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# Tutor profile: Elizabeth K.

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Elizabeth K.
Math teacher and tutor
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## Questions

### Subject:Trigonometry

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Question:

If a triangle has angles measuring 25 \$\$ ^\circ \$\$ and 28 \$\$ ^\circ \$\$ and the length of the side opposite the angle measuring 28 \$\$ ^\circ\$\$ is 10 feet, what are the lengths of the other two sides?

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Elizabeth K.

First we can use the law of sines to find the answer. \$\$ a/sinA = b/sinB =c/sin C\$\$ Let \$\$ a = 10\$\$. Then \$\$A=28\$\$. Side opposite the angle. Let \$\$ B=25\$\$. And since the sum of the angles of a triangle must equal 180, then \$\$ A+B+C =180\$\$ \$\$ 28+25+C=180\$\$ \$\$ 53 +C = 180\$\$ \$\$ C= 127\$\$ Let's find side \$\$b\$\$ first. \$\$ a/sinA = b/sinB \$\$ \$\$ 10/ sin(28) = b/sin(25)\$\$ \$\$ 9 = b\$\$ Now side \$\$c\$\$. \$\$ a/sinA=c/sinC\$\$ \$\$10/sin(28)=c/sin(127)\$\$ \$\$17 = c\$\$ The sides of the triangle are 17, and 9 feet.

### Subject:Pre-Algebra

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Question:

The sum of three consecutive numbers is 72. What are the numbers?

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Elizabeth K.

Since the numbers are consecutive, it means that they follow each other. For example, 5,6, and 7 are three consecutive numbers. Let the first number be \$\$x\$\$. Then second number is one greater or \$\$x+1\$\$. And the third number is \$\$ x +2\$\$ or two greater than the first. These three numbers must add up to 72. Add up the three numbers and set them equal to 72. \$\$x + (x+1) + (x+2) =72\$\$ Simply. \$\$ 3x + 3 =72\$\$ Now find \$\$x\$\$. \$\$ 3x = 72-3 = 69\$\$ \$\$ 3x/3=69/3\$\$ \$\$x = 33\$\$ Therefore the numbers are 33, 34, and 35.

### Subject:Algebra

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Question:

Sue and Dave buy some fruit. Sue buys 5 apples and 2 bananas for \$2. Dave buys 2 apples and 3 bananas for \$1.35. Find the cost of one apple and one banana.

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Elizabeth K.

Let \$\$ a =\$\$ one apple. Let \$\$ b=\$\$ one banana. Convert \$2 to 200 cents and \$1.35 to 135 cents. Sue buys \$\$ 5 a + 2 b = 200\$\$ Dave buys \$\$ 2 a + 3 b = 135\$\$ Now we can solve this set of simultaneous equations. Multiply the first equation by 3 and the second by 2. \$\$ 15 a + 6 b = 600\$\$ \$\$ 4 a + 6 b = 270 \$\$ Next subtract the second equation from the first. \$\$ (15-4) a + (6-6) b = (600-270)\$\$ \$\$ 11 a + 0 b = 330 \$\$ \$\$ 11 a = 330 \$\$ Solve for \$\$a\$\$ by dividing both sides of the equation by 11. \$\$ 11/11 a = 330/11 \$\$ \$\$ a = 30\$\$ Now find \$\$b\$\$ by substituting \$\$a\$\$ back into the first equation. \$\$ 5 (30) + 2 b = 200\$\$ \$\$ 150 + 2 b = 200\$\$ Solve for \$\$b\$\$. \$\$ 2 b = 200-150\$\$ \$\$ 2 b = 50\$\$ \$\$ b = 50/2 = 25\$\$ Therefore \$\$ a = 30 \$\$ cents\$\$ = \$0.30\$\$ = cost of one apple \$\$ b= 25\$\$ cents \$\$= \$0.25\$\$ = cost of one banana

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