What value should take the place of 18

Compare the perimeters of the two regular figures. Which statement is true?

adell [148]

Answer:

(A). The perimeter of the octagon is greater than that of the hexagon.

Step-by-step explanation:

Since, hexagon consists of 6 sides and 6 angles, thus the measure of one angle of the hexagon will be= $\frac{(n-2){\timeS}180^{\circ}}{6}$

= $\frac{(6-2){\timeS}180^{\circ}}{6}$

= $\frac{(4){\timeS}180^{\circ}}{6}$

= $120^{\circ}$

Now, since MQ is the angle bisector of the one of the angle of the hexagon, therefore ∠QMP=60°.

Now, from ΔQMP. we have

$\frac{MP}{MQ}=cos60^{\circ}$

$MP=\frac{1}{2}$

Thus, the perimeter of the hexagon is:

$P=12{\times}MP$

$P=12{\times}\frac{1}{2}$

$P=6 units$

Thus, the perimeter of hexagon is 6 units.

Also, Since, octagon consists of 8 sides and 8 angles, thus the measure of one angle of the octagon will be= $\frac{(n-2){\timeS}180^{\circ}}{8}$

= $\frac{(8-2){\timeS}180^{\circ}}{8}$

= $\frac{(6){\timeS}180^{\circ}}{8}$

= $135^{\circ}$

Now, since AP is the angle bisector of the one of the angle of the octagon, therefore ${\angle}PAC=cos\frac{135}{2}$ .

From ΔAPC, we have

$AC=cos\frac{135}{2}$

Now, Perimeter of octagon is:

$P=16{\times}cos\frac{135}{2}$

$P=16{\times}0.382$

$P=6.122 units$

Thus, the perimeter of octagon is 6.122 units.

Now, the perimeter of octagon is greater than perimeter of the hexagon, thus option A is correct that is The perimeter of the octagon is greater than that of the hexagon.

4 0

3 years ago

Find the distance between the two points in simplest radical form.

Jlenok [28]

Answer:

$d=\sqrt{58}\approx7.6$

Step-by-step explanation:

To find the distance between any two points, we can use the distance formula:

$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2$

Our first point, A, is at (1, 1) and our second point, B, is at (-2, 8).

Let's let A(1, 1) be (x₁, y₁) and B(-2, 8) be (x₂, y₂). Substitute this into the distance formula:

$d=\sqrt{(-2-1)^2+(8-1)^2$

Subtract:

$d=\sqrt{(-3)^2+(7)^2$

Square:

$d=\sqrt{9+49}$

Add:

$d=\sqrt{58}$

This cannot be simplified.

So, the distance between the two points is √58 or about 7.6 units.

And we're done!

So... where's my cookie :)?

6 0

3 years ago

The composite figure shown has a surface area of 844 square centimeters.

kolezko [41]

Given the surface area of the composite figure, the height of the rectangular prism is approximately 8 centimeters.

<h3>What is the height of the rectangular prism?</h3>

First we calculate the surface area of the rectangular pyramid;

S.A = lw + (1/2)w√(4h²+l²) + (1/2)l√(4h²+w²)

Given that;

w = 10cm
l = 18cm
h = 12cm

S.A = lw + (1/2)w√(4h²+l²) + (1/2)l√(4h²+w²)

S.A = (18cm×10cm) + (1/2)10cm√(4(12cm)²+18cm²) + (1/2)18cm√(4(12cm)²+(10cm)²)

S.A = (180cm²) + 5cm√(576cm² + 324cm²) + 9cm√(576² + 100cm²)

S.A = (180cm²) + 5cm(30cm) + 9cm(26cm)

S.A = 180cm² + 150cm² + 234cm²

S.A = 564cm²

Now, surface Area of the rectangular prism will be;

= Area of composite figure - surface area of the rectangular pyramid

= 1844cm² - 564cm²

= 1280cm²

Now surface area of rectangular prism is expressed as;

SA = 2lw + 2lh + 2hw

w = 10cm
l = 18cm
h = x

SA=2lw + 2lh + 2hw

SA - 2lw = h( 2l + 2w)

h = (SA - 2lw) / ( 2l + 2w)

h = (1280cm² - ( 2×18cm×10cm)) / ( 2×18cm + 2×10cm)

h = (1280cm² - 360cm²) / ( 36cm + 20cm)

h = 1020cm² / 56cm

h = 8cm

Given the surface area of the composite figure, the height of the rectangular prism is approximately 8 centimeters.

Learn more about Prism and Pyramid here: brainly.com/question/9796090

#SPJ1

8 0

1 year ago

What is the median of 82, 4, 94, 4, 60, 91<br> And what is the mode and range

Dimas [21]

Answer:

The median is 55.833

The range is 90

The mode is 4

Step-by-step explanation:

To find median you

1. Arrange your numbers in numerical order.

2. Count how many numbers you have.

3. If you have an odd number, divide by 2 and round up to get the position of the median number.

4.If you have an even number, divide by 2. Go to the number in that position and average it with the number in the next higher position to get the median.

To find mode you put the numbers in order from least to greatest and count how many times each number occurs. The number that occurs the most is the mode. To find range you first put all the numbers in order. Then subtract (take away) the lowest number from the highest. The answer gives you the range of the list.

4 0

3 years ago

What are the values of x and y?

ss7ja [257]

Answer: x=35 and y=72.5

Step-by-step explanation:

Everything os 360, so x is 35 because it los like it has the same measure as the another 35, so if you substract 70 360=290 and 290/4 = 72.5

5 0

3 years ago