Answer:
k = -9.
Step-by-step explanation:
As the triangle is right-angled at Q, by Pythagoras:
PR^2 = PQ^2 + RQ^2
So, substituting the given data and using the distance formula between 2 points:
(7 - 1)^2 + (k - 4)^2 = (-4-4)^2 + (-3-1)^2 + (7 - (-3))^2 + (k - (-4))^2
36 + (k - 4)^2 = 64 + 16 + 100 + ( k + 4)^2
(k - 4)^2 - (k + 4)^2 = 180 - 36
k^2 - 8k + 16 - (k^2 + 8k + 16) = 144
-16k = 144
k = -9.
Notice how on both sides of the equation there is one coefficient (number being multiplied by x) and a constant (just a plain number). You want all constants to be on one side and all coefficients on the other. He’s how do to that:
2x+14=-21-5
I am choosing that all constants will be on the right side, so I will do the inverse operation of any constant on the left side to remove it. Here, a constant on the left side is 14. I will subtract 14 from both sides of the equation. Positive 14 minus 14 is zero, so it cancels out and removes it.
2x+14-14 = -21-5x
2x = -35-5x
See how the 14 is now gone? The equation looks much simpler now. Okay next, you can see that there is a coefficient on the “constant side” that I’ve chosen, so I am going to remove that. Negative 5 plus positive 5 equals zero. Do this on both sides of the equation.
2x+5x = -35-5x+5x
7x = -35
Now the equation is just two numbers. All that is left to do is divide by the last coefficient, 7, in this case.
7x/7 = -35/7
x = -5
Answer:6.25
Step-by-step explanation:
2.5x2.5=6.25
Answer:
x is equal to negative one, and y is equal to negative four.
Step-by-step explanation:
You can do this by solving one of the equations by either x or y, then substituting it into the other. Let's solve the second one for y:
Now we'll substitute that into the first equation:
So we now know that x is equal to -1. We can simply substitute that into one of the original equations to find y:
We now know that x is equal to -1, and y is equal to -4. We can also check our answer by plugging that -4 into the other equation, and see if we still get -1:
So we know that our answer is correct.
Answer:
m∠CDE = 35°
Step-by-step explanation:
The exterior angle CDE is equal to the sum of the opposite interior angles, BCD and DBC. So, you have ...
6x -13 = (2x+10) +(x +1)
3x -24 = 0 . . . . . . . . . . . . subtract the right side, simplify
x -8 = 0 . . . . . . . . . . . . . . divide by 3
x = 8 . . . . . . . . . . . . . . . . . add 8
6x -13 = 6·8 -13 = 35 . . . . substitute for x in the expression for CDE
The measure of angle CDE is 35°.
