Answer:
B: (x, y) --> (x + 4, y - 3)
Step-by-step explanation:
the shape DEF went to the right along the x axis wich <em>increased</em> x and then went down the y axis or <em>decreased </em>y to make D'E'F'
some good way to remember these translations and orders are...
- x is first when plotting points, then y (x, y)
- x increases going right, and decreases going left, as well as y increasing going up, then decreasing going down
BONUS FACT:
the symbol ( ' ) is called a prime when refering to transformations and geometry ((as in D' is pronounced D prime))
Answer:
40 rubber bands are needed
5 rubber bands will be left from 5 bags of of rubber band
Step-by-step explanation:
Each student will need five rubber bands.
There are eight students
Total rubber bands needed = rubber bands per student × number of students
= 5 × 8
= 40
Total rubber bands needed = 40
Rubber bands come in bags of nine.
Number of bags needed = Total rubber bands needed / number of rubber bands in each bag
= 40 / 9
= 4.44 bags
It is impossible to get decimal number of rubber bands bag, so, the next whole number after 4 is 5
5 rubber bands bags will be bought which = 5 × 9
= 45 rubber bands
Only 40 rubber bands are needed
Left over rubber bands = 45 - 40
= 5 rubber bands
Answer:
Step-by-step explanation:
We have to find the equation of plane that is parallel to the vectors
The plane also passes through the point (2,0,-1).
Hence, the equation of plane s given by:
![\displaystyle\left[\begin{array}{ccc}x-2&y-0&z+1\\3&0&3\\0&1&3\end{array}\right]\\\\=(x-2)(0-3) - (y-0)(9-0) + (z+1)(3-0)\\=-3(x-2)-9y+3(z+1)\\\Rightarrow -3x + 6 - 9y + 3z + 3 = 0\\\Rightarrow 3x + 9y -3z -9 = 0\\\Rightarrow x + 3y -z - 3 = 0](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Dx-2%26y-0%26z%2B1%5C%5C3%260%263%5C%5C0%261%263%5Cend%7Barray%7D%5Cright%5D%5C%5C%5C%5C%3D%28x-2%29%280-3%29%20-%20%28y-0%29%289-0%29%20%2B%20%28z%2B1%29%283-0%29%5C%5C%3D-3%28x-2%29-9y%2B3%28z%2B1%29%5C%5C%5CRightarrow%20-3x%20%2B%206%20-%209y%20%2B%203z%20%2B%203%20%3D%200%5C%5C%5CRightarrow%203x%20%2B%209y%20-3z%20-9%20%3D%200%5C%5C%5CRightarrow%20x%20%2B%203y%20-z%20-%203%20%3D%200)
It is the required equation of plane.
(8x^2-9y^2-4x)+(x^2-3y^2-7x)
First, get rid of the parentheses and combine like terms
(8x^2+x^2)(-9y^2-3y^2)(-4x-7x)
9x^2-12y^2-11x is your answer
Answer:
The question is asking to solve a problem that'll "add up", or in other words, makes sense; through the use of Trigonometric functions. The leaning ladder is the hypotenuse of 17ft, adjacent to that is a wall that measures 16.5ft above the ground. The angle both sides make must be <=70°. The function here is Opposite over Hypotenuse i.e 16.5/17 . We use the inverse operation of Sin which is Sin^(-1) to find if the angle is < or = to 70°. Using a calculator, we find the angle to be 76.06°, which is > more than, 70°.
Thus, the ladder will not be safe for its height and therefore won't make sense.
