Answer: Lucie is 8 and her brother is 13
Step-by-step explanation: the only possible way for Lucie to be half her brother's age while being 5 years younger at the same time, is if she's 5 and he's 10. that's how old they were 3 years ago. now you just add 3 to 5 and 10 to find their current ages; 5+3=8 so Lucie is 8, and 10+3=13 so her brother is 13.
:)
In a 45-45-90 triangle, the two legs are congruent. Let's call them x. The hypotenuse is equal to 1 as we're using the unit circle. The hypotenuse of the triangle is the same as the radius of the unit circle.
a = x
b = x
c = 1
Use those values in the Pythagorean theorem to solve for x.
a^2 + b^2 = c^2
x^2 + x^2 = 1^2
2x^2 = 1
x^2 = 1/2
x = sqrt( 1/2 )
x = sqrt(1)/sqrt(2)
x = 1/sqrt(2)
x = sqrt(2)/2 ... rationalizing the denominator
So this right triangle has legs that are sqrt(2)/2 units long. Once we know the legs of the triangle, we can divide them over the hypotenuse to find the sine and cosine values.
sin(angle) = opposite/hypotenuse
sin(45) = (sqrt(2)/2) / 1
sin(45) = sqrt(2)/2
and
cos(angle) = adjacent/hypotenuse
cos(45) = (sqrt(2)/2) / 1
cos(45) = sqrt(2)/2
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For a 30-60-90 triangle, we would have
a = 1
b = x
c = 2
so,
a^2+b^2 = c^2
1^2+x^2 = 2^2
1+x^2 = 4
x^2 = 4-1
x^2 = 3
x = sqrt(3)
The missing leg is sqrt(3) units long.
Once we know the three sides of the 30-60-90 triangle, you should be able to see that
sin(30) = 1/2
sin(60) = sqrt(3)/2
cos(30) = sqrt(3)/2
cos(60) = 1/2
Answer:
Step-by-step explanation:
![\text{Use}\ a^\frac{1}{n}=\sqrt[n]{a}\\\\\sqrt{x+3}=\sqrt[2]{x+3}=(x+3)^\frac{1}{2}](https://tex.z-dn.net/?f=%5Ctext%7BUse%7D%5C%20a%5E%5Cfrac%7B1%7D%7Bn%7D%3D%5Csqrt%5Bn%5D%7Ba%7D%5C%5C%5C%5C%5Csqrt%7Bx%2B3%7D%3D%5Csqrt%5B2%5D%7Bx%2B3%7D%3D%28x%2B3%29%5E%5Cfrac%7B1%7D%7B2%7D)
Answer:
B. secondary roads
Step-by-step explanation:
While all of streets, county roads, and secondary roads are generally designed to carry less traffic and/or have lower speed limits than interstate highways, the generic name for such roads is ...
secondary roads.
