X = 25.5 mm.

Using the similarity statement given, that ΔABC ~ ΔDEF, we set up a proportion:

8.5/x = 4/12

Cross multiply:
4*x = 8.5*12
4x = 102

Divide both sides by 4:
4x/4 = 102/4
x = 25.5

7 0

3 years ago

Give the y-interecept

Inessa05 [86]

Answer:

(0, 5)

Step-by-step explanation:

3x + y = 5

Plug x = 0

3*0 + y = 5

0 + y = 5

y = 5

y-intercept = (0, 5)

5 0

3 years ago

Simplify remove all the perfect squares from inside the square root 45

denpristay [2]

Answer:

3 $\sqrt5}$

8 0

3 years ago

The population of a bee hive is growing with a monthly percentage rate compounded continuously. The population doubles in 3 mont

agasfer [191]

Answer:

$r = \frac{\ln{2}}{3}$

Step-by-step explanation:

The exponential growth function is:

$P(t) = P(0)e^{rt}$

In which P(t) is the population after t months, P(0) is the initial population and r is the monthly percentage rate.

The population doubles in 3 months.

This means that $P(3) = 2P(0)$

We use this to find r.

$P(t) = P(0)e^{rt}$

$2P(0) = P(0)e^{3r}$

$e^{3r} = 2$

$\ln{e^{3r}} = \ln{2}$

$3r = \ln{2}$

$r = \frac{\ln{2}}{3}$

8 0

3 years ago