Anna and Belle are asked to solve −2x − 15 = 6x + 9. Identify where one of them made an error. Anna Belle −2x − 15 = 6x + 9 −2x
2 answers:
Answer:
<h2>Belle is wrong.</h2>Step-by-step explanation:
The given expression is
The steps Anna did are
If you look carefuly, you would notice that Anna didn't make any mistakes, her steps and result is correct.
Belle steps are
Notice that this step is wrong, because she's not adding -9 to eliminate that term.
, this step is also wrong, because 9 + 9 = 18.
Therefore, Belle is wrong.
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Answer:
- AH = 3.2
- CH = 1.8
- BH = 2.4
Step-by-step explanation:
It can be convenient to compute the length of the hypotenuse of this triangle (AC). The Pythagorean theorem tells you ...
AC^2 = AB^2 + CB^2
AC^2 = 4^2 + 3^2 = 16 + 9 = 25
AC = √25 = 5
The altitude divides ∆ABC into similar triangles ∆AHB and ∆BHC. The scale factor for ∆AHB is ...
scale factor ∆ABC to ∆AHB = AB/AC = 4/5 = 0.8
And the scale factor to ∆BHC is ...
scale factor ∆ABC to ∆BHC = BC/AC = 3/5 = 0.6
Then the side AH is 0.8·AB = 0.8·4 = 3.2
And the side CH is 0.6·BC = 0.6·3 = 1.8
These two side lengths should add to the length AC = 5, and they do.
The remaining side BH can be found from either scale factor:
BH = AB·0.6 = BC·0.8 = 4·0.6 = 3·0.8 = 2.4
_____
The sides of interest are ...
AH = 3.2
CH = 1.8
BH = 2.4
