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3 years ago

Which of the following statements are true of the hypotenuse of a right triangle?

Mathematics

2 answers:

denis-greek [22]3 years ago

6 0

Answer:

<h2>It is the longest side of a right triangle.</h2><h2>It is opposite the right angle.</h2>

Step-by-step explanation:

First of all, remember that the hypothenuse of a right triangle is the largest side of all three. Also, the hypothenuse is always in front of the right angle. Those two characteristics are used to determined which side is the hypothenuse in a right triangle.

So, basically, the first choice is correct: It is the longest side of a right triangle.

The third choice is also correct: It is opposite the right angle.

Additionally, the legs are the ones which form the right triangle and the length of the hypothenuse is not the sum of the lengths of the other two sides, because that actually violates the triangular inequality which defined all existing triangles.

Therefore, the right answers are first and third choices.

kodGreya [7K]3 years ago

5 0

It is the longest side of a right triangle.

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Sever21 [200]

All you need to do is plug in the numbers and you'll get the sides.

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3 years ago

Which graph represents the inequality y>3−x?

nekit [7.7K]

Answer:

Step-by-step explanation:

The first step is to draw the line y = 3 - x to see what the line itself looks like. Is it going from left to right as in A and C is going up as you go from right to left as in B and D? The graph on the left (below) gives you the answer. It is going up as you progress from right to left.

The next step is to answer which is it: B or D.

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3 years ago

A man travels 20 km by car from Town P to Town Q at an average speed of x km/h. He finds that the time of the journey would be s

yuradex [85]

Answer:

x = 20.

Step-by-step explanation:

First, you should remember the relation:

Distance = Speed*Time.

First, we know that a man travels a distance of 20km at a speed of x km/h, in a time T.

We can write this as:

20km = (x km/h)*T

We know that the time is shortened by 12 minutes if the speed is increased by 5km/h

Rewriting these 12 minutes in hours (remember that 60min = 1 hour)

12 min = (12/60) hours = 0.2 hours

Then from this, he can travel the same distance of 20km in a time T minus 0.2 hours if the speed is increased by 5 km/h

We can write this as:

20km = (x + 5 km/h)*(T - 0.2 h)

Then we have a system of two equations, and we want to find the value of x:

20km = (x km/h)*T

20km = (x + 5 km/h)*(T - 0.2 h)

First, we should isolate the variable T in one of the equations, if we isolate it in the first one, we will get:

20km/(x km/h) = T

Replacing that in the other equation we get:

20km = (x + 5 km/h)*(T - 0.2 h)

20km = (x + 5 km/h)*( 20km/(x km/h) - 0.2 h)

Now we can solve this for x.

Removing the units (that we know that are correct) so the math is easier to read, we get:

20 = (x + 5)*(20/x - 0.2)

We only want to solve this for x.

20 = x*20/x - x*0.2 + 5*20/x - 5*0.2

20 = 20 - 0.2*x + 100/x - 1

subtracting 20 in both sides we get:

20 - 20 = 20 - 0.2*x + 100/x - 1 - 20

0 = -0.2*x + 100/x - 1

If we multiply both sides by x we get:

0 = -0.2*x^2 + 100 - x

-0.2*x^2 - x + 100 = 0

This is just a quadratic equation, we can solve it using the Bhaskara's equation, the solutions are:

$x = \frac{-(-1) \pm \sqrt{(-1)^2 - 4*(-0.2)*100} }{2*-0.2} = \frac{1 \pm 9 }{-0.4}$

Then the two solutions are:

x = (1 + 9)/-0.4 = -25

x = (1 - 9)/-0.4 = 20

As x is used to represent a speed, the negative solution does not make sense, so we should use the positive one.

x = 20

then the average speed initially is 20 km/h

3 0

3 years ago

G/2h + 3f = k <br> Solve for g

Mama L [17]

Answer: if i did this correctly its {x,y} = {3,6}

Step-by-step explanation:

6 0

3 years ago

Help me pls? thank you

Katyanochek1 [597]

i think its c (a picture of a city )

7 0

3 years ago

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