Answer:
4. SR= 17 (opposite angle of parallogram are equal)
<u>We are given:</u>
An even number 'n', multiplied by the next consecutive even number is 168
<u>Solving for n:</u>
From the given statement, we can say that:
n(n+2) = 168 [<em>n multiplied by the next even number 'n+2'</em>]
n² + 2n = 168
n² + 2n - 168 = 0 [<em>subtracting 168 from both sides</em>]
We can see that we now have a quadratic equation, solving using splitting the middle term
n² + 14n - 12n - 168 = 0
n(n + 14) -12(n + 14) = 0 <em>[factoring out common terms</em>]
(n-12)(n+14) = 0
Here, we can divide both sides by either (n-12) OR (n+14)
Checking the result in both the cases:
(n + 14) = 0/(n-12) (n-12) = 0/(n+14)
n + 14 = 0 n - 12 = 0
n = -14 n = 12
Both these values are even and since we are not told if the number 'n' is positive or negative, both 12 and -14 are the possible values of n
Answer:
Step-by-step explanation:
Given
x = hours spent on cardiovascular work
y = hours spent on weight training
From the first statement,
Each week: he spends at least 9 hours
This is represented as:
From the second statement,
Each week: he spends a max of 12 hours on weights
This is represented as:
From the third statement,
Each week: he spends a max of 6 hours on cardio works
This is represented as:
So, the inequalities are:
See attachment for the graph where the solution are also highlighted
From the attachment, the solutions are:
1) A student will study German for at least 3 years. x≥3
2) All employees work less than 40 hours. x<40
3) There are at least 35 people in the emergency room. x≥35
4) The carton holds at most 12 eggs. x≤12
5) There are no more than 10 gallons of gas in the tanks. x≤10
6) There are fewer than 10 yards of fabric left. x<10
7) The temperature is above 32°F. x>32
8) Years of experience cannot be less than 5 years. x≥5
The answer would be -2x + 8.
3 - x - (x - 5)
3 - x - x + 5
3 + (-x - x) + 5
3 - 2x + 5
(<u>-2x + 8).</u>
