Answer: 5
Step-by-step explanation:
Since
, by the corresponding angles theorem,
. This means
by AA.
As corresponding sides of similar triangles are proportional,
![\frac{10}{x+3}=\frac{10+x}{12}\\(10)(12)=(10+x)(x+3)\\120=x^{2}+13x+30\\x^{2}+13x-90=0\\(x+18)(x-5)=0\\x=-18, 5](https://tex.z-dn.net/?f=%5Cfrac%7B10%7D%7Bx%2B3%7D%3D%5Cfrac%7B10%2Bx%7D%7B12%7D%5C%5C%2810%29%2812%29%3D%2810%2Bx%29%28x%2B3%29%5C%5C120%3Dx%5E%7B2%7D%2B13x%2B30%5C%5Cx%5E%7B2%7D%2B13x-90%3D0%5C%5C%28x%2B18%29%28x-5%29%3D0%5C%5Cx%3D-18%2C%205)
However, as distance must be positive, we consider the positive solution, x=5.
Therefore, the answer is <u>5</u>
Answer:
x = -44
Step-by-step explanation:
-8 = x/4 + 3
-8 - 3 = x/4 + 3 - 3
-11 = x/4
-11 x 4 = (x/4) x 4
-44 = x
I'll explain it simply for you
1st question
Of course you know phythagoras theorm
You even wrote it up there
It states that the sum of the square of the two sides of an equilateral triangle is equal to the square of the hypotenuse
![{a}^{2} + {b}^{2} = {c}^{2}](https://tex.z-dn.net/?f=%20%7Ba%7D%5E%7B2%7D%20%20%2B%20%20%7Bb%7D%5E%7B2%7D%20%20%20%3D%20%20%7Bc%7D%5E%7B2%7D%20)
Where C is the hypotenuse
*NOTE* :
HYPOTENUSE is the greatest side in a triangle!!
And that's where your mistake is!
So you should take the greatest side as C
So in Q3. 7, 24 and 26 are the given numbers
You'll make the smaller two numbers a and b and the greatest number C
Using the Formula you'll solve the left side first which is
![{a}^{2} + {b}^{2}](https://tex.z-dn.net/?f=%20%7Ba%7D%5E%7B2%7D%20%20%2B%20%20%7Bb%7D%5E%7B2%7D%20)
Then the right side which is
![{c}^{2}](https://tex.z-dn.net/?f=%20%7Bc%7D%5E%7B2%7D%20)
And if both are equal then it is a right triangle otherwise it isn't!
Let
a=7
b=24
c=26
a^2 + b^2
7^2 + 24^2
49 + 576 = 625
GREAT, Now the right side
26^2 = 676
Since they aren't equal it isn't a right angled triangle...
Then let
a=7.5
b=10
c=12.5
7.5^2 + 10^2
= 56.25 + 100
= 156.25
12.5^2 = 156.25
They are EQUAL
Therefore it is a right triangle too
Hopefully I helped
Answer: <span>Postulate 4: If two points lie in a plane, the line containing them lies in that plane.
</span>That is because two points, call them A and B, always form a line, and so, given that they form the line AB and they are in the plane Q, the line AB is in the plane Q.<span />