<span>2x + x = 12
=> x =12/3 =4
so, original number is 84. </span>
Answer:
x = -9
Step-by-step explanation:
First, divide both sides by 12 to isolate the expression, x + 11
12(x + 11)/12 = 24/12
x + 11 = 2
Then, subtract 11 from both sides
x + 11 = 2
- 11 - 11
x = -9
Hi Vance :)
a=leg unknow
b=leg
c=hypotenuse
a²+b²=c²
a²=c²-b²
a²=145² - 144²
a²=21,025 - 20,736
a²=289
a=√289
a=17
unknow leg = 17 units
<h3>2
Answers: Choice C and choice D</h3>
y = csc(x) and y = sec(x)
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Explanation:
The term "zeroes" in this case is the same as "roots" and "x intercepts". Any root is of the form (k, 0), where k is some real number. A root always occurs when y = 0.
Use GeoGebra, Desmos, or any graphing tool you prefer. If you graphed y = cos(x), you'll see that the curve crosses the x axis infinitely many times. Therefore, it has infinitely many roots. We can cross choice A off the list.
The same applies to...
- y = cot(x)
- y = sin(x)
- y = tan(x)
So we can rule out choices B, E and F.
Only choice C and D have graphs that do not have any x intercepts at all.
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If you're curious why csc doesn't have any roots, consider the fact that
csc(x) = 1/sin(x)
and ask yourself "when is that fraction equal to zero?". The answer is "never" because the numerator is always 1, and the denominator cannot be zero. If the denominator were zero, then we'd have a division by zero error. So that's why csc(x) can't ever be zero. The same applies to sec(x) as well.
sec(x) = 1/cos(x)
Answer:
480 different sandwiches
Step-by-step explanation:
To find how many sandwiches can be made, we need to find the number of possibilities for each choice: bread, protein, cheese, vegetables.
Bread: 3 types -> combination of 3 choose 1 -> 3
Protein: 4 types -> combination of 4 choose 1 -> 4
Cheese: 4 types -> combination of 4 choose 1 -> 4
Vegetables: 5 types -> combination of 5 choose 2 -> 5!/(3!*2!) = 5*4/2 = 10
So the number of different sandwiches is:
3 * 4 * 4 * 10 = 480
