Answer:
17
Step-by-step explanation:
4x5=20 20 - 3= 17
Create equations:
10X+15y=2575.
X+Y=210.
Solve for X: X=210-Y, and sub it into the other equation: 10(210-Y)+15Y=2575. Solve for Y: 2,100-10y+15y=2575, 5y=475, y=95.
Sub Y into the original problem: X+95=210. Solve: X=115.
The first mechanic charges $115 per hour and the second charges $95 :)
We have that
y=x²----> equation 1<span>
y=x+2-----> equation 2
multiply equation 1 by -1
-y=-x</span>²
add equation 1 and equation 2
-y=-x²
y=x+2
------------
0=-x²+x+2-------------> -x²+x+2=0-----> x²-x-2=0
Group terms that contain the same variable, and move the
constant to the opposite side of the equation
(x²-x)=2
<span>Complete
the square. Remember to balance the equation by adding the same constants
to each side
</span>(x²-x+0.5²)=2+0.5²
Rewrite as perfect squares
(x-0.5)²=2+0.5²
(x-0.5)²=2.25-----> (x-0.5)=(+/-)√2.25-----> (x-0.5)=(+/-)1.5
x1=1.5+0.5-----> x1=2
x2=-1.5+0.5---- > x2=-1
for x=2
y=x²----> y=2²----> y=4
the point is (2,4)
for x=-1
y=x²----> y=(-1)²---> y=1
the point is (-1,1)
the answer isthe solution of the system are the points(2,4) and (-1,1)
Answer:
a. The probability is not equal to 1
b. P (A') = 0.70
c. P ( A U B ) = 0.80
d. P ( A' ∩ B' ) = 0.20
Step-by-step explanation:
a. Because these A and B are disjoint
b. since the probability of A is 0.30 then the probability of A compliment is
P(A compliment ) = 1 - P (A)
P(A compliment ) = 1-0.30
P(A compliment ) = 0.70
c. Since event are disjoint then intersection of A and B is 0, so probability of A U B is;
P ( A U B ) = P (A) + P(B) - P(A∩ B)
P ( A U B ) = 0.30 + 0.50 - 0
P ( A U B ) = 0.80
d. The inetrsection of compilments of A and B are:
by using De Morgan's Law we have,
P ( A' ∩ B' ) = P [(A U B )']
P ( A' ∩ B' ) = 1 - P ( A U B )
P ( A' ∩ B' ) = 1 - 0.80
P ( A' ∩ B' ) = 0.20
We want to find h and k so that
3x³ - 6x² + 4x - 2 ≡ (x-2)(3x² + hx + 4) + k
Expand the right side.
(x-2)(3x² + hx + 4) + k
= 3x³ + hx² + 4x - 6x² - 2hx - 8 + k
= 3x³ + (h-6)x² + (4 - 2h)x + k - 8
Match coefficients of x²:
h - 6 = -6
h = 0
Match coefficients of x:
4 - 2h = 4 (Correct because h=0)
Match constants.
k - 8 = -2
k = 6
Answer: h=0, k=6
