Answer:
w > 7
Step-by-step explanation:
L = 3w
2L + 2w > 56
sub for L
2(3w) + 2w > 56
6w + 2w > 56
8w > 56
w > 7
Check: L = 3(8)
L = 24
2(24) + 2(8) > 56
48 + 16 > 56
64 > 56
10 <0.25 (x + 1) <11
We must solve two inequalities in this case.
Inequality 1:
10 <0.25 (x + 1)
10 / 0.25 <x + 1
40 <x + 1
40-1 <x
39 <x
Inequality 2:
0.25 (x + 1) <11
(x + 1) <11 / 0.25
(x + 1) <44
x <44-1
x <43
The final result is:
39 <x <43
Answer:
39 <x <43
Answer:
90 in²
Step-by-step explanation:
The figure's area is that of four right triangles, each with legs of 6 in and 7.5 in. The area of each triangle is half the product of the leg lengths, so is ...
triangle area = (1/2)(6 in)(7.5 in)
Then the area of 4 of those triangles is ...
figure area = 4 · triangle area = 2(6 in)(7.5 in) = 90 in²
The slope of f(x) is 10 and the slope of g(x) is 5; g(x) has the greater y-intercept.
To find the slope of f(x), we use the slope formula: m=(y₂-y₁)/(x₂-x₁) = (-1--11)/(0--1) = (-1+11)/(0+1) = 10/1 = 10.
To find the slope of g(x), we just look at the form it is in. It is written in slope-intercept form, y=mx+b, where m is the slope. The number in g(x) that would correspond to m is 5.
The y-intercept of f(x) is found by looking at the points. Any y-intercept will have an x-coordinate of 0; the only point like this in the table is (0, -1) so the y-intercept is -1.
For g(x), we again look at the form y=mx+b. The number that corresponds with b is the y-intercept; in this case, it is 1. 1>-1, so g(x) has the larger y-intercept.
