Mathematics, 09.07.2019 11:40 dad46

Kayla has $500 in her account, and she spends $40 a week on food. if she falls below $30 in her account, she must pay a penalty. what is an inequality that can represent this situation?

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She starts with $500; that's a given. If she's spending $40 a week, that means that she'll be subtracting $40 from her account for each week (let's call the number of weeks that've gone by "w"), leaving her with 500-40w dollars after week w.

Now we have to compare this somehow to $30. Our inequality is going to look like:

500-40w ? 30

Where the ? is a stand-in for an inequality sign. Which inequality sign should we pick? Take a look at the question and see if you can find any keywords that might give you a hint. "If she falls below" is the big one I'm seeing. If she can't fall below $30, that means she'll always have to stay at or above $30 to avoid paying the penalty. What inequality sign represents at or above?

Answer from: Quest

gregory's graph is incorrect because it shows 2 inches of growth for each week when it should show 0.75 inches of growth each week.

Answer from: Quest

the system of inequity is

$y\leq -x+4$

$3y> x$

step-by-step explanation:

from the given graph it is noticed that we have two related lines. one is solid and another is dashed.

if a line passing through two points, then the equation of line is

$y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)$

the solid line passing through the points (0,4) and (4,0).

$y-4=\frac{0-4}{4-0}(x-0)$

$y=-x+4$

the related equation of solid line is $y=-x+4$ .

similarly, find the related equation of dashed line. the dashed liune passing through the points (0,0) and (3,1).

$y-0=\frac{0-1}{3-0}(x-0)$

$3y=x$

the related equation of dashed line is $3y=x$

from the given graph it is noticed that the point (0,1) lies on the shaded region, therefore the point (0,1) must be satisfied by the related equations.

check the related equations by the point (0,1).

$1=-0+4$

$1=4$

this statement is true if the sign of inequality is < instead of equality. since it is an solid line therefore the sign of inequality will be $\leq$ . the required inequality is

$y\leq -x+4$

similarly, check the second related equation.

$3(1)=0$

it is a dashed line, so this statement is true if the sign of inequality is > . the required inequality is

$3y> x$

15 points write a system of inequalities to represent the shaded portion of the graph

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Kayla has $500 in her account, and she spends $40 a week on food. if she falls below $30 in her acco...