D because one thousand nine hundred twenty divided by 8 equals two hundred and forty
The train traveled 60 miles per hour since 360 miles divided by 6 hours gives you 60 mph
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.
Answer:
750 mm, 7.5 cm
Step-by-step explanation:
Verify each case
case a) 2.5 km, 2,500 m
we know that
1 km ------> 1.000 m
so
2.5 km=2,500 m
therefore
The pair of measurements is equivalent
case b) 750 mm, 7.5 cm
we know that
1 cm ------> 10 mm m
so
7.5 cm=75 mm
therefore
<u>The pair of measurements is not equivalent</u>
case c) 3 m, 3,000 mm
we know that
1 m ------> 1.000 mm
so
3 m=3,000 mm
therefore
The pair of measurements is equivalent
case d) 120 cm, 1.2 m
we know that
1 m ------> 100 cm
so
1.2 m=120 cm
therefore
The pair of measurements is equivalent
Answer:
1
Step-by-step explanation:
21 = 3*7
65 = 5*13
CGF: to find the greatest common factor, multiply those factors both numbers have in common
GCF :1 since there are no factors in common
