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LekaFEV
7 days ago
13

A group of dragons and sheep are randomly divided into 2 equal rows. Each animal in one row is directly opposite an animal in th

e other row. If 75 of the animals are dragons, and the number of sheep opposite sheep is 10 more than the number of dragons opposite dragons, find the total number of animals in the group.
Mathematics
1 answer:
Zina [12.3K]7 days ago
8 0
The total count of animals in the group amounts to 170. To elaborate: let the sheep number be a; there are 75 dragons within the group. Opposing dragons total 37, and only one sheep opposes a dragon, leaving a - 1 remaining. The number of sheep opposing fellow sheep exceeds that of dragons opposing dragons by ten, leading to a - 1 = 94, thus a equals 95. Hence, the overall animal tally is 95 plus 75, which equals 170.
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Two planes A and B can each fly through still air at 550 mph. The distance from Paris to Los Angeles is 5000 miles. Wind blows f
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Answer:2688.63 miles

Step-by-step explanation:

Given

The distance from Paris to Los Angeles d=5000 miles

Wind traveling at 100 mph from Los Angeles to Paris

The velocity of the plane through still air is v=550 mph

Relative velocity of Plane A is v_a=550-100 =450 mph since Plane A is heading against the wind

Relative velocity of Plane B is v_b=550+100=650 mph

Plane A departs at noon

Distance covered by Plane A in 1 hour =450\times 1=450 miles

The total separation distance between the planes is 5000-450=4550 miles

Assuming they meet after t hours

Distance covered by Plane B in that time frame =v_b\times t=650\times t

Distance traveled by Plane A in t hours is =v_a\times t=450 t

The total distance equals 4550 miles

4550=650t+450t

t=\frac{4550}{1100}

t=4.13 hr

Distance traveled by B is =650\times 4.136=2688.63 miles

thus, they meet at a point 2688.63 miles away from Los Angeles.

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1 month ago
Why might the triangulation method not always produce an exact point (other than any measurement errors)
Zina [12379]

Answer:

The triangulation technique may not always yield a precise result (aside from any errors in measurement) for the following reasons:

It employs a variety of data sources, different researchers, and multiple theories or viewpoints.

Step-by-step explanation:

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Kennedy has a gross income of $95,000. What is her total tax due?
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Answer:

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Step-by-step explanation:

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1 month ago
Each leg of a 45°-45°-90° triangle measures 12 cm. Triangle X Y Z is shown. Angle X Y Z is a right angle and angles Y Z X and Z
babunello [11817]
Using the Pythagorean theorem: In a right triangle where legs are labeled a and b, and hypotenuse is c. Given the triangle ΔXYZ has a right angle at Y, with angles YZX and ZXY both measuring 45 degrees, and ZY = YX = 12 cm. The task is to find the length of XZ.
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1 month ago
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Given: △ABC, m∠A=60° m∠C=45°, AB=8 Find: Perimeter of △ABC, Area of △ABC
Svet_ta [12734]

We are given the triangle

△ABC, with m∠A=60° and m∠C=45°, and AB=8.

To start, we will calculate all angles and sides.

Finding angle B:

The total of all angles in a triangle equals 180.

m∠A + m∠B + m∠C = 180.

Substituting the known values,

60° + m∠B + 45° = 180.

This gives us m∠B = 75°.

Calculating BC:

Using the law of sines,

\frac{AB}{sin(C)}=\frac{BC}{sin(A)}

We can substitute in the values.

\frac{8}{sin(45)}=\frac{BC}{sin(60)}

BC=\frac{8}{sin(45)} \times sin(60)

BC=9.798

Finding AC:

\frac{AB}{sin(C)}=\frac{AC}{sin(B)}

Now we'll input the values.

\frac{8}{sin(45)}=\frac{AC}{sin(75)}

AC=\frac{8}{sin(45)} \times sin(75)

AC=10.928

Calculating Perimeter:

p=AB+BC+AC

We substitute values here as well.

p=10.928+8+9.798

p=28.726

Calculating Area:

Using the area formula,

A=\frac{1}{2}AB \times AC \times sin(A)

we can then insert values.

A=\frac{1}{2}8 \times 10.928 \times sin(60)

A=37.85570...............Answer

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1 month ago
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