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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?

Inactive
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.

Inactive
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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