If you're only provided with the lengths of a triangle, and you're asked to determine whether or not the triangle is right or not, you'll need to rely on the Pythagorean Theorem to help you out. In case you're rusty on it, the Pythagorean Theorem defines a relationship between the <em>legs</em> of a right triangle and its <em>hypotenuse</em>, the side opposite its right angle. That relationship is a² + b² = c², where a and b are the legs of the triangle, and c is its hypotenuse. To see if our triangle fits that requirement, we'll have to substitute its lengths into the equation.
How do we determine which length is the hypotenuse, though? Knowledge that the hypotenuse is always the longest length of a right triangle helps here, as we can clearly observe that 8.6 is the longest we've been given for this problem. The order we pick the legs in doesn't matter, since addition is commutative, and we'll get the same result regardless of the order we're adding a and b.
So, substituting our values in, we have:
(2.6)² + (8.1)² = (8.6)²
Performing the necessary calculations, we have:
6.76 + 65.61 = 73.96
72.37 ≠ 73.96
Failing this, we know that our triangle cannot be right, but we <em>do </em>know that 72.37 < 73.96, which tells us something about what kind of triangle it is. Imagine taking a regular right triangle and stretching its hypotenuse, keeping the legs a and b the same length. This has the fact of <em>increasing the angle between a and b</em>. Since the angle was already 90°, and it's only increased since then, we know that the triangle has to be <em>obtuse</em>, which is to say: yes, there's an angle in it larger than 90°.
Answer:
2x+5y
Step-by-step explanation:
5x + 5y - 3x
=2x+5y
Answer:
The length of the triangle is 3x given
The no of sides is 3x 3x 3x so 3x+3x+3x= 180
9x=180 x= 20
3x =3*20=60
3x=3*20=60
3x=3*20=60
Answer:
(x+1)(x-14)(x+3)
Step-by-step explanation:
The first step in factorising polynomials is to find the smallest factor first. The way to do this is with trial and error. Lets see if x+1 is a factor.
According to the factor theorem, (x-a) is a factor of P(x) if and only when P(a) = 0
In this case we will use f(x) = ((x)^3)-((10x)^2)-53x-42
f(-1) = 0
Therefore (x+1) is a factor of the polynomial.
Now we divide the polynomial with (x+1) via long division to get (x^2)-11x-42.
We now factorise (x^2)-11x-42 using whatever method you would like. I'm going to use the AC method, where we find a number that multiplies to AC and adds to B, In this case AC = -42, and B = -11.
Therefore (x^2)-11x-42 factosied is (x-14)(x+3)
Now merge (x+1) with (x-14)(x+3)
The final answer is (x+1)(x-14)(x+3)
If this has helped, please consider making this the Brainliest answer!
Answer:area of big square is 9x6 = 54 sq ft. Area of smaller square is 6x4 = 24 square feet. So if you throw a dart, you have a 24/54 or 4/9 chance of hitting the shaded spot.
Step-by-step explanation:
