x,y - the numbers
one positive number is 5 less than twice a second number
(1) x - 5 = 2y
their product is 117
(2) xy = 117
(1) x - 5 = 2y <em>add 5 to both sides</em>
x = 2y + 5 <em>substitute it to (2)</em>
(2y + 5)y = 117 <em>use distributive property</em>
(2y)(y) + (5)(y) = 117
2y² + 5y = 117 <em>subtract 117 from both sides</em>
2y² + 5y - 117 = 0
2y² + 18y - 13y - 117 = 0
2y(y + 9) - 13(y + 9) = 0
(y + 9)(2y - 13) = 0 ↔ y + 9 = 0 ∨ 2y - 13 = 0
y + 9 = 0 <em>subtract 9 from both sides</em>
y = -9
2y - 13 = 0 <em>add 13 to both sides</em>
2y = 13 <em>divide both sides by 2</em>
y = 6.5
<em>substitute the values of y to (1)</em>
x = 2(-9) + 5 = -18 + 5 = -13 < 0
x = 2(6.5) + 5 = 13 + 5 = 18
<h3>Answer: x = 18 and y = 6.5</h3>
Answer:
1/36
Step-by-step explanation:
On the first throw, the probability of rolling any particular number, 1 through 6, is 1 out of 6. So the chance of rolling a 4 is 1/6.
On the second roll, your probability of rolling a 2 is 1/6.
The 'trick' is knwoing what to do with those two numbers.
Here's the rule: If events are dependent on one another, you multiply the probabilities.
Any time you see a scenario where X has to happen <u>and then </u>some other thing (X, Y, or whatever) has to happen, the events are dependent.
Probability of rolling a 4 <u>and then</u> rolling a 2 = 1/6 * 1/6 = 1/36
Hope this helps.
The degree of the polynomial is 5, therefore are 5 zeros (real or imaginary).
The given zeros are
1/3, 4 - 6i, and -2 + 11i.
Because complex zeros always occur as conjugate pairs, the remaining complex zeros are
4 + 6i and -2 - 11i.
Answer: 4 + 6i, -2 - 11i.
(n+1)x 2=10
2n+2=10
2n=8
n=4
