Answer:
see explanation
Step-by-step explanation:
Given a line with a slope of zero.
This is a horizontal line parallel to the x- axis.
The equation of the line is y = c
where c is the value of the y- coordinates the line passes through.
The line passes through (0, 4 ) with a y- coordinate of 4, thus
Equation of line is y = 4
Thus
The line is horizontal
The line goes through (4, 4 )
The y- values are all 4
Ada 1 penyelesaian kerana mereka itu = antara satu sama lain.
Answer:
45 ways
Step-by-step explanation:
Total number of kids = 10
We have to select the 2 kids
So the number ways to select two kids ![^{10}C_2](https://tex.z-dn.net/?f=%5E%7B10%7DC_2)
We know that ![^{n}C_r=\frac{n!}{r!(n-r)!}](https://tex.z-dn.net/?f=%5E%7Bn%7DC_r%3D%5Cfrac%7Bn%21%7D%7Br%21%28n-r%29%21%7D)
So ![^{10}C_2=\frac{10!}{2!(10-2)!}=\frac{10!}{2!\times 8!}=\frac{10\times 9\times 8!}{2\times 8!}=45](https://tex.z-dn.net/?f=%5E%7B10%7DC_2%3D%5Cfrac%7B10%21%7D%7B2%21%2810-2%29%21%7D%3D%5Cfrac%7B10%21%7D%7B2%21%5Ctimes%208%21%7D%3D%5Cfrac%7B10%5Ctimes%209%5Ctimes%208%21%7D%7B2%5Ctimes%208%21%7D%3D45)
So there are 45 ways to select 2 competitors
Answer:
![\mathrm{Minimum}\space\left(\frac{7}{2},\:-\frac{33}{4}\right)](https://tex.z-dn.net/?f=%5Cmathrm%7BMinimum%7D%5Cspace%5Cleft%28%5Cfrac%7B7%7D%7B2%7D%2C%5C%3A-%5Cfrac%7B33%7D%7B4%7D%5Cright%29)
Step-by-step explanation:
![y=x^2-7x+4\\\mathrm{The\:vertex\:of\:an\:up-down\:facing\:parabola\:of\:the\:form}\:y=ax^2+bx+c\:\mathrm{is}\:x_v=-\frac{b}{2a}\\\mathrm{The\:parabola\:params\:are:}\\a=1,\:b=-7,\:c=4\\x_v=-\frac{b}{2a}\\x_v=-\frac{\left(-7\right)}{2\cdot \:1}\\\mathrm{Simplify}\\x_v=\frac{7}{2}\\\mathrm{Plug\:in}\:\:x_v=\frac{7}{2}\:\mathrm{to\:find\:the}\:y_v\:\mathrm{value}\\y_v=\left(\frac{7}{2}\right)^2-7\cdot \frac{7}{2}+4\\](https://tex.z-dn.net/?f=y%3Dx%5E2-7x%2B4%5C%5C%5Cmathrm%7BThe%5C%3Avertex%5C%3Aof%5C%3Aan%5C%3Aup-down%5C%3Afacing%5C%3Aparabola%5C%3Aof%5C%3Athe%5C%3Aform%7D%5C%3Ay%3Dax%5E2%2Bbx%2Bc%5C%3A%5Cmathrm%7Bis%7D%5C%3Ax_v%3D-%5Cfrac%7Bb%7D%7B2a%7D%5C%5C%5Cmathrm%7BThe%5C%3Aparabola%5C%3Aparams%5C%3Aare%3A%7D%5C%5Ca%3D1%2C%5C%3Ab%3D-7%2C%5C%3Ac%3D4%5C%5Cx_v%3D-%5Cfrac%7Bb%7D%7B2a%7D%5C%5Cx_v%3D-%5Cfrac%7B%5Cleft%28-7%5Cright%29%7D%7B2%5Ccdot%20%5C%3A1%7D%5C%5C%5Cmathrm%7BSimplify%7D%5C%5Cx_v%3D%5Cfrac%7B7%7D%7B2%7D%5C%5C%5Cmathrm%7BPlug%5C%3Ain%7D%5C%3A%5C%3Ax_v%3D%5Cfrac%7B7%7D%7B2%7D%5C%3A%5Cmathrm%7Bto%5C%3Afind%5C%3Athe%7D%5C%3Ay_v%5C%3A%5Cmathrm%7Bvalue%7D%5C%5Cy_v%3D%5Cleft%28%5Cfrac%7B7%7D%7B2%7D%5Cright%29%5E2-7%5Ccdot%20%5Cfrac%7B7%7D%7B2%7D%2B4%5C%5C)
![\mathrm{Simplify\:}\left(\frac{7}{2}\right)^2-7\cdot \frac{7}{2}+4:\quad -\frac{33}{4}\\y_v=-\frac{33}{4}\\Therefore\:the\:parabola\:vertex\:is\\\left(\frac{7}{2},\:-\frac{33}{4}\right)\\\mathrm{If}\:a0,\:\mathrm{then\:the\:vertex\:is\:a\:minimum\:value}\\a=1\\\mathrm{Minimum}\space\left(\frac{7}{2},\:-\frac{33}{4}\right)](https://tex.z-dn.net/?f=%5Cmathrm%7BSimplify%5C%3A%7D%5Cleft%28%5Cfrac%7B7%7D%7B2%7D%5Cright%29%5E2-7%5Ccdot%20%5Cfrac%7B7%7D%7B2%7D%2B4%3A%5Cquad%20-%5Cfrac%7B33%7D%7B4%7D%5C%5Cy_v%3D-%5Cfrac%7B33%7D%7B4%7D%5C%5CTherefore%5C%3Athe%5C%3Aparabola%5C%3Avertex%5C%3Ais%5C%5C%5Cleft%28%5Cfrac%7B7%7D%7B2%7D%2C%5C%3A-%5Cfrac%7B33%7D%7B4%7D%5Cright%29%5C%5C%5Cmathrm%7BIf%7D%5C%3Aa%3C0%2C%5C%3A%5Cmathrm%7Bthen%5C%3Athe%5C%3Avertex%5C%3Ais%5C%3Aa%5C%3Amaximum%5C%3Avalue%7D%5C%5C%5Cmathrm%7BIf%7D%5C%3Aa%3E0%2C%5C%3A%5Cmathrm%7Bthen%5C%3Athe%5C%3Avertex%5C%3Ais%5C%3Aa%5C%3Aminimum%5C%3Avalue%7D%5C%5Ca%3D1%5C%5C%5Cmathrm%7BMinimum%7D%5Cspace%5Cleft%28%5Cfrac%7B7%7D%7B2%7D%2C%5C%3A-%5Cfrac%7B33%7D%7B4%7D%5Cright%29)
<em>x</em> kg of Maxwell House coffee contains 0.13<em>x</em> kg of Columbian beans.
<em>y</em> kg of Folgers contains 0.21<em>y</em> kg of beans.
You want a mixture weighing 70 kg, so
<em>x</em> + <em>y</em> = 70
You also want this blend to consist of 19% Columbian beans, or 0.19 (70 kg) = 13.3 kg, so
0.13<em>x</em> + 0.21<em>y</em> = 13.3
Solve for <em>x</em> and <em>y</em> :
<em>x</em> + <em>y</em> = 70 ===> <em>y</em> = 70 - <em>x</em>
0.13<em>x</em> + 0.21<em>y</em> = 13.3 ===> 0.13<em>x</em> + 0.21 (70 - <em>x</em>) = 13.3
0.13<em>x</em> + 14.7 - 0.21<em>x</em> = 13.3
14.7 - 13.3 = 0.21<em>x</em> - 0.13<em>x</em>
1.4 = 0.08<em>x</em>
<em>x</em> = 17.5
<em>y</em> = 52.5