hectictar

area = ½ × base × height

Plug in the numbers for base and height.

area = ½ × 5 × 5

Just put that into a calculator to get that

area = 12.5 square units

34/16

Plug this into a calculator to turn it into a decimal.

34/16 = 2.125

Multiply by 100 to turn it into a percent.

2.125*100 = 212.5%

Yay!! 

First I'm just going to simplify the left side:

\(\frac{5}{8} - \frac{2y}{3} +y-\frac{2}{6}-3y+\frac{1}{144} \\ \frac{5(18)}{144} - \frac{2y(48)}{144} +\frac{144y}{144}-\frac{2(24)}{144}-\frac{3y(144)}{144}+\frac{1}{144} \\ \frac{90-96y+144y-48+-432y+1}{144} \\\frac{43-384y}{144}\)

Next I will simplify the right side:

\(1-y+3y-\frac{2}{36}+\frac{7y}{12}-3y-\frac{4}{16} \\ \frac{144}{144}-\frac{144y}{144}+\frac{3y(144)}{144}-\frac{2(4)}{144}+\frac{7y(12)}{144}-\frac{3y(144)}{144}-\frac{4(9)}{144} \\ \frac{144-144y+432y-8+84y-432y-36}{144} \\ \frac{100-60y}{144}\)

Now put the two sides together:

\(\frac{43-384y}{144} \geq \frac{100-60y}{144} \\ 43-384y \geq 100-60y \\ -384y \geq 57-60y \\ -324y \geq 57 \\ y \leq -\frac{57}{324} \\ y \leq -\frac{19}{108}\)

That's what I got...I checked over it twice and didn't catch any errors, but it is possible that I made an error somewhere of course.

Are you trying to make an equation that has z = -1.72 and z = 1.17 as the solutions?

Hmm it looks like O can only into 2 pieces. the letters F, S, H, all tie at 4 pieces. M beats them all with 5 pieces.

This reminds me of several games I have played,

Well let's look at the third one.

They tell us that the radius is 19 yards.

So how can we find the diameter?

Look at the equation for diameter.

diameter = 2 × radius

Oh, but we know what the radius is!

So let's replace the word "radius" with what we know the radius is, 19 yards.

diameter = 2 × 19 yards

Now just grab your calculator and type in, "2 × 19." Whatever you get is the diameter.

diameter = 38 yards

Does that make any sense?

Ah you can do these! I believe in you!

Just use these equations and plug in what you know:

radius = ½ × diameter

diameter = 2 × radius

circumference = 3.14 × diameter

area = 3.14 × radius²

1)

radius = 11 inches

diameter = 2 × radius = 2 × 11 = 22 inches

circumference = 3.14 × diameter = 3.14 × 22 = 69.08 inches

area = 3.14 × 11² = 3.14 × 121 = 379.94 square inches

2)

radius = ½ × diameter = ½ × 20 = 10 feet

diameter = 20 feet

circumference = 3.14 × diameter = 3.14 × 20 = 62.8 feet

area = 3.14 × radius² = 3.14 × 10² = 3.14 × 100 = 314 square feet

I hope this made sense!

Can you do the third one by yourself? It's almost identical to the first one.

I'm guessing that 144 goes under the radical.

\(\sqrt{\frac{45}{144}} \\~\\ \frac{\sqrt{45}}{\sqrt{144}} \\~\\ \frac{\sqrt{(3)(3)(5)}}{12} \\~\\ \frac{3\sqrt{5}}{12} \\~\\ \frac{\sqrt{5}}{4}\)

If 144 is not under the radical:

\(\frac{3\sqrt{5}}{144} = \frac{\sqrt{5}}{48}\)

9¾ + 4¾ + 3/10 + 3/10

\(9\frac34 + 4\frac34 +\frac3{10}+ \frac3{10} \\~\\ = \frac{39}{4} + \frac{19}{4} + \frac3{10}+ \frac3{10} \\~\\ = \frac{390}{40} + \frac{190}{40} + \frac{12}{40}+ \frac{12}{40} \\~\\ = \frac{390 +190+12+12}{40} = \frac{604}{40} = \frac{151}{10} = 15.1\)