (-6 * -2) - 8 = 12 - 8 = 4

Check on the graph to verify that this equation holds

144 x m - 309.6 = 50.4

Add 309.6 to both sides:

144 - 309.6 + 309.6 = 50.4 + 309.6

Simplify the arithmetic:

144 x m = 50.4 + 309.6

Simplify the arithmetic:

144 x m =360

m = 5/2

Answer:

9

Step-by-step explanation:

GCF of 27 and 45 is 9.

Look at the image... I hope this image helps you.

Answer: 83 degrees

Step-by-step explanation:

In order to find theta, you must take the arccosine of both sides. The arccosine eliminates the cosine, and extracts the argument. Therefore:

[tex]cos(x)=\frac{2}{16} =\frac{1}{8}[/tex]

[tex]arccos(cos(x))=arccos(\frac{1}{8} )=x[/tex]

Use a calculator the find the arccosine of 1/8. Its nearly impossible to find the exact answer without one:

[tex]x=arccos(\frac{1}{8} )[/tex]

[tex]x=83[/tex]

Answer: 42.0

Step-by-step explanation:

Answer:

1.77 Tones = 1770 Kilograms

Step-by-step explanation:

Multiply the value of the tone by 1000 to get KG

1.77 x 1000 = 1770

Answer:

gradient = 2

Step-by-step explanation:

calculate the gradient (slope) m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (0, - 1) and (x₂, y₂ ) = (2, 3) ← 2 points on the line

m = [tex]\frac{3-(-1)}{2-0}[/tex] = [tex]\frac{3+1}{2}[/tex] = [tex]\frac{4}{2}[/tex] = 2

Answer:

B.

Step-by-step explanation:

Answer:

35.4

Step-by-step explanation:

divide 72.8 by 6.5 to get the other two sides. Then you will have all four sides. From there you can add all four sides. 6.5 + 6.5 + 11.2 + 11.2 = 35.4. Hope that helps!

A dot plot or for chart is a statistical plot consisting of data points that are plotted on a scale using dots.

Your information is incomplete. Therefore, an overview of a dot plot will be given. A dot plot is a data visualization where the day points are plotted as dots on the graph.

Dot plots are used for relatively small data sets. It uses the dots to show where the data values in the distribution are.

Learn more about dot plot on:

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Hope this helps!! :)

Answer:

Sam can do the job in 20 min. So he can do the whole job at the rate of 1 job in 20 minutes.

So he does 1/20 of the job per minute.

.

Rob can do the job in 30 min. His rate is 1/30 of the job per minute.

.

Working together how does it take?

.

1/20*x + 1/30*x = 1 job done

, where x = minutes.

.

Step-by-step explanation:

A function is a relation where there is only one output for every input. In other words for every x value, there is only one y value.

Example : Multiply by 3 is a very simple function.

Input : 0 Output : 0

Input : 1 Output : 3

Input : 2 Output : 6

Input : 3 Output :9

And so on!

Hope this helps!

Answer:

a bit more than 48°

Step-by-step explanation:

We use the law of cosines for this.

The theorem is an extension of pythagoras' theorem, working for all triangles. In our case

[tex]\overline{BC}^2=\overline{AB}^2+\overline{AC}^2-2\overline{AB}\cdot\overline{AC}cos \hat A[/tex]

Let's replace all the values we have and find whatever is left.

[tex]10^2=11^2+13^2-2(11)(13)cos \hat A\\-286cos\hat A = -190\\cos \hat A\approx 0.6643 \rightarrow \hat A \approx 48\°[/tex]

Answer:

Radius = 8 in

Area = πr2 = 3.14 x (8)2= 3.14 x (64)

Area = 201.1429 in²

Step-by-step explanation:

hope this helps if not please let me now

Answer:

1st option

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

here m = - [tex]\frac{4}{5}[/tex] , then

y = - [tex]\frac{4}{5}[/tex] x + c

to find c substitute (5, 1 ) into the equation

1 = - 4 + c ⇒ c = 1 + 4 = 5

y = - [tex]\frac{4}{5}[/tex] x + 5 ( multiply through by 5 to clear the fraction )

5y = - 4x + 25 ( add 4x to both sides )

4x + 5y = 25 ← in standard form

Using it's concept, it is found that there is a There is a 0.1667 = 16.67% probability that the sum is less than 8 if the pink die shows a number less than 4.

A probability is given by the number of desired outcomes divided by the number of total outcomes.

In this problem, the possible outcomes for the pair of dice are given by:

(1,1), (1,2), (1,3), (1,4), (1,5), (1,6)

(2,1), (2,2), (2,3), (2,4), (2,5), (2,6)

(3,1), (3,2), (3,3), (3,4), (3,5), (3,6)

(4,1), (4,2), (4,3), (4,4), (4,5), (4,6)

(5,1), (5,2), (5,3), (5,4), (5,5), (5,6)

(6,1), (6,2), (6,3), (6,4), (6,5), (6,6)

We want to find the probability that the sum is less than 8 if the first die(the pink one) shows a number less than 4.

There are 18 total outcomes in which the pink die is less than 4, and in 3, the sum is less than 4, hence:

p = 3/18 = 1/6 = 0.1667.

There is a 0.1667 = 16.67% probability that the sum is less than 8 if the pink die shows a number less than 4.

More can be learned about probabilities at https://brainly.com/question/14398287

Answer:

Statements #1:  <L (congruent sign) <I

Statements #2: <H (congruent sign) <K

Statements #3: GH (congruent sign) MK

Reasons #2: given

Reasons #3: given

Reasons #4: angle angle side

Answer:

If it is a conjunction that uses the word and, the solution must work in both inequalities and the solution is in the overlap region of the graph. If it is a disjunction that uses the word or, the solution must work in either one of the equations.

Step-by-step explanation:

Answer:

G

Step-by-step explanation:

The answer is statement G