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alexira [117]
2 years ago
13

The Red Line in the figure is an altitude of triangle hjl. Using right angle trig and properties of equality, y sin L = x = z si

n H, write the Law of Sines for this triangle
​

Mathematics
2 answers:
aivan3 [116]2 years ago
7 0

Answer:

\Large \boxed{\mathrm{\bold{C}}}

Step-by-step explanation:

\sf \displaystyle sin(\theta) =\frac{opposite}{hypotenuse }

\sf \displaystyle sin(L) =\frac{x}{y}

\sf \displaystyle sin(H) =\frac{x}{z}

\displaystyle \sf \frac{sinL}{z} =\frac{sinH  }{y}

\displaystyle \sf \frac{\frac{x}{y} }{z} =\frac{\frac{x}{z} }{y}

Simplifying the expression.

\sf \displaystyle \frac{x}{yz } = \frac{x}{yz} \ (true)

\displaystyle \sf \frac{z}{sinL} =\frac{y}{sinH}

\displaystyle \sf \frac{z}{\frac{x}{y}} =\frac{y}{\frac{x}{z}}

Multiplying both sides by x.

\sf yz=yz  \ (true)

Alexxx [7]2 years ago
5 0

Answer:

d

Step-by-step explanation:

The law of Sines applied to a Δ ABC is

\frac{a}{sinA} = \frac{b}{sinB} = \frac{c}{sinC}

Using this in Δ HJL

\frac{z}{sinL} = \frac{y}{sinH} → (b)

Which may be expressed in reciprocal form as

\frac{sinL}{z} = \frac{sinH}{y} → (a)

Thus the law of Sines can be expressed as either (a) or (b)

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4 0
3 years ago
H(x) = -3(x²)<br><br><br> describe the transformation
Shkiper50 [21]

Answer:

The parent function is the simplest form of the type of function given.

g

(

x

)

=

x

2

The transformation being described is from  

g

(

x

)

=

x

2

to  

h

(

x

)

=

−

3

x

2

.

g

(

x

)

=

x

2

→

h

(

x

)

=

−

3

x

2

The horizontal shift depends on the value of  

h

. The horizontal shift is described as:

h

(

x

)

=

f

(

x

+

h

)

- The graph is shifted to the left  

h

units.

h

(

x

)

=

f

(

x

−

h

)

- The graph is shifted to the right  

h

units.

In this case,  

h

=

0

which means that the graph is not shifted to the left or right.

Horizontal Shift: None

The vertical shift depends on the value of  

k

. The vertical shift is described as:

h

(

x

)

=

f

(

x

)

+

k

- The graph is shifted up  

k

units.

h

(

x

)

=

f

(

x

)

−

k

- The graph is shifted down  

k

units.

In this case,  

k

=

0

which means that the graph is not shifted up or down.

Vertical Shift: None

The graph is reflected about the x-axis when  

h

(

x

)

=

−

f

(

x

)

.

Reflection about the x-axis: Reflected

The graph is reflected about the y-axis when  

h

(

x

)

=

f

(

−

x

)

.

Reflection about the y-axis: None

Compressing and stretching depends on the value of  

a

.

When  

a

is greater than  

1

: Vertically stretched

When  

a

is between  

0

and  

1

: Vertically compressed

Vertical Compression or Stretch: Stretched

Compare and list the transformations.

Parent Function:  

g

(

x

)

=

x

2

Horizontal Shift: None

Vertical Shift: None

Reflection about the x-axis: Reflected

Reflection about the y-axis: None

Vertical Compression or Stretch: Stretched

image of graph

The parent function is the simplest form of the type of function given.

g

(

x

)

=

x

2

The transformation being described is from  

g

(

x

)

=

x

2

to  

h

(

x

)

=

−

3

x

2

.

g

(

x

)

=

x

2

→

h

(

x

)

=

−

3

x

2

The horizontal shift depends on the value of  

h

. The horizontal shift is described as:

h

(

x

)

=

f

(

x

+

h

)

- The graph is shifted to the left  

h

units.

h

(

x

)

=

f

(

x

−

h

)

- The graph is shifted to the right  

h

units.

In this case,  

h

=

0

which means that the graph is not shifted to the left or right.

Horizontal Shift: None

The vertical shift depends on the value of  

k

. The vertical shift is described as:

h

(

x

)

=

f

(

x

)

+

k

- The graph is shifted up  

k

units.

h

(

x

)

=

f

(

x

)

−

k

- The graph is shifted down  

k

units.

In this case,  

k

=

0

which means that the graph is not shifted up or down.

Vertical Shift: None

The graph is reflected about the x-axis when  

h

(

x

)

=

−

f

(

x

)

.

Reflection about the x-axis: Reflected

The graph is reflected about the y-axis when  

h

(

x

)

=

f

(

−

x

)

.

Reflection about the y-axis: None

Compressing and stretching depends on the value of  

a

.

When  

a

is greater than  

1

: Vertically stretched

When  

a

is between  

0

and  

1

: Vertically compressed

Vertical Compression or Stretch: Stretched

Compare and list the transformations.

Parent Function:  

g

(

x

)

=

x

2

Horizontal Shift: None

Vertical Shift: None

Reflection about the x-axis: Reflected

Reflection about the y-axis: None

Vertical Compression or Stretch: Stretched

image of graph

Step-by-step explanation:

8 0
3 years ago
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