Answer:
Step-by-step explanation:
Here a equation of the line is given to us and we need to find out the equation of line which passes through the given point and parallel to the given line , the given equation is ,
Firstly convert it into <em>s</em><em>l</em><em>o</em><em>p</em><em>e</em><em> </em><em>i</em><em>n</em><em>t</em><em>e</em><em>r</em><em>c</em><em>e</em><em>p</em><em>t</em><em> </em><em>f</em><em>o</em><em>r</em><em>m</em><em> </em>of the line which is <u>y</u><u> </u><u>=</u><u> </u><u>m</u><u>x</u><u> </u><u>+</u><u> </u><u>x</u><u> </u>, as ;
On comparing it to <em>y</em><em> </em><em>=</em><em> </em><em>m</em><em>x</em><em> </em><em>+</em><em> </em><em>c</em><em> </em>, we have ,
Now as we know that the <em>s</em><em>l</em><em>o</em><em>p</em><em>e</em><em> </em><em>o</em><em>f</em><em> </em><em>t</em><em>w</em><em>o</em><em> </em><em>p</em><em>a</em><em>r</em><em>a</em><em>l</em><em>l</em><em>e</em><em>l</em><em> </em><em>l</em><em>i</em><em>n</em><em>e</em><em>s</em><em> </em><em>i</em><em>s</em><em> </em><em>s</em><em>a</em><em>m</em><em>e</em><em> </em>. Therefore the slope of the parallel line will be ,
Now we may use <em>p</em><em>o</em><em>i</em><em>n</em><em>t</em><em> </em><em>s</em><em>l</em><em>o</em><em>p</em><em>e</em><em> </em><em>f</em><em>o</em><em>r</em><em>m</em><em> </em>of the line as ,
On substituting the respective values ,
Again the equation can be rewritten as ,

The value of x is
and 
Step-by-step explanation:
The equation is 
Subtracting by
on both sides,

Taking LCM,

Multiplying by 3x on both sides,

Dividing by (-) on both sides,

Using quadratic formula, we can solve for x.

Taking out common term 2, we get,

Thus, the value of x is
and 
Answer:
1
+
sec
2
(
x
)
sin
2
(
x
)
=
sec
2
(
x
)
Start on the left side.
1
+
sec
2
(
x
)
sin
2
(
x
)
Convert to sines and cosines.
Tap for more steps...
1
+
1
cos
2
(
x
)
sin
2
(
x
)
Write
sin
2
(
x
)
as a fraction with denominator
1
.
1
+
1
cos
2
(
x
)
⋅
sin
2
(
x
)
1
Combine.
1
+
1
sin
2
(
x
)
cos
2
(
x
)
⋅
1
Multiply
sin
(
x
)
2
by
1
.
1
+
sin
2
(
x
)
cos
2
(
x
)
⋅
1
Multiply
cos
(
x
)
2
by
1
.
1
+
sin
2
(
x
)
cos
2
(
x
)
Apply Pythagorean identity in reverse.
1
+
1
−
cos
2
(
x
)
cos
2
(
x
)
Simplify.
Tap for more steps...
1
cos
2
(
x
)
Now consider the right side of the equation.
sec
2
(
x
)
Convert to sines and cosines.
Tap for more steps...
1
2
cos
2
(
x
)
One to any power is one.
1
cos
2
(
x
)
Because the two sides have been shown to be equivalent, the equation is an identity.
1
+
sec
2
(
x
)
sin
2
(
x
)
=
sec
2
(
x
)
is an identity
Step-by-step explanation:
Answer:
no
Step-by-step explanation:
Given
1 + 4(3x - 10) - 12x ← distribute the parenthesis
= 1 + 12x - 40 - 12x ← collect like terms
= 1 - 40
= - 39 ≠ - 9
Answer: (30m-9n)/270
First we start with m/9-n/30.
We multiply the denominators to get 270.
Then we multiply the numerators by the original denominators to get (30m-9n).
To check, we can use m=2, and n=4
2/9-4/30=4/45
(30*2-9*4)/270=24/270=4/45