Answer:
A 2
Step-by-step explanation:
When we divide x by 9 there is some whole number we will call y plus a remainder of 4
x/9 = y remainder 4
Writing this in fraction form
x/9 = y + 4/9
Multiplying each side by 9
9*x/9 = 9* y + 4/9 *9
x = 9y +4
Multiply each side by 2
2x = 2*(9y+4)
2x = 18y +8
Add 3 to each side
2x+3 = 18y +8+3
2x+3 = 18y +11
Divide each side by 9
(2x+3)/9 = 18y/9 +11/9
= 2y + 9/9 +2/9
=(2y+1 + 2/9)
We know y is a whole number and 1 is a whole number so we can ignore 2y +1 when looking for a remainder)
2/9 is a fraction
Taking this back from fraction form to remainder from
(2y+1) remainder 2
There are 14 chairs and 8 people to be seated. But among the 8. three will be seated together:
So 5 people and (3) could be considered as 6 entities:
Since the order matters, we have to use permutation:
¹⁴P₆ = (14!)/(14-6)! = 2,162,160, But the family composed of 3 people can permute among them in 3! ways or 6 ways. So the total number of permutation will be ¹⁴P₆ x 3!
2,162,160 x 6 = 12,972,960 ways.
Another way to solve this problem is as follow:
5 + (3) people are considered (for the time being) as 6 entities:
The 1st has a choice among 14 ways
The 2nd has a choice among 13 ways
The 3rd has a choice among 12 ways
The 4th has a choice among 11 ways
The 5th has a choice among 10 ways
The 6th has a choice among 9ways
So far there are 14x13x12x11x10x9 = 2,162,160 ways
But the 3 (that formed one group) could seat among themselves in 3!
or 6 ways:
Total number of permutation = 2,162,160 x 6 = 12,972,960
Answer:
The first loan covers 80 percent of the home’s price, while the second covers the remaining 20 percent.
Step-by-step explanation:
they are still a home price percentage
Question 7:
Diameter = 6.2 cm so Radius = 3.1 cm
A=πr² = 3.14 × 3.1² = 30.1754 cm² = 30.18 cm²
Question 8:
Circumference = 2πr
16π = 2πr
therefore 16 = 2r so r = 8cm
Answer:
(x, y) = (0, -2248)
Step-by-step explanation:
<u>Substitution</u>
Substitute for y:
300x -2248 = 350x -2248
0 = 50x . . . . . . . . add 2248-300x to both sides
x = 0
y = 300·0 -2248
The solution is (x, y) = (0, -2248).
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<u>Elimination</u>
Subtract the first equation from the second.
(y) -(y) = (350x -2248) -(300x -2248)
0 = 50x
x = 0
y = 300·0 -2248
The solution is (x, y) = (0, -2248).
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<em>Additional comment</em>
If you think for a bit about what the graph looks like, you realize both lines cross at their y-intercept, (0, -2248). That point of intersection is the solution to the system of equations.
