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What is the length of BC¯¯¯¯¯ ?

balandron [24]

Answer:

The length of BC is 17

Step-by-step explanation:

When we construct a triangle with the data, we will end up a isosceles triangle.

In a isosceles triangle , we know that tow angles and two sides are equal

The questions states that

$\angle b = \angle c$

Then sides AC and AB are also equal

On equation their values

2X - 8 = X+9

2X = X + 9 +8

2X = X + 17

2X - X = 17

X = 17

The length of BC = X = 17

4 0

4 years ago

Dana is filling a 1.5 gallon watering can at a rate of 0.75 gallon per minute. What is the domain of the function that represent

Butoxors [25]

Answer:

0 ≤ x ≤ 2

Step-by-step explanation:

A function show the relationship between an independent variable and a dependent variable. The independent variable (input) does not depend on other variables while the dependent variable (output) depend on other variables.

In this question, the volume of the water is the dependent variable and the time taken is the independent variable. Let y represent the volume of the water and x represent the time taken. Therefore:

y = 0.75x

The domain of the function is the set of independent variable, it can be gotten by determining x when y is minimum and maximum. Hence:

For y = 0

0 = 0.75x

x = 0/ 0.75 = 0

For y = 1.5 gallon

1.5 = 0.75x

x = 1.5/0.75 = 2

Hence, the domain = 0 ≤ x ≤ 2

6 0

3 years ago

A population of bacteria is initially 6000. After three hours the population is 3000. If this rate of decay continues, find the

serious [3.7K]

Answer:

The equation is $A=6000e^{-0.23t}$ at a rate of -23%.

Step-by-step explanation:

Decay can be represented by the equation $A=A_0e^{rt}$ . We can find the rate at which it decays by using t=3 hours and A=3000. This means $A_0=6000$ in this context.

$A=A_0e^{rt}\\3000=6000e^{r(3)}$

$0.5=e^{(24.5)r}$

After substituting, we divided by 6000 to each side to get 0.5 on the left. Now to solve for r, we will take the natural log of both sides and use log rules to isolate r.

$ln 0.5=ln e^{(3)r}\\ln 0.5=3r (ln e)\\\frac{ln0.5}{3} =r$