Each person should ride the bike for 4 miles, so that every one has to walk 8 miles and ride 4 miles.
If they had 2 bikes, each person will ride for 8 miles, 4 miles on each bike, and then walk 4 miles.
since 1.5 is half of 3.0 all ouj havr t o do is multiply by 2 2.4*2=4.8 answer
Answer:
51 m^2
Step-by-step explanation:
The shaded area is the difference between the area of the overall figure and that of the rectangular cutout.
The applicable formulas are ...
area of a triangle:
A = (1/2)bh
area of a rectangle:
A = bh
area of a trapezoid:
A = (1/2)(b1 +b2)h
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We note that the area of a triangle depends only on the length of its base and its height. The actual shape does not matter. Thus, we can shift the peak of the triangular portion of the shape (that portion above the top horizontal line) so that it lines up with one vertical side or the other of the figure. That makes the overall shape a trapezoid with bases 16 m and 10 m. The area of that trapezoid is then ...
A = (1/2)(16 m + 10 m)(5 m) = 65 m^2
The area of the white internal rectangle is ...
A = (2 m)(7 m) = 14 m^2
So, the shaded area is the difference:
65 m^2 -14 m^2 = 51 m^2 . . . . shaded area of the composite figure
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<em>Alternate approach</em>
Of course, you can also figure the area by adding the area of the triangular "roof" to the area of the larger rectangle, then subtracting the area of the smaller rectangle. Using the above formulas, that approach gives ...
(1/2)(5 m)(16 m - 10 m) + (5 m)(10 m) - (2 m)(7 m) = 15 m^2 + 50 m^2 -14 m^2
= 51 m^2
When roots of polynomials occur in radical form, they occur as two conjugates.
That is,
The conjugate of (a + √b) is (a - √b) and vice versa.
To show that the given conjugates come from a polynomial, we should create the polynomial from the given factors.
The first factor is x - (a + √b).
The second factor is x - (a - √b).
The polynomial is
f(x) = [x - (a + √b)]*[x - (a - √b)]
= x² - x(a - √b) - x(a + √b) + (a + √b)(a - √b)
= x² - 2ax + x√b - x√b + a² - b
= x² - 2ax + a² - b
This is a quadratic polynomial, as expected.
If you solve the quadratic equation x² - 2ax + a² - b = 0 with the quadratic formula, it should yield the pair of conjugate radical roots.
x = (1/2) [ 2a +/- √(4a² - 4(a² - b)]
= a +/- (1/2)*√(4b)
= a +/- √b
x = a + √b, or x = a - √b, as expected.
