Mathematics, 24.11.2019 08:31 daltondespain2

Consuela is planning her 7-day vacation. she has budgeted $250 to rent a moped for the week. the rental company charges $10 a day plus 30 cents per mile. write and solve a first degree inequality to determine the number of miles (m) consuela can drive and still stay within her budget.

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Answer from: Kjcampbell2

The equation is $0.3x\leq 180$ and consuela can drive maximum 600 miles.

Step-by-step explanation:

Given:

Consuela Budget= $\$250$

Rental Company Charges = $\$10 \ per\ day$

Additional Cost = 30 cents per mile = $0.3 per miles.

Number of days for vacation = 7

We need to find the number of miles Consuela can drive and still be in budget.

Let number of miles she can drive be

Rental Company Charges for per day $\times$ number of days + Additional Cost per mile $\times$ Number of miles she can drive sholud be less than or equal to Consuela Budget

Now the equation will be.

$10\times 70 +0.3x \leq 250\\70 +0.3 x\leq 250\\0.3x\leq 250-70\\0.3x\leq 180\\x\leq \frac{180}{0.3}\\\\x\leq 600 \ miles$

Hence Consuela can drive maximum of 600 miles to stay within her budget.

Answer from: Quest

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Answer from: Quest

$y> \frac{1}{3}x$ and y≤ -x +4 .

step-by-step explanation:

we are given a graph for system of inequalities.

in order to write the system of inequalities for the given graph, we need to find the inequality for each of the line separately.

let us find the slope of dotted line first.

taking two coordinates on the graph.

let us say (0,0) and (3,1).

let us find the slope of the line now.

slope of the dotted line would be = $\frac{1-0}{3-0} = \frac{1}{3}$ .

y-intercept of dotted line is y=0 only.

plugging slope m= $\frac{1}{3}$ and b=0 in slope-intercept form y=mx+b, we get

$y=\frac{1}{3}x$ .

the line is shaded up of that dotted line.

therefore, for shading up we would take greater than inequality symbol > .

and because it's a dotted line we would take only > symbol in place of = sign in above equation of line.

therefore, inequality for dotted line would be

$y> \frac{1}{3}x$ .

let us take two points (3,1) and (0,4) on the solid line.

slope of the solid line would be = $\frac{4-1}{0-3} = \frac{3}{-3}=-1$ .

for the solid line we have y-intercept b= 4.

plugging slope m= -1 and b=4 in slope-intercept form y=mx+b, we get

y = -1x + 4.

the line is shaded down of that solid line.

therefore, for shading down we would take less than inequality symbol < .

and because it's a solid line we would take ≤ symbol in place of = sign in above equation of line.

therefore, inequality for solid line would be

y≤ -x +4 .
Write a system of inequalities to represent the shaded portion of the graph.

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