If triangle JKL≈ triangle BCA which statement must be true?

Mathematics

1 answer:

kolezko [41]4 years ago

7 0

The correct answer is b

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Alan drew a scale drawing of a house and its lot. The scale he used was 1 millimeter: 5 meters. In the drawing, the lawn in the

Marat540 [252]

50 meters

Explanation

you can easily solve this by using a rule of three.

Step 1

Let

$\begin{gathered} 1\text{ milemeter}\rightarrow5\text{ meters} \\ \text{the proportion is} \\ \frac{1\text{ mm}}{5\text{ mt}} \end{gathered}$

x represents the length of the actual lawn

then

$\begin{gathered} 10\text{ mm}\rightarrow x\text{ mt} \\ \text{the proportion is} \\ \frac{10\text{ mm}}{\text{xmt}} \end{gathered}$

the proportion is the same, so

Step 2

$\begin{gathered} \frac{1}{5}=\frac{10}{x} \\ \text{solve for x} \\ 1\cdot x=5\cdot10 \\ x=50 \end{gathered}$

so, the length is 50 meters

6 0

2 years ago

The population of bacteria in a culture doubles every 14 hours. How long will it take for

Snezhnost [94]

Answer: 22 hours 11 minutes

<u>Step-by-step explanation:</u>

$P=P_o\cdot e^{(kt)}\\\\\text{Since the initial population is doubled in 14 hours, then:}\\2P_o=P_o\cdot e^{k\cdot 14}\\2=e^{14k}\\ln\ 2=ln\ e^{14k}\\ln\ 2=14k\\\\\dfrac{ln\ 2}{14}=k\\\\0.0495=k\\\\\\\text{Now that the k-value has been determined, we can find the time when the}\\\text{population is tripled:}\\3P_o=P_o\cdot e^{0.0495t}\\3=e^{0.0495t}\\ln\ 3=ln\ e^{0.0495t}\\ln\ 3=0.0495t\\\\\dfrac{ln\ 3}{0.0495}=5\\\\22.19=t\\\\22\ hrs +0.19\ hrs$