For the first one, you did good. I will just suggest a couple things.
Statement Reason
JK ≅ LM Given
<JKM ≅ < LMK Given (You did both of these steps so well done.)
MK ≅ MK Reflexive Property (Your angle pair is congruent but isn't one of the interior angle of the triangles you are trying to prove.)
ΔJMK ≅ ΔLKM SAS
Problem 2: (You also have a lot of great stuff here.)
Statement Reason
DE ║ FG Given
DE ≅ FG Given
<DEF≅<FGH Given
<EDF≅<GFH Corresponding Angles (You don't need to know that F is the midpoint but you got corresponding angle pair which is correct.)
ΔEDF≅ΔGFH ASA
<DFE≅<FHG CPCTC
Answer:
Step 1: Simplify both sides of the equation.
8−2(3−x)=4x+6
8+(−2)(3)+(−2)(−x)=4x+6(Distribute)
8+−6+2x=4x+6
(2x)+(8+−6)=4x+6(Combine Like Terms)
2x+2=4x+6
2x+2=4x+6
Step 2: Subtract 4x from both sides.
2x+2−4x=4x+6−4x
−2x+2=6
Step 3: Subtract 2 from both sides.
−2x+2−2=6−2
−2x=4
Step 4: Divide both sides by -2.
−2x
−2
=
4
−2
Step-by-step explanation:
Triangular sequence = n(n + 1)/2
If 630 is a triangular number, then:
n(n + 1)/2 = 630
Then n should be a positive whole number if 630 is a triangular number.
n(n + 1)/2 = 630
n(n + 1) = 2*630
n(n + 1) = 1260
n² + n = 1260
n² + n - 1260 = 0
By trial an error note that 1260 = 35 * 36
n² + n - 1260 = 0
Replace n with 36n - 35n
n² + 36n - 35n - 1260 = 0
n(n + 36) - 35(n + 36) = 0
(n + 36)(n - 35) = 0
n + 36 = 0 or n - 35 = 0
n = 0 - 36, or n = 0 + 35
n = -36, or 35
n can not be negative.
n = 35 is valid.
Since n is a positive whole number, that means 630 is a triangular number.
So the answer is True.
(<u>−1</u>
2 )(n^3)+
<u>1</u>
2 n^2+4.6n+(−
<u>1</u>
2)(n^3)+
<u>1</u>
2 n^2+4.5n
=
<u>−1</u>
2 n^3+
1
2 n^2+4.6n+
−1
2 n^3+
1
2 n^2+4.5n
Combine Like Terms:
=
<u>−1</u>
2 n^3+
<u>1</u>
2 n^2+4.6n+
<u>−1</u>
2 n^3+
<u>1</u>
2 n^2+4.5n
=(<u>−1</u>
2 n^3+
<u>−1</u>
2 n^3)+(
<u>1</u>
2 n^2+
<u>1</u>
2 n^2)+(4.6n+4.5n)
=−n^3+n^2+9.1n
Answer:
=−n^3+n^2+9.1n
Everything underlined means its a fraction/divided hope this helps <em>:D</em>
