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  1. The ladder will be unsafe because its angle with the ground is greater than 70°.

    Step-by-step explanation: hope that helps

  2. All the given points are collinear, so we have ...
      AB +BC = AC
      BC +CS +SD = BD
    The problem statement tells us
      BD = AC
      BC +CS +SD = AB +BC . . . . . substituting for BD and AC
      BC +CS +2 = 4 +BC . . . . . . . . substituting given lengths
      CS = 2 . . . . . . . . . . . . . . . . . . . subtract (2+BC)

    CS is the radius of Circle C, so its diameter is twice that: 4. The radius of Circle D is the diameter of Circle C plus SD, so is 4 +2 = 6. The diameter of Circle D is twice that: 12.

    The diameter of Circle C is 4.
    The diameter of Circle D is 12.

  3. 24cm²

    Step-by-step explanation:

    Perimeter of rectangle ABCF = 20 cm

    One of the sides AB = 6 cm (AB)(Let it be L)

    other side of Rectangle=B.

    Perimeter of Rectangle = 2 (Length + width)

    20 = 2(L+W) = 2(6 + W)

    [tex]\frac{20}{2}[/tex]=6+B

    10=6+B

    B =  10-6

    B = 4 cm

    Width of Rectangle, W = 4 cm (BC)

    Length of side of trapezium, CD = BD - BC = 9 - 4 = 5 cm

    And length of EF = 3 cm

    Area of Trapezium = [tex]\frac{1}{2}[/tex]×(CD+EF)×CF

    [tex]\frac{1}{2}[/tex]×(5+3)×6

    [tex]\frac{8}{2}[/tex]×6

    4×6=24

  4. Given:

    The base of the given triangle has two part:

    Left( left side of the hypotenuse) = 25

    Right ( right side of the hypotenuse) = x

    The altitude (h) = 60

    To find the value of x.

    Formula:

    By Altitude rule we know that, the altitude of a triangle is mean proportional between the right and left part of the hypotenuse,

    [tex]\frac{left}{altitude} =\frac{altitude}{right}[/tex]

    Now,

    Putting,

    left = 25, altitude = 60 and right = x we get,

    [tex]\frac{25}{60} =\frac{60}{x}[/tex]

    or, [tex](25)(x )=(60)(60)[/tex] [ by cross multiplication]

    or, [tex]x = \frac{3600}{25}[/tex]

    or, [tex]x = 144[/tex]

    Hence,

    The value of x is 144.

  5. Secants from the same point have the same product of length to the near intersection times length to the far intersection from the point.

    1) 5(5+x) = 6(6+4)

    ... 25 + 5x = 60 . . . . eliminate parentheses using the distributive property

    ... 5x = 35 . . . . . . . . subtract 25

    ... x = 7 . . . . . . . . . . . divide by 5

    2) The same rule applies.

    ... 3(3+5) = 4(4+x)

    ... 24 = 16 + 4x . . . . . eliminate parentheses

    ... 8 = 4x . . . . . . . . . . . subtract 16

    ... 2 = x . . . . . . . . . . . . divide by 4

  6. There are 3 grams of fiber in 1/2 cup of oatmeal. Therefore, the number of grams of fiber in 1 (which is twice as large as 1/2) cup of oatmeal is:
    3 g fiber *2= 6 g fiber.

    There is 6 g fiber in 1 cup of oatmeal. Therefore, the number of fiber in 1 1/8 (which is 1 1/8 times as large as 1) cups of oatmeal is:
    6 g fiber *(1 1/8)= 6.75 g fiber.

    There is 6.75 g of fiber left in the box.

    Hope this would help~

  7. Answer=6 3/4 grams

     3 grams of fiber        x fiber
    =
          1/2 cup              1 1/8 cup

    Cross multiply
    1/2x=3 3/8
    divide both sides by 1/2
    x=6.75 or 6 3/4
    There is 6 3/4 grams of fiber in 1 1/8 cups of oatmeal.

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