Answer:
a = - 2, b = - 6
Step-by-step explanation:
Substitute the values of the zeros into the polynomial and equate to zero.
x² +(a + 1)x + b
x = - 2 → (- 2)² - 2(a + 1) + b = 0 , that is
4 - 2a - 2 + b = 0
2 - 2a + b = 0 ( subtract 2 from both sides )
- 2a + b = - 2 → (1)
x = 3 → 3² + 3(a + 1) + b = 0, that is
9 + 3a + 3 + b = 0
12 + 3a + b = 0 ( subtract 12 from both sides )
3a + b = - 12 → (2)
Subtract (1) from (2) term by term to eliminate b
5a = - 10 ( divide both sides by 5 )
a = - 2
Substitute a = - 2 into either of the 2 equations and evaluate for b
Substituting into (2)
3(- 2) + b = - 12
- 6 + b = - 12 ( add 6 to both sides )
b = - 6
Thus a = - 2 and b = - 6
Answer:
23. $ 62.76 to the nearest cent
$63.00 to the nearest dollar
24. $ 38.42 to the nearest cent
$38.00 to the nearest dollar
Step-by-step explanation:
When we round to the nearest cent we round the second number after the decimal. We look at the third number after the decimal. If it is 5 or above we round up.
When we round to the nearest dollar, we round the number befroe the decimal. We look at the number after the decimal. If it is 5 or above we round up.
23. $62.756 we round the 5 so we look at the 6 6>= 5 so we round up
$ 62.76 to the nearest cent
$62.756 we round the 2 so we look at the 7 7>= 5 so we round up
$63.00 to the nearest dollar
24. $38.415 we round the 1 so we look at the 5 5>= 5 so we round up
$ 38.42 to the nearest cent
$38.415 we round the 8 so we look at the 4 4< 5 so we leave alone
$38.00 to the nearest dollar
-253 IS deeper than -280 in water. As your going into the negatives, The smaller numbers are bigger than the big numbers. It is the opposite when it comes to positive numbers.
Answer:
Step-by-step explanation:
Let the age be xy or 10x + y.
Reverse the two digits of my age, divide by three, add 20, and the result is my age, convert this to equation:
- (10y + x)/3 + 20 = 10x + y
- (10y + x)/3 = 10x + y - 20
- 10y + x = 3(10x + y - 20)
- 10y + x = 30x + 3y - 60
- 30x - x + 3y - 10y = 60
- 29x - 7y = 60
We should consider both x and y are between 1 and 9 since both the age and its reverse are 2-digit numbers.
Possible options for x are:
- 29x ≥ 7*1 + 60 = 67 ⇒ x > 2, at minimum value of y,
and
- 29x ≤ 7*9 + 60 = 123 ⇒ x < 5, at maximum value of y.
So x can be 3 or 4.
<h3>If x = 3</h3>
- 29*3 - 7y = 60
- 87 - 7y = 60
- 7y = 27
- y = 27/7, discarded as fraction.
<h3>If x = 4</h3>
- 29*4 - 7y = 60
- 116 - 7y = 60
- 7y = 56
- y = 8
So the age is 48.