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frez [133]
4 years ago
6

(GEOMETRY PLS HELP SERIOUSLY) A treasure map says that a treasure is buried so that it partitions the distance between a rock an

d a tree in a 5:9 ratio. Marina traced the map onto a coordinate plane to find the exact location of the treasure.
What are the coordinates of the treasure? If necessary, round the coordinates to the nearest tenth.

A.(11.4, 14.2)

B.(7.6, 8.8)

C.(5.7, 7.5)

D.(10.2, 12.6)

Mathematics
2 answers:
anygoal [31]4 years ago
8 0

Answer:

(7.6,8.8)

Step-by-step explanation:

second option

pogonyaev4 years ago
5 0

You have coordinates of tree T(16,21) and of rock R(3,2). Let S be a point that denotes treasure. Since treasure is buried so that it partitions the distance between a rock and a tree in a 5:9 ratio, you can state that

\dfrac{\overrightarrow{RS}}{\overrightarrow{ST}}=\dfrac{5}{9}.

Find the coordinates of these vectors:

\overrightarrow{RS}=(x_S-3,y_S-2), \\
\overrightarrow{ST}=(16-x_S,21-y_S).

Then

\dfrac{x_S-3}{16-x_S} =\dfrac{5}{9} and \dfrac{y_S-2}{21-y_S} =\dfrac{5}{9}.

Solve these two equations:

1.

9(x_S-3)=5(16-x_S),\\ 9x_S-27=80-5x_S,\\ 9x_S+5x_S=80+27,\\14x_S=107,\\ \\x_S=\dfrac{107}{14}\approx 7.6.

2.

9(y_S-2)=5(21-y_S),\\9y_S-18=105-5y_S,\\9y_S+5y_S=105+18,\\14y_S=123,\\ \\y_S=\dfrac{123}{14}\approx 8.8.

Answer: the treasure are placed at point (7.6,8.8), so the correct choice is B.

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Which set of numbers is correctly ordered from greatest to least?
shepuryov [24]

Answer:

Step-by-step explanation:

Here is the corrected question and options:

Option 1:

7\frac{1}{3} , \frac{221}{30} , 7.36, 3.16\sqrt{2e}

Option 2:

7\frac{1}{3} , 7.36 , \frac{221}{30} , 3.16\sqrt{2e}

Option 3:

3.16\sqrt{2e}, 7.36 , \frac{221}{30} , 7\frac{1}{3}

Option 4:

3.16\sqrt{2e},  \frac{221}{30} , 7.36 , 7\frac{1}{3}

Solution:

Lets write each of the above given numbers in a simplified form:

7\frac{1}{3}

Simplify this by converting it into a decimal form:

This becomes:

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So

7\frac{1}{3} = 7.3

\frac{221}{30}

Simplify this by converting it into a decimal form:

This becomes:

221/30 = 7.3666666667

So,

\frac{221}{30} = 7.367

7.36

This number comes with a bar sign on .36 which means that the number has a non terminating repeating decimal expansion as 7.3636363636...

So after rounding it off this becomes:

7.36

3.16\sqrt{2e}

Simplify this by converting it into a decimal form:

The value of e = 2.718

This becomes:

3.16 \sqrt{2*2.718}

= 3.16 (√5.436)

= 3.16 * 2.331523

=  7.3679949818

= 7.368

So

3.16\sqrt{2e} = 7.368

7.367995

Now we get the numbers in decimal form:

7\frac{1}{3} = 7.333333 = 7.3

\frac{221}{30} = 7.3666666667 = 7.367

7.36 = 7.3636363636

3.16\sqrt{2e} = 7.3679949818 = 7.368

Now lets order the numbers from greatest to least:

3.16\sqrt{2e}

\frac{221}{30}

7.36

7\frac{1}{3}

So the correct option is:

Option 4

3.16\sqrt{2e},  \frac{221}{30} , 7.36 , 7\frac{1}{3}  

7 0
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