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suter [353]
3 years ago
7

max earns 1800 per month plus a comission of 3 % of his sales he wants to earn at least 3000 this month what amount of salws doe

s max need this month
Mathematics
1 answer:
r-ruslan [8.4K]3 years ago
6 0
He earns 1800 so, 3000 minus 1800 is 1200, if u set this up as a proportional relationship you'll get  1200 = 3
                                      x      100

cross multiply the relationship, 1200 by 100 is 120,000, 3 by x is 3x, 3x=120,000            isolate the variable so you divide 3x by 3 and get 1x,
                                      what you do to one side you have to do to the other 
                                       so 120,000 divide by 3 is 40,000. If max wants to earn at least 3000 this month he will have to sell at least 40,000 dollars in items
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Option D: O(0,0), S(a,0), T(a,a), W(0,a)

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Option A: O(0,0), S(0,a), T(a,a), W(a,0)

To find the sides of a square, let us use the distance formula,

d=\sqrt{\left(x_{2}-x_{1}\right)^{2}+\left(y_{2}-y_{1}\right)^{2}}

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\begin{array}{l}{\text { Length } O S=\sqrt{(0-0)^{2}+(a-0)^{2}}=\sqrt{a^{2}}=a} \\{\text { Length } S T=\sqrt{(a-0)^{2}+(a-a)^{2}}=\sqrt{a^{2}}=a} \\{\text { Length } T W=\sqrt{(a-a)^{2}+(0-a)^{2}}=\sqrt{a^{2}}=a} \\{\text { Length } O W=\sqrt{(a-0)^{2}+(0-0)^{2}}=\sqrt{a^{2}}=a}\end{array}

Thus, the square with vertices O(0,0), S(0,a), T(a,a), W(a,0) has sides of length a.

Option B: O(0,0), S(0,a), T(2a,2a), W(a,0)

Now, we shall find the length of the square,

\begin{aligned}&\text { Length } O S=\sqrt{(0-0)^{2}+(a-0)^{2}}=\sqrt{a^{2}}=a\\&\text {Length } S T=\sqrt{(2 a-0)^{2}+(2 a-a)^{2}}=\sqrt{5 a^{2}}=a \sqrt{5}\\&\text {Length } T W=\sqrt{(a-2 a)^{2}+(0-2 a)^{2}}=\sqrt{2 a^{2}}=a \sqrt{2}\\&\text {Length } O W=\sqrt{(a-0)^{2}+(0-0)^{2}}=\sqrt{a^{2}}=a\end{aligned}

This is not a square because the lengths are not equal.

Option C: O(0,0), S(0,2a), T(2a,2a), W(2a,0)

Now, we shall find the length of the square,

\begin{array}{l}{\text { Length OS }=\sqrt{(0-0)^{2}+(2 a-0)^{2}}=\sqrt{4 a^{2}}=2 a} \\{\text { Length } S T=\sqrt{(2 a-0)^{2}+(2 a-2 a)^{2}}=\sqrt{4 a^{2}}=2 a} \\{\text { Length } T W=\sqrt{(2 a-2 a)^{2}+(0-2 a)^{2}}=\sqrt{4 a^{2}}=2 a} \\{\text { Length } O W=\sqrt{(2 a-0)^{2}+(0-0)^{2}}=\sqrt{4 a^{2}}=2 a}\end{array}

Thus, the square with vertices O(0,0), S(0,2a), T(2a,2a), W(2a,0) has sides of length 2a.

Option D: O(0,0), S(a,0), T(a,a), W(0,a)

Now, we shall find the length of the square,

\begin{aligned}&\text { Length OS }=\sqrt{(a-0)^{2}+(0-0)^{2}}=\sqrt{a^{2}}=a\\&\text { Length } S T=\sqrt{(a-a)^{2}+(a-0)^{2}}=\sqrt{a^{2}}=a\\&\text { Length } T W=\sqrt{(0-a)^{2}+(a-a)^{2}}=\sqrt{a^{2}}=a\\&\text { Length } O W=\sqrt{(0-0)^{2}+(a-0)^{2}}=\sqrt{a^{2}}=a\end{aligned}

Thus, the square with vertices O(0,0), S(a,0), T(a,a), W(0,a) has sides of length a.

Thus, the correct answers are option a and option d.

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