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3 years ago

Find the missing parts of the triangle. Round to the nearest tenth when necessary or to the nearest minute as appropriate.

Mathematics

1 answer:

Katena32 [7]3 years ago

3 0

Answer:

A) A = 27.3°, B = 56.1°, C = 96.6°

Step-by-step explanation:

Use the Law of Cosines:

A = arccos [(b² + c² - a²)/(2bc)] = arccos [(13.2² + 15.8² - 7.3²)/(2*13.2*15.8)] = 27.3°
B = arccos [(a² + c² - b²)/(2ac)] = arccos [(7.3² + 15.8² - 13.2²)/(2*7.3*15.8)] = 56.1°
C = 180° - (A + B) = 180° - (27.3° + 56.1°) = 96.6°

Correct choice is A.

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Hich statement best describes a graph of paired points that form a proportional relationship?

Yanka [14]

Answer:

A. A straight line can be drawn through all the points and the line passes through the point (0,0) .

Step-by-step explanation:

See comment for options

Given

A graph with proportional relationship

Required

Which of options (a to d) describes the graph

A graph with a proportional relationship is represented as:

$y = kx$ and

$(x,y) = (0,0)$ is a paired point on the graph

This implies that options (b) and (c) are not true

Option (d) is also incorrect because if the graph does not pass through all points, then it is not proportional.

Hence, (a) is correct

6 0

3 years ago

Copies of a famous painting were created at the local art museum for visitors to purchase. The copies had a 30% smaller area tha

lina2011 [118]

Answer:

12.6 square feet

Step-by-step explanation:

So first we set it up:

18ft is 100% of the original

and the area of the copies are 70%

Copies: x

x/70 = 18/100

70(18) = 1260

1260/100 = 12.6

x = 12.6

6 0

3 years ago

Please answer this now in two minutes

Firlakuza [10]

Answer:

x = 6.6

Step-by-step explanation:

Data obtained from the question include the following:

Angle X = 15°

Angle Y° = 23°

Side y = 10

Side x =..?

The value of side x can be obtained by using the sine rule as shown below:

x/Sine X = y/Sine Y

x/Sine 15 = 10/Sine 23

Cross multiply

x × Sine 23 = 10 × Sine 15

Divide both side by Sine 23

x = (10 × Sine 15) / Sine 23

x = 6.6

Therefore, the value of x is 6.6.

7 0

3 years ago

Find the solution of the initial value problem dy/dx=(-2x+y)^2-7 ,y(0)=0

Leokris [45]

Substitute $v(x)=-2x+y(x)$ , so that $\dfrac{\mathrm dv}{\mathrm dx}=-2+\dfrac{\mathrm dy}{\mathrm dx}$ . Then the ODE is equivalent to

$\dfrac{\mathrm dv}{\mathrm dx}+2=v^2-7$

which is separable as

$\dfrac{\mathrm dv}{v^2-9}=\mathrm dx$

Split the left side into partial fractions,

$\dfrac1{v^2-9}=\dfrac16\left(\dfrac1{v-3}-\dfrac1{v+3}\right)$

so that integrating both sides is trivial and we get

$\dfrac{\ln|v-3|-\ln|v+3|}6=x+C$

$\ln\left|\dfrac{v-3}{v+3}\right|=6x+C$

$\dfrac{v-3}{v+3}=Ce^{6x}$

$\dfrac{v+3-6}{v+3}=1-\dfrac6{v+3}=Ce^{6x}$

$\dfrac6{v+3}=1-Ce^{6x}$

$v=\dfrac6{1-Ce^{6x}}-3$

$-2x+y=\dfrac6{1-Ce^{6x}}-3$

$y=2x+\dfrac6{1-Ce^{6x}}-3$

Given the initial condition $y(0)=0$ , we find

$0=\dfrac6{1-C}-3\implies C=-1$

so that the ODE has the particular solution,

$\boxed{y=2x+\dfrac6{1+e^{6x}}-3}$

5 0

3 years ago

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Nat2105 [25]

I hope this helps you

8 0

3 years ago