Answer:
Infinite amount of solutions
Step-by-step explanation:
Parallel lines have no solution
Same lines have infinite solutions
Intersecting lines have 1 solution
Step 1: Write out equation
-14(x - 5) = -14x + 70
Step 2: Distribute -14
-14x + 70 = -14x + 70
Here we see that we have 2 exact same lines. Therefore, we have infinite amount of solutions.
Alternatively, we can plug in any number <em>x </em>and it would work. So then we would have infinite amount of solutions as well.
<span>D. 20 + 2âš10 units
To solve this, you simply need to calculate the length of each side of the triangle with the vertexes of A(3,4), B(-5,-2), and C(5,-2). The length of each side is simply calculated using the pythagoras theorem. Note that it doesn't matter what order you do the subtraction. The absolute value will be the same and if it happens to be negative, not a problem since it will become positive once you square the values.
So the length of side AB is
sqrt((3-(-5))^2 + (4-(-2))^2) = sqrt(8^2 + 6^2) = sqrt(64 + 36) = sqrt(100) = 10.
The length of side BC is
sqrt((-5 - 5)^2 + (-2 - (-2))^2) = sqrt(-10^2 + 0^2) = sqrt(100+0) = sqrt(100) = 10.
And finally, the length of side AC is
sqrt((3-5)^2 + (4-(-2))^2) = sqrt(-2^2 + 6^2) = sqrt(4+36) = sqrt(40)
= 2 * sqrt(10)
Finally, add all the lengths together.
10 + 10 + 2âš10 = 20 + 2âš10</span>
The answer to this problem is -5x=8
Answer: 912
===================================
Work Shown:
The starting term is a1 = 3. The common difference is d = 5 (since we add 5 to each term to get the next term). The nth term formula is
an = a1+d(n-1)
an = 3+5(n-1)
an = 3+5n-5
an = 5n-2
Plug n = 19 into the formula to find the 19th term
an = 5n-2
a19 = 5*19-2
a19 = 95-2
a19 = 93
Add the first and nineteenth terms (a1 = 3 and a19 = 93) to get a1+a19 = 3+93 = 96
Multiply this by n/2 = 19/2 = 9.5 to get the final answer
96*9.5 = 912
I used the formula
Sn = (n/2)*(a1 + an)
where you add the first term (a1) to the nth term (an), then multiply by n/2
-----------------
As a check, here are the 19 terms listed out and added up. We get 912 like expected.
3+8+13+18 +23+28+33+38 +43+48+53+58 +63+68+73+78 +83+88+93 = 912
There are 19 values being added up in that equation above. I used spaces to help group the values (groups of four; except the last group which is 3 values) so it's a bit more readable.
You would set it up: .5/100 = x/490 and then cross multiply .5 time 490 and 100 times x, and end up with: 245=100x. divide by 100, and get 2.45
