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Masteriza [31]
2 years ago
15

This is a map of three towns. It shows the train line and the highway that connects the towns. The north direction is shown. The

map is drawn to scale. The distance between Tounouse and Avaria is 250 kilometers. A new train line is to be built between Tounouse and Mt.Monotti. Estimate the distance between these two towns.

Mathematics
1 answer:
vlada-n [284]2 years ago
4 0

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.

__

<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:

  • ∠TMA ≈ 107°
  • ∠TAM ≈ 24°
<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.

__

<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.

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lina2011 [118]

Answer:

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Step-by-step explanation:

to find the points of intersection equate the 2 equations , that is

7x - 15 = 10 + 12x - 6x² ( subtract 10 + 12x - 6x² from both sides )

6x² - 5x - 25 = 0 ← factor the quadratic on left side

consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term

product = 6 × - 25 = - 150 and sum = - 5

the factors are - 15 and + 10

use these factors to split the x- term

6x² - 15x + 10x - 25 = 0 ( factor the first/second and third/fourth terms )

3x(2x - 5) + 5(2x - 5) = 0 ← factor out (2x - 5) from each term

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equate each factor to zero and solve for x

3x + 5 = 0 ⇒ 3x = - 5 ⇒ x = - \frac{5}{3}

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3 0
1 year ago
How do I factor x^4-5x^2+6?
Vilka [71]

Answer:

=(x^2-3)(x^2-2)

Step-by-step explanation:

So we have the expression:

x^4-5x^2+6

And we wish to factor it.

First, let's make a substitution. Let's let u be equal to x². Therefore, our expression is now:

=u^2-5u+6

This is a technique called quadratic u-substitution. Now, we can factor in this form.

We can use the numbers -3 and -2. So:

=u^2-2u-3u+6

For the first two terms, factor out a u.

For the last two terms, factor out a -3. So:

=u(u-2)-3(u-2)

Grouping:

=(u-3)(u-2)

Now, substitute back the x² for u:

=(x^2-3)(x^2-2)

And this is the simplest form.

And we're done!

3 0
3 years ago
A video game has 25 levels. At level one, a player has 5 points. Each additional level increases the player's points by 10. If
ozzi

Answer:

<u>B. (3,25)</u>

Step-by-step explanation:

x = level of the video game

y = number of points

At level 1, a player has 5 points.

At level 2, the player has 5 + 10 = 15 points

Therefore, we can use the function notation this way:

f(x) = 5x + 10

<u>The only ordered pair given that is from this function is:</u>

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The remaining three don't represent this function.

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3 years ago
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kolbaska11 [484]
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The distance between the two buildings is 844.23 feet apart, we go this answer by simply applying the SOH CAH TOA method

<h3>Trigonometry</h3>

Given Data

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  • Angle of Elevation θ = 35°
  • Distance between the buildings Adj = ??

Applying the SOH CAH TOA Approach we have

Tan  θ = Opp/Adj

Substituting our given data we have

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make x subject of the formula we have

x = 400/0.4738

x = 844.23 feet

learn more about trigonometry here:

brainly.com/question/24349828

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