Answer:
Distance is 8.485
Midpoint is (3,4)
Step-by-step explanation:
Use the points (-1,7) and (5,1)
Insert them into the equation and solve for D
![D=\sqrt{x} ((5-(-1))^2 + (1-7)^2)\\D=\sqrt{x} ((6)^2 + (-6)^2)\\D=\sqrt{x} (36+36)\\D=\sqrt{x} (72)\\D=8.485](https://tex.z-dn.net/?f=D%3D%5Csqrt%7Bx%7D%20%28%285-%28-1%29%29%5E2%20%2B%20%281-7%29%5E2%29%5C%5CD%3D%5Csqrt%7Bx%7D%20%28%286%29%5E2%20%2B%20%28-6%29%5E2%29%5C%5CD%3D%5Csqrt%7Bx%7D%20%2836%2B36%29%5C%5CD%3D%5Csqrt%7Bx%7D%20%2872%29%5C%5CD%3D8.485)
Insert points into second equation to find midpoint
![(\frac{_1+5}{2} , \frac{7+1}{2}) \\(\frac{6}{2} ,\frac{8}{2} )\\(3,4)](https://tex.z-dn.net/?f=%28%5Cfrac%7B_1%2B5%7D%7B2%7D%20%2C%20%5Cfrac%7B7%2B1%7D%7B2%7D%29%20%5C%5C%28%5Cfrac%7B6%7D%7B2%7D%20%2C%5Cfrac%7B8%7D%7B2%7D%20%29%5C%5C%283%2C4%29)
Answer:
Number of Muhammad's swim suits = k - 8
Step-by-step explanation:
Given:
Number of Charlie's swim suits = K
Number of Muhammad's swim suits = 8 less than Charlie
Find:
Expression [Number of Muhammad's swim suits]
Computation:
Number of Muhammad's swim suits = 8 less than Charlie
Number of Muhammad's swim suits = k - 8
Answer:
The value of a will be ![a=-\frac{1}{2}](https://tex.z-dn.net/?f=a%3D-%5Cfrac%7B1%7D%7B2%7D)
Step-by-step explanation:
Start by graphing the parabola and the three points of the triangle. These points are at intersections of y=a(x-1)(x-4) and the axes
so the y = 0 points are (1,0) and (4,0).
The x = 0 intersection is when y=a(-1)(-4) or (0,4a)
The base and height of this triangle are
The base would be the distance between the y=0 intersections and the height would be the y value of the other vertex.
Hence, base=3 units and height = 4a units. Thus, area can be calculated as
![A = \frac{1}{2}\times b\times h =\frac{1}{2}\times 3\times 4a = 3](https://tex.z-dn.net/?f=A%20%3D%20%5Cfrac%7B1%7D%7B2%7D%5Ctimes%20b%5Ctimes%20h%20%3D%5Cfrac%7B1%7D%7B2%7D%5Ctimes%203%5Ctimes%204a%20%3D%203)
![a=\frac{1}{2}](https://tex.z-dn.net/?f=a%3D%5Cfrac%7B1%7D%7B2%7D)
∵ the parabola opens downward therefore a will be negative.
hence, ![a=-\frac{1}{2}](https://tex.z-dn.net/?f=a%3D-%5Cfrac%7B1%7D%7B2%7D)
The surface area of a rectangular prism needs an formula.
For a rectangular prism you have to understand some about the shape.
It is a 3D shape consisting of 6 sides
all are rectangles
to determine the area of one rectangle is the base multiplied by the height or in this case length times with.
but you also need to account for all sides and the height.
so the Surface area formula would be like
![sa = l \times w + l \times h + w \times h](https://tex.z-dn.net/?f=sa%20%3D%20l%20%5Ctimes%20w%20%2B%20l%20%5Ctimes%20h%20%2B%20w%20%5Ctimes%20h)
this accounts for 3 of the sides of the rectangular prism.
the top,bottom,and side.
so to get the surface area of a rectangle prism you must mutiply each side by 2 to account for all sides of the rectangular prism.
so the surface area formula for a rectangular prism is
![SA = 2\\ \times l \times w +2 \times l \times h+2 \times h \times w](https://tex.z-dn.net/?f=SA%20%3D%202%5C%5C%20%20%5Ctimes%20l%20%5Ctimes%20w%20%2B2%20%5Ctimes%20l%20%5Ctimes%20h%2B2%20%5Ctimes%20h%20%5Ctimes%20w)
I won't solve it for you but just plug in your values for l,w,and h into that formula and you will get your answer in metres squared or m
<span>Simplifying
2x + -1y = 9
Solving
2x + -1y = 9
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add 'y' to each side of the equation.
2x + -1y + y = 9 + y
Combine like terms: -1y + y = 0
2x + 0 = 9 + y
2x = 9 + y
Divide each side by '2'.
x = 4.5 + 0.5y
Simplifying
x = 4.5 + 0.5y
Hope this helps :)
~I tried to space it out so it wont look like a bunch of mess scrambled up xD~</span>