DEF is a isosceles right triangle, so DE =EF. apply Pythagoras:
DF² = DE² + EF² , BUT DE = DF .then DB² = 2DE² = 28²
DE² = 28/2 = 14 and DE = √14 = 3.71 ≈3.7
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Answer:
see attached
Step-by-step explanation:
I started with triangle GHJ on the right. It is isosceles, so ...
g = 48°
h = 2(90 -g) = 84°
k = 180° -h = 96°
Then, on the lower right, we have ...
a = 180° -143° = 37°
b = 143°
c = e = a = 37°
f = 90° -e = 53°
At vertex D, we also have ...
85° +d = b ⇒ d = 143° -85° = 58°
In triangle DGH, we have ...
m + d = h ⇒ m = h -d = 84° -58° = 26°
The sum of angles in triangle DGP is 180°, so ...
p = 180° -85° -26° = 69°
Finally, ...
s = p = 69°
r = 180° -p = 111°
_____
The relationships we used are ...
- corresponding angles are congruent (at a transversal of parallel lines)
- alternate interior angles are congruent
- an exterior angle equals the sum of remote interior angles
- acute angles in a right triangle are complementary
- angles in a triangle sum to 180°
- linear pair angles are supplementary
- angle sum theorem
Answer:
x=23
y=12
Step-by-step explanation:
Start by making two separate equations. One for each answer it gives you. So you know you will have two different numbers, therefore you need two different variables. I'm going to use x and y. The first part of the sentence says that the sum is 35 meaning we are going to add two numbers to get 35.
x+y=35
The second part says the difference of two numbers is 11, which means you are subtracting two numbers to get 11.
x-y=11
Now you can either decide to you substitution or elimination. I prefer elimination, so thats what I will be using. To do this you need to line up both equations.
x+y=35
x-y=11 Now you can add straight down. x+x=2x; y-y=0; 35+11=46. Write out what you have left
2x+0=46 You do not have to write the zero in the equation, I did so that you could see that the y's cancell each other.
It can also look like this 2x=46. Now you need to divide by 2 to get x by itself.
x=23
To find y you take the 23 and plug it for x in one of the equations you started with. I'm going to use the (x+y=35). No matter whihc you use your answer will be the same.
23+y=35 Subtract the 23 over to get y alone.
-23 -23
y=12
Answer:
1
Step-by-step explanation:
1st way: We can find the slope of the line by plugging the two points into the slope formula. If you do, slope would be (-3/2-3/2)/(-3/2-3/2) which simplifies to -3/-3 which is 1. The slope is 1.
2nd way: You can just use logic to figure it out because since the x and y in both of the points are equal to each other, we know that the slope has to be 1.
