Answer:
See image
Step-by-step explanation:
To graph the inequality
-2x + y >= -10
Change it to y = mx + b form, use a solid line (bc of the "or equal to" underline)
y >= 2x - 10 We have y-intercept at -10 and slope 2/1, shading goes above the line.
The other graph is an absolute value graph; it has a v-shape. The 7 makes it stretched 7 times taller (and skinnier) the -4 by the x shifts the whole graph to the right 4 units. The -4 at the end of the equation shifts the whole graph down 4 units. See image. The shading goes above the V (kind of looks like inside)
The solution to the system is where the shading of the two overlap. It is mostly the shading for the absolute value graph except for a tiny triangle at the bottom. See image.
Answer:
6 in
Step-by-step explanation:
To find the height, just divide the volume by the base area
c=36+g
c:g:s=5:2:1
The ratio gives us two equations so that's three equations in three unknowns. Actually we're after the total t; let's put that in to solve for directly.
c:g:s:t = 5 : 2 : 1 : 5+2+1
We turn the ratio to fraction equations. s has the one; let's write everything in terms of s.
c/s = 5/1, g/s = 2/1, t/s = 8/1
Clearing the fractions,
c = 5s, g = 2s, t = 8s
Our other equation is
c = 36 + g
Substituting in for c and g,
5s = 36 + 2s
Solving,
3s = 36
s = 12
That's right; let's just get the total t.
t = 8s = 72
Answer: 72
Answer:
626.7 
Step-by-step explanation:
Consider the figure as a circle with radius 7.5 and a rectangle with width 30 and length 15.
CIRCLE
A = pi*r*r = pi*7.5*7.5 = 56.25pi =176.7
RECTANGLE
A = l*w = 15*30 = 450
176.7 + 450 = 626.7
The area of a sector is given by the formula
... A = (1/2)r²·θ . . . . . where r is the radius, and θ is the central angle is radians
Your angle is given in degrees, so we need to multiply it by π/180° to find its equivalent in radians.
... A = (1/2)(7.13 ft)²·(50°)·(π/180°) ≈ 7.0607π ft² ≈ 22.2 ft²
