We can’t see the rotation
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: 0.15(40) + 0.6(x – 40) = 0.25(x)
Step-by-step explanation:
Hi, to answer this question we have to write an equation with the information given:
Fifteen percent of the pigment in paint color A is black
15% = 15/100 = 0.15 (decimal form)
0.15 A
Sixty percent of the pigment in paint color B is black
0.6 B
An unknown amount of paint color B is mixed with 40 ml of paint color A,
SO:
0.15 (0.40)
0.6 (x-0.40)
x = total amount of paint in the mixture of the two colors
The result is a paint that contains 25% (0.25 in decimal form)black pigment (x)
0.15(40) + 0.6(x – 40) = 0.25(x)
Feel free to ask for more if needed or if you did not understand something.
So you subtitute y=3x into
2x+y=15
so
2x+(3x)=15
add like terms
5x=15
divide both sides by 5
x=3
subtitute x=3 into first equation (y=3x)
y=3(3)
y=9
Answer:
D) x=9 ; y=3√(3)
Step-by-step explanation:
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Therefore, x=9 and y=3√(3)
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