Coordinate points are set up as (x, y) so...
x = 3
y = -3
Step 1: Plug 3 into x and -3 in to y in the equation: y = 4x - 1
-3 = 4(3) - 1
Step 2: Solve using basic order of operation
-3 = 12 - 1
-3 = 11
If the end result is equal to each other othen it is on the line y = 4x - 1. If not then the point isn't on the line
Hope this helped!
Answer:
A) Tammy: 10x + 5y > 200
Keith: 12x + 3y > 180
B) A possible combination is x = 16 and y = 4
Step-by-step explanation:
x: number of lawns they each mow
y: number of yards they each rake
A) Tammy earns $10 for each lawn she mows and $5 for each yard she rakes, then the total money she earns is computed by:
10x + 5y
She wants to earn more than $200, so her inequality is:
10x + 5y > 200
Keith earns $12 for each lawn he mows and $3 for each yard he rakes. He wants to earn more than $180. Then, his inequality is:
12x + 3y > 180
B) Keith had met his goal but Tammy did not meet her goal, then:
12x + 3y > 180
10x + 5y < 200
Let's suppose x = 16:
12(16) + 3y > 180
y > (180 - 192)/3
y > -4
10(16) + 5y < 200
y < (200 - 160)/5
y < 8
Then, a possible combination is x = 16 and y = 4
Answer:
3,247,695
Step-by-step explanation:
We want the coefficient of the term with x^8
So Use Newton's Binomial Expansion formula
Formula is (x + y) ^n = Sum for i=0 to n (n choose i) x^(n-i)*y^i
here (x^2 + 3) ^ 12
( 12 choose i) * (x^2)^(12-i) * (3)^i
i needs to equal 8 for us to get x^8
(12 choose 8) * (x^2)^(12-8) * (3^8)
= (12 choose 8) * x^8 * (3^8)
so a = (12 choose 8) * 
a = (12! /(8! * 4!) ) *
a = ( 12*11*10*9/ 4*3*2*1) *
a = (11*5*9) *
a = 11*5*9 * 6561
a = 3,247,695
Answer:
The probability of 1 or less children from that group to learn how to swim before 6 years of age is 0.072
Step-by-step explanation:
In this case we need to compute the probability of none of these 12 children learns to swim before 6 years of age. This is given by:
p(0) = (1 - 0.312)^(12) = 0.688^(12) = 0.01124
We now need to calculate the probability that one child learns to swim before 6 years of age.
p(1) = 12*0.312*(1 - 0.312)^(11) = 3.744*(0.688)^(11)
p(1) = 3.744*0.01634
p(1) = 0.0612
The probability of 1 or less children from that group to learn how to swim before 6 years of age is:
p = p(0) + p(1) = 0.01124 + 0.0612 = 0.07244
Larger is x
the other is called y
sum of squares is 394
x^2+y^2=394
one is 2 less that other
x>y so
y+2=x
subsitute y+2 for x
(y+2)^2+y^2=394
expand
y^2+4y+4+y^2=394
add like terms
2y^2+4y+4=394
divideboth sides by 2
y^2+2y+2=197
subtract 197 from both sides
y^2+2y-195=0
factor
(y+15)(y-13)=0
set each to zero
y+15=0
y=-15
impossible since it is stated that they are positive so get rid of this solution
y-13=0
y=13
find other
y+2=x
13+2=x
15=x
numbers are 13 and 15
