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maria [59]
3 years ago
12

(a) use the pythagorean theorem to determine the length of the unknown side of the triangle, (b) determine the perimeter of the

triangle, and (c) determine the area of the triangle. the figure is not drawn to scale.
a. the length of the unknown side is ___

b. the perimeter of the triangle is ___

c. the area of the triangle is ___

Mathematics
1 answer:
Kisachek [45]3 years ago
8 0

Answer:

(A) 40 km

(B) 90 km

(C) 180 km²

Step-by-step explanation:

To find the missing side of this triangle, let's use the Pythagorean theorem.

a^2+b^2=c^2, assuming that a and b are legs, and c is the hypotenuse.

Assuming the 9km side is a, we need to find the value of b, so we can substitute into the equation.

9^2+b^2=41^2\\81+b^2=1681\\b^2=1681-81\\b^2=1600\\\\b = \sqrt{1600} \\b=40

So, the length of the missing side is 40. Now that we know this piece of information, we can find the perimeter and area of the triangle.

The perimeter is all the sides added together, so 41+9+40 = 90 km is the perimeter.

The area are the two legs multiplied divided by 2.

So,

\frac{9\cdot40}{2} \\\\\frac{360}{2}\\\\180

So the area of this triangle is 180 cm²

I hope this helped!

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stira [4]

Answer:

1) When x is 1, y is 4, and vice versa

2) When x is -6, y is 42, and when x is 7, y is 114

3) When x is -2, y is 2, and when x is 8, y is 42

Step-by-step explanation:

1)

y=x^2-6x+9

y+x=5 which can be rearranged as y=5-x.

Substituting this lone y into the first equation, you get:

5-x=x^2-6x+9

Move everything to one side:

x^2-5x+4=0

Factor:

(x-4)(x-1)=0

x=1, 4

y=4, 1

2)

y-30=12x which can be rearranged as y=12x+30.

y=x^2+11x-12

Let's use elimination this time and subtract the first equation from the second:

0=x^2-x-42

Factor:

(x-7)(x+6)=0

x=-6, 7

y= -42, 114

3)

y=x^2-2x+6

y=4x+10

Let's set the two equations equal to each other through substitution:

x^2-2x-6=4x+10

Move everything to one side:

x^2-6x-16=0

Factor:

(x-8)(x+2)=0

x=-2, 8

y= 2, 42

Hope this helps!

6 0
3 years ago
Help me plz I need help
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