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Math Help - a few questions I need help with. thank you

  1. #1
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    a few questions I need help with. thank you

    Okay I am almost done with this lesson. Once again I need help. UGH.. I already did this but received an F and I am fixing all the wrong answers.

    Please show me how you got the answers. I would still like to learn instead of just knowing the answer. Plus I need to know what I did wrong.

    1. What is the equation of a horizontal line that passes through the point at (-2,-3)?


    2. In a circle whose diameter is 20inches, a chord is 6inches from the center. What is the length of the chord?

    3. Use the Law of Syllogism to determine a conclusion.
    (1) All squares are rhomubuses
    (2) The diagonals of a rhombus are perpendicular.

    4. What are the coordinates of the image of the point at (-3, -5) after a reflection over the y-axis?

    5.Find the measure of an angle if its measure is 4 times the measure of its comlement.

    6. Write an equation of the line that passes through the point at (4,4) and is perpendicular to the line whose equation is 2x+y=7.

    7. Classify triangle ABC by its angles if m<B=26 and m<A=64.

    8. Find the length to the nearest tenth, of the apothem of a regular octagon whose sides are 10inches long.

    9. Solve the system of equation:
    3x+2y=17
    2x-y=9



    Please help.. I already did this. I have to redo to get a better grade. I already fixed most of them on my own.
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  2. #2
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    Quote Originally Posted by jessicamelia1983 View Post
    ...

    1. What is the equation of a horizontal line that passes through the point at (-2,-3)?
    A horizontal line is the locus of points which have the same displacement to the x-axis. Thus the y-value must not change. Therefore the equation of such a line is:
    y = -3


    Quote Originally Posted by jessicamelia1983 View Post
    2. In a circle whose diameter is 20inches, a chord is 6inches from the center. What is the length of the chord?
    From the diameter you know that the radius is 10'' long. Draw a rough sketch of the situation. You can see a right triangle with the radius as hypotenuse and the displacement of the chord to the centre as one leg. Use Pythagorean theorem to calculate the missing leg. That would be half of the chord. The complete chord is 16'' long.

    ...

    Quote Originally Posted by jessicamelia1983 View Post
    4. What are the coordinates of the image of the point at (-3, -5) after a reflection over the y-axis?
    Use the properties of reflection over an axis. If P is the original point and P' is the image of P then PP' perpendicular to the y-axis and the y-axis bisect the distance PP'. Thus P'(3, -5)

    Quote Originally Posted by jessicamelia1983 View Post
    5.Find the measure of an angle if its measure is 4 times the measure of its comlement.
    Use the property: angle + compliment = 180.
    With your problem the angle = 5 * compliment. Therefore:

    5*compliment + compliment = 180
    6* compliment = 180
    compliment = 30
    thus angle = 5*compliment = 150

    Quote Originally Posted by jessicamelia1983 View Post
    6. Write an equation of the line that passes through the point at (4,4) and is perpendicular to the line whose equation is 2x+y=7.
    From 2x + y = 7 ==> y = -2x + 7.
    Therefore the slope of the given line is m = -2. A perpendicular line has the slope m' =
    Now use point-slope formula to get the equation of the line:

    \frac{y-4}{x-4}= \frac{1}{2}+\Longrightarrow~y= \frac{1}{2}x+2

    Quote Originally Posted by jessicamelia1983 View Post
    7. Classify triangle ABC by its angles if m<B=26 and m<A=64.
    Because \angle(A) + \angle(B) = 90^\circ the angle at C must be a right angle. Therefore you are dealing with a right triangle.

    Quote Originally Posted by jessicamelia1983 View Post
    8. Find the length to the nearest tenth, of the apothem of a regular octagon whose sides are 10inches long.
    An octagon consists of 8 congruent sosceles triangles. If s is the side of the octagon, the half diameter of the octagon is r, the apothem is a and the angle at the centre of the octagon is \alpha = \frac{360^\circ}{8} = 45^\circ then you can use some trigonometric formulae:

    r = \frac{\frac{1}{2}~s}{\sin(22.5^\circ)}

    a = \frac{\frac{1}{2}~s}{\tan(22.5^\circ)}

    Plug in the values you know: a\approx 12.1

    Quote Originally Posted by jessicamelia1983 View Post
    9. Solve the system of equation:
    3x+2y=17
    2x-y=9
    I don't know which method you use to solve such a system....

    3x+2y=17
    2x-y=9 multiply this equation by 2

    3x+2y=17
    4x-2y=18 add columnwise(?)

    7x = 35 divide by 7

    x = 5 substitute 5 instead of x in the 2nd equation:

    10 - y = 9 ==> y = 1
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