9514 1404 393
Answer:
10. (x, y) = (-3/8, 2 9/16)
11. k = -1
Step-by-step explanation:
10. The value of x at the vertex is ...
x = -b/(2a)
x = -(-3)/(2(-4)) = -3/8
The corresponding value of y is ...
y = 2 +(-3/8)(-3 +(-3/8)(-4)) = 2 +(-3/8)(-3/2) = 2 +(9/16)
The vertex is (x, y) = (-3/8, 2 9/16).
__
11. The discriminant is zero when the roots are equal.
b² -4ac = 0
(k-1)² -4(1)(-k) = 0
k² -2k +1 +4k = 0
k² +2k +1 = 0 . . . . . collect terms
(k +1)² = 0 . . . . . . . . write as a square
k = -1 . . . . . . . . . . . . the value of k that satisfies
<em>Check</em>
x² -2x +1 = (x -1)² = 0 . . . . has equal roots: x=1.
Answer:
$ 37.642
Step-by-step explanation:
Total Bill : $ 32.45
Tip : 16% of the bill.
= 16% x 32.45
=32.45 x (16/100)
= $ 5.192
hence ,
Total bill = Tip + bill charged
= 5.192 + 32.45
= $ 37.642
The excluded values are the values that the variable cannot take on because it makes the overall expression undefined.
For example, we can't have in the expression because is undefined.
For both of these problems you do the same sort of thing, with some factorization along the way:
If or , the denominator is 0 and we have an undefined expression, so these are the excluded values.
If or , we get an undefined expression.
Answer:
it's not possible
Step-by-step explanation:
let's say that we have
so twice the last integer is
and the second integer is
so the sum of both is 212
so as we can see there aren't those integers
Answer:
(2, -2)
Step-by-step explanation:
Multiply the first equation by -3,and multiply the second equation by 1.
−3(5x+6y=−2)
1(15x+4y=22)
Becomes:
−15x−18y=6
15x+4y=22
Add these equations to eliminate x:
−14y=28
Then solve−14y=28for y:
−14y=28
−14y
−14
=
28
−14
(Divide both sides by -14)
y=−2
Now that we've found y let's plug it back in to solve for x.
Write down an original equation:
5x+6y=−2
Substitute−2foryin5x+6y=−2:
5x+(6)(−2)=−2
5x−12=−2(Simplify both sides of the equation)
5x−12+12=−2+12(Add 12 to both sides)
5x=10
5x
5
=
10
5
(Divide both sides by 5)
x=2
Answer:
x=2 and y=−2