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tigry1 [53]
2 years ago
6

Point B has coordinates (−4, −2). The x-coordinate of point A is 5. The distance between points A and B is 15 units. What are th

e possible coordinates of point A?
Mathematics
1 answer:
GaryK [48]2 years ago
7 0

~~~~~~~~~~~~\textit{distance between 2 points} \\\\ A(\stackrel{x_1}{5}~,~\stackrel{y_1}{y})\qquad B(\stackrel{x_2}{-4}~,~\stackrel{y_2}{-2})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ \stackrel{AB}{15}=\sqrt{[-4 - 5]^2 + [-2 - y]^2}\implies 15^2=(-9)^2+(-2-y)^2

225=81+(-2-y)(-2-y)\implies 225=81+\stackrel{F~O~I~L}{(4+4y+y^2)} \\\\\\ 144=4+4y+y^2\implies 0=y^2+4y-140\implies 0=(y-10)(y+14) \\\\\\ y= \begin{cases} 10\\ -14 \end{cases}\qquad \qquad \qquad A(5~~,~~10)\qquad A(5~~,~~-14)

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4 0
3 years ago
The denarius was a unit of currency in ancient rome. Suppose it costs the roman government 101010 denarii per day to support 444
givi [52]

<u>the correct question is</u>

The denarius was a unit of currency in ancient rome. Suppose it costs the roman government 10 denarii per day to support 4 legionaries and 4 archers. It only costs 5 denarii per day to support 2 legionaries and 2 archers. Use a system of linear equations in two variables. Can we solve for a unique cost for each soldier?

Let

x-------> the cost to support a legionary per day

y-------> the cost to support an archer per day

we know that

4x+4y=10 ---------> equation 1

2x+2y=5 ---------> equation 2

If you multiply equation 1 by 2

2*(2x+2y)=2*5-----------> 4x+4y=10

so

equation 1 and equation 2 are the same

The system has infinite solutions-------> Is a consistent dependent system

therefore

<u>the answer is</u>

We cannot solve for a unique cost for each soldier, because there are infinite solutions.

5 0
3 years ago
On a map, 2 inches represents an actual distance of 64 miles. Towns A and B are 608 miles apart. Find the distance between the t
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Answer: The distance in the map is 19 inches.

Step-by-step explanation:

On the map. 2 inches represent an actual distance of 64 miles.

The actual distance between town A and town B is equal to 608 miles, we need to divide this distance into groups of 64 miles.

N = 608/64 = 9.5

And each one of those 9.5 groups is represented with 2 inches in the map, then the distance in the map is:

d = 9.5*2 inches = 19 inches.

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3 years ago
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Answer:

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Step-by-step explanation:

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3 years ago
Urgent help neededddd
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Answer:

176

Step-by-step explanation:

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2 years ago
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