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AfilCa [17]
3 years ago
8

Brittany received 8 silver dollars on her eighth birthday. After her next birthday she had 15 and after the next she had 22. Aft

er her eleventh birthday she had 29 silver dollars. How many silver dollars will she have after her 16th birthday if her collection increases at the same rate every year?
Mathematics
2 answers:
max2010maxim [7]3 years ago
8 0
Ever year she gets 15 silver dollars, so she will have 64 silver dollars
elena55 [62]3 years ago
7 0
Every year Brittany receives 7 silver dollars, therefore she will receive 64 silver dollars on her 16th birthday.
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The set A satisfying the given inequality is A = (-\infty, -10].

<h3>What are some properties of an inequality relation? </h3>

Following are some facts which are true for an inequality relation:

  • Equal numbers can be added or subtracted from both sides of an inequality without affecting the inequality sign.
  • The Inequality sign is unchanged if both sides are multiplied or divided by a positive number, but when multiplied or divided by a negative number the inequality sign is reversed.

\frac{5x-2}{8} - \frac{3x-5}{10} &\ge& x+y\\\\\Rightarrow\;\; \frac{13}{40}x + \frac{1}{4}&\ge& x+y\\\\\Rightarrow\;\;\;\;\;\; -\frac{27}{40}x &\ge & y - \frac{1}{4}\\\\\Rightarrow\;\;\;\;\;\;\;\;\;\; -x &\ge & \frac{40}{27}\left( y-\frac{1}{4} \right).\hspace{1cm}(1)

Since y ∈ B, -2 ≤ y ≤ 7. So,

\;\;\;\;\;\;\;\,-2 - \frac{1}{4}\; \le\; y - \frac{1}{4} \;\le\; 7 - \frac{1}{4}\\\\\Rightarrow\;\;\;\;\;\;\;\;\; -\frac{9}{4}\; \le\;  y - \frac{1}{4} \;\le\; \frac{27}{4}\\\\\Rightarrow\;\;\; -\frac{9}{4}\cdot \frac{40}{27} \;\le\; \frac{40}{27} \left( y-\frac{1}{4} \right) \;\le \;\frac{27}{4}\cdot \frac{40}{27}\\\\\Rightarrow\;\;\;\;\;\;\;\; -\frac{10}{3} \;\le\; \frac{40}{27}\left( y - \frac{1}{4} \right)\; \le\; 10.

The set {-x | inequality (1) holds ∀ y ∈ B} is [10, \infty) i.e.

10 ≤ -x ≤ \infty.

Multiplying -1 throughout gives

-10 ≥ x ≥ -\infty.

x, thus, lies in the range A = (-\mathbf{\infty}, -10}.

Learn more about the inequality here.

brainly.com/question/17801003

Disclaimer: The question was incomplete. Please find the full content below.

<h3>Question </h3>

Find the set A such that for x ∈ A

\frac{5x - 2}{8} - \frac{3x - 5}{10} \ge x + y

∀y ∈ B = {y ∈ R | -2 ≤ y ≤ 7}.

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