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2 years ago

"Which triangle can be proven congruent to ABC using the ASA criterion?.

Mathematics

2 answers:

Virty [35]2 years ago

4 0

ABC is congruent to XYZ using ASA since angle A is congruent with angle X, angle B is congruent with angle Y, and side AB is congruent with side XY

alekssr [168]2 years ago

3 0

Answer: $\triangle{XYZ}$

Step-by-step explanation:

The ASA postulate of congruence says that two triangles are said to be congruent if two corresponding angles and the side in between are congruent.

When we look at $\triangle{ABC}$ , it can be seen that segment AB is the included side in between ∠A and ∠B.

The only triangle that has a segment with measure 5 lies between two corresponding congruent angles is $\triangle{XYZ}$ .

Hence, by ASA postulate

$\triangle{XYZ}\cong\triangle{ABC}$

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During optimal conditions, the rate of change of the population of a certain organism is proportional to the population at time

Lana71 [14]

Answer:

The population is of 500 after 10.22 hours.

Step-by-step explanation:

The rate of change of the population of a certain organism is proportional to the population at time t, in hours.

This means that the population can be modeled by the following differential equation:

$\frac{dP}{dt} = Pr$

In which r is the growth rate.

Solving by separation of variables, then integrating both sides, we have that:

$\frac{dP}{P} = r dt$

$\int \frac{dP}{P} = \int r dt$

$\ln{P} = rt + K$

Applying the exponential to both sides:

$P(t) = Ke^{rt}$

In which K is the initial population.

At time t = 0 hours, the population is 300.

This means that K = 300. So

$P(t) = 300e^{rt}$

At time t = 24 hours, the population is 1000.

This means that P(24) = 1000. We use this to find the growth rate. So

$P(t) = 300e^{rt}$

$1000 = 300e^{24r}$

$e^{24r} = \frac{1000}{300}$

$e^{24r} = \frac{10}{3}$

$\ln{e^{24r}} = \ln{\frac{10}{3}}$

$24r = \ln{\frac{10}{3}}$

$r = \frac{\ln{\frac{10}{3}}}{24}$

$r = 0.05$

$P(t) = 300e^{0.05t}$

At what time t is the population 500?

This is t for which P(t) = 500. So

$P(t) = 300e^{0.05t}$

$500 = 300e^{0.05t}$

$e^{0.05t} = \frac{500}{300}$

$e^{0.05t} = \frac{5}{3}$

$\ln{e^{0.05t}} = \ln{\frac{5}{3}}$

$0.05t = \ln{\frac{5}{3}}$

$t = \frac{\ln{\frac{5}{3}}}{0.05}$

$t = 10.22$

The population is of 500 after 10.22 hours.

7 0

2 years ago

the probabilities that Kojo and Adwoa will pass an examination are 3/4 and 3/5 respectively. Find the probability that both will

olga_2 [115]

Assuming that their exam success is independent then
P(both fail) = 1/4 x 2/5 = 2/20 or 1/10

5 0

2 years ago

According to a commercial, 4 out of 5 dentist recommend a certain brand of toothpaste. Suppose There are 120 dentist in your are

Genrish500 [490]

4/5 recommend, so about 4/5(120) = 96 doctors recommend the brand.

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2 years ago

5TH GRADE LEVEL QUESTION: LOOK AT PHTO AND ANSWER HANDING OUT BRAINLIEST.

mafiozo [28]

Answer:

The volume of Jill's rectangular prism is 40 cm^3

Step-by-step explanation:

w*l*h=area

2*2*10

4*10

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Hope this helps!!

5 0

2 years ago

In the diagram Shown a 2 foot wide flower border surrounds the heart shaped pond.What is the area of the border?

Dimas [21]

This figure is what we would call a composite figure. A composite figure is a shape that is made up of multiple other shapes. when looking at the pond and the border that surrounds it, we can see that this heart shape is made up of two semi circles and a square. To find the area of the border, we will use the area formulas for semi circles and for squares:

Semi Circle Area Formula: $\pi r^{2}$ ÷ 2
Square Area Formula: length x width

Pi = 3.14
Radius = Half of the diameter, in this case 6

After finding the area of each shape, we can subtract the 2 ft width to find the area of the flower bed border.

8 0

3 years ago

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