The equivalent equation of 4y – 1 = 15 is 20x - 13 = 15
The equations are given as:
4y – 1 = 15 and y = 5x – 3.
Substitute y = 5x – 3. in 4y – 1 = 15
4(5x – 3) – 1 = 15
Expand
20x- 12 - 1 = 15
Evaluate the like terms
20x - 13 = 15
Hence, the equivalent equation of 4y – 1 = 15 is 20x - 13 = 15
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{\text{Direction of parabola depends on the sign of quadratic coefficient of a }} \hfill \\
{\text{quadratic equation}}. \hfill \\
{\text{For given quadratic equation}}. \hfill \\
a{x^2} + bx + c = 0 \hfill \\
{\text{The parabola is in the upward direction if }}a{\text{ }} > {\text{ }}0{\text{ and in downward direction if }}a < 0 \hfill \\
{\text{Here, the equation of given parabola is }} \hfill \\
{x^2} - 6x + 8 = y \hfill \\
\Rightarrow y = \left( {{x^2} - 6x + 9} \right) - 9 + 8 \hfill \\
\Rightarrow y = {\left( {x - 3} \right)^2} - 1. \hfill \\
{\text{Thus, the parabola is in the upward direction}} \hfill \\
Answer:
see explanation
Step-by-step explanation:
Using the sum/ difference → product formula
cos x - cos y = - 2sin( )sin ( )
sin x - sin y = 2cos ( )sin ( )
Given
(cosA - cosB)² + (sinA - sinB )²
= [ - 2sin()sin( ) ]² + [ 2cos( )sin( ) ]²
= 4sin² ( )sin² ( ) + 4cos² ( )sin² ( )
= 4sin² ( )[ sin² ( ) + cos² ( ) ← sin²x + cos²x = 1
= 4sin² ( ) × 1
= 4sin² ( ) = right side ⇒ proven
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a. 8
b. 114
a.
36/6 = 48/x
36x = 288
x = 8
b.
12/72 = 19/x
1/6 = 19/x
x = 114