Answer:
or 
Step-by-step explanation:
The question is
Find the slope intercept form of the line parallel to the line 5x+8y=120 passing through (4,5)
step 1
Find the slope of the given line
we have
isolate the variable y
The slope of the given line is m=-5/8
step 2
Find the slope of the line parallel to the given line
we know that
If two lines are parallel, then their slopes are the same
so
The slope of the parallel line to given line is m=-5/8
step 3
Find the equation of the line into slope intercept form
The equation of the line into slope intercept form is equal to
we have
m=-5/8 and point (4,5)
substitute and solve for b
substitute
or
X=16/3 or 5.33333 based on the fact that the angles are congruent
The piece of unknown metal is in thermal equilibrium with water such that Q of metal is equal to Q of the water. We write this equality as follows:
-Qm = Qw
Mass of metal (Cm)(ΔT) = Mass of water (Cw) (ΔT)
where C is the specific heat capacities of the materials.
We calculate as follows:
-(Mass of metal (Cm)(ΔT)) = Mass of water (Cw) (ΔT)
-68.6 (Cm)(52.1 - 100) = 42 (4.184) (52.1 - 20)
Cm = 1.717 -----> OPTION C
Answer:
2) (-∞, 17]
Step-by-step explanation:
The leading coefficient of the function is negative, so the parabola opens downward. The vertex will be a maximum, the upper end of the range. The lower end of the range will be -∞.
The vertex of the function lies on the axis of symmetry. The maximum can be found by evaluating the function at x=-4.
y = -(-4)² -8(-4) +1 = -16 +32 +1 = 17
The range of the function is (-∞, 17].
