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3 years ago

The base of this right prism is a right-angled triangle. What is the surface area of the prism?

Mathematics

2 answers:

lianna [129]3 years ago

8 0

Answer:

○ D) 1720 mm.²

Explanation:

$hb(c + b + a)(h) = S. A. \\ \\ (8 \times 15)(17 + 15 + 8)(8) = 120(40)(8) = 38400 \\ \\ 38400 ≈ 1720$

This is not the best explanation, but I have you one.

I hope this is correct, and as always, I am joyous to assist anyone at any time.

brilliants [131]3 years ago

7 0

Answer:

D. 1720 mm^2.

Step-by-step explanation:

This consists of 5 surfaces.

Area of 2 triangles + area of base + area of the side + area of the sloping side.

= 2 * 1/2 * 8 * 15 + 40*17 + 8*40 + 15*40

= 120 + 680 + 320 + 600

= 1720.

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P1= (5,-4); p2=(8,-3);p3=(7,-10) find the length of each side of the triangle determined by three points

Dima020 [189]

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$\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ P2(\stackrel{x_2}{8}~,~\stackrel{y_2}{-3})\qquad P3(\stackrel{x_2}{7}~,~\stackrel{y_2}{-10}) \\\\\\ P2P3=\sqrt{[7-8]^2+[-10-(-3)]^2}\implies P2P3=\sqrt{(7-8)^2+(-10+3)^2} \\\\\\ P2P3=\sqrt{(-1)^2+(-7)^2}\implies P2P3=\sqrt{50}\implies \boxed{P2P3=5\sqrt{2}}\\\\[-0.35em] \rule{34em}{0.25pt}$

$\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ P3(\stackrel{x_2}{7}~,~\stackrel{y_2}{-10})\qquad P1(\stackrel{x_1}{5}~,~\stackrel{y_1}{-4}) \\\\\\ P3P1=\sqrt{[5-7]^2+[-4-(-10)]^2}\implies P3P1=\sqrt{(5-7)^2+(-4+10)^2} \\\\\\ P3P1=\sqrt{(-2)^2+6^2}\implies P3P1=\sqrt{40}\implies \boxed{P3P1=2\sqrt{10}}$

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3 years ago

The Asian elephant is an endangered species with a current population of 45,000. This species is said to be experinceing a decli

hram777 [196]

Answer:

5 years

Step-by-step explanation:

Given that

The current population is 45,000

The rate of interest in declining would be 4.5% per year

The expected population is 35,746

We need to find out the no of years

Since the rate of interest decrease by 4.5% per year so after decreasing it the percentage would be 0.955

Now

Year 1 = 45,000 × 0.955 = 42,975

Year 2 = 42,975 × 0.955 = 41,041.125

Year 3 = 41,041.125 × 0.955 = 39,194.27

Year 4 = 39,194.27 × 0.955 = 37,430.53

Year 5 = 37,430.53 × 0.955 = 35,746.16

Hence, the no of years would be 5

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3 years ago

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Luden [163]

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Step-by-step explanation: Given that a sail boat leaves port and sails 12 kilometers west and then 9 kilometers north.

We are to find the distance between the sailboat from the port in kilometers.

Since the directions west and north are at right-angles, we can visualize the movement of the sailboat in the form of a right-angled triangle as shown in the attached figure.

The sailboat moves leaves the port at P and reach O after sailing 12 km west. From point O, again it moves towards north 9 km and reach the point S.

PS = ?

Using the Pythagoras theorem, we have from right-angled triangle SOP,

$PS^2=OS^2+OP^2=9^2+12^2=81+144=225\\\\\Rightarrow PS=15~\textup{km}.$

Thus, the sailboat is at a distance of 15 km from the port.

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