The answer is FALSE. Theorem, as applied in mathematics, is a statement
that has been proved having a basis of laborious mathematical reasoning. The statement
that is assumed to be true without proof is called axiom or postulate. Theorems
are proved using axioms.
Answer:
57
Step-by-step explanation:
1) According to PEMDAS, <em>multiply </em>first: 27+ 5x6= 27+30
2) Then <em>add</em>: 27+30=57
The correct answer is –6x + 15 < 10 – 5x.
We can tell this by solving for x.
–3(2x – 5) < 5(2 – x) ----> Multiply to the parenthesis.
-6x + 15 < 10 - 5x ----> This is answer #3 and now we add 5x to both sides
-x + 15 < 10 ----> subtract 15 from both sides
-x < -5 ----> Divide by -1
x > 5 (Note that you have to change the direction of the sign when dividing by a -1. Therefore it does not match answer #1).
Ok so basically solve for y
x-y=12
27+3y=2x
27+3y=2x
subtract 3y from both sides
27=2x-3y
2x-3y=27
x-y=12
multiply by -2
-2x+2y=-24
add them
2x-3y=27
<u>-2x+2y=-24 +</u>
0x-1y=3
-y=3
y=-3
y coordinate is -3
2.
y=2x+14
-4x-y=4
y=2x+14
subtract 2x from both sides
y-2x=14
mulitply both sides by -2
-2y+4x=-28
add the 2 equations
-2y+4x=-28
<u /><u>-y-4x=4 +</u>
-3y+0x=-24
-3y=-24
divide both sides by -3
y=8
y coordinate is 8
1. y coordinate is y=-3
2. y coordinate is y=8<u>
</u>
Since they are similar, that means they are proportionally the same.
So KL is similar to PN
JL is similar to PM
So,
You need to find how much bigger is the second triangle from first.
It is proportionally scaled up.
KL/JL = PN/ PM
You basically put in order of triangles. Left triangle on left side of equal sign and right triangle on right side of equal sign. You put in denominator the similar sides and numerator the similar sides (the side that is similar to the side of the other triangle)
5/6 = PN / 9
Cross-multiply
PN * 6 = 5*9
6PN = 45
PN =45/6
PN =7.5
