Answer:
b=-a
Step-by-step explanation:
if the distance from origin 0 of b is the same as the distance of a from b but in opposite directions, this makes b differ from a by polarity but with similar values.
Answer:
Rule is (x, y+k)
New point is (-3,9)
Step-by-step explanation:
A point translated vertically k units up means the x coordinate remains the same in the translation but the y coordinate is increased by k units
This can be represented mathematically as;
Let;s assume the point to be A with coordinates (x,y) then to get the image of the point under a vertical translation k units up you add k to the y coordinate value.
Given ;

where T is the translation
In the question
Given (-3,-6) and T is (0,5) the new coordinate will be

This is a 30-60-90 triangle and we can apply rules to easily identify the hypotenuse of this triangle, which is denoted by <em>x</em>.
The length of the longer side of the triangle is given in the problem. To solve the hypotenuse of this triangle, let's solve first for the length of the shorter side of the triangle.
The shorter side can be solved by just dividing the length of the longer side by the square root of 3. Hence, we have
![short=\frac{4}{\sqrt[]{3}}](https://tex.z-dn.net/?f=short%3D%5Cfrac%7B4%7D%7B%5Csqrt%5B%5D%7B3%7D%7D)
Since we already have the values for the length of the shorter side and longer side, we can solve for the hypotenuse using the Pythagorean theorem.
![\begin{gathered} c=\sqrt[]{a^2+b^2} \\ c=\sqrt[]{4^2+(\frac{4}{\sqrt[]{3}})^2} \\ c=\sqrt[]{16+\frac{16}{3}} \\ c=\sqrt[]{\frac{64}{3}} \\ c=\frac{8}{\sqrt[]{3}}\cdot\frac{\sqrt[]{3}}{\sqrt[]{3}} \\ c=\frac{8\sqrt[]{3}}{3} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20c%3D%5Csqrt%5B%5D%7Ba%5E2%2Bb%5E2%7D%20%5C%5C%20c%3D%5Csqrt%5B%5D%7B4%5E2%2B%28%5Cfrac%7B4%7D%7B%5Csqrt%5B%5D%7B3%7D%7D%29%5E2%7D%20%5C%5C%20c%3D%5Csqrt%5B%5D%7B16%2B%5Cfrac%7B16%7D%7B3%7D%7D%20%5C%5C%20c%3D%5Csqrt%5B%5D%7B%5Cfrac%7B64%7D%7B3%7D%7D%20%5C%5C%20c%3D%5Cfrac%7B8%7D%7B%5Csqrt%5B%5D%7B3%7D%7D%5Ccdot%5Cfrac%7B%5Csqrt%5B%5D%7B3%7D%7D%7B%5Csqrt%5B%5D%7B3%7D%7D%20%5C%5C%20c%3D%5Cfrac%7B8%5Csqrt%5B%5D%7B3%7D%7D%7B3%7D%20%5Cend%7Bgathered%7D)
Hence, the value of hypotenuse for this right triangle is
Answer: 10 cm
Step-by-step explanation:
The circumference of the CD = 22\pi
We know that the formula of the circumference is:
Circumference = 2\pi r
We will substitute the value of circumference to find the radius:
22 pi = 2 x pi x r
r = 11
Therefore its radius will be 22 / 2 = 11 cm
Jamie wants to cut the CD from the middle of the CD to one side but leaving one cm. To find the measurement of the cut portion, we will subtract 1 from 11 to get:
11 - 1 = 10 cm
Step-by-step explanation:
3.14×6×6 = X
3.14×9×9 = Y
take Y-X