Answer:
about 106 km
Step-by-step explanation:
The distance between the two towns can be estimated several ways. In the attachment, we chose to measure the angles on the map. Using the law of sines, we can estimate the unknown distance.
The distance can also be estimated using the Tounouse-Avaria distance as a ruler. For best results, that ruler would need to be subdivided to an appropriate level.
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<h3>angle measures</h3>
The angles in the triangle can be measured using a protractor or some other tool. The attachment shows the results from a geometry program:
<h3>law of sines</h3>
The law of sines tells us the distances are proportional to the sines of the opposite angles:
TM/sin(TAM) = TA/sin(TMA)
TM = sin(24°)×(250 km)/sin(107°) ≈ 106.3 km
The distance from Tounouse to Mt. Monotti is estimated to be about 106 km.
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<em>Alternate solution</em>
Using a compass or dividers to project the TM distance onto TA, we find it is between 0.4 and 0.5 of the TA distance. The difference between 2×TM and TA can be estimated to be about 0.4×TM. That is, ...
TM ≈ TA/2.4 ≈ (250 km)/2.4 ≈ 104.2 km
This estimate is consistent with the one found using angle measures.
Answer:1.17
Step-by-step explanation:
Answer:
- m = 4/3; b = -4
- m = 3; b = -6
Step-by-step explanation:
In each case, <em>solve for y</em>. You do this by getting the y-term by itself, then dividing by the coefficient of y.
<h3>1.</h3>
-3y = -4x +12 . . . . . subtract 4x
y = 4/3x -4 . . . . . . . divide by -3
The slope is 4/3; the y-intercept is -4.
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<h3>2.</h3>
y = 3x -6 . . . . . . divide by 2
The slope is 3; the y-intercept is -6.
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<em>Additional comment</em>
Whatever you do to one side of the equation, you must also do to the other side. When we say "subtract 4x", that means 4x is subtracted from both sides of the equation. The reason for doing that in the first equation is to eliminate the 4x term from the left side.
(Sometimes, you may see operations described as "move ...". There is no property of equality called "move." There are <em>addition</em>, <em>subtraction</em>, <em>multiplication</em>, <em>division</em>, and <em>substitution</em> properties of equality. Any equation solving process will make use of one or more of these.)
Answer:
(2,-10)
Step-by-step explanation:
I used a graphing tool to graph the system of equations. The the two lines intercept at the point (2,-10). So, (2,-10) is the solution.
