The total surface area of this cuboid is 112 cm, Find the value of x. X cm 2 cm 10 cm

The area of a regular octagon is 35 cm 2 what is the area of a regular octagon with sides three times as large

Maurinko [17]

The area of a polygon = n*side^2 / (4 * tan(180/n))
where "n" is the number of sides

Let's calculate area for side = 2
area = 8*2^2 / (4 * tan(180/8))
area = 32 / (4 * tan(22.5))
area = 32 / 4*0.41421
 area = 19.3138746047 

Now, let's calculate area for side = 6
area = 8*6^2 / (4 * tan(180/8))
area = 288 / 1.65684 
area = 173.824871442 

 173.824871442 / 19.3138746047 = 9

So, the area would be 9 times larger.

ALSO, looking at the formula
n*side^2 / (4 * tan(180/n))
we can see that the side length appears just once in the formula and we are to square it in the calculation. So, if we increase the side length is increased by 3, then the area increases by 3^2 or 9.

5 0

4 years ago

Rectangle ABCD is similar to rectangle RSTU .

Alenkasestr [34]

Answer:

The scale factor of a dilation from ABCD to RSTU is $\frac{1}{2}$

Step-by-step explanation:

We know that the rectangle ABCD is similar to rectangle RSTU.

Given that in rectangle ABCD the longest sides are DC and AB and in the rectangle RSTU the longest sides are UT and RS ⇒ The scale factor of a dilation will transform the sides DC and AB into UT and RS

Working with the lengths of the sides :

DC.(Scale factor) = UT

AB.(Scale factor) = RS

Replacing with the values of the lengths (Scale factor : SF) :

$DC.SF=UT\\(90ft).(SF)=45ft\\SF=\frac{45ft}{90ft} \\SF=\frac{1}{2}$

$AB.SF=RS\\(90ft).(SF)=45ft\\SF=\frac{45ft}{90ft} \\SF=\frac{1}{2}$

Notice that the scale factor is dimensionless.

We can verify this result with the sides AD and BC :

$AD.SF=UR\\50ft.(\frac{1}{2})=25ft\\ 25ft=25ft$

$BC.SF=TS\\50ft.(\frac{1}{2})=25ft\\ 25ft=25ft$

The scale factor (SF) is $\frac{1}{2}$

7 0

3 years ago

Read 2 more answers

1. Ten slips of paper labeled from 1 to 10 are placed in a hat. The first slip of paper is NOT replaced before selecting the sec

Oduvanchick [21]

1. If we get an odd number first (probability 5/10 = 1/2), then the only way to get a number greater than 9 is the 10 (probability 1/9, since only 9 papers remain). This gives 1/2 * 1/9 = 1/18.

2. We would expect that P(2 white cards) = P(1 white card)*P(2nd white card given 1 white card).This gives the equation 14/95 = 2/5 * x
Solving for x gives x = 7/19.

3. There are a total of 4 favorable results: 1, 4, 5, 6. Out of the 6 possibilities, this is a probability of 4/6 = 2/3.

8 0

3 years ago

Can some one help with this question?

vesna_86 [32]

Answer:

Step-by-step explanation:

log₂125 = log₂(5²) = 2log₂5 = 2k

3 0

3 years ago

What is the vertex of the quadratic function f(x)=(x-8)(x-2)?

7nadin3 [17]

Change the function into vertex form:
f(x)=x²-10x+16
make a square by (adding half of -10)², which is 25, then subtract it:
f(x)=x²-10x+25-25+16
f(x)=(x-5)²-9
so the vertex is at (5,-9)

another way to do it:
f(x)=x²-10x+16
the vertex is when x=- $\frac{b}{2a}$ , b=-10, a=1 in this case.
x=-(-10/2*1)=5
plug x=5 into the quadratic function, you get f(x)=-9

4 0

3 years ago

The total surface area of this cuboid is 112 cm,Find the value of x.X cm2 cm10 cm​

The total surface area of this cuboid is 112 cm,Find the value of x.X cm2 cm10 cm