Answer:
7x + 3y = 44
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c (m is the slope and c the y- intercept )
Rearrange - 3x + 7y = 5 into this form by adding 3x to both sides
7y = 3x + 5 ( divide all terms by 7 )
y = x +
← in slope- intercept form
with slope m =
Given a line with slope m then the slope of a line perpendicular to it is
= -
= -
= -
, thus
y = - x + c ← is the partial equation
To find c substitute (5, 3) into the partial equation
3 = - + c ⇒ c = 3 +
=
y = - x +
← in slope- intercept form
Multiply through by 3
3y = - 7x + 44 ( add 7x to both sides )
7x + 3y = 44 ← in standard form
Answer:
36 cups of water
Step-by-step explanation:
Make a proportion, where x is the number of cups of water needed:
=
Cross multiply and solve for x:
2x = 72
x = 36
So, 36 cups of water will be needed
Answer:
1 + cosa sina
Step-by-step explanation:
cos³a - sin³a ← is a difference of cubes and factors in general as
a³ - b³ = (a - b)(a² + ab + b²) , then
cos³a - sin³a
= (cosa - sina )(cos²a + cosa sina + sin²a)
= (cosa - sina)(1 + cosa sina) [ sin²a + cos²a = 1 ]
Then
= ← cancel (cosa - sina) on numerator/ denominator
= 1 + cosa sina