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denpristay [2]
3 years ago
5

Just number 2 please i’ve tried many times... i need an equation and the answer :)

Mathematics
1 answer:
Triss [41]3 years ago
7 0

Keller collected $62.48 and Izzy collected $47.83 and J collected $19.98

Step-by-step explanation:

Step 1; Assume that J collected $x, Keller collected $y and Izzy collected $z. All three combined collected $125.95, so

x + y + z = 125.95, take this as equation 1.

From the given data, the following equations can be formed.

y = 42.50 + x or x = y - 42.50 take this as equation 2 and

y = 15 + z, take this as equation 3.

Step 2; Now we must determine x and y in terms of z, so that equation 1 can be solved (the equations can be in terms of any term x, y or z.)

Rearranging equation 2 and 3,

we get 15 + z so  x = y - 42.50, y = x = 15 + z - 42.50, take this as equation 4,

If we substitute equations 4, 2 in 1, we get

(15 + z - 42.50) + (15 + z) + z = 125.95,

3z - 12.5 = 129.95,

3z = 142.45, so z = 47.833.

Substitute z = 47.833 in equation 3.

y = 15 + 47.8333 = 62.4833.

Substitute y = 62.4833 in equation 2,

x = 62.4833 - 42.50 = 19.9833.

Rounding of the values of x,y, and z to nearest hundredth we get

x = $19.98, y = $62.48 and z = $47.48.

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Answer:

Approximately 14.65 kilometers.

Step-by-step explanation:

Please refer to the drawing.

So, to find our distance, we essentially just need to find the value of x.

To do so, we can use the Law of Sines.

Note that ∠a corresponds to the 12km, and ∠c corresponds to x.

So, let's find each of the angles first.

Note that from our ending point, the bearing to the lighthouse is 125°.

This means, if you refer to the drawing:

a+b=90

This is because they are complementary.

We also know that:

90+b=125

From our bearing.

So, let's solve for b. Subtract 90 from both sides:

b=35

Substitute this back into our first equation to acquire:

a+35=90

Subtract 35 from both sides:

a=55\textdegree

Now, we can use the fact that the interior angles of a triangle sum to 180 to find c. We already know that one angle is 36 and the other is 55. So:

36+55+c=180

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Subtract 91 from both sides:

c=89\textdegree

Now, we can use the Law of Sines, which states:

\frac{\sin(A)}{a}=\frac{\sin(B)}{b}=\frac{\sin(C)}{c}

It doesn't really matter which ratio we use as long as we align the sides and angles correctly.

Recall that ∠a correspond to 12km while ∠c corresponds to x.

So, let's substitute 12 for a, 55 for A, x for b, and 89 for B. This yields:

\frac{\sin(55)}{12}=\frac{\sin(89)}{x}

So, to find the distance traveled, we just have to find x.

Cross-multiply:

12\sin(89)=x\sin(55)

Divide both sides by sin(55). This yields:

x=\frac{12\sin(89)}{\sin(55)}

Divide. Use a calculator. Make sure you're in Degrees mode. This gives us:

x\approx14.65

So, the ship approximately traveled 14.65 kilometers from Point A to Point B.

And we're done!

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3 years ago
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