Answer:
420
Step-by-step explanation:
Each of the 7 appetizers can be paired with one of 10 entrees, and each entree can be paired with one of 6 desserts. So the number of combinations is:
7 × 10 × 6 = 420
REPOST IT A BIT CLEARER sorry i was on caps and im to lazy to elete what i wworte and repost it
Answer:
Part A:
![4 + x = y](https://tex.z-dn.net/?f=4%20%2B%20x%20%3D%20y)
![0.5*4 + 1*x = 0.7*y](https://tex.z-dn.net/?f=0.5%2A4%20%2B%201%2Ax%20%3D%200.7%2Ay)
![x = 8/3\ quarts\ of\ 100\%\ solution](https://tex.z-dn.net/?f=x%20%3D%208%2F3%5C%20quarts%5C%20of%5C%20100%5C%25%5C%20solution)
![y = 20/3\ quarts\ of\ 70\%\ solution](https://tex.z-dn.net/?f=y%20%3D%2020%2F3%5C%20quarts%5C%20of%5C%2070%5C%25%5C%20solution)
Part B:
![x + y = 10](https://tex.z-dn.net/?f=x%20%2B%20y%20%3D%2010)
![2x + 3y = 23](https://tex.z-dn.net/?f=2x%20%2B%203y%20%3D%2023)
and ![y = 3](https://tex.z-dn.net/?f=y%20%3D%203)
Step-by-step explanation:
Part A:
The inicial concentration of the lemonade is 50%, and the volume is 4 quarts, and we will add x quarts of a lemonade with a concentration of 100%, so the total volume will be y, and the concentration will be 0.7, so we have that:
![4 + x = y](https://tex.z-dn.net/?f=4%20%2B%20x%20%3D%20y)
![0.5*4 + 1*x = 0.7*y](https://tex.z-dn.net/?f=0.5%2A4%20%2B%201%2Ax%20%3D%200.7%2Ay)
Using the value of y from the first equation in the second one, we have:
![2 + x = 0.7*(4 + x)](https://tex.z-dn.net/?f=2%20%2B%20x%20%3D%200.7%2A%284%20%2B%20x%29)
![2 + x = 2.8 + 0.7x](https://tex.z-dn.net/?f=2%20%2B%20x%20%3D%202.8%20%2B%200.7x)
![0.3x = 0.8](https://tex.z-dn.net/?f=0.3x%20%3D%200.8)
![x = 8/3\ quarts](https://tex.z-dn.net/?f=x%20%3D%208%2F3%5C%20quarts)
![y = 4 + 8/3 = 20/3\ quarts](https://tex.z-dn.net/?f=y%20%3D%204%20%2B%208%2F3%20%3D%2020%2F3%5C%20quarts)
Part B:
If he shoots a total of ten targets, we can write the equation:
![x + y = 10](https://tex.z-dn.net/?f=x%20%2B%20y%20%3D%2010)
Each stationary target is 2 points, and each moving target is 3 points, so if the total points is 23, we have:
![2x + 3y = 23](https://tex.z-dn.net/?f=2x%20%2B%203y%20%3D%2023)
If we subtract the second equation by two times the first one, we have:
![2x + 3y - 2*(x + y) = 23 - 2*10](https://tex.z-dn.net/?f=2x%20%2B%203y%20-%202%2A%28x%20%2B%20y%29%20%3D%2023%20-%202%2A10)
![2x + 3y - 2x - 2y = 23 - 20](https://tex.z-dn.net/?f=2x%20%2B%203y%20-%202x%20-%202y%20%3D%2023%20-%2020)
![y = 3](https://tex.z-dn.net/?f=y%20%3D%203)
⇒ ![x = 7](https://tex.z-dn.net/?f=x%20%3D%207)
Answer:
y=x+4
Step-by-step explanation:
So, let's start with the fact that we have two numbers. Let's call one of them "x" and the other one "y." Let's also assume that "y" is the larger number and "x" is the smaller number.
We know that both of them added together (the sum) gives us 74. Mathematically, that means:
x+y=74.
We also know that the larger number ("y") is 4 more than the smaller number ("x"). Another way to say this is, if you have the smaller number and add 4 more to it, you'll end up with the larger number. Mathematically, this means:
y=x+4
Since we know that y=x+4, we can put "x+4" into the first equation for "y", giving us:
x+(x+4)=74
Simplifying gives us:
2x+4=74
-4 -4
---------
2x=70
--- ---
2 2
x=35
Since we now know that x=35, and we know that y=x+4, we now know that:
y=(35)+4
y=39
Now that we have both of the numbers, we should check our work to ensure it's correct:
Does 39+35=74? Yes it does.
Is 39 (the larger of the two numbers) four more than the smallest number (35)? Yes it is.
A function can be represented verbally. For example, the circumference of a square is four times one of its sides.
A function can be represented algebraically. For example, 3x+6 3 x + 6 .
A function can be represented numerically.
A function can be represented graphically.