Answer :- parallelogram
Step-by-step explanation:
Anthony has a square-shaped, wooden board. To build a door, he uses the board and cuts 3 feet off of its width. The new area of the wooden board is given by the expression below, where x represents the length in feet.
x(x-3)
Which statement best describes the term (x - 3)?
Answer:
y = -2(x -2)^2 + 11
Step-by-step explanation:
It works well to factor the leading coefficient from the first two terms.
... y = -2(x^2 -4x) +3
Now we want to add the square of half the x-coefficient inside parentheses, and subtract the equivalent quantity outside parentheses.
... y = -2(x^2 -4x +4) +3 - (-2·4)
... y = -2(x -2)^2 +11 . . . . . . . . simplify
_____
The form given in the problem statement is called "vertex form," where the vertex of the parabola is (h, k). A graph shows us the vertex is (2, 11), so we can write the function immediately as ...
... y = -2(x -2)^2 +11
Answer:
<em>The points that are 10 units from P(-17,-2) are (-23,6) and (-11,6)</em>
Step-by-step explanation:
<u>Distance Between Points in the Plane
</u>
Given two points A(x,y) and B(w,z), the distance between them is:
![d=\sqrt{(z-y)^2+(w-x)^2}](https://tex.z-dn.net/?f=d%3D%5Csqrt%7B%28z-y%29%5E2%2B%28w-x%29%5E2%7D)
It can be also expressed as:
![d^2=(z-y)^2+(w-x)^2](https://tex.z-dn.net/?f=d%5E2%3D%28z-y%29%5E2%2B%28w-x%29%5E2)
Substituting the values of both points, and knowing the distance is 10:
![10^2=(6-(-2))^2+(x+17)^2](https://tex.z-dn.net/?f=10%5E2%3D%286-%28-2%29%29%5E2%2B%28x%2B17%29%5E2)
![100=8^2+(x+17)^2](https://tex.z-dn.net/?f=100%3D8%5E2%2B%28x%2B17%29%5E2)
Swapping both sides:
![64+(x+17)^2=100](https://tex.z-dn.net/?f=64%2B%28x%2B17%29%5E2%3D100)
Moving the constants to the right side:
![(x+17)^2=100-64=36](https://tex.z-dn.net/?f=%28x%2B17%29%5E2%3D100-64%3D36)
Taking the square root:
![x+17=\pm 6](https://tex.z-dn.net/?f=x%2B17%3D%5Cpm%206)
We get two possible answers:
![x=-17-6=-23](https://tex.z-dn.net/?f=x%3D-17-6%3D-23)
![x=-17+6=-11](https://tex.z-dn.net/?f=x%3D-17%2B6%3D-11)
Thus the points that are 10 units from the point P(-17,-2) are (-23,6) and (-11,6)
Answer:
![\frac{15+6}{10-3}](https://tex.z-dn.net/?f=%5Cfrac%7B15%2B6%7D%7B10-3%7D)
Step-by-step explanation:
Sum of 15 and 6 = 15 + 6
Difference of 10 and 3 = 10 - 3
So, the expression is
![\frac {15 + 6}{10-3}](https://tex.z-dn.net/?f=%5Cfrac%20%7B15%20%2B%206%7D%7B10-3%7D)
This is the required expression.