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3 years ago

A tree casts a shadow of 24 feet at the same time as a 5-foot tall man casts a shadow of 4feet. Find the height of the tree.

Mathematics

1 answer:

Nitella [24]3 years ago

7 0

Answer:

30 ft

Step-by-step explanation:

This is a problem of similar triangles.

| \

h | \

| \

| 5|\

| | 4\

<----24---->

tree man

The height of the man is 5 ft.

The shadow of the tree is 24 ft.

The shadow of the man is 4 ft.

We have similar triangles, so the lengths of their sides are proportional.

h/24 = 5/4

Cross multiply.

4h = 24 * 5

Divide both sides by 4.

h = 6 * 5

h = 30

Answer: 30 ft

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A conjecture and the two-column proof used to prove the conjecture are shown.

aliina [53]

Answer: the statements and resons, from the given bench, that fill in the blank are shown in italic and bold in this table:

Statement Reason

1. K is the midpoint of segment JL Given

2. segment JK ≅ segment KL Definition of midpoint

3. L is the midpoint of segment KM Given

4. segment KL ≅ segment LM Definition of midpoint

5. segment JK ≅ segment LM Transitive Property of

Congruence

Explanation:

1. First blank: you must indicate the reason of the statement "segment JK ≅ segment KL". Since you it is given that K is the midpoint of segment JL, the statement follows from the very Definition of midpoint.

2. Second blank: you must add a given statement. The other given statement is segment KL ≅ segment LM .

3. Third blank: you must indicate the statement that corresponds to the definition of midpoint. That is segment KL ≅ segment LM .

4. Fourth and fith blanks: you must indicate the statement and reason necessary to conclude with the proof. Since, you have already proved that segment JK ≅ segment KL and segment KL ≅ segment LM it is by the transitive property of congruence that segment JK ≅ segment LM.

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4 years ago

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If N is the population of the colony and t is the time in days, express N as a function of t. Consider Upper N 0 is the origina

lesya [120]

Answer:

(a) $N(t)=Noe^{kt}$

(b)5,832 Mosquitoes

Step-by-step explanation:

(a)Given an original amount $N_o$ at t=0. The population of the colony with a growth rate $k \neq 0$ , where k is a constant is given as:

$N(t)=Noe^{kt}$

(b)If $N_o=1000$ and the population after 1 day, N(1)=1800

Then, from our model:

N(1)=1800

$1800=1000e^{k}\\$Divide both sides by 1000\\e^{k}=1.8\\$Take the natural logarithm of both sides\\k=ln(1.8)$

Therefore, our model is:

$N(t)=1000e^{t*ln(1.8)}\\N(t)=1000\cdot1.8^t$

In 3 days time

$N(3)=1000\cdot1.8^3=5832$

The population of mosquitoes in 3 days time will be approximately 5832.

(c)If the population N(t)=20,000,we want to determine how many days it takes to attain that value.

From our model

$N(t)=1000\cdot1.8^t\\20000=1000\cdot1.8^t\\$Divide both sides by 1000\\20=1.8^t\\$Convert to logarithm form\\Log_{1.8}20=t\\\frac{Log 20}{Log 1.8}=t\\ t=5.097\approx 5\; days$

In approximately 5 days, the population of mosquitoes will be 20,000.

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3 years ago

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Use inverse operation to solve the question 2/3z = -4 Z= ?

sweet [91]

Answer:

z=(-6)

Step-by-step explanation:

(2/3)*z=(-4)

2*z=3*(-4) --> We move the 3 from the left to the right part of the equation. It was dividing, so we move it multiplying.

2*z=(-12)

z=(-12)/2 --> It's the inverse case of before. 2 was multiplying, so we move it to the right by dividing it.

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3 years ago

12 more than the quotient of 54 and 9

Tema [17]

Answer:

Step-by-step explanation:

54/9 + 12

6 + 12

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3 years ago

Would I set this problem up as 5x-20=2x+37 ?

Harman [31]

Answer:

Yes I believe so is that algebra i think you set up the equation correctly I'm in a college statistic class our equations that we work with much more similar to algebra.

Step-by-step explanation:

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3 years ago

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