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Ksivusya [100]
3 years ago
9

Use the law of sines to find the value of w.

Mathematics
2 answers:
worty [1.4K]3 years ago
7 0

Answer:

it is the answer b 4.0 cm

Step-by-step explanation:

Lunna [17]3 years ago
4 0

Option B: 4.0 cm is the value of w

Explanation:

It is given that \angle W= 39, \angle U=31, VW=3.3 and UV=w

Using the law of sines, we have,

\frac{sin U}{3.3} =\frac{sin W}{w}

Substituting the values, we have,

\frac{\sin 31}{3.3}=\frac{\sin 39}{w}

Cross multiplying, we get,

(sin31) w=3.3( \sin 39)

Simplifying, we have,

0.515w=2.077

Dividing both sides by 0.515, we have,

w=4.0

Thus, the value of w is 4.0 cm

Hence, Option B is the correct answer.

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A line is perpendicular to x + 3y - 4 = 0 and has the same y-intercept as 2x + 5y - 20 = 0. Find the equation for the line.​
yawa3891 [41]
<h3>Answer:  -3x+y-4 = 0   (standard form)</h3>

This is equivalent to y = 3x+4 (slope intercept form)

By "standard form", I mean the form Ax+By+C = 0.

====================================================

Explanation:

Let's solve the first equation for y

x+3y-4 = 0

x+3y = 4

3y = 4-x

3y = -x+4

y = (-x+4)/3

y = (-x/3) + (4/3)

y = (-1/3)x + (4/3)

The equation is now in y = mx+b form, aka slope intercept form, with m = -1/3 as the slope and b = 4/3 as the y intercept. We'll focus on the slope.

Apply the negative reciprocal to this so that we go from -1/3 to +3/1 or simply 3. Flip the fraction and the sign. Note how -1/3 and 3 multiply to -1. Perpendicular slopes always multiply to -1, assuming neither line is vertical.

So this mystery perpendicular line we're after has a slope of 3.

It has the same y intercept as 2x+5y-20 = 0. Plug in x = 0 and solve for to determine the y intercept.

2x+5y-20 = 0

2(0)+5y-20 = 0

5y-20 = 0

5y = 20

y = 50/5

y = 4

The y intercept of 2x+5y-20 = 0 is y = 4, so it's also the y intercept of our final answer. Let b = 4.

-------------------------------------

We found that:

  • m = 3 is the slope of the perpendicular line
  • b = 4 is the y intercept of the perpendicular line

So we know that,

y = mx+b

y = 3x+4

is the slope intercept form of the answer. Since your teacher gave you the equations in standard form (one version of it anyway), let's convert y = 3x+4 to that form as well

y = 3x+4

y-3x = 4

-3x+y = 4 .... one way to express standard form

-3x+y-4 = 0 .... another standard form

Some math textbooks use Ax+By = C as standard form, while others use Ax+By+C = 0. Unfortunately, it's a bit confusing because the same phrasing is used.

7 0
2 years ago
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