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3 years ago

Solve the triangle. Round your answers to the nearest tenth.

Mathematics

1 answer:

Tresset [83]3 years ago

6 0

Answer:

<B = 47°

<C = 28°

b = AC = 28.0

Step-by-step explanation:

Given:

∆ABC

AB = c = 18

BC = a = 37

<A = 105°

Required:

Length of AC = b

measure of angle B and angle C

SOLUTION:

==>Use the sine rule, sin A/a = sinC/c to find the angle of C:

SinA = sin(105) = 0.9659

a = 37

sinC = ?

c = 18

0.9659/37 = sinC/18

Cross multiply

0.9659*18 = 37*sinC

17.3862 = 37*sinC

Divide both sides by 37

17.3862/37 = sinC

0.4699 = sinC

sinC = 0.4699

C = Sin-¹(0.4699)

C = 28.0° (nearest tenth)

==>Find angle B using sum of angles in a triangle:

Angle B = 180 - (105+28)

Angle B = 180 - 133

Angle B = 47°

==>Find length of b using sine rule, b/sinB = c/sinC:

SinC = sin(28) = 0.4695

SinB = sin(47) = 0.7314

c = 18

b = ?

b/0.7314 = 18/0.4695

Cross multiply

b*0.4695 = 18*0.7314

b*0.4695 = 13.1652

Divide both sides by 0.4695

b = 13.1652/0.4695

b = 28.0 (nearest tenth)

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Who can answer this? I’ll mark brainliest!!

Vesna [10]

Answer:

y = 0.48(x - 0.5)² - 3

y = 0.48(x² - x - 6)

Step-by-step explanation:

From the graph the zeros are

x = {-2, 3}

The x coordinate of the vertex is the midpoint of the roots

x = (-2 + 3) / 2

x = 0.5

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vertex = (0.5, -3)

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

Merhod I - vertex

Vertex form is

y = a(x - h)² + k

plug in the vertex

y = a(x - 0.5)² - 3

to find a plug in either root

using x = 3

0 = a(3 - 0.5)² - 3

0 = a(2.5)² - 3

0 = 6.25a - 3

3 = 6.25a

a = 3/6.25

a = 0.48

y = 0.48(x - 0.5)² - 3

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

Method II - roots

y = a(x + 2)(x - 3)

-3 = a(0.5 + 2)(0.5 - 3)

-3 = a(2.5)(-2.5)

-3 = -6.25a

3/6.25 = a

0.48 = a

y = 0.48(x + 2)(x - 3)

Expand

y = 0.48(x² - x - 6)

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Step-by-step explanation:

Here, The club charges $y an hour for each child and $x an hour for each adult.

And, according to the question,

In the family 3 children and 2 adults visited a health club such that the family does not want to spend more than $30 an hour at the health club.

That is, $2x + 3y\leq 30$

Which is the required inequality.

Since at origin, $2\times 0 + 3\times \leq 30$ (true)

That is, the inequality must contains the origin.

Therefore, shaded region will occur below the line.

Also, x-intercept of the given line is (15,0)

And, y-intercept of the given line is (0,10)

Thus the line will join the order pairs (15,0) and (0,10)

Also, $x\geq 0$ and $y\geq 0$ ( because charges can not be negative)

Therefore the shaded region will only contain the first quadrant.

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