The inequality representation of the scenario is :
- 5m + 8c ≤ 25
- m = 1 and c = 1
- Number of mugs = m
- Cost per mug = $5
- Number of ground coffee = c
- Cost per ground coffee = $8
- Total amount to spend = $25
- (Number of mug × cost per mug) + (Number of ground coffee × cost of ground coffee) ≤total amount to spend
- Representing as an inequality : 5m + 8c ≤ 25
Combination of m and c that makes the inequality true :
- Using trial by error :
- m = 1 and c = 1
- 5(1) + 8(1) ≤ 25 ; 13 ≤ 25
Hence, m = 1 and c =1 are valid values for the expression.
Learn more : brainly.com/question/15748955
Cubic inches. Think how small a lunchbox is.
Equation of a straight line is normally in the form: y = mx + c.
Where, m and c are constants in which;
m = gradient
c = y-intercept.
Comparing this standard way way of writing the equation of a straight line with the current scenario, this equation can be rewritten as;
y = b1x + b0.
This way, b1 = gradient of the line while b0 = y-intercept.
let's firstly convert the mixed fractions to improper fractions and then proceed.
![\stackrel{mixed}{4\frac{1}{2}}\implies \cfrac{4\cdot 2+1}{2}\implies \stackrel{improper}{\cfrac{9}{2}}~\hfill \stackrel{mixed}{1\frac{1}{4}}\implies \cfrac{1\cdot 4+1}{4}\implies \stackrel{improper}{\cfrac{5}{4}} \\\\[-0.35em] ~\dotfill](https://tex.z-dn.net/?f=%5Cstackrel%7Bmixed%7D%7B4%5Cfrac%7B1%7D%7B2%7D%7D%5Cimplies%20%5Ccfrac%7B4%5Ccdot%202%2B1%7D%7B2%7D%5Cimplies%20%5Cstackrel%7Bimproper%7D%7B%5Ccfrac%7B9%7D%7B2%7D%7D~%5Chfill%20%5Cstackrel%7Bmixed%7D%7B1%5Cfrac%7B1%7D%7B4%7D%7D%5Cimplies%20%5Ccfrac%7B1%5Ccdot%204%2B1%7D%7B4%7D%5Cimplies%20%5Cstackrel%7Bimproper%7D%7B%5Ccfrac%7B5%7D%7B4%7D%7D%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill)
![\begin{array}{ccll} miles&hours\\ \cline{1-2} \frac{9}{2}&\frac{5}{4}\\[1em] x&1 \end{array}\implies \cfrac{~~ \frac{9}{2}~~}{x}=\cfrac{~~ \frac{5}{4}~~}{1}\implies \cfrac{~~ \frac{9}{2}~~}{\frac{x}{1}}=\cfrac{5}{4}\implies \cfrac{9}{2}\cdot \cfrac{1}{x}=\cfrac{5}{4} \\\\\\ \cfrac{9}{2x}=\cfrac{5}{4}\implies 36=10x\implies \cfrac{36}{10}=x\implies \cfrac{18}{5}=x\implies 3\frac{3}{5}=x](https://tex.z-dn.net/?f=%5Cbegin%7Barray%7D%7Bccll%7D%20miles%26hours%5C%5C%20%5Ccline%7B1-2%7D%20%5Cfrac%7B9%7D%7B2%7D%26%5Cfrac%7B5%7D%7B4%7D%5C%5C%5B1em%5D%20x%261%20%5Cend%7Barray%7D%5Cimplies%20%5Ccfrac%7B~~%20%5Cfrac%7B9%7D%7B2%7D~~%7D%7Bx%7D%3D%5Ccfrac%7B~~%20%5Cfrac%7B5%7D%7B4%7D~~%7D%7B1%7D%5Cimplies%20%5Ccfrac%7B~~%20%5Cfrac%7B9%7D%7B2%7D~~%7D%7B%5Cfrac%7Bx%7D%7B1%7D%7D%3D%5Ccfrac%7B5%7D%7B4%7D%5Cimplies%20%5Ccfrac%7B9%7D%7B2%7D%5Ccdot%20%5Ccfrac%7B1%7D%7Bx%7D%3D%5Ccfrac%7B5%7D%7B4%7D%20%5C%5C%5C%5C%5C%5C%20%5Ccfrac%7B9%7D%7B2x%7D%3D%5Ccfrac%7B5%7D%7B4%7D%5Cimplies%2036%3D10x%5Cimplies%20%5Ccfrac%7B36%7D%7B10%7D%3Dx%5Cimplies%20%5Ccfrac%7B18%7D%7B5%7D%3Dx%5Cimplies%203%5Cfrac%7B3%7D%7B5%7D%3Dx)
