How many pounds of each does he use?
Hello Guest!
\(x+y=400\\ y=400-x\\ 2.7x+3.2y=3\cdot400\\ 2.7x+3.2(400-x)=1200\\ 2.7x-3.2x=-1280+1200\\ -0.5x=-80\\ \color{blue}x=160\ \text{pounds a 2.70 \$}\\ \color{blue}y=240\ \text{pounds a 3.20 \$} \)
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How many pages can he type before the meeting starts?
\(n=\dfrac{3}{4}h\times \dfrac{2}{\dfrac{1}{8}h}= \dfrac{3}{4}h\times \dfrac{2\cdot 8}{h}=\color{blue}12\)
d. 12 pages can he type before the meeting starts.
What is the value of n?
\(400,000^2=160,000,000,000=1.6\cdot 10^{11}\)
The value of n is 11.
Sind 1 liter 0,000 000 811 03 acre-foot?
Hallo Gast!
Das acre-foot ist definiert durch das Volumen, das notwendig ist, um eine Fläche von 1 acre mit einer Tiefe von 1 foot (Fuß) mit Wasser zu überfluten. Ein acre ist exakt 43.560 ft² (Quadratfuß) groß. Somit umfasst ein acre-foot ein Volumen von exakt 43,560 ft³ (Kubikfuß).
\(\frac{1\ acre-foot}{43560\ ft^3}\cdot \frac{1\ ft^3}{30,48^3cm^3}\cdot\frac{10^3cm^3}{l}=1\\ 1l=\frac{1\ acre-foot}{43560\ ft^3}\cdot \frac{1\ ft^3}{30,48^3cm^3}\cdot 10^3cm^3=8,107\ 131\ 9\cdot 10^{-7}\text{acre-foot}\\ \color{blue}1l=0,000\ 000\ 810\ 713\ 19\ \text{acre-foot}\)
Find the area of triangle ACD.
\(f(x)=\sqrt{8^2-x^2}\\ g(x)=\sqrt{20^2-(x-17)^2}\\ \sqrt{8^2-x^2}=\sqrt{20^2-(x-17)^2}\\64-x^2=400-x^2+34x-289\\ 34x=-47\\ x=-\dfrac{47}{34}\\ y=\sqrt{8^2-(-\frac{47}{34})^2}\)
\(A_{ACD}=\dfrac{xy}{2}\\ A_{ACD}=\dfrac{1.382\cdot 7.8985}{2}\\ \color{blue}A_{ACD}=5.469 \)
What is the slope of the line?
If the area of the triangle is 16, the line must intersect the y-axis at 4, because 8*4/2=16.
The slope of the line it 4 : 8 = 0.5
Solve the inequality
\(-4(x + 4) > x + 7 + 5(x + 2)\\ -4x-16>x+7+5x+10\\ -10x>33\\ \color{blue}x<-3.3\)
\(\color{blue}x\in \mathbb R \ |\ \) \(\color{blue}-\infty\) < x < -3.3
Solve the inequality 2x - 5 <= -x + 12 - 3x + 19
\(2x - 5 <= -x + 12 - 3x + 19 \\ 6x\leq 36\\ x\leq 6 \)
\(\color {blue}x\in\mathbb R\ |\ \)\(\color{blue}-\infty < x \le 6\)
Simplify
\((2y-1)(4y^{10}+2y^9+4y^8+2y^7 + y^6)\\ =y^6(2y-1)(y^4+2y^3+4y^2+2y+1)\\ =y^6(2y-1)((8y^3+2y^2+4y+2)y+1)\\ =y^6(2y-1)((((8y+2)y+4)y+2)y+1)\\ =y^6 (2 y - 1) (8 y^4 + 2 y^3 + 4 y^2 + 2 y + 1\\ \color{blue}=16 y^{11} - 4 y^{10} + 6 y^9 - y^6 \)
Solve the equation.
\( x + \sqrt{x - 2} = 4\\ \sqrt{x - 2} = 4-x\\ x-2=x^2-8x+16\\ x^2-9x+18=0\\ x=4.5\pm \sqrt{4.5^2-18}\\ x=4.5\pm 1.5\\ \color{blue}x\in\{3,6\}\)
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