Given:
The equation of a line is:
A line is parallel to the given line and passes through the point (3,-4).
To find:
The equation of the line in the slope intercept form.
Solution:
The slope intercept form of a line is:
...(i)
Where, m is the slope and b is the y-intercept of the line.
We have,
...(ii)
On comparing (i) and (ii), we get
Slope of the given line is 1.
We know that the slopes of parallel lines are equal. So, the slope of the required line is 1.
The required line passes through the point (3,-4) with slope 1. So, the equation of the required line is:
Subtracting 4 from both sides, we get
Therefore, the equation of the required line is .
Answer:
(a) 2.6 m^2
(b) 3.9 m^3
Step-by-step explanation:
(a)
ABCD is a trapezoid.
A = (B + b)h/2
A = (1.7 m + 2.3 m)(1.3 m)/2 = 2.6 m^2
(b)
The skip is shaped like a prism with trapezoidal bases.
V = area of base * height
V = 2.6 m^2 * 1.5 m = 3.9 m^3
Answer:
Step-by-step explanation:
Given: sin x + cos x
To change the given trigonometry expression in term of sine only.
Trigonometry identity:-
Expression: 
We get rid of cos x from expression and write as sine form.
Expression: 
Hence, The final expression is only sine function.
Since 1 < x < 5, adding each side by a, where a is negative, gives
a > ax > 5a
and adding b to each side gives
a + b > ax + b > 5a + b
or
5a + b < ax + b < a + b
Since 7 < f(x) < 23, it follows that
5a + b = 7
a + b = 23
Solve for a by eliminating b :
(5a + b) - (a + b) = 7 - 23
4a = -16
a = -4
Solve for b :
-4 + b = 23
b = 27
