Answer:
y = 18 and x = -2
Step-by-step explanation:
y = x^2+bx+c To find the turning point, or vertex, of this parabola, we need to work out the values of the coefficients b and c. We are given two different solutions of the equation. First, (2, 0). Second, (0, -14). So we have a value (-14) for c. We can substitute that into our first equation to find b. We can now plug in our values for b and c into the equation to get its standard form. To find the vertex, we can convert this equation to vertex form by completing the square. Thus, the vertex is (4.5, –6.25). We can confirm the solution graphically Plugging in (2,0) :
y=x2+bx+c
0=(2)^2+b(2)+c
y=4+2b+c
-2b=4+c
b=-2+2c
Plugging in (0,−14) :
y=x2+bx+c
−14=(0)2+b(0)+c
−16=0+b+c
b=16−c
Now that we have two equations isolated for b , we can simply use substitution and solve for c . y=x2+bx+c 16 + 2 = y y = 18 and x = -2
The volume of the prism 121.6 cube in.
Step-by-step explanation:
Given,
The base is right angle triangle whose two sides are equal.
So,
Base (b) = 8 in
Another side of right angle triangle (l) = 8 in
Height (h) of the prism = 3.8 in
To find the volume of the prism.
Formula:
V = 
bhl
Now,
V = ×8×8×3.8 cube in
= 121.6 cube in.
Given:
A(-5,4)
B(3,4)
C(3,-5)
So point D is:
so point D is (-5,-5)
For AB is
Distance between two point is:
![\begin{gathered} (x_1,y_1)and(x_2,y_2) \\ D=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20%28x_1%2Cy_1%29and%28x_2%2Cy_2%29%20%5C%5C%20D%3D%5Csqrt%5B%5D%7B%28x_2-x_1%29%5E2%2B%28y_2-y_1%29%5E2%7D%20%5Cend%7Bgathered%7D)
so distance between A(-5,4) and B(3,4) is:
![\begin{gathered} D=\sqrt[]{(3-(-5))^2+(4-4)^2} \\ =\sqrt[]{(8)^2+0^2} \\ =8 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20D%3D%5Csqrt%5B%5D%7B%283-%28-5%29%29%5E2%2B%284-4%29%5E2%7D%20%5C%5C%20%3D%5Csqrt%5B%5D%7B%288%29%5E2%2B0%5E2%7D%20%5C%5C%20%3D8%20%5Cend%7Bgathered%7D)
So AB is 8 unit apart.
For B(3,4) and C(3,-5).
![\begin{gathered} D=\sqrt[]{(3-3)^2+(-5-4)^2} \\ =\sqrt[]{0^2+(-9)^2} \\ =9 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20D%3D%5Csqrt%5B%5D%7B%283-3%29%5E2%2B%28-5-4%29%5E2%7D%20%5C%5C%20%3D%5Csqrt%5B%5D%7B0%5E2%2B%28-9%29%5E2%7D%20%5C%5C%20%3D9%20%5Cend%7Bgathered%7D)
So BC is 9 unit apart.
For fourth bush point is (-5,-5) it left of point C(3,-5) is:
![\begin{gathered} D=\sqrt[]{(3-(-5))^2+(-5-(-5))^2} \\ =\sqrt[]{(8)^2+0^2} \\ =8 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20D%3D%5Csqrt%5B%5D%7B%283-%28-5%29%29%5E2%2B%28-5-%28-5%29%29%5E2%7D%20%5C%5C%20%3D%5Csqrt%5B%5D%7B%288%29%5E2%2B0%5E2%7D%20%5C%5C%20%3D8%20%5Cend%7Bgathered%7D)
so fourth bush is 8 unit left of C.
For fourth bush(-5,-5) below to point A(-5,4)
![\begin{gathered} D=\sqrt[]{(-5-(-5))^2+(4-(-5))^2} \\ =\sqrt[]{0^2+9^2} \\ =9 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20D%3D%5Csqrt%5B%5D%7B%28-5-%28-5%29%29%5E2%2B%284-%28-5%29%29%5E2%7D%20%5C%5C%20%3D%5Csqrt%5B%5D%7B0%5E2%2B9%5E2%7D%20%5C%5C%20%3D9%20%5Cend%7Bgathered%7D)
so fourth bush 9 units below of A.
Answer:
6x^2 + 8x
Step-by-step explanation:
the 2 is on top of x, so its squared
Answer:
x=5/2 + a/2, y= 5/2 - a/2
Step-by-step explanation:
We can solve this system using addition of the equations
x+y=5
<u>x-y=a</u>
2x =(5+a)
x=(5+a)/2= 5/2 +a/2
x=5/2 +a/2
x-y=a
y = x - a , x=5/2 + a/2
y= 5/2 + a/2-a
y= 5/2 - a/2
