Answer:
Step-by-step explanation:
-3(3x - 4) = -9x + 12
-9x + 12 = -9x + 12
0 = 0
infinitely many solutions
Answer:
33x - 13 = 13x + 7
Step-by-step explanation:
If "G" is the midpoint of line FH, then both segments (lines FG and GH) must be the same length. Therefore, to find "x", you can set both segments equal to each other. After doing this, you can simplify and isolate to find "x".
FG = 33x - 13
GH = 13x + 7
FG = GH
33x - 13 = 13x + 7
Answer:
∠MLP = 72° , ∠LJK = 22° , ∠JKL = 72° , ∠KLJ = 86°
Step-by-step explanation:
Here, given In ΔJLK and ΔMLP
Here, JK II ML, LM = MP
∠JLM = 22° and ∠LMP = 36°
Now, As angles opposite to equal sides are equal.
⇒ ∠MLP = ∠MPL = x°
Now, in ΔMLP
By <u>ANGLE SUM PROPERTY</u>: ∠MLP + ∠MPL + ∠LMP = 180°
⇒ x° + x° + 36° = 180°
⇒ 2 x = 180 - 36 = 144
or, x = 72°
⇒ ∠MLP = ∠MPL = 72°
Now,as JK II ML
⇒ ∠LJK = ∠JLM = 22° ( Alternate pair of angles)
Now, by the measure of straight angle:
∠MLP + ∠JLM + ∠JLK = 180° ( Straight angle)
⇒ 72° + 22° + ∠JLK = 180°
or, ∠JLK = 86°
In , in ΔJLK
By <u>ANGLE SUM PROPERTY</u>: ∠JKL + ∠JLK + ∠LJK = 180°
⇒ ∠JKL + 86° + 22° = 180°
⇒ ∠JKL = 180 - 108 = 72 , or ∠JKL = 72°
Hence, from above proof , ∠MLP = 72° , ∠LJK = 22° , ∠JKL = 72° ,
∠KLJ = 86°
Answer:
The equation used to predict the number of people living in the town after x years is y = 32,000 (1.08)x
Step-by-step explanation:
Hi, to answer this question we have to analyze the information given:
- <em>Initial population: 32,000
</em>
- <em>Growth per year: 8%
</em>
So, to obtain "y" (the number of people living in the town after x years), we have to multiply the initial population by 1+ 0.08 (the growth rate is 8%/100=0.08 and the original value) and the number of years (x).
Mathematically speaking:
y = 32,000 (1+0.08) x
y= 32,000 (1.08) x
The equation used to predict the number of people living in the town after x years is y = 32,000 (1.08)x
