Hello :
the normal vector of the plane is : d' = [4,-1,5]...(vector perpendicular to the plane)<span>
d </span><span>⊥ d' because : (4)(2)+(-1)(3)+(5)(1)=0
</span>the line is perpendicular to the plane .
Answer:
y = (1/4)x
Step-by-step explanation:
"Direct variation" here signifies y = kx, where k is the constant of proportionality.
Then y = kx. Here we are to find k using the info that x = 12 and y = 3:
3 = k(12), or
k = 3/12, or k = 1/4
Then y = (1/4)x
Number 19 you are comparing one measurement to another. Since it says 1/2 inch equals 4 ft, we want to find out how many more inches are needed if the given scale was 2/3 = 4 ft. Now lets find a common denominator for both scales stated in inches. We have 2/3 inch and 1/2 inch. Our denominator are the bottom parts of the fraction where we need to find a common factor for the denominator so we can add or subtract fractions. We have a 3 and a 2. You may always use the multiplication between two denominators to find a common factor such as 3 times 2 which equals 6 for both denominators. Now we multiplied the 3 by 2 to get 6 so the top part (numerator needs to be multiplied the the 2 because we changed the bottom part by 2 as well. You should notice that when you reduce your fraction now 4/6 is 2/3. Just a self check example there. As for 1/2 we multiplied a 3 to get 6 for the denominator so we need to multiply the numerator by 3 as well. You now should have 4/6 and 3/6. Since the question asks for how many more inches we need to subtract 4/6 from 3/6 and we get 1/6 inch for our answer.
let's notice the tickmarks on the left and right sides, meaning those two sides are twins, and therefore equal, so the perimeter is simply 2.5+2.5+3.5+2.5 = 11 ft.
the trapezoid has an altitude/height of 2 ft, thus
![\bf \textit{area of a trapezoid}\\\\ A=\cfrac{h(a+b)}{2}~~ \begin{cases} a,b=\stackrel{bases}{parallel~sides}\\ h=height\\[-0.5em] \hrulefill\\ a=2.5\\ b=3.5\\ h=2 \end{cases}\implies A=\cfrac{2(2.5+3.5)}{2}\implies A=6](https://tex.z-dn.net/?f=%5Cbf%20%5Ctextit%7Barea%20of%20a%20trapezoid%7D%5C%5C%5C%5C%20A%3D%5Ccfrac%7Bh%28a%2Bb%29%7D%7B2%7D~~%20%5Cbegin%7Bcases%7D%20a%2Cb%3D%5Cstackrel%7Bbases%7D%7Bparallel~sides%7D%5C%5C%20h%3Dheight%5C%5C%5B-0.5em%5D%20%5Chrulefill%5C%5C%20a%3D2.5%5C%5C%20b%3D3.5%5C%5C%20h%3D2%20%5Cend%7Bcases%7D%5Cimplies%20A%3D%5Ccfrac%7B2%282.5%2B3.5%29%7D%7B2%7D%5Cimplies%20A%3D6)
According to Google, a Variable is <span>any factor, trait, or condition that can exist in differing amounts or types. If you type in variable in the Google search bar, it will give you the definition in a little box at the very top of the page :).
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