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SashulF [63]
2 years ago
8

Which of the following is a true proportion of the figure based on the triangle proportionality theorem?

Mathematics
1 answer:
prisoha [69]2 years ago
6 0

Answer:

The correct option is A.

Step-by-step explanation:

When we have two congruent figures, the correspondent sides of the figures are related by the same constant C.

In the case of the image.

h is the left side of the smaller triangle.

h + j is the left side of the larger triangle.

Then we have the relation:

(h + j) = C*h

If we isolate C, we get:

C = (h + j)/h

We can also write this for the other side (the bottom one)

k*C = (k + i)

C = (k + i)/k

Then we have:

(h + j)/h = (k + i)/k

We can rewrite this as:

h/h + j/h = k/k + i/k

1 + j/h = 1 + i/k

We can subtract 1 in each side to get:

j/h = i/k

This is almost the same we can see in option A (its inversed)

If we apply the inverse to both sides, we get:

(j/h)^-1 = (i/k)^-1

h/j = k/i

Which is the same equation that we can see in option A.

Then the correct option is A.

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Answer this question
Murljashka [212]

Answer:

a = p * q

b = p * s + q * r

c = r * s

Step-by-step explanation:

In the trinomial ax² + bx + c

a is the coefficient of x²

b is the coefficient of x

c is the numerical term

∵ The trinomial is ax² + bx + c

∵ Its factors are (px + r) and (qx + s)

∴ ax² + bx + c = (px + r)(qx + s)

∵ (px + r)(qx + s) = (px)(qx) + (px)(s) + r(qx) + (r)(s)

∴ (px + r)(qx + s) = pqx² + (psx + qrx) + rs

∴ ax² + bx + c = pqx² + (ps + qr)x + rs

→ By comparing the two sides

∵ ax² = pqx² ⇒ divide both sides by x²

∴ a = pq

∵ bx = (ps + qr)x ⇒ Divide both sides by x

∴ b = ps + qr

∴ c = rs

∴ a = p * q

∴ b = p * s + q * r

∴ c = r * s

5 0
2 years ago
2.7 times a number equals 8.37?
KIM [24]

Answer:

22.599

PLEASE SAID THANKS

4 0
2 years ago
Read 2 more answers
A climber is on a hike. After 2 hours he is at an altitude of 400 feet. After 6 hours he is at an altitude of 700 feet. Is the r
cluponka [151]

Answer:

  not enough information

Step-by-step explanation:

Dividing altitude by hours, we find the ratios to be 400/2 = 200 ft/h and 700/6 = 116 2/3 ft/h.

These are not the same ratio, so altitude is not proportional to time.

___

However, that's not what the question asks. It ask about rate of change. We only have enough information to determine the rate of change between hour 2 and hour 6 is 300 ft in 4 hours, or 75 ft/hour. Since we don't have any other rate of change information, we cannot determine if the rate of change is proportional to anything.

_____

<em>Comment on the question</em>

We suspect the question is simply worded poorly, and that we're supposed to determine if altitude is proportional to hours. (It is not). If that is actually the question, "rate of change" needs to be left out of the question.

6 0
3 years ago
A person trying to gain access to a bank vault must pass through a series of three security doors. If an attempt to pass through
ExtremeBDS [4]

Answer:

C) S = {F, PF, PPF, PPP}

Step-by-step explanation:

For this case, we know that a person is trying to gain access to a bank vault and needs to go through 3 security doors, and we know that if the person does not pass a door, then he/she has no other attempts. We denote P= Successful pass , F= Failed pass

And we are interested on the sample space, we need to remember that the sample is the set with all the possible values for an experiment.

For this case the person can fail at the 1,2 or 3 try

For the case that fails at the 1 try we have F

For the case that fails at the 2 try we have PF

For the case that fails at the 3 try we have PPF

And the last option is that the person not fails at any try and we have PPP

So then the sample space would be given by:

C) S = {F, PF, PPF, PPP}

6 0
2 years ago
Mackenzie is working two summer jobs, making $7 per hour babysitting and making $13 per hour landscaping. In a given week, she c
Harrizon [31]

Answer:

$ 18.00

Step-by-step explanation:

8 0
3 years ago
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