3. The point where two rays meet to form an angle is called the

1. Find the cost of levelling the ground in the form of a triangle having the sides 51 m, 37 m and 20 m at the rate of ₹ 3 per m

Flauer [41]

1. Find the cost of levelling the ground in the form of a triangle having the sides 51 m, 37 m and 20 m at the rate of ₹ 3 per m².

a = 51 m, b = 37 m, c = 20 m

semiperimeter: p = (51+37+20):2 = 54 m

Area of triangle:

$A=\sqrt{p(p-a)(p-b)(p-c)}\\\\A=\sqrt{54(54-51)(54-37)(54-20)}\\\\A=\sqrt{54\cdot3\cdot17\cdot34}\\\\A=\sqrt{9\cdot2\cdot3\cdot3\cdot17\cdot17\cdot2}\\\\A=3\cdot2\cdot3\cdot17\\\\A=306\,m^2$

Rate: ₹ 3 per m².

Cost: ₹ 3•306 = ₹ 918

2. Find the area of the isosceles triangle whose perimeter is 11 cm and the base is 5 cm.

a = 5 cm

a+2b = 11 cm ⇒ 2b = 6 cm ⇒ b = 3 cm

p = 11:2 = 5.5

$A=\sqrt{5.5(5.5-3)^2(5.5-5)}\\\\ A=\sqrt{5.5\cdot(2.5)^2\cdot0.5}\\\\ A=\sqrt{11\cdot0.5\cdot(2.5)^2\cdot0.5}\\\\A=0.5\cdot2.5\cdot\sqrt{11}\\\\A=1.25\sqrt{11}\,cm^2\approx4.146\,cm^2$

3. Find the area of the equilateral triangle whose each side is 8 cm.

a = b = c = 8 cm

p = (8•3):2 = 12 cm

$A=\sqrt{12(12-8)^3}\\\\ A=\sqrt{12\cdot4^3}\\\\ A=\sqrt{3\cdot4\cdot4\cdot4^2}\\\\A=4\cdot4\cdot\sqrt{3}\\\\A=16\sqrt3\ cm^2\approx27.713\ cm^2$

4. The perimeter of an isosceles triangle is 32 cm. The ratio of the equal side to its base is 3 : 2. Find the area of the triangle.

a = 2x

b = 3x

2x + 2•3x = 32 cm ⇒ 8x = 32 cm ⇒ x = 4 cm ⇒ a = 8 cm, b = 12 cm

p = 32:2 = 16 cm

$A=\sqrt{16(16-8)(16-12)^2}\\\\ A=\sqrt{16\cdot8\cdot4^2}\\\\ A=\sqrt{2\cdot8\cdot8\cdot4^2}\\\\ A=8\cdot4\cdot\sqrt2\\\\ A=32\sqrt2\ cm^2\approx45.2548\ cm^2$

8 0

2 years ago

Use the angle and the given side to solve for the value of x. Round to the nearest tenth.57°6.х

Svetllana [295]

Given data:

The first angel given is ∠1=54 degrees.

T

7 0

1 year ago

Multiply: 5 • (-3)

slamgirl [31]

Answer:

$-15$

Step-by-step explanation:

We can factor out a 1 from -3 to get $5\cdot(-3)=5\cdot-1\cdot3=-1(5\cdot3)$ .

We know from simple arithmetic that $5\cdot3=5+5+5=10+5=15$ .

So, our answer is $-1(15)=\boxed{-15}$

6 0

3 years ago

Read 2 more answers

Given <img src="https://tex.z-dn.net/?f=f%28x%29%20%3Dx%5E2%20-6x%2B8%20and%20g%28x%29%20%3Dx-2" id="TexFormula1" title="f(x) =x

Eva8 [605]

For this case we have the following functions:

$f (x) = x ^ 2-6x + 8\\g (x) = x-2$

We must subtract the functions:

$f (x) -g (x) = x ^ 2-6x + 8- (x-2)\\f (x) -g (x) = x ^ 2-6x + 8-x + 2\\f (x) -g (x) = x ^ 2-7x + 10$

We build a table of values for $x = 0,1,2,3.$

$x = 0, f (x) -g (x) = 0 ^ 2-7 (0) + 10 = 10\\x = 1, f (x) -g (x) = 1 ^ 2-7 (1) + 10 = 1-7 + 10 = 4\\x = 2, f (x) -g (x) = 2 ^ 2-7 (2) + 10 = 4-14 + 10 = 0\\x = 3, f (x) -g (x) = 3 ^ 2-7 (3) + 10 = 9-21 + 10 = -2$

Answer:

$f (x) -g (x) = x ^ 2-7x + 10$

8 0

3 years ago

I'm in 7th grade and need help have a final tomorrow

inna [77]

I can maybe help, what's the question

7 0

3 years ago