Answer:
17
Step-by-step explanation:
Answer:
x-intercept: (2,0)
y-intercept: (0,4)
Step-by-step explanation:
x-intercept: when y = 0
y = -2x + 4
0 = -2x + 4
x = 2
y-intercept: when x = 0
y = -2x + 4
y = -2(0) + 4
y = 4
<h3>5) Find the solution set of the inequality
![230 \leq 10c + 30](https://tex.z-dn.net/?f=230%20%5Cleq%20%2010c%20%2B%2030)
</h3>
From given,
![230 \leq 10c + 30](https://tex.z-dn.net/?f=230%20%5Cleq%20%2010c%20%2B%2030)
![\mathrm{Switch\:sides}\\\\10c+30\ge \:230\\\\\mathrm{Subtract\:}30\mathrm{\:from\:both\:sides}\\\\10c+30-30\ge \:230-30\\\\\mathrm{Simplify}\\\\10c\ge \:200\\\\\mathrm{Divide\:both\:sides\:by\:}10\\\\\frac{10c}{10}\ge \frac{200}{10}\\\\\mathrm{Simplify}\\\\c\ge \:20](https://tex.z-dn.net/?f=%5Cmathrm%7BSwitch%5C%3Asides%7D%5C%5C%5C%5C10c%2B30%5Cge%20%5C%3A230%5C%5C%5C%5C%5Cmathrm%7BSubtract%5C%3A%7D30%5Cmathrm%7B%5C%3Afrom%5C%3Aboth%5C%3Asides%7D%5C%5C%5C%5C10c%2B30-30%5Cge%20%5C%3A230-30%5C%5C%5C%5C%5Cmathrm%7BSimplify%7D%5C%5C%5C%5C10c%5Cge%20%5C%3A200%5C%5C%5C%5C%5Cmathrm%7BDivide%5C%3Aboth%5C%3Asides%5C%3Aby%5C%3A%7D10%5C%5C%5C%5C%5Cfrac%7B10c%7D%7B10%7D%5Cge%20%5Cfrac%7B200%7D%7B10%7D%5C%5C%5C%5C%5Cmathrm%7BSimplify%7D%5C%5C%5C%5Cc%5Cge%20%5C%3A20)
The solution set is:
![230\le \:10c+30\quad :\quad \begin{bmatrix}\mathrm{Solution:}\:&\:c\ge \:20\:\\ \:\mathrm{Interval\:Notation:}&\:[20,\:\infty \:)\end{bmatrix}](https://tex.z-dn.net/?f=230%5Cle%20%5C%3A10c%2B30%5Cquad%20%3A%5Cquad%20%5Cbegin%7Bbmatrix%7D%5Cmathrm%7BSolution%3A%7D%5C%3A%26%5C%3Ac%5Cge%20%5C%3A20%5C%3A%5C%5C%20%5C%3A%5Cmathrm%7BInterval%5C%3ANotation%3A%7D%26%5C%3A%5B20%2C%5C%3A%5Cinfty%20%5C%3A%29%5Cend%7Bbmatrix%7D)
6)
<h3>Write an inequality that represents all solutions to
![4(2x + 8) \leq 40](https://tex.z-dn.net/?f=4%282x%20%2B%208%29%20%5Cleq%20%2040)
</h3>
From given,
![4(2x + 8) \leq 40](https://tex.z-dn.net/?f=4%282x%20%2B%208%29%20%5Cleq%20%2040)
![\mathrm{Divide\:both\:sides\:by\:}4](https://tex.z-dn.net/?f=%5Cmathrm%7BDivide%5C%3Aboth%5C%3Asides%5C%3Aby%5C%3A%7D4)
![\frac{4\left(2x+8\right)}{4}\le \frac{40}{4}](https://tex.z-dn.net/?f=%5Cfrac%7B4%5Cleft%282x%2B8%5Cright%29%7D%7B4%7D%5Cle%20%5Cfrac%7B40%7D%7B4%7D)
![\mathrm{Simplify}\\\\2x+8\le \:10\\\\\mathrm{Subtract\:}8\mathrm{\:from\:both\:sides}\\\\2x+8-8\le \:10-8\\\\\mathrm{Simplify}\\2x\le \:2\\\\\mathrm{Divide\:both\:sides\:by\:}2\\\\\frac{2x}{2}\le \frac{2}{2}\\\\\mathrm{Simplify}\\\\x\le \:1](https://tex.z-dn.net/?f=%5Cmathrm%7BSimplify%7D%5C%5C%5C%5C2x%2B8%5Cle%20%5C%3A10%5C%5C%5C%5C%5Cmathrm%7BSubtract%5C%3A%7D8%5Cmathrm%7B%5C%3Afrom%5C%3Aboth%5C%3Asides%7D%5C%5C%5C%5C2x%2B8-8%5Cle%20%5C%3A10-8%5C%5C%5C%5C%5Cmathrm%7BSimplify%7D%5C%5C2x%5Cle%20%5C%3A2%5C%5C%5C%5C%5Cmathrm%7BDivide%5C%3Aboth%5C%3Asides%5C%3Aby%5C%3A%7D2%5C%5C%5C%5C%5Cfrac%7B2x%7D%7B2%7D%5Cle%20%5Cfrac%7B2%7D%7B2%7D%5C%5C%5C%5C%5Cmathrm%7BSimplify%7D%5C%5C%5C%5Cx%5Cle%20%5C%3A1)
The solution set is:
![4\left(2x+8\right)\le \:40\quad :\quad \begin{bmatrix}\mathrm{Solution:}\:&\:x\le \:1\:\\ \:\mathrm{Interval\:Notation:}&\:(-\infty \:,\:1]\end{bmatrix}](https://tex.z-dn.net/?f=4%5Cleft%282x%2B8%5Cright%29%5Cle%20%5C%3A40%5Cquad%20%3A%5Cquad%20%5Cbegin%7Bbmatrix%7D%5Cmathrm%7BSolution%3A%7D%5C%3A%26%5C%3Ax%5Cle%20%5C%3A1%5C%3A%5C%5C%20%5C%3A%5Cmathrm%7BInterval%5C%3ANotation%3A%7D%26%5C%3A%28-%5Cinfty%20%5C%3A%2C%5C%3A1%5D%5Cend%7Bbmatrix%7D)
6)
<h3>What is the solution set of the inequality 6(2 - r) < 18 ?</h3>
From given,
![6(2 - r) < 18](https://tex.z-dn.net/?f=6%282%20-%20r%29%20%3C%2018)
![\mathrm{Divide\:both\:sides\:by\:}6\\\\\frac{6\left(2-r\right)}{6}](https://tex.z-dn.net/?f=%5Cmathrm%7BDivide%5C%3Aboth%5C%3Asides%5C%3Aby%5C%3A%7D6%5C%5C%5C%5C%5Cfrac%7B6%5Cleft%282-r%5Cright%29%7D%7B6%7D%3C%5Cfrac%7B18%7D%7B6%7D%5C%5C%5C%5C%5Cmathrm%7BSimplify%7D%5C%5C%5C%5C2-r%3C3%5C%5C%5C%5C%5Cmathrm%7BSubtract%5C%3A%7D2%5Cmathrm%7B%5C%3Afrom%5C%3Aboth%5C%3Asides%7D%5C%5C%5C%5C2-r-2%3C3-2%5C%5C%5C%5C%5Cmathrm%7BSimplify%7D%5C%5C%5C%5C-r%3C1%5C%5C%5C%5C%5Cmathrm%7BMultiply%5C%3Aboth%5C%3Asides%5C%3Aby%5C%3A-1%5C%3A%5Cleft%28reverse%5C%3Athe%5C%3Ainequality%5Cright%29%7D)
When, we multiply or divide both sides by negative number, we must flip the inequality sign
![\left(-r\right)\left(-1\right)>1\cdot \left(-1\right)\\\\\mathrm{Simplify}\\\\r>-1](https://tex.z-dn.net/?f=%5Cleft%28-r%5Cright%29%5Cleft%28-1%5Cright%29%3E1%5Ccdot%20%5Cleft%28-1%5Cright%29%5C%5C%5C%5C%5Cmathrm%7BSimplify%7D%5C%5C%5C%5Cr%3E-1)
The solution set is:
![6\left(2-r\right)-1\:\\ \:\mathrm{Interval\:Notation:}&\:\left(-1,\:\infty \:\right)\end{bmatrix}](https://tex.z-dn.net/?f=6%5Cleft%282-r%5Cright%29%3C18%5Cquad%20%3A%5Cquad%20%5Cbegin%7Bbmatrix%7D%5Cmathrm%7BSolution%3A%7D%5C%3A%26%5C%3Ar%3E-1%5C%3A%5C%5C%20%5C%3A%5Cmathrm%7BInterval%5C%3ANotation%3A%7D%26%5C%3A%5Cleft%28-1%2C%5C%3A%5Cinfty%20%5C%3A%5Cright%29%5Cend%7Bbmatrix%7D)
7)
<h3>Solve the inequality 4(-3b + 4) - b > -16b + 12</h3>
From given,
![4(-3b + 4) - b > -16b + 12](https://tex.z-dn.net/?f=4%28-3b%20%2B%204%29%20-%20b%20%3E%20-16b%20%2B%2012)
![-12b + 16 - b > -16b + 12\\\\-13b + 16>-16b+12\\\\\mathrm{Subtract\:}16\mathrm{\:from\:both\:sides}\\\\-13b+16-16>-16b+12-16\\\\\mathrm{Simplify}\\\\-13b>-16b-4\\\\\mathrm{Add\:}16b\mathrm{\:to\:both\:sides}\\\\-13b+16b>-16b-4+16b\\\\\mathrm{Simplify}\\\\3b>-4\\\\\mathrm{Divide\:both\:sides\:by\:}3\\\\\frac{3b}{3}>\frac{-4}{3}\\\\\mathrm{Simplify}\\\\b>-\frac{4}{3}](https://tex.z-dn.net/?f=-12b%20%2B%2016%20-%20b%20%3E%20-16b%20%2B%2012%5C%5C%5C%5C-13b%20%2B%2016%3E-16b%2B12%5C%5C%5C%5C%5Cmathrm%7BSubtract%5C%3A%7D16%5Cmathrm%7B%5C%3Afrom%5C%3Aboth%5C%3Asides%7D%5C%5C%5C%5C-13b%2B16-16%3E-16b%2B12-16%5C%5C%5C%5C%5Cmathrm%7BSimplify%7D%5C%5C%5C%5C-13b%3E-16b-4%5C%5C%5C%5C%5Cmathrm%7BAdd%5C%3A%7D16b%5Cmathrm%7B%5C%3Ato%5C%3Aboth%5C%3Asides%7D%5C%5C%5C%5C-13b%2B16b%3E-16b-4%2B16b%5C%5C%5C%5C%5Cmathrm%7BSimplify%7D%5C%5C%5C%5C3b%3E-4%5C%5C%5C%5C%5Cmathrm%7BDivide%5C%3Aboth%5C%3Asides%5C%3Aby%5C%3A%7D3%5C%5C%5C%5C%5Cfrac%7B3b%7D%7B3%7D%3E%5Cfrac%7B-4%7D%7B3%7D%5C%5C%5C%5C%5Cmathrm%7BSimplify%7D%5C%5C%5C%5Cb%3E-%5Cfrac%7B4%7D%7B3%7D)
The solution set is:
![\left(-3b+4\right)-b>-16b+12\quad :\quad \begin{bmatrix}\mathrm{Solution:}\:&\:b>-\frac{4}{3}\\\\\:\mathrm{Interval\:Notation:}&\:\left(-\frac{4}{3},\:\infty \:\right)\end{bmatrix}](https://tex.z-dn.net/?f=%5Cleft%28-3b%2B4%5Cright%29-b%3E-16b%2B12%5Cquad%20%3A%5Cquad%20%5Cbegin%7Bbmatrix%7D%5Cmathrm%7BSolution%3A%7D%5C%3A%26%5C%3Ab%3E-%5Cfrac%7B4%7D%7B3%7D%5C%5C%5C%5C%5C%3A%5Cmathrm%7BInterval%5C%3ANotation%3A%7D%26%5C%3A%5Cleft%28-%5Cfrac%7B4%7D%7B3%7D%2C%5C%3A%5Cinfty%20%5C%3A%5Cright%29%5Cend%7Bbmatrix%7D)
Answer:
B
Step-by-step explanation:
trust me bro i gotchu
Answer: 2/3
Step-by-step explanation:
14 is 2/3 of 21 so 2/3 cup per loaf