Answer:
Yes
Step-by-step explanation:
Yes.
Let's first start with even numbers. (N - even number)
Any even number squared, is an even number. Then, we add that squared even number to another even number which would give us an even number.
Now, let's see odd numbers.
Any odd number squared would be an odd number. When you add "N", it would be adding an odd number to an odd number, which gives you an even number.
OR
We can start by factoring the expression:
This is essentially multiplying two consecutive numbers, which in turn means that one number has to be even, and one has to be odd. An odd number multiplied by an even number will always be even.
Answer:
1. X = 14
2.X =13
Step-by-step explanation:
The angles are 90 degrees. I did math to check if the x values are correct and they are.
2 Answers:
- B) The lines are parallel
- C) The lines have the same slope.
Parallel lines always have equal slope, but different y intercepts.
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Explanation:
Let's solve the second equation for y
3y - x = -7
3y = -7+x
3y = x-7
y = (x-7)/3
y = x/3 - 7/3
y = (1/3)x - 7/3
The equation is in y = mx+b form with m = 1/3 as the slope and b = -7/3 as the y intercept. We see that the first equation, where y was already isolated, also has a slope of m = 1/3. The two equations of this system have the same slope. Choice C is one of the answers.
However, they don't have the same y intercept. The first equation has y intercept b = -4, while the second has b = -7/3. This means that they do not represent the same line. They need to have identical slopes, and identical y intercepts (though the slope can be different from the y intercept of course) in order to have identical lines. So we can rule out choice D and E because of this.
Because the two equations have the same slope, but different y intercepts, this means the lines are parallel. Choice B is the other answer.
Parallel lines never touch or intersect, which in turn means there is no solution point. A solution point is where the lines cross. We can rule out choice A.
I recommend using your graphing calculator, Desmos, GeoGebra, or any graphing tool (on your computer or online) to graph each equation given. You should see two parallel lines forming. I used GeoGebra to make the graph shown below.
Let's put this on the usual Cartesian grid just so we can talk about it without drawing a picture. We'll use map conventions, right is east, up is north.
The ball starts at (0,0). 10.3 feet northwest means we have an isosceles right triangle whose diagonal is 10.3 feet. It's isosceles because northwest means equal parts north and west.
The sides of these triangles are in ratio
so the coordinates after the first putt are
The negative sign indicates west, which doesn't really matter for this problem. The distance from the origin to this point is 10.3 as required.
Now a second putt of 3.8 feet north puts us at
The squared distance to the origin is exactly
A little calculator work tells us
Third choice.
