Answer:
![15x^2+5xy-125=0](https://tex.z-dn.net/?f=15x%5E2%2B5xy-125%3D0)
Step-by-step explanation:
We are give the following in the question:
Dimensions of rectangle:
Length , l =
![l = x\sqrt{100} = 10x](https://tex.z-dn.net/?f=l%20%3D%20x%5Csqrt%7B100%7D%20%3D%2010x)
Width of rectangle, w =
![w = \dfrac{y}{2} +\dfrac{3x}{2}](https://tex.z-dn.net/?f=w%20%3D%20%5Cdfrac%7By%7D%7B2%7D%20%2B%5Cdfrac%7B3x%7D%7B2%7D)
Area of rectangle = 125 square cm.
Area of rectangle =
![A =l\times w](https://tex.z-dn.net/?f=A%20%3Dl%5Ctimes%20w)
Putting values, we get,
![125 = 10x\times (\dfrac{y}{2}+\dfrac{3x}{2})\\\\125 = 5xy+15x^2\\15x^2+5xy-125=0](https://tex.z-dn.net/?f=125%20%3D%2010x%5Ctimes%20%28%5Cdfrac%7By%7D%7B2%7D%2B%5Cdfrac%7B3x%7D%7B2%7D%29%5C%5C%5C%5C125%20%3D%205xy%2B15x%5E2%5C%5C15x%5E2%2B5xy-125%3D0)
is the required equation.
Answer:
<h3>
x₁ = -1, x₂ = 3</h3>
Step-by-step explanation:
![4x^2-8x-12=0\\{}\qquad\qquad^{\div4\qquad\div4}\\x^2-2x-3=0\\\\x^2+x-3x-3=0\\\\x(x+1)-3(x+1)=0\\\\(x+1)(x-3)=0\\\\x+1=0\quad\vee\quad x-3=0\\\\x=-1\quad\vee\quad x=3](https://tex.z-dn.net/?f=4x%5E2-8x-12%3D0%5C%5C%7B%7D%5Cqquad%5Cqquad%5E%7B%5Cdiv4%5Cqquad%5Cdiv4%7D%5C%5Cx%5E2-2x-3%3D0%5C%5C%5C%5Cx%5E2%2Bx-3x-3%3D0%5C%5C%5C%5Cx%28x%2B1%29-3%28x%2B1%29%3D0%5C%5C%5C%5C%28x%2B1%29%28x-3%29%3D0%5C%5C%5C%5Cx%2B1%3D0%5Cquad%5Cvee%5Cquad%20x-3%3D0%5C%5C%5C%5Cx%3D-1%5Cquad%5Cvee%5Cquad%20x%3D3)
Answer:
![2(a^3+b^2+11)+1(3+a^3+b+11)=3a^3+2b^2+b+36](https://tex.z-dn.net/?f=2%28a%5E3%2Bb%5E2%2B11%29%2B1%283%2Ba%5E3%2Bb%2B11%29%3D3a%5E3%2B2b%5E2%2Bb%2B36)
Step-by-step explanation:
I assume that you need simplification of the given expression.
The given expression is:
![2(a^3+b^2+11)+1(3+a^3+b+11)](https://tex.z-dn.net/?f=2%28a%5E3%2Bb%5E2%2B11%29%2B1%283%2Ba%5E3%2Bb%2B11%29)
Using distributive property and multiplying 2 inside the parenthesis and 1 inside the other parenthesis. This gives,
![2(a^3+b^2+11)=2\times a^3+2\times b^2+2\times 11\\2(a^3+b^2+11)=2a^3+2b^2+22\\\\1(3+a^3+b+11)=1\times 3+1\times a^3+1\times b+1\times 11\\1(3+a^3+b+11)=3+a^3+b+11=a^3+b+14](https://tex.z-dn.net/?f=2%28a%5E3%2Bb%5E2%2B11%29%3D2%5Ctimes%20a%5E3%2B2%5Ctimes%20b%5E2%2B2%5Ctimes%2011%5C%5C2%28a%5E3%2Bb%5E2%2B11%29%3D2a%5E3%2B2b%5E2%2B22%5C%5C%5C%5C1%283%2Ba%5E3%2Bb%2B11%29%3D1%5Ctimes%203%2B1%5Ctimes%20a%5E3%2B1%5Ctimes%20b%2B1%5Ctimes%2011%5C%5C1%283%2Ba%5E3%2Bb%2B11%29%3D3%2Ba%5E3%2Bb%2B11%3Da%5E3%2Bb%2B14)
Therefore,
is equal to:
![2a^3+2b^2+22+a^3+b+14](https://tex.z-dn.net/?f=2a%5E3%2B2b%5E2%2B22%2Ba%5E3%2Bb%2B14)
Now, combining like terms using the commutative property of addition, we get:
![=(2a^3+a^3)+2b^2+b+(22+14)\\=3a^3+2b^2+b+36](https://tex.z-dn.net/?f=%3D%282a%5E3%2Ba%5E3%29%2B2b%5E2%2Bb%2B%2822%2B14%29%5C%5C%3D3a%5E3%2B2b%5E2%2Bb%2B36)
Therefore, the simplified form is ![3a^3+2b^2+b+36](https://tex.z-dn.net/?f=3a%5E3%2B2b%5E2%2Bb%2B36)
Answer:
see below
Step-by-step explanation:
— 7x — бу = — 15
To find the x intercept set y = 0 and solve for x
-7x - 0 = -15
-7x= -15
Divide by -7
-7x/-7 = -15/-7
x = 15/7
The x intercept is (15/7,0)
To find the y intercept set x = 0 and solve for y
o— бу = — 15
— бу= -15
Divide by -6
— бу/-6= -15/-6
у= 5/2
The y intercept is (0,5/2)
Yes bdndjsjshshdjbfbdbejsbsbdjsjsnrjrnbdnrnr fork