All categories

2 years ago

Pentagon ABCDE is shown on the coordinate plane below:

Mathematics

1 answer:

Sonbull [250]2 years ago

3 0

Answer:

the answer is (-1,2)

x = -1

y = 2

You might be interested in

The following picture is a square pyramid where DE=8 cm and m∠ADE=60°.

Goryan [66]

Given:

The length of DE is 8 cm and the measure of ∠ADE is 60°.

We need to determine the surface area of the pyramid.

Length of AD:

The length of AD is given by

$cos 60^{\circ}=\frac{FD}{8}$

$4=FD$

Length of AD = 8 cm

Slant height:

The slant height EF can be determined using the trigonometric ratio.

Thus, we have;

$sin \ 60^{\circ}=\frac{EF}{8}$

$sin \ 60^{\circ} \times 8=EF$

$\frac{\sqrt{3}}{2} \times 8=EF$

$4\sqrt{3}=EF$

Thus, the slant height EF is 4√3

Surface area of the square pyramid:

The surface area of the square pyramid can be determined using the formula,

$SA=Area \ of \ square + \frac{1}{2} (Perimeter \ of \ base ) (slant \ height)$

Substituting the values, we have;

$SA=8^2+\frac{1}{2}(8+8+8+8)(4 \sqrt{3})$

$SA=64+\frac{1}{2}(32)(4 \sqrt{3})$

$SA=64+(16)(4 \sqrt{3})$

$SA=64+64 \sqrt{3}$

The exact form of the area of the square pyramid is $64+64 \sqrt{3}$

Substituting √3 = 1.732 in the above expression, we have;

$SA = 64 + 110.848$

$SA = 174.848$

Rounding off to one decimal place, we get;

$SA = 174.8$

Thus, the area of the square pyramid is 174.8 cm²

7 0

3 years ago

Read 2 more answers

A 150 cm pendulum swings through an arc which measured 100pi cm. In exact radians, through what angle does it swing?

choli [55]

Answer:

Pendulum will swing by an angle 0.666π

Step-by-step explanation:

We have given arc = $100\pi cm$

And length of the pendulum l = 150 cm

Length of the pendulum will be equal to radius of the pendulum so r = 150 cm

Arc is given by $arc=radius\times angle$

So $100\pi =150\times\times \Theta$

$\Theta =0.666\pi$

So pendulum will swing by an angle 0.666π

5 0

3 years ago

I need help on this 3,4,and 2 help me solve one please

Mrrafil [7]

3) 12 divided by 3= 4

4 x 2= 8

4 0

3 years ago

Find the slope of the line passing through the points D (10, 8) and E (-4,4)

RUDIKE [14]

Answer:

Slope=2/7

Step-by-step explanation:

Slope=rise/run

$rise = 8 - 4 = 4 \\ run = 10 - ( - 4) = 14 \\ slope = \frac{4}{14} = \frac{2}{7}$

8 0

3 years ago

What is the surface area and volume? PLEASE EXPLAIN IN DETAIL.

Effectus [21]

Check the picture below.

so to find the surface area of the triangular prism, we simply add the areas of each of the figures composing it, as you can see is really just 2 triangles an 3 rectangles.

$\bf \stackrel{\textit{\Large Areas}}{\stackrel{triangles}{2\left[ \cfrac{1}{2}(4)(3) \right]}+\stackrel{\textit{rectangles}}{(3\cdot 10)+(4\cdot 10)+(5\cdot 10)}}\implies 12+30+40+50\implies 132$

now, to get the volume is simply the area of the triangular face times the length, well, we know the area of one of the triangles is 6, times 10 is just 6*10 = 60.

7 0

3 years ago