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LuckyWell [14K]
2 years ago
14

Which statement correctly compares Line segment AB Which statement correctly compares Line segment AB and Line segment FD? And L

ine segment FD?
Mathematics
1 answer:
GenaCL600 [577]2 years ago
6 0

Answer:

AB is longer FD

Step-by-step explanation:

Given

See attachment for triangles ABC and FDE

Required

Compare line segments AB and FD

From the attachment, we have:

AC = FE --- equal line segments

The measure of angles will then be used to compare the line segments;

\angle C = 72^o

\angle F = 65^o

The longer the angle of depression, the shorter the required line segment

72 > 65 implies that AB is longer

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Suppose you want to build a small walkway around your garden so that there is someplace to walk around and work on your vegetabl
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Answer:

Approximately 3.5 feet - Option B

Step-by-step explanation:

Imagine that you have this walkway around the garden, with dimensions 30 by 20 feet. This walkway has a difference of x feet between it's length, and say the dimension 30 feet. In fact it has a difference of x along both dimensions - on either ends. Therefore, the increases length and width should be 30 + 2x, and 20 + 2x, which is with respect to an increases area of 1,000 square feet.

( 30 + 2x ) * ( 20 + 2x ) = 1000 - Expand "( 30 + 2x ) * ( 20 + 2x )"

600 + 100x + 4x^2 = 1000 - Subtract 1000 on either side, making on side = 0

4x^2 + 100x - 400 = 0 - Take the "quadratic equation formula"  

( Quadratic Equation is as follows ) - x_{1,\:2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a},

x=\frac{-100+\sqrt{100^2-4\cdot \:4\left(-400\right)}}{2\cdot \:4}:\quad \frac{5\left(\sqrt{41}-5\right)}{2},

x=\frac{-100-\sqrt{100^2-4\cdot \:4\left(-400\right)}}{2\cdot \:4}:\quad -\frac{5\left(5+\sqrt{41}\right)}{2}

There can't be a negative width of the walkway, hence our solution should be ( in exact terms ) \frac{5\left(\sqrt{41}-5\right)}{2}. The approximated value however is 3.5081...or approximately 3.5 feet.

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What is the area of the figure?<br>​
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Answer:

5.4 in.

Step-by-step explanation:

Figuring out the area of shapes like these are quite simple, you first have to break apart this shape to make solving this easier. If you draw a line and break off the triangle from the square you will get 2 different shapes. A square with all the sides being 2 inches, and a triangle that is 2 inches tall and 1.4 inches across (you subtract 3.4 by 2). Next you just use the equation (2 * 2) + ((1.4 * 2)/2). Multiply 2 by 2 (which is 4) and you get the area of the square (you multiply the base by the width). And for the triangle you multiple 1.4 by 2 (you get 2.8)... But because it's a triangle you have to divide that number by 2 since the triangle is half of a square. So 2.8 / 2 is going to be 1.4. After that you now have the equation 4 + 1.4 and the answer is going to be 5.4.

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